Category Archives: Hints and Tips

General thoughts on teaching…

Glossary

Glossary of English Grammar Terms

Some people have said that teachers teach English differently from foreign languages. They don’t use the right technical terms for the cases, such as nominative or accusative, and that means children don’t have such a strong command of grammar.

I don’t know how true that is, but it was certainly true in my own schooling, and I’ve seen the effects when teaching myself.

Whatever your level of grammatical knowledge, I thought it would help a few pupils if I wrote down the most common terms and what they all mean with simple examples (with each term shown in red).

66 and 99

This is just another name for quotation marks or speech marks (see article) because they look like the numbers in certain fonts, eg he said, Hello.

Abbreviation

A series of letters standing for different words, eg BBC for British Broadcasting Corporation.

Abstract noun

A noun for an idea, eg peace.

Accent

Punctuation mark in words that come from French (usually the acute accent that slopes up) or that have an extra syllable (the grave accent that slopes down), eg née or learnèd.

Acronym

An abbreviation that can be pronounced as a word, eg Var for Video Assistant Referee. (Note that you only use a capital for the first letter of acronyms.)

Adjective

A word to describe a noun or a pronoun, eg the man is cool or he is cool.

Adverb

A word to describe a verb, adjective or another adverb, eg he ran quickly, he was really jealous or she ran really fast.

Ampersand

A symbol used to stand for the word and, eg Marks & Spencer.

Antonym

A word that means the opposite of another word, eg cold is an antonym for hot.

Apostrophe

A punctuation mark to show a contraction or the possessive, eg its raining or Marks book.

Article

A word that introduces a noun, eg a tree (the indirect article) or the table (the direct article).

Asterisk

A punctuation mark to link to a footnote or replace bad language, eg * see footnote or he was a real s**t.

Auxiliary (or helping) verb

The first part of the continuous present, future, imperfect, conditional, perfect or the pluperfect tense, eg he is giving, he was giving, he will be giving, he would be giving, he has given or he had given. The one ending in -ing is called the present participle while the other one is called the past participle.

Brackets

Punctuation marks to separate less important information, an abbreviation or a definition in the middle of a sentence, eg he loved to swim (when he got the chance), he worked for the North Atlantic Treaty Organisation (NATO) or the painter used chiaroscuro (light and shade).

Collective noun

A noun for a collection of animals, eg a dazzle of zebras.

Concrete (or common) noun

A noun for something you can physically touch, eg concrete.

Circumflex

A punctuation mark that looks like a hat over vowels in words that come from French, eg rôle.

Colon

A punctuation mark that introduces a list if the first part could be a sentence on its own, eg he bought everything he needed for dinner: pizza, salad and a bottle of wine.

Comma

A punctuation mark to separate different parts of a sentence (see article), eg he liked playing rugby, football and cricket.

Complex sentence

A sentence that contains at least one subordinating conjunction or a relative pronoun, eg He went outside because it was so hot or She was the woman who had been in the café.

Compound sentence

A sentence that contains at least one coordinating conjunction, eg Richard was happy, but Jane was sad.

Conditional tense

The tense that shows what might happen given a certain condition. It can be used in the present or perfect tense, both in the simple or continuous form, eg I would give, I would be giving, I would have given or I would have been giving.

Conjunction

A word that can either join two sentences together or separate words in a list (see article), eg he went outside because it was hot or he liked to pay with a credit card or cash.

Contraction

A shortening of two words using an apostrophe, eg isn’t for is not.

Curly brackets

Punctuation marks that are rarely used in English but appear in music and Mathematics, eg the set of odd numbers = {1, 3, 5, 7…}

Definite article

The word the, eg the table. (Note that you pronounce it with a short ‘e’ before words that start with a consonant sound, such as table, but with a long ‘e’ before words that start with a vowel sound, such as our or hour.

Determiner

A word that describes or introduces a noun, eg that book or his homework. A determiner can be an article or a possessive pronoun, so it’s not really a separate category in the parts of speech.

Direct object

The direct object of a sentence is whatever suffers the action of the verb—in other words, whatever has something done to it, eg he kicked the football.

Exclamation mark

A punctuation mark that shows someone is shouting, making a joke or giving a command, eg Shut up!, Two elephants fly off a cliff—jumbo jets! or Open the door!

FANBOYS

A mnemonic or way of remembering all the coordinating conjunctions using the first letter of each in an acrostic, ie For, And, Nor, But, Or, Yet and So.

Fragment

A sentence that’s missing a word or words, eg Because he was annoyed.

Fronted adverbial

A phrase at the start of a sentence (also called an opener or sentence starter) to describe when, where or how something happens, eg At the corner of the street, At five past 10 or With great difficulty.

Full-stop

A punctuation mark to show an abbreviation that doesn’t end with the same letter as the original word or the end of a sentence, eg Prof. Jackson or He went to the shops.

Future tense

The tense that shows something will happen in the future. It comes in two forms for any verb: the simple and continuous, eg I will have or I will be having. You can also create a kind of future tense by using to go as a modal verb, eg I am going to visit my sister.

Hashtag

A punctuation mark that stands for the word ‘number’ or that precedes a tag on social media such as Facebook or Instagram, eg #1 or #wildlifephotography.

Homophone

A word that sounds like another word although it’s spelt differently, eg there, they’re and their are homophones.

Indefinite article

The word a or an, eg a table or an apple.

Indirect object

Usually, the person who benefits from a transaction, eg he gave him the book.

Infinitive

The basic form of any verb, eg he wanted to go swimming.

Interjection

An expression of emotion or a word that helps you play for time when answering a question, eg wow or well.

Inverted commas

Loosely, this is just another name for quotation marks or speech marks (see article). However, it should really only be the single variety used for quotations from a text, eg he said, Hello or the author talks about the sublime verdure.

Mood

Three main forms of any verb: the indicative, imperative and subjunctive, eg I am the best, be the best or if I were the best. In addition, you have active and passive moods, eg he taps the table or the table is tapped by him. Finally, there are a few weird ones like the pseudo-imperative, exclamative and optative, but not even I can recognise those!

Noun

A person, place or thing, eg woman, town or shoe. There are three types: collective, concrete (or common), abstract and proper nouns.

Object

The (direct) object of a sentence is whatever suffers the action of the verb—in other words, whatever has something done to it, eg he kicked the football.

Opener

A phrase at the start of a sentence (also called a fronted adverbial or sentence starter) to describe when, where or how something happens, eg At the corner of the street, At five past 10 or With great difficulty.

Parts of speech

The nine main types of words, ie adjectives, adverbs, articles, conjunctions, interjections, nouns, prepositions, pronouns and verbs.

Participle

The final part of the continuous present, future, imperfect, conditional, perfect or the pluperfect tense, eg he is giving, he will be giving, he was giving, he would be giving, he has given or he had given. The one ending in -ing is called the present participle while the other one is called the past participle. (Note that the present participle is called a gerund if it’s used as a noun, eg Typing is a good skill to have.)

Past tense

The tense that shows something happened in the past or used to happen. There are four different past tenses: the simple past or preterite (I did), the imperfect (eg I was doing), the perfect (eg I have done) and the pluperfect (eg I had done). The perfect and pluperfect also have a continuous as well as simple form, eg I have been doing or I had been doing.

Per cent sign

Punctuation mark showing the percentage value, eg 30%.

Personal pronoun

A pronoun used to represent a noun that is either the subject, direct object or indirect object of the sentence, eg he kicked the dog or the criminal tricked him or she sent him the letter.

Phrase

A group of words that belong together, eg railway bridge.

Possessive pronoun

A pronoun used to represent a person, animal or thing that owns something else, eg his shoes, its collar or their windows.

Preposition

A word that shows position in time or space, eg at four o’clock or under the bridge.

Present tense

The tense that shows something is happening now. It comes in three forms for any verb: the simple, continuous (or progressive) and emphatic, eg I have, I am having or I do have.

Pronoun

A word that stands for a noun, eg he.

Proper noun

A noun that is the name of something or someone, eg London or Harrison Ford.

Question mark

Punctuation mark that goes after a question, eg what time is it?

Quotation marks

This is just another name for speech marks or 66 and 99 (see article), eg he said, Hello.

Relative pronoun

A word that relates to someone or something that’s just been mentioned in the same sentence, eg the woman whom I saw this morning or the shoe that was on the floor.

Semicolon

Punctuation mark that either stands for because or so in a sentence or separates items in a list that already have commas in them, eg It was hot; he had to go outside or London, England; Paris, France and Berlin, Germany.

Sentence

A full sentence can take many forms (see article), but it usually has at least a subject and verb (plus direct and indirect objects and other words sometimes), eg The cat sat on the mat. There are three different types of sentences: simple, compound and complex.

Sentence starter

A phrase at the start of a sentence (also called an opener or fronted adverbial) to describe when, where or how something happens, eg At the corner of the street, At five past 10 or With great difficulty.

Simple sentence

A sentence that doesn’t have a conjunction or a relative pronoun in it, eg He tapped the table.

Speech marks

This is just another name for quotation marks or 66 and 99 (see article), eg he said, Hello.

Square brackets

Punctuation marks that are similar to regular brackets, but they’re usually used to show that the writer has added extra letters or words so that a quotation makes sense, eg He love[s] roses.

Stroke

Punctuation mark (slash in US English) that means and/or and is also the equivalent of the division sign in Maths, eg he wanted different men/women or the answer was 2/3.

Synonym

A word that means the same as another word, eg small is a synonym for little.

Subject

The subject of a sentence is the word or words that control the finite verb in the main clause of a sentence. It may be just a pronoun or a noun phrase including a/an or the, eg she headed the football or the woman parked her car.

Tilde

Punctuation mark usually over the n in words that come from Spanish, eg señor.

Umlaut

Punctuation mark (diaeresis in English) over the a, o or u in words that usually come from German, eg über.

Verb

A doing word, eg skips. The words be and become (in all their forms) are also verbs.

Wabits (or Wabbits)

A mnemonic or way of remembering all the subordinating conjunctions using the first letter of some of them in an acrostic, eg When, Although, Because, (Before,) If, Though and Since.

Word

A morphological unit or collection of letters side-by-side on a page, eg text.

 

 

 

If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.

Interview preparation

Interview Preparation

Every year, thousands of 11+ and 13+ candidates go to what might be their very first interviews. They’re hoping for a place at their target schools, but they’ll probably be nervous about going through the whole process.

Interview prep is important to give yourself the best chance of impressing the teacher and the school. Teachers generally want to teach bright, enthusiastic, polite pupils who are interested in the world around them, so that’s the impression you want to give during your interviews!

It’s also important to do your research about possible target schools so that you can talk about the differences between them. These might involve all kinds of aspects, including the facilities, activities, curriculum, alumni and values (or ‘ethos’).

Here’s a quick guide to the right behaviour and how to create and rehearse answers to the kinds of questions you might be asked.

Let’s start with a few basics.

Appearance

You’ll probably be sent a letter before the interview telling you how you’re expected to dress. It’ll usually be just your school uniform, but it’s worth checking. You want to make the best possible first impression, so you don’t want to stand out like a sore thumb!

Manners

You should be polite, friendly and respectful. That means following any instructions you’re given and getting the basics right.

When you’re called into the interview room, you’ll probably be met by a teacher who’ll offer you a handshake. How to shake hands properly is an important social skill. You should simply grip and shake the hand firmly for a second or two and then let it go, smiling and keeping eye contact throughout. (You can probably afford to grip the hands of male teachers a bit more firmly!)

After that, the teacher might sit down, but you shouldn’t sit down yourself until you’ve been invited to do so. That’s not polite. Not everyone cares about these things, but it’s better to be safe than sorry!

After the interview, you might have to shake hands again, but you just need to follow the same procedure as before.

Body Language

The way you sit and stand and how you position your hands, arms and legs are important in making the right impression. I once starred in a Channel 4 documentary on mating habits, so I had to learn all about body language!

There are many different signs, both good and bad. Here are a few to bear in mind:

Dos

  • Keep eye contact while you’re listening to the teacher.
  • If you’re speaking yourself, you should look into the teacher’s eyes at least half the time.
  • Mirror the body position of the teacher, eg if the teacher leans forward, it’s a good idea to lean forward as well.
  • Find a neutral position for your hands, eg clasping them together and resting them in your lap.

Don’ts

  • Don’t show any bad habits, eg playing with a pencil or picking your nose.
  • Don’t cross your arms. It puts up a barrier and makes you look defensive—or just plain bored!

Questions

There are lots of questions you might be asked in an interview, but some of the most common ones crop up again and again. It’s always worth preparing and rehearsing your answers—even to the simplest of questions.

If you’re asked a difficult question, feel free to take a moment to work out what to say. A short pause is much better than ‘waffling’ vaguely without really saying anything!

Typically, you’ll be asked a mixture of ‘open’ and ‘closed’ questions.

  • Open questions invite you to provide information or your opinion on something in a sentence or two.
  • Closed questions only need a one-word answer, but you shouldn’t settle for that. For instance, if someone asks you about your favourite subject, you shouldn’t just say English or Maths. You should be prepared to explain why without any prompting. Otherwise, you might end up with a lot of awkward pauses! Instead, try to imagine that each question comes with the words ‘and why’ at the end. That will help you to remember to explain everything.

It’s worth coming up with a list of possible questions and then writing out ‘model answers’ to each of them. Here are a few that might crop up:

Personal

  • What’s your name?
  • Where do you live?
  • What close family do you have?

Academic

  • What’s your favourite subject?
  • What’s your least favourite subject?
  • Which subject do you think is most important?
  • Is there any extra subject you think should be taught?
  • What makes a good teacher?
  • What makes a good lesson?
  • Is learning facts at school more important than developing skills?
  • Is it better to be good at Maths or English?
  • How important is it to learn a foreign language?

Likes and Dislikes

  • What do you like to do outside school?
  • What are your favourite things to do with your friends?
  • Do you like sport?
  • How important is sport at school?
  • How important are music and drama at school?
  • What’s your favourite kind of music?
  • Do you play an instrument?
  • Do you have any hobbies or extracurricular activities?
  • Have you recently been to a cultural event like a play, a concert or an exhibition?
  • If you could travel anywhere in the world, where would you go?
  • If you could live abroad, which city or country would you choose?
  • If you won millions of pounds in the lottery, what would you spend it on?

Current Affairs

  • Do you ever read a newspaper or listen to the news?
  • Have you seen a news story recently that you were especially interested in?
  • What do you think are the most important issues in the world today?
  • Do you think we should try to save the planet or learn to live with climate change?
  • Which is more important, Science or the Arts?
  • What do you think of the current government?

Self-awareness

  • How would you describe yourself?
  • Do you think you are talented?
  • Why do you think you deserve a place at this school?
  • If people who know you well had to describe you in three words, what would they say?
  • What are your strengths and weaknesses?
  • Has there ever been a big challenge in your life that you’ve had to overcome?

Values

  • Is it better to be an adult or a child?
  • Is it important to be intelligent and well-educated?
  • Is it more important to be kind or clever?
  • How important is it to be creative?
  • Who are the people who inspire you?

School Choice

  • Why did you apply to this school?
  • How does it compare to other schools you know about?
  • What qualities do you think we’re looking for in potential pupils?
  • If you could change anything about your current school, what would it be?
  • Which other schools did you apply to?
  • What did you like about the other schools?

Boarding

  • What makes a good boarder?
  • What extra problems do you think you would face as a boarder?
  • What do you think are the benefits of boarding?

At the end of the interview, the teacher will usually ask if you have any questions. Interviews are a two-way street, so it’s not just a case of the school choosing the pupils—the pupils also need to choose the school!

That means it’s worth thinking of a good question to ask. It shouldn’t be too basic because that just means you couldn’t be bothered to look it up online! It should be about something important to you and relevant to your application.

Here are a few examples:

  • What do you most enjoy about this school?
  • Why do you think I should want to study here?
  • How do you think I’ll fit in with the other pupils?
  • How do you think your facilities will benefit me personally?
  • What are the opportunities for me to…? (Fill in the blank with what you’re most interested in, such as sport, music or drama.)

Practice

After you’ve done your preparation, you should rehearse by asking an adult to play the part of the teacher and conduct a mock interview. This is called rôle playing. You’re the candidate, and your mum, dad, tutor or other adult plays the part of the interviewer.

You should try to mirror the conditions of the interview as closely as possible. That means wearing the same clothes, knocking on the door, shaking hands, sitting down and answering questions just as you would in the real thing—and for the same amount of time, if possible.

Try to keep up the act. If you make a mistake, don’t say, “Sorry” or start again. Just keep going as best you can. Things always go wrong, so it’s good to practice recovering from your mistakes.

Afterwards, you can have a ‘debrief’, discussing what you think went well and what you might need to do better:

  • Did you smile?
  • Did you keep eye contact?
  • Did you offer a firm handshake?
  • Did you wait to be asked to sit down?
  • Did you answer the questions correctly?
  • Did you say what you wanted to say?
  • Were you confident, or did you keep saying, “Er” and “Erm” the whole time?

Verdict

Interview prep is important in making the best possible first impression at the school of your choice. Exams only give schools limited information about your suitability, so they have to measure your social skills and willingness to learn some other way. That’s where interviews come in.

If you prepare well and come across as polite, enthusiastic and bright, you’ll have a much better chance of being offered a place. Remember, though, the interview is not just for the school. It’s for you as well! This is your chance to find out if it’s going to be a good match, so pay attention to what you’re told and ask a question to find out whatever else you need to know.

 

 

 

 

If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.

Words have power

Persuasive Writing

More and more questions in school entrance exams involve persuasive writing. This is the attempt to change people’s minds about an issue, change how they feel about it or persuade them to do something. It can take many forms:

  • Essays
  • Speeches
  • Letters
  • Newspaper articles

The format of each of these is obviously different, and you can read up on how to write essays, letters and newspaper articles elsewhere on this site. However, they all rely on similar techniques, which will be covered in this article:

  • Rhetoric (or poetic devices or literary techniques)
  • Anecdote
  • Facts
  • Statistics
  • Emotion
  • Call to action

Rhetoric

Strictly speaking, rhetoric is the name given to skills and techniques involved in public speaking. It was taught by the Greeks thousands of years ago, so some of the terms derive from Greek, but it still survives today. It largely overlaps with poetic devices and literary techniques, such as rhetorical questions, similes and metaphors.

Rhetorical techniques can be used in any form of persuasive writing, and you can see a long list and explanation of the main poetic devices in my article on the subject. However, these are the main ones to consider when it comes to persuasive writing:

  • Rhetorical questions (and hypophora)
  • Tricolon (or rule of three)
  • Anaphora
  • Epistrophe
  • Hyperbole
  • Alliteration
  • Simile
  • Metaphor
  • Imagery
  • Sentence structure

Anecdote

An anecdote is a story or account of an event used to illustrate your point. It’s a good idea to make it funny if you can to get readers on your side. For example, if you were arguing that mobile phones should be banned at school, you might tell the tale of diving into a swimming pool with your iPhone still in your pocket!

Facts

If you’re trying to persuade someone who disagrees with you, it’s no good to say what you think without any evidence to back it up. This is known as mere assertion. Facts are much more convincing and help prove your point.

For example, you might be asked to write an essay on what people should eat for breakfast. Yes, you could say what you like to have, but that’s just your own personal preference. It’s far better to be able to talk about the nutritional benefits, such as the fibre in muesli or the vitamin C in orange juice.

Statistics

If you read the newspaper, you’ll often see articles using statistics to support the writers’ arguments. Statistics are just numbers that show what’s happening in the world, but they’re useful because they offer a precise measurement of the quantity of something or its change over time.

You don’t need to be good at Maths to use statistics, but it helps if you’re familiar with fractions, decimals and percentages. These are just different ways of showing the share of something or the rate of change. They often come up in discussions of economics (the study of markets and business).

For example, you might read that the economy had grown by 2.1% in a given year or that the amount of Government debt was 100% of Gross Domestic Product (a way of measuring the size of the economy).

If you’re doing an entrance exam, you might not know that many statistics, so you won’t be able to include them in your persuasive writing. However, you can always revise the topic beforehand so that you’re fully prepared!

Emotion

People are often persuaded by emotion rather than logical argument. If you can make them laugh or cry, they’re more likely to take your side.

Telling jokes is obviously a good way to make someone laugh—although they have to be funny! Telling a sad story about someone suffering is a good way to make them cry—or at least sympathise with the victim and therefore become easier to persuade.

Call to Action (or CTA)

One of the best ways to win converts to your cause and create a positive result is to include a call to action. This is something that your reader can actually do to help, such as write a letter to the local MP or turn up for a protest march.

It’s a common technique in advertising, which is designed usually to get you to buy the product. Most adverts have a catchphrase, and it’s often a call to action that invites the customer to visit a website or buy a particular brand of product.

For example, the ride-sharing app Lyft told people to ‘Ride and save’, and a Mexican restaurant chain called Chipotle told their customers to ‘Get my guac’ (or guacamole).

Verdict

If you want to persuade someone to think, feel or do something a certain way, you can’t just rely on the message itself. You have to back it up with other techniques, such as rhetoric, anecdotes, facts, statistics, emotion and a call to action.

Whether your writing an essay, a letter, a speech or a newspaper article, all these skills can help you persuade your readers—and help get you a better mark!

 

 

 

 

If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.

Checking Maths Answers

At the end of any kind of test, it’s important to check your work. It’s sometimes called ‘sanity checking’, which just means making sure your answers aren’t crazy!

Checking in English is relatively easy because you just have to look out for mistakes with spelling, capital letters, punctuation or other grammar. However, checking in Maths is much harder because there are so many different types of questions. So what’s the answer?

Well, you could always repeat your working for every single question, but that means any test would take twice as long! You don’t have time to do that, so there must be another way. In my experience, you should learn a few different ways of checking that are simple and quick to use.

If you have a mental checklist to go through, it should help you avoid silly mistakes.

Instructions

Have you read all the instructions on the front page? They might contain important guidelines about how to do the exam. For example, you might be told to show your working for every sum—even if there’s no mark scheme, which would usually mean there’s just one mark for a correct answer.

Units

The easiest and quickest way to check your answer is to make sure you’ve included the units! It may be true that 25 x £1.60 is £40, but you won’t get the mark unless you put in the pound sign…

Numbers

Have you copied down the numbers correctly in your sums? You’ll never get the right answer if you’re asking the wrong question…!

Addition

You can use the column method for as many numbers as you like. If you try to add 8, 7 and 5 one by one, there’s a danger you’ll end up saying 8 + 7 = 15 + 5 = 20, which is wrong!

Multiplication

There are a couple of ways of checking a multiplication sum.

Last Digits

  1. Multiply the last digits of both numbers together.
  2. Make sure the last digit of that number and your answer are the same.
  • Eg 3,792 x 26 must end with a 2 because 2 x 6 = 12, and 12 ends with a 2

Rounding

  1. Round both numbers to one (or two) significant figures.
  2. Multiply them together.
  3. Make sure the number you get and your answer are roughly the same size.
  • Eg 3,792 x 26 must be roughly 120,000 because 4,000 x 30 = 120,000 

     

     

     

    If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.

How to Write a Newspaper Article

In the good old days, 11+ or 13+ candidates were simply asked to do a comprehension and write a story in their English exams. However, the creative writing papers have changed recently, and candidates might have to do a wide range of creative writing tasks, such as writing a diary entry or a newspaper article. This post should help you understand the basic format of a newspaper article enough to write your own in a convincing way.

Format

The picture above shows a typical article taken from the online edition of The Daily Telegraph. It happens to be from the sport section, but it follows a similar pattern to most articles, whether they’re in news, opinion or any other section.

Here are the basic elements that you need to copy in your own article:

  1. Headline. This says what the news item actually is and will usually have only 5-10 words in it. This one’s a little longer, but it still leaves out one or two words, in this case the ‘a’ in front of the words ‘shock call-up’. Articles such as a, an and the are normally left out of the main headline, as are auxiliary verbs such as being and having. For example, if the headline was in the passive, it would read something like ‘Josh Tongue handed shock call-up’, not ‘Josh Tongue is handed shock call-up’. Notice also that it’s in the present tense—even though the event obviously happened in the past! That’s just a convention or habit, but you need to do the same.
  2. Subheadline. This explains the main headline in a bit more detail. This is generally a bit longer, so the rules are slightly less strict on leaving out words. Notice that the word ‘an’ makes it into this one, but there’s no ‘the’ before ‘nets’.
  3. Byline. This tells the reader who’s written the article and where it was written. In this case, it’s just the journalist’s name and location, but columnists sometimes have a mini-biography.
  4. Date. This shows the date and time when the article was published.
  5. Picture. You probably won’t have to draw a picture, but you might possibly have to show where it goes in the article and say what would be in it. In this case, it’s just a picture of Josh Tongue bowling at Lord’s Cricket Ground.
  6. Caption. The line under the picture usually repeats the headline again in different words, and there’s usually a credit for the photographer who took the picture or the agency that provided it. In this case, you can see it was Philip Brown via Getty Images.
  7. Lede. The first paragraph is called the ‘lede’ for historical reasons that aren’t important now! It usually repeats the headline with a bit more explanatory detail, including the five Ws:
    Who?
    What?
    Where?
    When?
    Why?
  8. Other paragraphs. There’s no set number of paragraphs for a newspaper article, so you’ll need to check the question to work out how much to write. However, most newspaper articles include the most important information at the top of the article and less important details further down. These usually include a mix of the following:
    • Background. This is not part of the actual story, but it helps explain what’s going on. For example, in the second paragraph of this article, we find that ‘Tongue has never played at Lord’s before’.
    • Interviews. The usual sources journalists use to back up a story are interviews with the people concerned. In political stories, you might find quotations from both sides of a controversial argument. In this case, all we see is a short quotation from Chris Woakes, who ‘spoke of a “dark” summer in 2022’.
    • Statistics. Another way to confirm a story is by using numbers. This is common in articles about economics. However, in this case, we find that Woakes ‘averages 61.2 with the bat and 11.3 with the ball’.
    • Anecdotes. Journalists often try to ‘hook’ the reader or generate an emotional reaction by telling a story. In this case, we hear how Woakes ‘was sidelined by a knee injury and wondered if he would add to his 45 Test caps’.

Conventions

Every newspaper has a ‘style guide’ that helps journalists decide how to write the story. These cover all kinds of grammatical points, including such things as how to capitalise words or where to use commas. Here are a couple of common usages:

  • Use people’s full names (and titles) when first mentioning them in the article. After that, just use their surnames. In this article, for instance, it’s ‘Josh Tongue’ in the first paragraph but ‘Tongue’ after that.
  • Use ‘elegant variation’ to avoid repeating people’s names too often. It can get a bit repetitive to use people’s names all the way through an article, so it’s normal to think of different ways to refer to them. In this article, Chris Woakes is referred to as the ‘seasoned international and Lord’s specialist’.
  • Treat what interviewees say as quotations rather than speech. That means you don’t need to put a comma before the spoken words, as with the word “dark” in this example. It also means you have to put the full-stop after the speech marks and not before.
  • Don’t write in the first person. Unless you’re supposed to be a columnist writing an opinion piece, you shouldn’t use the words ‘I’ or ‘me’.

Sample Questions

  1. Write a news article about a natural disaster, such as an earthquake, volcanic eruption or tsunami.
  2. Write a sports report about a football match.
  3. Write an article about the importance of saving the planet.
  4. Write a restaurant review.
  5. Write an obituary for a famous person who’s just died. 

     

     

     

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How to Hyphenate Words

Hyphenation

How not to do it…!

Hyphenation is not the most important thing in the world, but there’s a right way and a wrong way to do it. Here are the three rules you need to obey if you want to get it right.

  1. Hyphenate in between syllables. Syllables are just the different sounds in a word, and you can count them. For instance, happily has three syllables because there are three different sounds (hap-, -pi- and -ly). Putting the hyphen in between syllables just makes it easier to read. This also means that you can’t hyphenate words that have only one syllable. Sorry, but you just can’t…!
  2. Start the second part of the word on the next line with a consonant. Again, it just makes it easier to read if you start the second part with a consonant. Hence, the word ‘cleaning’ in the picture should be hyphenated before the ‘n’ and not after!
  3. If there’s a double consonant or two consonants in a row, put the hyphen in between the two. This almost always makes the word easier to read because it breaks the word in a ‘natural’ position. For instance, the word ‘railway’ naturally breaks into ‘rail-‘ and ‘way’.

And that’s it…! Here are a few sample questions to test yourself on.

Quiz

Hyphenate the following words correctly. (There may be more than one option!)

  1. cleaning
  2. happily
  3. hero
  4. barn
  5. rolling
  6. rhythm
  7. backward
  8. tiller
  9. begin
  10. merrily 

     

     

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Number triangle

Number Triangles

Number triangles are a useful way of working out how to rearrange a multiplication or division sum.

This is important if you have to ‘fill in the gaps’, for example.

Let’s say the question sets out a bus stop method division sum with the dividend missing. In other words, something divided by 9 is 38. You could work it out ‘backwards’, but it would be much easier to put the values into a number triangle and rearrange it so that the something is simply 9 x 38.

Method

If you draw an equilateral triangle and write the three values in the right corners, you can just put your finger over one of them to see what you have to do to work it out.

For example, if you know that a = bc (or a = b x c), then you should put a in the top corner of the triangle. That’s because the two other letters are now together at the bottom, forming bc. If you put your finger on the a, you just see bc—which is the formula for a.

It’s the same if you know what the formula for b or c is. All you need to do is put the b and the c in the bottom corners. The a has to go at the top because the formula for b is a over c (in other words, a divided by c), and the formula for c is a over b. That means if you put your finger over the b, you’ll get the formula for b, which is a over c.

The same goes for c. If you put your finger over the c, you’ll get the formula for c, which is a over b.

All that means that one triangle contains three formulas:

a = bc
b = a/c
c = a/b

Quiz

Rearrange these sums by drawing a number triangle and work out what the question mark stands for. (In other words, turn them into division or multiplication sums that start with “? =” and then work out the answer.)

  1. 36 = 9 x ?
  2. 108 = ? x 3
  3. 4 = 24 ÷ ?
  4. 5 = ? ÷ 15
  5. 2.5 = 300 ÷ ?

 

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Problem Questions

‘Problem questions’ are often the most difficult in 11+ and 13+ Maths papers.

There are several different kinds, but they all have one thing in common: they all ‘hide’ the sums that you have to do.

That means the first thing you have to do is work out the actual calculations you’re being asked for.

Here’s an example from a 10-11+ Bond book that I was going through today with one of my pupils:

What is the nearest number to 1000, but smaller than 1000, into which 38 will divide with no remainder?

He couldn’t answer it, so I told him something I always say in these situations. There are three ways of answering a question in Maths:

  1. Use a proper mathematical technique.
  2. Use trial and error.
  3. Guess!

Method 1

The first method is usually the most efficient and reliable. In this case, you need to do two calculations:

  1. 1000 ÷ 38 (ignoring any remainder)
  2. Multiply the answer by 38.

The first step should be done using long division and should give the answer 26.

 

 

 

 

 

 

 

The second should be done by long multiplication and give the answer 988.

Method 2

It’s all very well saying you have to use ‘proper’ Maths, but what if you don’t know how to do it? That’s when trial and error comes in handy.

Trial and error just means thinking of a number that you think is ‘about right’ and then adding or subtracting from it if the answer is too low or too high.

In this case, there’s no easy answer, but you might round up 38 to 40, and 40 goes into 1,000 25 times. However, that still leaves a difference of 25 lots of 2, which is 50, so the actual total is only 950. If you add on another 38, you get 988, which is the answer.

Method 3

If you’re doing a multiple choice paper, the worst mistake in the world is to leave an answer blank. It only takes a second to guess A, B, C, D or E, so it’s worth doing because you’ll always have a 20% chance of getting it right—and that beats zero!

The key is to make sure your guesses are at least possible. For example, if the question asks for a number between 1 and 10, don’t guess 12!

For this question, it isn’t easy to guess, but the answers to a lot of questions at 11+ or 13+ level can be narrowed down quite easily to a common fraction or a single-digit number.

As Sherlock Holmes once told Dr Watson, “Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth!”

Quiz

  1. Mark is 11 and Julie is 9 years old. If they get £80 pocket money shared according to their ages, how much does each of them get?
  2. If a dress costs £240 after VAT at 20% is added on, what is the original price?
  3. Candy floss is on sale at £2 for three sticks at Stall A and £2.50 for five sticks at Stall B. Which stall is cheaper per stick?
  4. A garden measures 10 x 8 metres in total. There’s a lawn surrounded by a path 1 metre wide around the outside. What’s the area of the grass?
  5. If school starts at 9.15am and there are four 45-minute lessons in the morning followed by three lessons of 1 hour 15 minutes in the afternoon with an hour for lunch, what time do the children go home? 

     

     

     

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Rounding

Rounding

Rounding is just a convenient way of keeping numbers simple. Nobody wants to have to remember all the decimals in 𝝅 (which is 3.14159265358979323846 to 20 decimal places), so people usually round it to 3.14 (or 22/7).

There are three ways of rounding numbers:

  • using a power of 10
  • using decimal places
  • using significant figures.

Powers of 10

We use a decimal number system, so it’s often useful to round values to the nearest power of 10, eg 10 (10¹), 100 (10²) or 1,000 (10³). In fact, when we round values to the nearest whole number, we’re still using a power of 10 as units are simply a multiple of one, which is 10⁰.

When you round to the nearest 10, for instance, you’re just saying which multiple of 10 is closest to your value, eg 23 is closer to 20 than 30, so 23 is 20 to the nearest 10.

But what if it’s halfway between? The number 25 is no closer to 20 than it is to 30, so what should you do? The answer is that mathematicians decided on a ‘convention’ (ie an agreed rule) that you should always round up if the next digit after the ones you need is five or more. That means 25 is 30 to the nearest 10 and not 20.

Sample Questions

  1. What is 5.5 to the nearest whole number?
  2. What is 46 to the nearest 10?
  3. What is 62 to the nearest 100?
  4. What is 236 to the nearest 1000?
  5. What is 500 to the nearest 1000?

Decimal Places (d.p.)

Using decimal places is helpful for long decimals that seem to go on forever. If you round to a certain number of decimal places (dp), the number must have that number of digits after the decimal point, eg 𝝅 to two decimal places (2 d.p.) is 3.14. 𝝅 is an irrational number that goes on forever, so that’s quite handy!

Every time you round a value, you have to check the next digit to see if it’s five or more. If it is, you have to add one to the previous digit, eg 𝝅 to three decimal places is 3.142 as the second 1 in 3.1415… is followed by a 5.

Trailing zeroes should be shown if you need them to reach the given number of decimal places, eg 10 to two decimal places is 10.00.

Sample Questions

  1. What is 5.24 to one decimal place?
  2. What is 18.2222… to one decimal place?
  3. What is 9.99 to one decimal place?
  4. What is 4 to 2 d.p.?
  5. What is 6.25 to three decimal places?

Significant Figures (or sig. fig.)

Using significant figures is good for both very big and very small numbers, so a lot of calculator papers in Maths will tell you to show your answers to three significant figures.

If you round to a certain number of significant figures, you start with the first digit that’s not zero and keep as many as you need, working from left to right as the bigger numbers are always on the left, eg 𝝅 to three significant figures is 3.14.

Every time you round to a certain number of significant figures, you have to check the next digit to see if it’s five or more. If it is, you have to add one to the previous digit, eg 𝝅 to five significant figures is 3.1416 as the 5 in 3.14159… is followed by a 9.

Significant figures can be confusing sometimes. If a number starts with one or more zeroes, you have to ignore them as they’re not ‘significant’ (ie important), so you’ll sometimes end up with very long strings of digits, eg 0.000025 is 0.00003 to just one significant figure even though it has six digits!

If you’re rounding a whole number to a certain number of significant figures, you should set to zero all the values between the last significant figure and the decimal point and ignore any decimal places, eg 1,234,567.89 to four significant figures is 1,235,000.

Values ending in lots of nines can look a bit weird when rounded, eg 9.99999 to three significant figures is 10.0…!

Sample Questions

  1. What is 13 to one significant figure?
  2. What is 7.89 to two significant figures?
  3. What is 2,495 to three significant figures?
  4. What is 1,254.36 to 2 sig. figs?
  5. What is 99.9 to 1 sig. fig.? 

     

     

     

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Pronunciation

Pronunciation

English is a funny old language. It’s such a mishmash of imported words and complicated constructions that it was once described as having French vocabulary and German grammar!

Unfortunately, that means the spelling and pronunciation of words are often different due to silent letters or letters that have different pronunciations depending on the context.

Two of those letters are c and g. Both can be ‘hard’ or ‘soft’:

  • C can be a hard /k/ sound as in ‘coat’ or a soft /s/ sound as in ‘ceiling’.
  • G can be hard /g/ sound as in ‘goat’ or a soft /j/ sound as in ‘suggest’.

The general rule is that both letters are soft before e, i or y and hard before any other letter (or at the end of a word).

However, there are exceptions, especially words with only one syllable such as ‘get’ or foreign words such as ‘ciao’, which is Italian for hello or goodbye and is pronounced ‘chow’.

Quiz

How do you pronounce the following words?

  1. coffee
  2. chorus
  3. gybe
  4. celebrate
  5. cellar
  6. metallic
  7. ageist
  8. gild
  9. gauge
  10. conger 

     

     

     

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Working out values from a pie chart

Working out Values from a Pie Chart

This is a typical question from a Dulwich College 11+ Maths paper that asks you to work out various quantities from a pie chart.

To answer questions like this, you have to be comfortable working with fractions and know that there are 360 degrees in a circle.

So how should you start?

The first question asks for the fraction of the school children who liked tennis.

To work this out, you just need to take the following steps:

  1. Put the number of degrees showing the tennis segment over 360 to create a fraction.
  2. Simplify the fraction.

The number of degrees is 45, so the fraction is 45/360.

The first step to simplifying fractions is to see if the numerator goes into the denominator, which it does in this case: 45/45 = 1 and 360/45 = 8, so the fraction is 1/8 in its lowest terms.

(By the way, for a complete guide to simplifying fractions, just read Working with Fractions.)

The second question asks how many of the children preferred cricket.

To answer this, you should be able to learn a bit from the first question.

To work this out, you just need to take the following steps:

  1. Put the number of degrees showing the cricket segment over 360 to create a fraction.
  2. Multiply that fraction by the number of school children in the survey, which is 240.

As with the first question, you need to work out the fraction of the children in the survey you’re dealing with.

In this case, it’s 60/360 or 1/6.

To find out the number of children, you just have to multiply by 240, which is 1/6 x 240 = 40.

The final question asks you to estimate (or guess) how many of the children would say their favourite sport was football out of the whole school of 1200 pupils.

To work this out, you just need to take the following steps:

  1. Work out the number of degrees taken up by the football segment of the pie chart.
  2. Put the number of degrees over 360 to create a fraction.
  3. Multiply that fraction by the number of children in the school, which is 1200.

To work out the number of degrees, it’s easier if you spot that the first half of the pie chart is composed of just football and tennis.

There are 180 degrees in total for that half, so taking away 45 degrees for the tennis-lovers gives you 135 degrees.

This works out at a fraction of 135/360 or 3/8.

Now, we only have data for the 240 children who’ve been surveyed, but that’s why we’re being asked to estimate the answer.

We have to assume that the other kids at school share the same preferences as the ones in the survey.

If we do that, all we need to do is multiply 3/8 by 1200 to get 3/8 x 1200 = 450.

And that’s it…!

 

 

 

 

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Reflecting shapes in a mirror line

Reflecting Shapes in a Mirror Line

This is a typical question from a Dulwich College 11+ Maths paper, and it asks you to draw a reflection of the triangle in the mirror line shown on the chart.

Dulwich papers tend to be a bit tricky, and this is not the easiest version of this kind of reflective symmetry question.

For a start, the mirror line is drawn at 45 degrees rather than being horizontal or vertical, and it doesn’t help that the diagram is a bit ‘squashed’, which means the mirror line is actually at around 40 degrees rather than 45!

So how should you do it?

The first thing to do is to imagine that you were looking at yourself in the mirror from, say, 30cm away.

Your reflection will appear ‘in’ the mirror, but it won’t be on the surface of the mirror, will it?

It’ll actually seem to be 30cm ‘behind’ the mirror – which is exactly the same distance as you are in front of it.

That’s important, and you’ll have to use that fact when you do the question.

The basic steps are these:

  1. Plot the ‘vertices’ (or corners) of the reflected shape one by one by drawing a small cross in pencil.
  2. Join them up using a ruler and pencil.

In order to plot each corner, you need to imagine that the corner is your face and that the mirror line is the mirror.

To see your reflection, you have to be standing right in front of the mirror – looking at an angle of 90 degrees to the mirror – so to ‘see’ the reflection of a corner, you have to do the same, looking at an angle of 90 degrees to the mirror line.

The distance from your face to the mirror is the same as the distance to the spot ‘behind’ the mirror where you see your reflection.

In the same way, the distance from the corner to the mirror line is the same as the distance to the spot ‘behind’ the mirror line where the reflected point should go.

If you use the diagram at the top of this article to help you, you should be able to see that the top of the triangle is one-and-a-half diagonal squares away from the mirror line.

That means you need to go another one-and-a-half diagonal squares the other side of the mirror line (continuing in the same direction) in order to plot the reflected point.

Now repeat this for the other corners of the triangle, which are four-and-a-half and three diagonal squares away from the mirror line.

Once you’ve done that, you can join up all three points using a ruler and pencil to make the reflected triangle.

Once you get the hang of it, you may not even need to plot all the corners: if it’s a simple shape like a square or a rectangle, then you might be able to draw it from scratch.

Just make sure you label the shape if the question asks you to.

And that’s it…!

 

 

 

 

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Why I Hate the Press!

I know why they do it (most of the time), but it’s still incredibly annoying and confusing.

I’m talking about grammatical mistakes in the papers.

Yes, it’s important for their copy to be readable, but we have rules on capital letters, spelling, punctuation and other grammar primarily to make language more understandable, not less, so there is a price to pay when mistakes are made.

In addition, newspapers these days employ far fewer copy editors to correct mistakes, so journalists are increasingly having to do spell checks and grammar checks themselves – with predictable results!

As a tutor, I’m in a difficult position. On the one hand, I accept that language changes over time, but my job depends on telling my pupils what is right and what is wrong.

I have to draw a line in the sand and tell people what I would do, but that’s based on the education I got forty years ago!

I’m far more comfortable with language changes that happen over a timescale of centuries rather than years or even decades, and I still teach people not to use words like ‘alright’ or ‘onto’ even though most people wouldn’t know what I was on about.

Anyway, feel free to make up your own mind. Here’s a quick list of the ways in which the ‘style guides’ of newspapers and magazines try to change the rules of English in order to make their articles more ‘readable’:

  • Paragraphs only include one or two sentences (meaning that you often have to check back to see who ‘he’ or ‘she’ is).
  • Commas are omitted before the word ‘and’.
  • Commas are omitted after openers/sentence starters/fronted adverbials.
  • Split infinitives are permitted.
  • ‘Sentences’ may start with conjunctions even though they are strictly speaking only clauses.
  • ‘Likely’ may be used as an adverb.

Writers also simply make mistakes, and my pet peeves are the use of ‘centre around’ (rather than ‘centre on’) and words like ‘focussing’ (rather than ‘focusing’).

I’m sure we can all think of a few more examples, but I thought I’d illustrate my point by putting together a list from just one newspaper on just one day – The Daily Telegraph on Thursday 2 September 2021.

Have a look at the quotations and see how many mistakes you can spot!

‘But, now 34 and in the twilight of his career, it is hard to see Solskjaer using Cavani in the sort of wide role supporting Ronaldo that he became accustomed to for a while at PSG in order to accommodate Ibrahimovic centrally.’

This is not a full sentence as it starts with ‘but’. It is actually only a main clause that needs another main clause before it. The other problem is that we don’t know who or what is 34. By the way it’s phrased, it looks like ‘it’ is 34, but that’s impossible, so maybe it’s Solskjaer, but that’s not right either. It’s actually Cavani!

‘The Norwegian has already admitted he “maybe overplayed” Fernandes and Marcus Rashford is currently sidelined until later next month following shoulder surgery after repeatedly being asked to play through the pain barrier.’

The comma before ‘and’ has been left out. This happens a lot in the papers, but you should be able to see from this example how confusing it is. Commas are a signal to pause when you’re reading, but without that pause It seems as though Solskjaer overplayed both Fernandes and Rashford because it looks like a list. However, the word ‘is’ lets us know that we’re actually entering another main clause. This is just plain confusing and results in readers having to reread sentences in order to make sense of them.

‘Any club sanctioned by Fifa would face further disciplinary action if they defied any ban on fielding affected players – although the teams would likely only do so if they planned on trying to overturn such a ban.’

Pronouns are a problem these days, often because writers don’t want to follow the convention of assuming that an individual is male when using the word ‘anyone’ or ‘everyone’. Using ‘them’ or ‘their’ is an ungrammatical cop-out. Here, the writer uses the plural pronoun ‘they’ to refer to the singular noun ‘club’, which is debatable to say the least. I’d say it was grammatically wrong, but I’ll admit that British English (though not American English) treats clubs as plural when using their names, for example in saying that ‘Liverpool have bought a defender’. That’s all well and good, but that’s not the case here. It’s not the name of a club that’s being used, just the word ‘club’. The other problem is the use of ‘likely’ as an adverb. This is a perfectly acceptable American usage, but ‘likely’ has always been an adjective in British English – until recently!

‘He said: “Monetary policy has always influenced fiscal outcomes — interest rate changes influence sovereign financing costs. But, with QE, the character of the relationship has changed.”’

Colons should be used when introducing a list rather than speech, and ‘sentences’ shouldn’t start with the word ‘but’.

‘In 2019, it was condemned by its own former chairman for celebrating the resignation of a Labour MP, who was chair of the party’s friends of Israel group, on its Twitter account.’

The problem here is the use of commas around the relative clause (‘who was chair of the party’s friends of Israel group’). Yes, a pair of commas may be used to fence off ‘extra information’ from the rest of the sentence, but relative clauses following ‘who’ and ‘that’ are a special case. They need commas if you’re describing something or someone, but not if you’re defining something or someone. Here, the writer is defining which Labour MP is meant, so no commas should be used. It’s the same when using ‘which’ and ‘that’. You should use ‘which’ with a comma to describe, but ‘that’ without a comma to define.

‘She put longevity above genuine achievement, and popularity above actually tackling Germany’s real problems.’

This is the reverse of the missing comma I mentioned before. The comma before the word ‘and’ here implies that a new main clause is about to start and that the reader should expect a verb after the word ‘popularity’, but in fact it’s just a list. Again, this causes confusion and reduces readability by forcing readers to reread the sentence to check the meaning.

‘Its economy only survives thanks to her predecessor’s labour market reforms, and the fact that the euro is much cheaper than the Deutsche Mark would have been.’

Again, this is another example of the redundant ‘Oxford comma’ in the middle of a list.

‘Reread some of your old columns, dust out your biography of Churchill, and, above all, stop trying to imitate Angela Merkel.’

This is yet another instance of the misplaced comma before the word ‘and’. I presume the writer means ‘dust off’ rather than ‘dust out’…!

‘Many centre-ground voters, while they may not allow themselves to become over-heated by the subject, will nevertheless acknowledge the fact that allowing such migrants to remain indefinitely in Britain when many thousands of others are rejected after applying through formal channels is unfair and unjust.’

All that’s wrong with this is the tautology at the end: ‘unfair’ means ‘unjust’, so you don’t need both adjectives.

‘It all adds up to an entangling web of sclerotic bureaucratic processes that will do little to actually protect the environment.’

I realise that the need to avoid the split infinitive was based on an arbitrary comparison with Latin, in which the infinitive literally can’t be split because it’s one word rather than two, but the convention is still common enough to make most people shiver when they read something like this.

‘There’s a clear need to reduce emissions to tackle climate change and conserve the environment. But we need an approach that doesn’t borrow tools from the old socialist handbook.’

The second ‘sentence’ is only a fragment as it starts with ‘but’.

‘Countries with the most economic freedom perform 50 per cent better on Yale and Columbia universities’ Environmental Performance Index, while those with controlled economies perform worse.’

‘While’ is a subordinating conjunction and so shouldn’t have a comma before it.

‘In response to climate change, the Adam Smith Institute and the British Conservative Alliance are focusing on three areas. First, a border-adjusted carbon tax that would account for the costs to the environment while encouraging innovation. Second, embracing nuclear energy by addressing the high fixed costs to design. And third, a clean free trade agenda including abolishing tariffs and quotas on environmental goods and joining the Agreement on Climate Change, Trade and Sustainability.’

This is just a list, so the writer should’ve used one sentence instead of piling up sentence fragments that don’t have a subject or a verb. The last ‘sentence’ shouldn’t start with ‘and’ either.

‘Former Prime Minister, Benjamin Disraeli once wrote, “ I am prepared for the worst, but hope for the best ”.’

Here, the comma before ‘Benjamin Disraeli’ shouldn’t be there because he is one of many prime ministers. If there’d been only one prime minister, then there should’ve been commas before and after his name, but there are no circumstances in which you should only have one comma.

‘A number of scenarios could unfold: among them a really bad flu epidemic, a new variant that evades the vaccines, or a brutally cold winter that fills the hospitals.’

The first problem here is the phrase ‘among them’. I’d say it was a grey area, but I would leave it out – the colon should introduce the list itself. The second problem is the comma before ‘or’. Yes, it’s a co-ordinating conjunction (or FANBOYS word), but that just means there should be a comma in front of it if it’s being used to join two sentences together, not when it’s separating items in a list. It’s the same for the word ‘and’ and other co-ordinating conjunctions.

‘Meanwhile the NHS is at full stretch to try to reduce the waiting times on operations and diagnostics, with its capacity is reduced by ongoing Covid precautions.’

First, there should be a comma after ‘meanwhile’ or any other adverb at the start of a sentence. Second, the word ‘is’ shouldn’t be there.

‘GPs are still reluctant to see patients face to face, and this is putting additional pressure on hospitals, with health problems spotted later and multiple problems are piling up.’

This is a similar problem, the word ‘are’ being left in by mistake after ‘problems’.

‘Even pre Covid, winter meant headlines screaming “ NHS in worst crisis ever”.’

‘Pre’ is only a prefix rather than a word, so it needs a hyphen. There is also an extra space left in by mistake before ‘NHS’.

‘So lets remember Disraeli’s wise words.’

‘Lets’ should be written with an apostrophe before the ‘s’ as it stands for ‘let us’.

‘We must rebuild the Nightingale hospitals now, this Autumn, before it is too late.’

While ‘Autumn’ is a proper noun, it is not capitalised in English.

‘Some 15,000 beds was prepared last year under the Nightingale plan.’

‘Beds’ is plural, but ‘was’ is singular.

‘There is a short, sharp army recruitment advert running at the moment. It’s slogan is Fail, Learn, Win.’

This time, the apostrophe is wrong. The word should be ‘its’, meaning ‘belonging to it’. You might also argue that there should be inverted commas around the slogan itself.

‘We were not prepared. So let’s learn the lesson. We must be prepared. Then we can win the battle against Covid.’

I know writers and politicians like short, sharp sentences, but this is getting ridiculous! The writer here manages to make two sentences into four…

‘We must now put many thousands of retired medics doctors, nurses on standby. A Medical Reserve, along the lines of the Territorial Army.’

This comes from the same article, which was full of mistakes. There should be a comma after ‘medics’, and the word ‘and’ should replace the comma before ‘nurses’ as it’s the last item in the list. The last ‘sentence’ has no subject or verb, so it should probably start with ‘It should be’.

‘Some 40,000 retired medics offered to come back to help last year, but only 1 in 8 were engaged due to overwhelming bureaucracy.’

Again, this shows the problem with plurals. The number ‘1’ is obviously singular, so how can you say ‘1 in 8 were engaged’?!

‘Yes it will cost money. But it will be cheap at the price if it helps avoid tier restrictions, more lockdowns, more furlough.’

There should be a comma after ‘yes’ as it’s an interjection, the full-stop before ‘But’ should be a comma, ‘But’ should start with a lower case ‘b’ and the word ‘and’ should replace the comma before ‘more furlough’. Apart from that, it’s fine…!

‘Every winter the NHS needs more capacity, we would have both beds and staff.’

There should be a comma after the phrase ‘every winter’ as it’s an opener, and the comma after ‘capacity’ should be a full-stop – this is known as a ‘comma splice’.

 

 

 

 

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Americanisms

In the words of Winston Churchill (or George Bernard Shaw or James Whistler or Oscar Wilde), Britain and America are “two nations divided by a single language”.

Quite a few of my pupils live outside the United Kingdom and/or go to foreign schools but are applying to English schools at 11+ or 13+ level.

One of the problems they face is the use of Americanisms.

There are a number of words that are spelled differently in American English, so you just have to watch out for them. English schools want pupils who are fluent in British English, not the American version – however similar it might be!

The first English dictionary was produced by Samuel Johnson, who published A Dictionary of the English Language in 1755.

However, after the War of Independence, Noah Webster was annoyed by all the ‘English’ textbooks in American schools and decided to try and prove that America had moved on from its colonial past by ‘simplifying’ English spelling and making it more consistent.

The result was A Compendious Dictionary of the English Language, published in 1806, and then An American Dictionary of the English Language, published in 1828.

If you’re trying to learn English, that was an unfortunate decision!

However, there are a few typical changes that are easy enough to reverse.

  • -ize should be -ise, eg ‘realize’ should be ‘realise’ (but ‘capsize’ is the same in both).
  • -yze should be -yse, eg ‘analyze’ should be ‘analyse’.
  • -se should be -ce, eg ‘defense’ should be ‘defence’.
  • -l- should be -ll-, eg ‘traveled’ should be ‘travelled’.
  • -or should be -our, eg ‘color’ should be ‘colour’.
  • -er should be -re, eg ‘center’ should be ‘centre’ (but ‘thermometer’ is the same in both).
  • -e- should be -oe- or -ae-, eg ‘encyclopedia’ should be ‘encyclopaedia’, and ‘diarrhea’ should be ‘diarrhoea’.

Some of Webster’s alterations caught on in Britain, such as deleting the silent -k in words such as ‘publick’ or spelling ‘connexion’ as ‘connection’, but there were many others that didn’t even make it in the States – phew!

1. Cloke — cloak

2. Soop — soup

3. Masheen — machine

4. Tung — tongue

5. Greef — grief

6. Dawter — daughter

7. Korus — chorus

8. Nightmar — nightmare

9. Turnep — turnip

10. Iland — island

11. Porpess — porpoise

12. Steddy — steady

13. Hainous — heinous

14. Thum — thumb

15. Gillotin — guillotine

16. Spunge — sponge

17. Ake — ache

18. Wimmin — women

19. Determin — determine

20. Giv — give

21. Bilt — built

22. Beleev — believe

23. Grotesk — grotesque

24. Stile — style

25. Neer — near

26. Sley — sleigh

 

 

 

 

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Parents at school gates with children

How do I Know if my Child Will Get a Place?

This is the question I get asked the most as a tutor. And even if parents don’t ask it directly, I know that it’s always lurking in the background somewhere…!

School entrance exams are very stressful for pupils and parents alike, and it would be nice to be able to reassure them by giving them all the pass marks for their target schools. Unfortunately, it’s much more complicated than that.

Schools adjust the marks from Common Entrance exams at 11+ and 13+ to allow for the different ages of the children. Some will have a birthday late in the school year, which means they’ll be ‘young for their year’, and it’s generally agreed that it would be unfair to penalise those children by asking them to compete directly against other pupils who might be up to 12 months older than they are.

That’s a big difference at such a young age, so schools ‘standardise’ marks using a formula that adjusts for the relative age of each pupil. That formula also includes adjustments for various other factors, so it’s impossible to know in advance what your child’s standardised score will be.

On top of that, schools don’t often publish their pass marks, so what are pupils and their parents to do?

Well, if you can get hold of your child’s standardised score – and that’s a big if! – then you can at least check whether that score has been good enough in the past to guarantee a place at certain schools. There’s a website called elevenplusexams.co.uk that has posted what they call ‘Entry Allocation Scores & Collated Cutoffs’ for a few schools in Essex. You can find the 2019 figures here, and you can also find out the results and offers for Bishop Vesey’s Grammar School, The Schools of King Edward VI in Birmingham and Sutton Coldfield Grammar School for Girls here. If your chosen schools are not on those sites, feel free to search for them online.

I’m sorry I can’t be of more help, but at least that’s a start.

Good luck…!

 

 

 

 

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Colons and Semicolons

Using colons and semicolons is often an easy way to get a tick in your homework, but it still involves taking a bit of a risk. If you get it right, you get a tick, but if you get it wrong, you get a cross. This article explains how to use both colons and semicolons so that you can be confident of getting far more ticks than crosses!

Colons (:)

Colons can only be used to introduce a list where the introductory phrase could form a sentence on its own. If not, you shouldn’t use any punctuation at all.

I went to the supermarket and bought the following items: apples, pears and bananas.

Or:

I went to the supermarket and bought apples, pears and bananas.

Note that you can still use colons even if there’s only one item in the list:

I only wanted one thing from my men: courage!

Sample questions

Have a go at the following questions and see if you can add the right punctuation. It’ll either be a colon, a semicolon, a comma or nothing at all.

  1. I love chocolate biscuits and milkshakes.
  2. He said “I always go the gym on Wednesdays.”
  3. There were three items on her shopping list flour, sugar and eggs.
  4. He prized only one quality in his players teamwork.
  5. He stayed in his room it was far too hot to go outside.

Semicolons (;)

Semicolons can be used either to separate two main clauses if one explains the other or to separate items in a list that are long and/or contain commas.

He was very careful not to make any spelling mistakes; his teacher was always having a go at him for bad spelling.

Or:

The entries to the competition came from London, England; Paris, France; and Berlin, Germany.

Note that the semicolon before the ‘and’ is optional. We don’t generally use commas before ‘and’ in a normal list, but some people think using a semicolon in the same situation makes things clearer.

Sample questions

Have a go at the following questions and see if you can add the right punctuation. It’ll either be a semicolon, a colon, a comma or nothing at all.

  1. I love chocolate biscuits and milkshakes I used to have them all the time as a kid.
  2. She said, “I always go the pool on Saturdays it’s the only day I get enough time.”
  3. There was only one thing she wanted to do go and get her hair cut.
  4. His team always scored great goals the other team just scored more.
  5. I never cook chicken I’m afraid of making myself sick. 

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Explaining humour

Explaining Humour

One of the things that children taking Common Entrance exams at either 11+ or 13+ find most difficult to explain is humour. Here’s a quick guide to various different types with explanations, examples and a short quiz at the end.

Slapstick Comedy or Farce

This is a type of physical comedy that relies on the fact that we find it funny when other people hurt themselves. It’s called ‘Schadenfreude’ in German, and it really shouldn’t be funny…but it is!

Example: A man slips on a banana skin and falls over.

Deadpan or Dry Humour

This is any joke that’s told with a very matter-of-fact tone.

Example: “It can hardly be a coincidence that no language on earth has ever produced the expression ‘As pretty as an airport’.”
The Long Dark Tea-time of the Soul, by Douglas Adams

Self-deprecation

This means putting oneself down in a self-mocking way.

Example: “If a book about failures doesn’t sell, is it a success?”
Jerry Seinfeld

Toilet and Bodily Humour

What we do in the toilet or in the bedroom has given rise to a LOT of jokes over the years…

Example: “It’s just a penis, right? Probably no worse for you than smoking.”
When You Are Engulfed in Flames, by David Sedaris

Puns, Wit and Wordplay

These are jokes based on double meanings or a play on words.

Example: “If not actually disgruntled, he was far from being gruntled.”
The Code of the Woosters, by P.G. Wodehouse

Epigrams

An epigram is just a saying, and some sayings can be very funny – whether deliberately or not!

Example: “Always go to other people’s funerals, otherwise they won’t come to yours.”
Yogi Berra

Dark Humour

Dark humour is usually about death or the gloomier aspects of life.

Example: I come from Des Moines. Somebody had to.”
The Lost Continent: Travels in Small-Town America, by Bill Bryson

Sarcasm and Irony

Sarcasm is saying exactly the opposite of what you mean, but irony is much richer and more popular because the meaning for the reader can be anything from the literal truth of the statement to its exact opposite. It’s up to you…

Example: “It is a truth universally acknowledged that a single man in possession of a good fortune must be in want of a wife.”
Pride and Prejudice, by Jane Austen

Innuendo

Finding a rude double meaning in a word or phrase is called innuendo.

Example: “Headline?” he asked.
“‘Swing Set Needs Home,'” I said.
“‘Desperately Lonely Swing Set Needs Loving Home,'” he said.
“‘Lonely, Vaguely Pedophilic Swing Set Seeks the Butts of Children,'” I said.”
The Fault in Our Stars, by John Green

Tongue-in-cheek

This expression just means the writer or speaker is being insincere in an ironic and/or mocking way.

Example: “In the beginning, the Universe was created. This has made a lot of people very angry and been widely regarded as a bad move.”
The Hitchhiker’s Guide to the Galaxy, by Douglas Adams

Exaggeration and Hyperbole

Exaggeration can lead to a powerful punchline in a joke because it relies on shocking the reader with something unexpected.

Example: “In our family, there was no clear line between religion and fly fishing.”
A River Runs Through It, by Norman Maclean

Parody and Mockery

Pretending to write in a certain style or copying the format of a particular writer or type of text can be done humorously – although the implied criticism may be affectionate.

Example: “It is a truth universally acknowledged that a zombie in possession of brains must be in want of more brains.”
Pride and Prejudice and Zombies, by Seth Grahame-Smith and Jane Austen

Satire

This is making fun of something usually in religion, politics or current affairs.

Example: “They say the world is flat and supported on the back of four elephants who themselves stand on the back of a giant turtle.”
The Fifth Elephant, by Terry Pratchett

The Surreal

‘Surreal’ just means absurd, nightmarish or like a fantasy.

Example: “As Gregor Samsa awoke one morning from uneasy dreams he found himself transformed in his bed into a gigantic insect.”
The Metamorphosis, by Franz Kafka

Character Humour

Like a lot of sit-coms this form of humour relies on the personality of the characters. Things are funny because they are so typical of a certain type of person – often a stereotype.

Example: “As a boy, I wanted to be a train.”
Machine Man, by Max Barry

Observational

A lot of stand-up comedy is based on observational humour, which means simply picking up on the typical habits of people in the world around us. We laugh because we recognise the behaviour and often the reason for it.

Example: “It’s a funny thing about mothers and fathers. Even when their own child is the most disgusting little blister you could ever imagine, they still think that he or she is wonderful.”
Matilda, by Roald Dahl

Insults

The shock value of an insult lends itself to humour.

Example: Two whales walk into a bar. The first whale says to the other, “WOOOOOO. WEEEEEEEEOOOOO. WEEEEEEEEEEEEOOOOOOOOO.” The second whale says, “Shut up Steve, you’re drunk.”

Awkward Situations

If a situation is particularly cringeworthy or awkward, then it will often generate nervous laughter.

Example: “I don’t know how other men feel about their wives walking out on them, but I helped mine pack.”
Breaking Up, by Bill Manville

Blue or Off-colour Jokes

Using rude words or swear words has the shock value that can generate humour.

Example: “If this typewriter can’t do it, then f*** it, it can’t be done.”
Still Life With Woodpecker, by Tom Robbins

Sample Questions

How would you explain the humour in these lines?

  1. “An unhappy alternative is before you, Elizabeth. From this day, you must be a stranger to one of your parents. your mother will never see you again if you do not marry Mr Collins, and I will never see you again if you do.”
    Pride & Prejudice, by Jane Austen
  2. “There’s a door,” he whispered.
    “Where does it go?”
    “It stays where it is, I think,” said Rincewind.
    Eric, by Terry Pratchett
  3. “It’s not because I want to make out with her.”
    “Hold on.”
    He grabbed a pencil and scrawled excitedly at the paper as if he’d just made a mathematical breakthrough and then looked back up at me.
    “I just did some calculations, and I’ve been able to determine that you’re full of s**t.”
    Looking for Alaska, by John Green
  4. “I came from a real tough neighborhood. Once a guy pulled a knife on me. I knew he wasn’t a professional: the knife had butter on it.”
    Rodney Dangerfield
  5. “A word to the wise ain’t necessary. It’s the stupid ones who need advice.”
    Bill Cosby
  6. “To win back my youth, Gerald, there is nothing I wouldn’t do – except take exercise, get up early or be a useful member of the community.”
    A Woman of No Importance, by Oscar Wilde
  7. “Some men are born mediocre, some men achieve mediocrity, and some men have mediocrity thrust upon them. With Major Major, it had been all three. Even among men lacking all distinction, he inevitably stood out as a man lacking more distinction than all the rest, and people were always impressed by how unimpressive he was.”
    Catch-22, by Joseph Heller
  8. “Build a man a fire, and he’ll be warm for a day. Set a man on fire, and he’ll be warm for the rest of his life.”
    Jingo, by Terry Pratchett
  9. “There are moments, Jeeves, when one asks oneself, ‘Do trousers matter?'”
    “The mood will pass, sir.”
    The Code of the Woosters, by PG Wodehouse
  10. “There was a boy called Eustace Clarence Scrubb, and he almost deserved it.”
    The Voyage of the Dawn Treader, by CS Lewis
  11. “I write this sitting in the kitchen sink.”
    I Capture the Castle, by Dodie Smith
  12. “You can lead a horticulture, but you can’t make her think.”
    Dorothy Parker
  13. “For a moment, nothing happened. Then, after a second or so, nothing continued to happen.”
    The Hitchhiker’s Guide to the Galaxy, by Douglas Adams
  14. “For the better part of my childhood, my professional aspirations were simple – I wanted to be an intergalactic princess.”
    Seven Up, by Janet Evanovich
  15. “It wasn’t until I had become engaged to Miss Piano that I began avoiding her.”
    Into Your Tent I’ll Creep, by Peter De Vries
  16. “To lose one parent, Mr. Worthing, may be regarded as a misfortune; to lose both looks like carelessness.”
    The Importance of Being Earnest, by Oscar Wilde 

     

     

     

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SOHCAHTOA

SOHCAHTOA (pronounced ‘soccer-toe-uh’) is a useful ‘mnemonic’ to remember the definitions of sines, cosines and tangents. Amazingly, I was never taught this at school, so I just had to look up all the funny numbers in a big book of tables without understanding what they meant. As a result, I was always a bit confused by trigonometry until I started teaching Maths and came across SOHCAHTOA quite by accident!

The reason it’s called SOHCAHTOA is because the letters of all three equations make up that word – if you ignore the equals signs…

First of all, let’s define our terms:

  • S stands for sine (or sin)
  • O stands for the opposite side of a right-angled triangle
  • H stands for the hypotenuse of a right-angled triangle
  • C stands for cosine (or cos)
  • A stands for the adjacent side of a right-angled triangle
  • T stands for tangent (or tan)
  • O stands for the opposite side of a right-angled triangle (again)
  • A stands for the adjacent side of a right-angled triangle (again)

Sines, cosines and tangents are just the numbers you get when you divide one particular side of a right-angled triangle by another. For a given angle, they never change – however big the triangle is.

Sine = Opposite ÷ Hypotenuse

Cosine = Adjacent ÷ Hypotenuse

Tangent = Opposite ÷ Adjacent

All these ratios were discovered by Indian and Arabic mathematicians some time before the 9th Century, but you can still use them today to help you work out the length of a side in a right-angled triangle or one of the angles.

Each of these formulas can be rearranged to make two other formulas. (If it helps, you can put the three values in a number triangle with the one in the middle at the top). Let’s take the sine formula first:

Sine = Opposite ÷ Hypotenuse means:

  • Hypotenuse = Opposite ÷ Sine
  • Opposite = Hypotenuse x Sine

As long as you know the angle and the length of the opposite side or the hypotenuse, you can work out the length of the other one.

  • Unknown: hypotenuse
    Known: opposite and angle
    • If one of the angles of a right-angled triangle is 45° and the opposite side is 5cm, the formula for the length of the hypotenuse must be opposite ÷ sin(45°). The sine of 45° is 0.707 (to three decimal places), so hypotenuse = 5 ÷ 0.707 = 7cm (to the nearest cm).
  • Unknown: opposite
    Known: hypotenuse and angle
    • If one of the angles of a right-angled triangle is 45° and the hypotenuse is 5cm, the formula for the length of the opposite side must be hypotenuse x sin(45°). The sine of 45° is 0.707 (to three decimal places), so opposite = 5 x 0.707 = 4cm (to the nearest cm).

Equally, as long as you know the the hypotenuse and opposite side lengths, you can work out the angle by using the ‘arcsine’ or ‘inverse sine’ function on your calculator, which works out the matching angle for a given sine and is written as sin-1, eg sin(45°) = 0.707, which means sin-1(0.707) = 45°.

  • Unknown: angle
  • Known: opposite and hypotenuse
    • If the opposite side of a right-angled triangle is 4cm and the hypotenuse is 5cm, the formula for the angle must be sin-1(4÷5), or the inverse sine of 0.8. The sine of 53° (to the nearest degree) is 0.8, so the angle must be 53°.

We can do the same kind of thing with the cosine formula, except this time we’re dealing with the adjacent rather than the opposite side.

Cosine = Adjacent ÷ Hypotenuse means:

  • Hypotenuse = Adjacent ÷ Cosine
  • Adjacent = Hypotenuse x Cosine

As long as you know the angle and the length of the adjacent side or the hypotenuse, you can work out the length of the other one.

  • Unknown: hypotenuse
    Known: adjacent and angle
    • If one of the angles of a right-angled triangle is 45° and the adjacent side is 5cm, the formula for the length of the hypotenuse must be adjacent ÷ cos(45°). The cosine of 45° is 0.707 (to three decimal places), so hypotenuse = 5 ÷ 0.707 = 7cm (to the nearest cm).
  • Unknown: adjacent
    Known: hypotenuse and angle
    • If one of the angles of a right-angled triangle is 45° and the hypotenuse is 5cm, the formula for the length of the adjacent side must be hypotenuse x cos(45°). The sine of 45° is 0.707 (to three decimal places), so adjacent = 5 x 0.707 = 4cm (to the nearest cm).

Equally, as long as you know the the hypotenuse and adjacent side lengths, you can work out the angle by using the ‘arccosine’ or ‘inverse cosine’ function on your calculator, which works out the matching angle for a given cosine and is written as cos-1, eg cos(45°) = 0.707, which means cos-1(0.707) = 45°.

  • Unknown: angle
  • Known: adjacent and hypotenuse
    • If the adjacent side of a right-angled triangle is 4cm and the hypotenuse is 5cm, the formula for the angle must be cos-1(4÷5), or the inverse cosine of 0.8. The sine of 37° (to the nearest degree) is 0.8, so the angle must be 37°.

Finally, we can do the same kind of thing with the tangent formula, except this time we’re dealing with the opposite and adjacent sides.

Tangent = Opposite ÷ Adjacent means:

  • Adjacent = Opposite ÷ Tangent
  • Opposite = Adjacent x Tangent

As long as you know the angle and the length of the opposite or adjacent side, you can work out the length of the other one.

  • Unknown: adjacent
    Known: opposite and angle
    • If one of the angles of a right-angled triangle is 45° and the opposite side is 5cm, the formula for the length of the adjacent side must be opposite ÷ tan(45°). The tangent of 45° is 1, so adjacent = 5 ÷ 1 = 5cm.
  • Unknown: opposite
    Known: adjacent and angle
    • If one of the angles of a right-angled triangle is 45° and the adjacent side is 5cm, the formula for the length of the opposite side must be adjacent x tan(45°). The tangent of 45° is 1, so opposite = 5 x 1 = 5cm.

Equally, as long as you know the the opposite and adjacent side lengths, you can work out the angle by using the ‘arctangent’ or ‘inverse tangent’ function on your calculator, which works out the matching angle for a given tangent and is written as tan-1, eg tan(45°) = 0.707, which means tan-1(0.707) = 45°.

  • Unknown: angle
  • Known: adjacent and hypotenuse
    • If the adjacent side of a right-angled triangle is 5cm and the hypotenuse is 5cm, the formula for the angle must be tan-1(5÷5), or the inverse tangent of 1. The tangent of 45° is 1, so the angle must be 45°.

Sample Questions

  1. If one of the angles of a right-angled triangle is 20° and the opposite side is 15cm, how long is the hypotenuse?
  2. If one of the angles of a right-angled triangle is 35° and the hypotenuse is 7cm, how long is the opposite side?
  3. If the opposite side of a right-angled triangle is 3cm and the hypotenuse is 8cm, what is the angle?
  4. If one of the angles of a right-angled triangle is 75° and the adjacent side is 12cm, how long is the hypotenuse?
  5. If one of the angles of a right-angled triangle is 45° and the hypotenuse is 5cm, how long is the adjacent side?
  6. If the adjacent side of a right-angled triangle is 15cm and the hypotenuse is 2cm, what is the angle?
  7. If one of the angles of a right-angled triangle is 15° and the opposite side is 20cm, how long is the adjacent side?
  8. If one of the angles of a right-angled triangle is 45° and the adjacent side is 5cm, how long is the opposite side?
  9. If the adjacent side of a right-angled triangle is 15cm and the hypotenuse is 12cm, what is the angle?
  10. If the adjacent side of a right-angled triangle is 4cm and the hypotenuse is 18cm, what is the angle?

     

     

     

     

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Long Multiplication

You can use short multiplication if you’re multiplying one number by another that’s in your times tables (up to 12). However, if you want to multiply by a higher number, you need to use long multiplication.

  • Write down the numbers one on top of the other with the smaller number on the bottom and a times sign on the left (just as you would normally), then draw three lines underneath to hold three rows of numbers.
This image has an empty alt attribute; its file name is Screenshot-2020-05-26-at-20.00.56.png
  • Multiply the top number by the last digit of the bottom number as you would normally.
This image has an empty alt attribute; its file name is Screenshot-2020-05-26-at-20.06.10.png
  • Write a zero at the end of the next answer line (to show that you’re multiplying by tens now rather than units).
This image has an empty alt attribute; its file name is Screenshot-2020-05-26-at-20.07.14.png
  • Multiply the top number by the next digit of the bottom number, starting to the left of the zero you’ve just added.
This image has an empty alt attribute; its file name is Screenshot-2020-05-26-at-20.10.49.png
  • Add the two answer lines together to get the final answer.
This image has an empty alt attribute; its file name is Screenshot-2020-05-26-at-20.13.54.png

Notes:

  • Some people write the tens they’ve carried right at the top of the sum, but that can get very confusing with three lines of answers!
  • Don’t forget to add the zero to the second line of your answer. If it helps, you can try writing it down as soon as you set out the sum (and before you’ve even worked anything out).
  • At 11+ level, long multiplication will generally be a three-digit number multiplied by a two-digit number, but the method will work for any two numbers, so don’t worry. If you have to multiply two three-digit numbers, say, you’ll just have to add another line to your answer.

Sample questions:

Have a go at these questions. Make sure you show your working – just as you’d have to do in an exam.

  1. 216 x 43
  2. 17 x 423
  3. 23 x 648
  4. 782 x 28
  5. 127 x 92

     

     

     

     

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How to Add, Subtract, Multiply and Divide

The most important things you need to do in Maths are to add, subtract, divide and multiply. If you’re doing an entrance exam, and there’s more than one mark for a question, it generally means that you have to show your working. Even if it’s easy enough to do in your head, you still have to write down the sum on paper. That way, the examiner knows that you didn’t just guess!

Here are the basic operations:

Addition

The standard way to add numbers is the ‘column method’.

  • Write down the numbers one on top of the other (however many there are), with two lines under them and a plus sign on the left.
  • Add the first column of numbers on the right and put the answer between the lines.
    • If the total is more than 9, ‘carry’ the tens by putting that number in small handwriting under the next space on the answer line.
  • Add the next column of numbers working from the right and put the answer between the lines, adding any numbers below the line that have been carried.
  • If you get to the final column of numbers and the total is more than 9, you can write both digits on the answer line.
  • If you have more than two columns of numbers and the total is more than 9, you’ll have to ‘carry’ any tens again by putting that number in small handwriting under the next space on the answer line.
  • You can then finish off as normal.

Notes:

  • You don’t need the second line if you don’t want to use it.
  • You can also choose to put the carried numbers above the top line of the sum, but that gets a bit messy if you’re doing long multiplication, so it’s best to get into the habit of using this method.

Sample Questions

Have a go at these questions. Don’t just do them in your head. That’s too easy! Make sure you show your working – just as you’d have to do in an exam.

  1. 8 + 5
  2. 17 + 12
  3. 23 + 19
  4. 77 + 88
  5. 127 + 899

Subtraction

The standard way to subtract one number from another is again the ‘column method’, but this time it’s slightly different. For a start, you can only use this method with two numbers (not three or more), and you can’t use it for negative numbers.

  • Write down the two numbers one on top of the other, with the bigger one on top, the usual two lines under them and a minus sign on the left.
  • Working from the right, take away the first digit in the second number from the first digit in the first and write the answer on the answer line.
    • If you can’t do it because the digit on the top row is too small, you’ll have to ‘borrow’ a 10 from the digit in the next column.
      • Place a 1 above and to the left of the top right-hand digit to make a new number, in this case 12.
      • Cross out the digit you’re borrowing from, subtract 1 and write the new digit above and to the left of the old one.
      • You can now subtract as normal, so 12 – 7 = 5 in this case.
  • Working from the right, subtract the next digit in the bottom number from the next digit in the top number and put the answer between the lines.
  • Repeat this step until you’ve finished the sum.
    • Note that in this case you have to borrow 1 from the 2, leaving 1, and then borrow 1 from the 4, writing it next to the 1 so it makes 11. It may look like you’re borrowing 11, but you’re not. You’ve just had to write the two 1s next to each other.

If you can’t borrow from a digit because it’s a zero, just cross it out, write 9 above and to the left and borrow from the next digit to the left. If that’s a zero, too, just do the same again until you reach one that’s not zero.

Notes:

  • You don’t need the second line if you don’t want to use it.
  • If the answer to the sum in the last column on the left is zero, you don’t need to write it down, so your answer should be 17, say, not 017.
  • You don’t need to put commas in numbers that are more than 1,000.
  • You could cross out the numbers from top left to bottom right instead, but that leaves less room to write any little numbers above and to the left (where they have to go), so it’s best to get into the habit of using this method.

Sample Questions

Have a go at these questions. Don’t just do them in your head. That’s too easy! Make sure you show your working – just as you’d have to do in an exam.

  1. 8 – 5
  2. 17 – 12
  3. 43 – 19
  4. 770 – 681
  5. 107 – 89

Multiplication (or short multiplication)

This is short multiplication, which is meant for multiplying one number by another that’s in your times tables (up to 12). If you want to multiply by a higher number, you need to use long multiplication.

  • Write down the numbers one on top of the other with the single-digit number on the bottom, two lines underneath and a times sign on the left.
  • Multiply the last digit of the top number by the bottom number and put the answer between the lines.
    • If the total is more than 9, ‘carry’ the tens by putting that number in small handwriting under the next space on the answer line.
  • Working from the right, multiply the next digit of the top number by the bottom number, adding any number below the answer line.
    • As with addition, if you get to the final column of numbers and the total is more than 9, you can write both digits on the answer line.

Notes:

  • You don’t need the second line if you don’t want to use it.
  • You can also choose to put the carried numbers above the top line of the sum, but that gets a bit messy if you’re doing long multiplication, so it’s best to get into the habit of using this method.
  • If you’re multiplying one or more numbers with a decimal point, take the decimal point(s) out first then multiply the numbers and put the decimal point in afterwards. You just need to make sure that the number of decimal places is the same as the total number of decimal places in the original numbers, eg 2.5 x 1.1 = 25 x 11 ÷ 100 = 275 ÷ 100 = 2.75.

Sample Questions

Have a go at these questions. Don’t just do them in your head. That’s too easy! Make sure you show your working – just as you’d have to do in an exam.

  1. 21 x 3
  2. 17 x 4
  3. 23 x 6
  4. 77 x 8
  5. 127 x 9

Division (or short division, or the ‘bus stop’ method)

This is short division, which is meant for dividing one number by another that’s in your times tables (up to 12). If you want to divide by a higher number, you need to use long division (see my article here). It’s called the ‘bus stop’ method because the two lines look a bit like the area where a bus pulls in at a bus stop.

  • Write down the number you’re dividing (the ‘dividend’), draw the ‘bus stop’ shape around it so that all the digits are covered and then write the number you’re dividing by (the ‘divisor’) on the left.
  • Try to divide the first digit of the dividend by the divisor. If it goes in exactly, write the answer on the answer line above the first digit of the dividend.
  • If it goes in, but there’s a remainder, write the answer on the answer line above the first digit of the dividend and then write the remainder above and to the left of the next digit in the dividend.
  • If it doesn’t go, then make a number out of the first two digits of the dividend and divide that number by the divisor, adding any remainder above and to the left of the next digit. Just make sure you don’t write a zero on the answer line – the only time you should do that is if the answer is a decimal, eg 0.375.
  • Repeat this process for each of the remaining digits, using any remainders to make a new number with the next digit.
  • If you divide one number by another in the middle of the dividend and it doesn’t go, then just put a zero on the answer line and combine the digit with the next one.

Notes:

  • If you have a remainder at the end of the sum, you can either show it as a remainder or you can put a decimal point above and below the line, add a zero to the dividend and carry on until you have no remainder left.
    • If the remainder keeps going, it’s likely to repeat the same digits over and over again. This is called a ‘recurring decimal’. Once you spot the pattern, you can stop doing the sum. Just put a dot over the digit that’s repeating or – if there’s more than one – put a dot over the first and last digit in the pattern.
  • If your handwriting is a bit messy, make sure you make the numbers quite large with a bit of space between them so that you can fit everything in!

Sample Questions

Have a go at these questions. Don’t just do them in your head. That’s too easy! Make sure you show your working – just as you’d have to do in an exam.

  1. 36 ÷ 3
  2. 172 ÷ 4
  3. 222 ÷ 6
  4. 816 ÷ 8
  5. 126 ÷ 9

     

     

     

     

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Who or Whom, Who’s or Whose?

The ‘W’ words are useful if you’re trying to understand or summarise a story, but who, whom, who’s and whose tend to cause problems. Here’s a quick guide to what they all mean and how to use them.

Who v Whom

Who and whom are both relative pronouns, which mean they relate to the person you’ve just been talking about. Note that they don’t relate to animals or things, just people. The difference is just one letter, but it signals that one of them stands for the subject (in the nominative case if you’ve ever done Latin) while the other stands for the object (in the accusative).

  • The subject of a sentence is the noun or pronoun that controls the verb, in other words the person or thing that’s ‘doing the doing’.
  • The object of a sentence is the noun or pronoun that is suffering the action the verb, in other words the person or thing that’s having something done to it.

For example, in the following sentence, ‘the girl’ is the subject, and ‘the boy’ is the object:

The girl tapped the boy on the shoulder.

We could also use pronouns, in which case ‘she’ is the subject, and ‘him’ is the object.

She tapped him on the shoulder.

Note that we use ‘him’ rather than ‘he’ in this case. That tells us that the boy is the object and not the subject. It’s the same with ‘who’ and ‘whom’. In fact, it’s the same letter – the letter ‘m’ – that tells us that ‘him’ and ‘whom’ are both the objects of the sentence, and that might be a good way to remember the difference.

For example, in the following sentence, ‘the girl’ is still the subject, so we use ‘who’:

They saw the girl who had tapped the boy on the shoulder.

In the next sentence, the boy is still the object, so we use ‘whom’:

They saw the boy whom the girl had tapped on the shoulder.

Note that neither who nor whom needs a comma before it in these cases. That’s because we are defining which people we’re talking about. It’s a bit like ‘which’ and ‘that’: ‘which’ describes things and needs a comma, but ‘that’ defines things and doesn’t. If we already know who people are and simply want to describe them, then we do use a comma.

They saw Patricia Smith, who had tapped the boy on the shoulder.

They saw Paul Jones, whom the girl had tapped on the shoulder.

In these cases, we know who the children are – Patricia and Paul – so all we’re doing is describing something that has happened. There is only one Patricia Smith and one Paul Jones, so we don’t need to define them. That means we need to use a comma in both cases.

I hope that all makes sense. Here are a few practice questions. Just decide in each case whether you should use ‘who’ or ‘whom’.

  1. They talked to Jim, who/whom lived in Stoke.
  2. He played football with the boy who/whom had red hair.
  3. She was friends with the girl who/whom played volleyball.
  4. Who/whom do you think will win the egg and spoon race?
  5. Who/whom did they put in prison?

Who’s v Whose

The words ‘who’s’ and ‘whose’ are homophones, which is another way of saying they sound the same but mean completely different things. ‘Who’s’ is short for ‘who is’ or ‘who has’ while ‘whose’ is a possessive pronoun that means ‘of whom the’ or ‘of which the’. For example, take these two sentences:

  • Who’s going to the cinema tonight?
  • He was a big man whose hands were larger than dinner plates.

The first means ‘Who is going to the cinema tonight?’ whereas the second means ‘He was a big man of whom the hands were larger than dinner plates’. The only reason we don’t say those things is that they’re a bit of a mouthful, so it’s easier to use ‘who’s’ or ‘whose’.

I hope that’s clear now. Here are a few practice questions. Just decide in each case whether you should use ‘who’s’ or ‘whose’.

  1. Who’s/whose in charge of the tennis rackets?
  2. Who’s/whose bag is this?
  3. He speaks to the woman who’s/whose behind the counter.
  4. She likes him to know who’s/whose boss.
  5. Who’s/whose been eating all the crisps?

     

     

     

     

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Could or Might?

Could and might mean different things, but a lot of people use them both to mean the same thing. Here’s a quick guide to avoid any confusion.

Here are two sentences that a lot of people think mean the same thing:

  • “I might [or may] go to the cinema.”
  • “I could go to the cinema.”

The first sentence means there is a chance the speaker will go to the cinema. The second sentence doesn’t. I know this is a bit picky and pedantic, but ‘could’ – like ‘can’ – comes from the verb ‘to be able to’, so the second sentence means either “I was able to go to the cinema” or “I would be able to go to the cinema.” Both of those are very different from the first sentence.

Adults might get away with confusing ability with probability, but if you’re taking an English exam any time soon, it’s probably a good idea to learn the difference!

 

 

 

 

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Homophones

Homophones are words that sound the same even though they’re spelt differently and mean different things. Getting them right can be tricky, but it’s worth it in the end.

The reason why homophones are important is not just to do with the general need to spell correctly. Many people think getting them wrong is a ‘worse’ mistake than simply mis-spelling a word because it means that you don’t really know what you’re doing. Anyone can make a spelling mistake, but using completely the wrong word somehow seems a lot worse. That may not sound fair, but that’s just how a lot of people think, so it’s worth learning the common homophones so you don’t get caught out.

Here’s a list of the main ones:

Spellings Meanings
a lot/allot much/distribute
ad/add notice/put together
ads/adds/adze notices/puts together/type of axe
aid/aide help/assistant
ail/ale trouble (verb)/beer
air/heir atmospheric gas/inheritor
aisle/isle/I’ll corridor/island/I will
all ready/already everything set/by a certain time
all together/altogether everyone in the same place/absolutely
all/awl totally/piercing tool
allowed/aloud permitted/out loud
alter/altar change/church table
ant/aunt insect/parent’s sister or brother’s wife
arc/ark part of circle/Biblical boat
assent/ascent agreement/rise
assistance/assistants help/helper
ate/eight consumed/8
aural/oral to do with hearing/to do with mouths
away/aweigh off/up (eg anchors aweigh)
ay/aye/eye/I yes/yes/organ of sight/1st person
bail/bale scoop water out/jump out
bait/bate food on hook/hold (eg bated breath)
ball/bawl sphere/
band/banned group/illegal
bard/barred poet/banned
bare/bear naked/tolerate or grizzly
baron/barren lord/arid
base/bass foundation/low note
be/bee exist/flying insect
beach/beech sandy area/type of tree
beat/beet hit/beetroot
beau/bow male admirer/bend down or front
bell/belle musical instrument/pretty girl
berry/bury fruit/inter
berth/birth sleeping place/arrival of baby
billed/build invoiced/construct
bite/byte nibble/unit of data
blew/blue forced air/colour
bloc/block group of countries/cuboid
boar/bore wild pig/boring person
board/bored flat object/weary
boarder/border lodger/edge
bode/bowed imply/curved
bolder/boulder braver/rock
born/borne created/tolerated
bough/bow branch/bend down or front of ship
boy/buoy male child/floating marker
brake/break slow down/shatter
breach/breech gap/part of gun
bread/bred food made with yeast/brought up
brewed/brood fermented/family
brews/bruise ferments/scar
bridle/bridal leather strap/to do with brides
broach/brooch open (a question)/piece of jewellery
browse/brows look through/hair above the eyes
but/butt although/water tank
buy/by/bye purchase/by means of/goodbye
cache/cash hidden hoard/notes and coins
callous/callus heartless/blister
cannon/canon gun/collection of artistic works
canvas/canvass sail fabric/ask questions of
capital/capitol upper case or city/government building
carat/carrot/caret/karat weight/vegetable/arrow/share of gold
carol/carrel song/cubicle
cast/caste thrown/social class
cede/seed give up/reproductive unit
ceiling/sealing roof/making watertight
cell/sell part of body/exchange for money
cellar/seller basement/person selling
censor/sensor ban (film etc)/measurement device
cent/scent/sent US penny/perfume/dispatched
cents/scents US pennies/perfumes
cereal/serial breakfast dish/TV show
cession/session giving up/period of course
chance/chants luck/songs
chased/chaste pursued/like a virgin
cheap/cheep inexpensive/bird sound
chews/choose nibbles/select
chilly/chilli cold/hot food
choir/quire group of singers/unit of paper
chord/cord group of notes/string
chute/shoot disposal passage/take shot at goal
cite/sight/site quote/seeing/location
clause/claws paragraph/talons
coarse/course rough/track or route
colonel/kernel army rank/stone in fruit
complement/compliment go well with/say something nice
coo/coup sound of dove/revolution
core/corps centre/army unit
correspondence/correspondents letters/letter-writers
council/counsel governing body/advice
councillor/counsellor governor/advisor
creak/creek whine/stream
crews/cruise teams/voyage
cue/queue snooker tool/line of people waiting
currant/current dried fruit/electric flow
cymbal/symbol musical instrument/icon
dam/damn river barrier/damnation
days/daze 24-hour periods/confuse
dear/deer expensive/type of mammal
defused/diffused made safe/circulated
desert/dessert sandy zone/pudding
dew/do/due water on grass/finish/owed
die/dye expire/colour (verb)
discreet/discrete not talkative/separate
doe/dough/doh female dear/unbaked bread/oh, no
done/dun finished/grey-brown
draft/draught practise writing/on tap (eg beer)
dual/duel in two parts/fight with swords etc
earn/urn/ern or erne make money/vase/type of bird
ewe/you/yew female sheep/2nd person/type of tree
faint/feint lose consciousness/fake attack
fair/fare just/food
fated/feted destined/celebrated
faun/fawn rural god/beige or young deer
faze/phase  disturb/stage
feat/feet achievement/plural of foot
find/fined seek/told to pay money
fir/fur type of tree/animal hide
flair/flare talent/bullet making bright light
flea/flee type of insect/run away
flew/flu/flue past tense of fly/influenza/chimney
flocks/phlox herds/type of plant
flour/flower ingredient for bread/plant
for/four/fore to the benefit of/4/in front
fort/forte castle/speciality
forth/fourth forwards/4th
foul/fowl disgusting/birds
friar/fryer  monk/pan
gait/gate way of walking/door outside
gene/jean DNA unit/trousers
gild/guild cover in gold/organisation
gilt/guilt covered in gold/having done wrong
gored/gourd holed/fruit or water container
gorilla/guerrilla type of ape/freedom fighter
grate/great fireplace/grand
grease/Greece lubrication/a country
groan/grown moan/past tense of grow
guessed/guest past tense of guess/invitee
hail/hale celebrate/healthy
hair/hare strands growing on head/rabbit
hall/haul room/pull
hangar/hanger storage for aircraft/hook in wardrobe
hay/hey dried grass/oy
heal/heel/he’ll make well/back of foot/he will
hear/here listen/in this place
heard/herd past tense of hear/group of animals
heed/he’d pay attention to/he would or he had
hertz/hurts frequency unit/causes pain
hew/hue/Hugh cut/colour/a name
hi/high hello/raised
higher/hire more raised/rent
him/hymn a pronoun/religious song
hoard/horde collection/mass of people
hoarse/horse rough (of voices)/an animal
hoes/hose garden tools/tube
hold/holed keep or carry/past tense of hole
hole/whole space/entire
holey/holy/wholly with holes/sacred/completely
hour/our 60 minutes/a pronoun
humorous/humerus funny/arm bone
idle/idol lazy/religious statue
illicit/elicit illegal/draw out
in/inn inside/hotel
instance/instants example/moments
intense/intents fierce/purposes
it’s/its it is/belonging to it
jam/jamb fruit spread/door frame
kernel/colonel core/army rank
knap/nap crest/doze
knead/kneed/need mix dough/hit with knee/require
knight/night warrior/dark time
knit/nit fit together/egg of louse
knot/not tied rope/negative
know/no/Noh be aware of/negative/type of drama
knows/nose is aware of/facial feature
laid/lade past tense of lay/load ship
lain/lane past participle of lay/alley
lay/lei place/flower necklace
leach/leech leak/blood-sucking worm
lead/led heavy metal/past tense of lead
leak/leek drop out/vegetable
leased/least past tense of lease/superlative of less
lee/lea shadow of wind/meadow
lessen/lesson make less/teaching session
levee/levy embankment/tax
liar/lyre person who lies/musical instrument
license/licence permit (verb)/permission
lichen/liken mould/compare
lie/lye falsehood/alkali solution
links/lynx connections/wild cat
load/lode put into/vein of metal in ground
loan/lone lending/single
locks/lox secures/smoked salmon (American)
loot/lute money/musical instrument
made/maid created/young woman
mail/male post/masculine
main/mane/Maine chief/hair/state in USA
maize/maze corn/labyrinth
manner/manor way/lord’s house
mantel/mantle mentalpiece/coat
marshal/martial army rank/to do with war
massed/mast brought together/upright post on ship
maybe/may be perhaps/might be
meat/meet/mete type of food/get together/distribute
medal/meddle award/interfere
metal/mettle shiny material/spirit
might/mite may/tiny spider
mince/mints ground beef/plural of mint
mind/mined brain/dug up
miner/minor/mynah digger/junior/type of bird
missed/mist past tense of miss/fog
moan/mown groan/past participle of mow
mode/mowed way/past tense of mow
moose/mousse elk/foam
morn/mourn morning/regret
muscle/mussel part of body/sea creature
mustard/mustered spicy dressing/broughted together
naval/navel to do with the navy/belly button
nay/neigh no (dated)/sound of horse
none/nun not one/female monk
oar/or/ore blade/alternatively/metal source
ode/owed poem/due
oh/owe/o ah/have a debt of/oh (poetic)
overseas/oversees foreign/manages
pail/pale bucket/faint
pain/pane ache/window panel
pair/pare/pear couple/shave/type of fruit
palate/palette/pallet part of mouth/artist’s tray/platform
passed/past past tense of pass/in the past
patience/patients tolerance/people in hospital
pause/paws break/animal hands and feet
pea/pee vegetable/urinate
peace/piece harmony/bit
peak/peek/pique summit/look quickly/annoyance
peal/peel sound of bells/take skin off
pearl/purl precious stone/knitting stitch
pedal/peddle foot lever/sell
pedalled/peddled cycled/sold
peer/pier look carefully/jetty
per/purr for each/sound of a cat
pi/pie 3.14/dish topped with pastry
plain/plane unexciting/2D object
pleas/please requests (noun)/if it pleases you
plum/plumb type of fruit/measure water depth
pole/poll rod/election or survey
pore/pour concentrate on/flow
practice/practise rehearsal/rehearse
pray/prey talk to God/victim
presence/presents being somewhere/gifts
prince/prints son of monarch/printed photographs
principal/principle main/rule of conduct
profit/prophet money made/religious seer
rack/wrack wire tray/shipwreck
rain/reign/rein water from clouds/rule/control strap
raise/rays/raze lift/plural of ray/destroy
rap/wrap hit/pack up (eg a present)
rapped/rapt/wrapped past tense of rap/spellbound/past tense of wrap
read/red past tense of read/scarlet
read/reed study/type of plant
real/reel genuine/cylinder for fishing line etc
reek/wreak smell bad/cause
rest/wrest relax/wrench away
retch/wretch vomit/poor soul
review/revue look over/stage performance
right/rite/write correct/ritual/form Leopardtters
ring/wring sound of bell/squeeze out water
road/rode/rowed street/past tense of ride/past tense of row
roe/row female deer/use oars
role/roll part in play/type of bread
root/route part of plant/roads to take
rose/rows type of flower/tiers
rote/wrote repetition/past tense of write
rough/ruff coarse/Elizabethan collar
rung/wrung past tense of ring/squeezed water out
rye/wry cereal plant/mocking
sail/sale canvas propulsion/selling
scene/seen situation/past tense of see
scull/skull row alone/head of skeleton
sea/see ocean/be aware of
seam/seem sewn connection/appear
seas/sees/seize oceans/is aware of/grab
serf/surf agricultural worker/waves
sew/so/sow connect with thread/thus/plant
shear/sheer cut/complete
shoe/shoo footwear/chase away
side/sighed edge/past tense of sigh
sighs/size breathes out/dimensions
slay/sleigh kill/sled
sleight/slight deceptive skill/faint
soar/sore rise/painful
soared/sword past tense of soar/bladed weapon
sole/soul only/spirit
some/sum a few/total
son/sun male child/star in the sky
staid/stayed unadventurous/past tense of stay
stair/stare step/look hard
stake/steak wooden post/joint of meat
stationary/stationery motionless/writing materials
steal/steel run off with/metal compound
step/steppe stair/European plains
stile/style fence steps/manner
straight/strait not bending/narrow strip of water
suite/sweet hotel rooms/sugary
summary/summery brief account/to do with summer
surge/serge rush/type of cloth
tacks/tax nails/levy
tail/tale back end/story
taught/taut past tense of teach/tight
tea/tee meal/golf ball holder
team/teem group of players/swarm
tear/tier teardrop/row
tern/turn type of bird/go round a corner
their/there/they’re belonging to them/in that direction/they are
theirs/there’s the one belonging to them/there is
threw/through past tense of throw/in and out of
thrown/throne past participle of throw/royal chair
thyme/time type of herb/progress of days or years
tic/tick habit/mark (if correct)
tide/tied flow of water/past tense of tie
to/too/two towards/as well/2
toad/towed frog/past tense of tow
toe/tow part of foot/pull
told/tolled past tense of tell/rang
trussed/trust bound (with rope)/belief
vain/vane/vein proud/fin/artery
vale/veil valley/lace face covering (for brides etc)
vial/vile test tube/evil
wade/weighed walk in water/past tense of weigh
wail/whale howl/type of ocean mammal
waist/waste middle of body/use carelessly
wait/weight delay or stay/mass
waive/wave give up/breaker
ware/wear/where pottery/put on clothes/which place
way/weigh/whey manner/measure weight/part of milk
ways/weighs manners/measures weight
we/wee pronoun/urination or little
weak/week feeble/seven days
weather/whether climatic conditions/if
we’d/weed we would or we had/unwanted plant
we’ll/wheel we will or we shall/round component
wet/whet liquid/sharpen
we’ve/weave we have/make cloth
which/witch pronoun/wizard
while/wile as/ruse or cunning plan
whine/wine whimper/alcoholic grape drink
who’s/whose who is or who has/of whom the
wood/would tree material/conditional marker
yoke/yolk part of plough/yellow part of egg
yore/your/you’re former times/belonging to you/you are
you’ll/Yule you will or you shall/Christmas

 

 

 

 

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French Regular Verbs – Present Subjunctive Tense

The subjunctive in French is generally used in the present tense after expressions such as ‘il faut que’ and some verbs that also take the word ‘que’ after them. These are generally the ones that express feelings or doubts (eg vouloir and craindre), especially when two parts of a sentence have different subjects, eg ‘I want her to be happy’ becomes ‘Je veux qu’elle soit contente’. Verbs ending in -er or -re have one set of endings, but  -ir verbs have another (shown here in red):

Verbs Ending in -er, eg Donner (to Give)

Je donne          (I may give)
Tu donnes          (You may give – informal)
Il/elle donne          (He/she may give)
Nous donnions          (We may give)
Vous donniez          (You may give – formal and/or plural)
Ils/elles donnent          (They may give – masculine or masculine and feminine/feminine only)

Verbs Ending in -re, eg Vendre (to Sell)

Je vende          (I may sell)
Tu vendes          (You may sell – informal)
Il/elle vende          (He/she may sell)
Nous vendions          (We may sell)
Vous vendiez          (You may sell – formal and/or plural)
Ils/elles vendent          (They may sell – masculine or masculine and feminine/feminine only)

Verbs Ending in -ir, eg Finir (to Finish)

Je finisse          (I may finish)
Tu finisses          (You may finish – informal)
Il/elle finisse          (He/she may finish)
Nous finissions          (We may finish)
Vous finissiez          (You may finish – formal and/or plural)
Ils/elles finissent          (They may finish – masculine or masculine and feminine/feminine only)

 

 

 

 

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Circle Theorems

This article explains circle theorems, including tangents, sectors, angles and proofs (with thanks to Revision Maths).

Isosceles Triangle

Two Radii and a chord make an isosceles triangle.

Perpendicular Chord Bisection

The perpendicular from the centre of a circle to a chord will always bisect the chord (split it into two equal lengths).

Angles Subtended on the Same Arc

Angles subtended on the same arc

Angles formed from two points on the circumference are equal to other angles, in the same arc, formed from those two points.

Angle in a Semi-Circle

angle in a semi-circle

Angles formed by drawing lines from the ends of the diameter of a circle to its circumference form a right angle. So c is a right angle.

Proof

We can split the triangle in two by drawing a line from the centre of the circle to the point on the circumference our triangle touches.

Divide the triangle in two

We know that each of the lines which is a radius of the circle (the green lines) are the same length. Therefore each of the two triangles is isosceles and has a pair of equal angles.

Two isosceles triangles

But all of these angles together must add up to 180°, since they are the angles of the original big triangle.

Therefore x + y + x + y = 180, in other words 2(x + y) = 180.
and so x + y = 90. But x + y is the size of the angle we wanted to find.

Tangents

A tangent to a circle is a straight line which touches the circle at only one point (so it does not cross the circle- it just touches it).

A tangent to a circle forms a right angle with the circle’s radius, at the point of contact of the tangent.

angle with a tangent

Also, if two tangents are drawn on a circle and they cross, the lengths of the two tangents (from the point where they touch the circle to the point where they cross) will be the same.

Tangents from an external point are equal in length

Angle at the Centre

Angle at the centre

The angle formed at the centre of the circle by lines originating from two points on the circle’s circumference is double the angle formed on the circumference of the circle by lines originating from the same points. i.e. a = 2b.

Proof

You might have to be able to prove this fact:

proof diagram 1

OA = OX since both of these are equal to the radius of the circle. The triangle AOX is therefore isosceles and so ∠OXA = a
Similarly, ∠OXB = b

proof diagram 2

Since the angles in a triangle add up to 180, we know that ∠XOA = 180 – 2a
Similarly, ∠BOX = 180 – 2b
Since the angles around a point add up to 360, we have that ∠AOB = 360 – ∠XOA – ∠BOX
= 360 – (180 – 2a) – (180 – 2b)
= 2a + 2b = 2(a + b) = 2 ∠AXB

Alternate Segment Theorem

Alternate segment theorem

This diagram shows the alternate segment theorem. In short, the red angles are equal to each other and the green angles are equal to each other.

Proof

You may have to be able to prove the alternate segment theorem:

proof of alternate segment theorem

We use facts about related angles

A tangent makes an angle of 90 degrees with the radius of a circle, so we know that ∠OAC + x = 90.
The angle in a semi-circle is 90, so ∠BCA = 90.
The angles in a triangle add up to 180, so ∠BCA + ∠OAC + y = 180
Therefore 90 + ∠OAC + y = 180 and so ∠OAC + y = 90
But OAC + x = 90, so ∠OAC + x = ∠OAC + y
Hence x = y

Cyclic Quadrilaterals

cyclic quadrilateral is a four-sided figure in a circle, with each vertex (corner) of the quadrilateral touching the circumference of the circle. The opposite angles of such a quadrilateral add up to 180 degrees.

Area of Sector and Arc Length

A sector

If the radius of the circle is r,
Area of sector = πr2 × A/360
Arc length = 2πr × A/360

In other words, area of sector = area of circle × A/360
arc length = circumference of circle × A/360

 

 

 

 

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Verbal Reasoning

Verbal Reasoning

Verbal Reasoning (VR) tests were invented to test pupils’ logic and language skills – although they do sometimes includes questions about numbers. In order to do well in a VR test, the most important thing is to be systematic, to have a plan for what to do if the question is hard.

Fortunately, there are plenty of past papers available online (including on this website!), so the types of question are well known. Here is a guide to the different kinds of problems and the best ways to approach them. I’m sorry that there are so many, but it’s best to be ready for anything…!

First of all, let’s just talk briefly about exam technique. Verbal Reasoning tests are always multiple choice, so it’s very important to answer every question. If you don’t know the answer, you should work by process of elimination until you have as few options left as possible and then guess.

Guessing is fine in Verbal Reasoning: the only thing worse than a wrong answer is no answer at all! You can then mark those questions by circling or underlining the question numbers or putting an asterisk next to them so that you can easily review your guesses if you have any time left after finishing the paper.

It’s very tempting to give up when you see a difficult question, but that won’t get you any marks. Having said that, you shouldn’t spend too long on the hardest questions. In general, you get around 40-60 seconds for each question, so you should be prepared to guess after roughly that amount of time. 

Another part of exam technique is to read the questions carefully. You’re never going to get the right answer to the wrong question, so feel free to read the question again if you’re not quite sure what it means.

Muddled Words (Anagrams)

Anagrams are words in which the letters have been muddled up. A typical question asks you to complete a sentence by putting the letters of one of the words in the correct order.

The easiest way to do this is to write out all the letters in a three-by-three grid (or a circle). That way, you force your brain to look for new possibilities rather than focusing too much on what’s there already.

For example, if you’re told that ‘A hammer is used to drive in SLAIN’, you don’t want to think about the word ‘SLAIN’ because you know it’s not the right answer, so you should write the letters out in a grid like this:

     A
S   N    L
      I

Write the letters out in pairs from the original word, making sure each pair is on opposite sides of the grid, ie the S and L are on the left and right, the A and I are top and bottom and the N is on its own, so you can put it in the middle. Obviously, there might be gaps in the grid, but that’s fine.

Once you’ve completed the grid, think about the context of the sentence. What would make sense? In this case, what would a hammer be hitting? Sometimes, it’s so obvious you don’t need to worry about the anagram, but if it’s not, try to think of words that would make sense beginning with each possible letter. 

Insert a Letter

One common type of question asks you to say which letter will start and finish two pairs of words, eg PRES( )TAND and WIND( )TAIN. Sometimes the answer is obvious (‘S’ in this case), but, if it’s not, the best thing to do is to look at all four words one after the other to see which letter might fit and then try that letter in the other words.

If that doesn’t work, you should at least be able to work out if it’s a vowel or a consonant that’s missing, and it’s also useful to know the most common letters in the English language, which are (in order) E, T, A, O, N, I, R, S and H.

Finally, you might just have to go through every letter of the alphabet, but there are only 26, so it shouldn’t take too long! Bear in mind that there are different ways of pronouncing letters and different places to put the emphasis, so try writing down the likely options as well as saying them in your head.

Find the Odd Words

In this kind of question, you’re given five words, and you have to spot the two that don’t fit with the others, eg Lorry, Helicopter, Taxi, Bus, Plane. The best way is to try and find the three words that go together – whatever is left must be the odd ones out.

Don’t just try to find a pair of words that go together. If you do, you might get the answer wrong if there’s another word that goes with them. You might also get it wrong because the ‘odd ones out’ don’t have anything in common. In this case, ‘Helicopter’ and ‘Plane’ ARE related, but they don’t have to be.

If there are one or more words you don’t know, you can at least work out which parts of speech they are. Once you know that, you will probably be able to see which ones belong together. For example, look at this list of words: spade, dig, cultivate, grow, bulb.

If you don’t know what ‘cultivate’ means, you should write down ‘noun’ next to spade and bulb and ‘verb’ next to dig and grow. After that, you can ask yourself if spade and bulb have anything in common. They don’t, but dig and grow do, so that means ‘cultivate’ must belong with them, and the odd ones out must be spade and bulb.

Alphabet Codes/Code Words

Here, you’ll be asked either to put a word into code or to decode a word. To do that, you’ll be given a word and the coded version, and it’s up to you to work out how the code works, eg STRAW might become UVTCY.

Normally, you just have move one or two spaces forwards or backwards in the alphabet (in this case, it’s +2), but look out for other combinations. They might involve changing direction or a change to the number of spaces or a combination of both, eg -1, +2, -3, +4.

The good news is that you’ll usually have an alphabet printed next to the question, so you can put your pencil on a letter and ‘walk’ forwards or backwards to get the coded version, but you can also write down the code underneath the word and write down how to get each letter with a positive or negative number – just make sure you don’t get confused between coding and decoding!

Synonyms (Similar Meaning)

Synonyms are words that have similar meanings, such as cold and chilly. In synonym questions, you’re given two groups of three words, and you have to find two synonyms, one from each group, eg (FILTER MATCH BREAK) (DENY DRAIN CONTEST).

The first thing to do is to have a quick look at all the words to see if the answer’s obvious (MATCH and CONTEST, in this case). If it is, write it down. If it’s not, you have to be systematic: start with the first word in the first group and compare it with the first, second and third words in the other group. If that doesn’t work, repeat for the second and third words of the first group.

Just be careful to think about ALL the possible meanings of a word, eg ‘minute’ can mean 60 seconds, but it can also mean very small! If you still can’t do the question (because you don’t know one or more of the words), try to work by process of elimination.

That means narrowing down the options by getting rid of any pairs of words that definitely don’t mean the same. Once you’ve done that, feel free to guess which one of the leftover pairs is the answer.

One way of checking words mean the same thing is to think of a phrase or sentence containing one of them and then try substituting all the other options. For example, if the words are (cook, meal, room) and (oven, space, eat), start with ‘I like to cook dinner’ and then try all three of the other words.

Does ‘I like to oven dinner’ mean the same? What about ‘I like to space dinner’ or ‘I like to eat dinner’? If none of the words fits exactly, then move on to the next word in the left-hand bracket and then the last one, if necessary. In the end, you should find the answer, which in this case is ‘room’ and ‘space’.

You can also narrow down the options by checking the parts of speech. If you’re looking for a word that means the same, it will have to be the same part of speech as the other word, eg a noun, verb or adjective.

Hidden Words

These questions ask you to find ‘hidden’ four-letter words between two other words in a sentence, using the last few letters from one word and the first few from the next, eg ‘The bird sat on the roof’.

Again, scan the sentence quickly to see if the answer’s obvious. If it is, write it down. If it’s not, check every possibility by starting with the last three letters of the first word and the first letter of the second word, moving forward one letter at a time and then checking the next pair of words.

You might want to put your fingers on each pair of words with a four-letter gap in the middle so that you can see all the options as they appear just by moving your fingers along the line. In this example, the possible words are theb, hebi, ebir, irds, rdsa, dsat, sato, aton, tont, onth, nthe, ther, hero and eroo, so the answer is obviously ‘hero’, but note that ‘tont’ is spread over three words (sat, on and the), and some words are not long enough to have the usual number of possibilities.

Find the Missing Word

These questions ask you to find a missing set of three letters that make up a word, eg There is an INITE number of stars in the sky. First of all, look at the word in capitals and try to work out what it’s meant to be in the context of the rest of the sentence.

If it’s not obvious, try working out where the letters might be missing – is it after the first letter or the second or the third etc? Sometimes you might not know the word (‘INFINITE’ and therefore ‘FIN’ in this case), but, again, it’s worth a guess – just make sure your made-up word sounds reasonable!

Algebra (Calculating with Letters)

This is one type of question that’s easier if you’re good at Maths! Algebra uses letters to stand for numbers and is a way of creating useful general formulas for solving problems. In Verbal Reasoning tests, you’ll generally have to add, subtract, multiply and/or divide letters, eg A = 1, B = 2, C = 3, so what is A – B + C?

The first step is to convert the letters to numbers, and then you can simply work out the answer as you would in Maths. Just make sure you’re aware of BIDMAS/BODMAS. This is an acronym that helps you remember the order of operations: Brackets first, then Indices/Order (in other words, powers such as x squared), then Division and Multiplication and lastly Addition and Subtraction.

Note that addition doesn’t actually come before subtraction – they belong together, so those sums should be done in the order they appear in the question, eg in this case, A – B must be done first (1 – 2 = -1) and then C added on (-1 + 3 = 2).

Antonyms (Opposite Meaning)

Antonyms are words that have opposite meanings, such as hard and soft. In antonym questions, you’re given two groups of three words, and you have to find two antonyms, one from each group, eg (GROW WATER WILD) (SLICE FREE TAME).

The first thing to do is to have a quick look at all the words to see if the answer’s obvious (WILD and TAME, in this case). If it is, write it down. If it’s not, you have to be systematic: start with the first word in the first group and compare it with the first, second and third words in the other group.

If that doesn’t work, repeat for the second and third words of the first group. Just be careful to think about ALL the possible meanings of a word, eg ‘minute’ can mean 60 seconds, but it can also mean very small!

If you still can’t do the question (because you don’t know one or more of the words), try to work by process of elimination. That means narrowing down the options by getting rid of any pairs of words that definitely don’t mean the opposite to each other. Once you’ve done that, feel free to guess which one of the leftover pairs is the answer.

Complete the Calculation

This is another number question, and it again means you need to know BIDMAS/BODMAS. You’ll be given an equation (or number sentence), and you just have to fill in the missing number to make sure it balances, eg 24 – 10 + 6 = 8 + 7 + ( ).

First of all, work out what the complete side of the equation equals, and then add, subtract, divide or multiply by the numbers in the other side to work out the answer (in this case, 24 – 10 + 6 = 20, and 20 – 8 – 7 = 5, so 5 is the answer). Don’t forget you’re working backwards to the answer, so you have to use the opposite operators!

Rearrange to Make Two New words

In these questions, you’re given two words, and you have to take a letter from the first word and put it in any position in the second word to leave two new words, eg STOOP and FLAT.

Again, check first to see if the answer’s obvious, but then work through systematically, picking letters from the first word one by one and trying to fit it into each position in the second word. (In this case, the answer is STOP and FLOAT.) Remember that both the new words must make sense!

Number Relationship

This is another Maths question in which you’ll be given three sets of numbers in brackets with the middle one in square brackets. The middle number in the final set is missing, though, so you have to calculate it using the two on either side, based on what happens in the first two sets, eg (3 [15] 5) (2 [8] 4) (7 [ ] 3).

The calculation will only involve the four basic operations (addition, subtraction, multiplication and division), but it gets much harder when the numbers appear more than once!

In this example, all you need to do is multiply the outside numbers to get the answer (3 x 5 = 15 and 2 x 4 = 8, so 7 x 3 = 21), but you might get more complicated questions like this one: (16 [40] 8) (11 [27] 5) (4 [ ] 11). Here, you have to add the first number to itself and then add the other one (16 + 16 + 8 = 40 and 11 + 11 + 5 = 27, so 4 + 4 + 11 = 19).

These kinds of questions can be very difficult, so try not to spend too long on them. If it takes more than a minute or so to answer a question, it’s time to move on. You can always come back later if you have time at the end of the test.

Alphabet Series/Sequence

These questions are a variation on number sequences in Maths – except using letters – and you answer them in the same way. You’re presented with several pairs of letters, and you have to fill in the blanks by working out what the patterns are, eg AB BD CF ??.

The best way to do this is to focus on the first and second letters of each pair separately as there will always be a pattern that links the first letters of each pair and a pattern that links the second letters of each pair, but there usually won’t be a pattern that links one letter to the next.

There’ll be a printed alphabet next to the question, so just do the same as you would for a number sequence question in Maths, drawing loops between the letters and labelling the ‘jump’ forwards or backwards in the alphabet, eg +1 or -2. Once you know what the pattern is, you can use it to work out the missing letters.

Just watch out for sequences with two patterns mixed together, eg CD TS GH RQ KL PO ?. Here, the first, third and fifth pairs of letters make up the sequence (with two letters missing between each pair), so the answer is OP. 

Analogies (Complete the Sentence)

In this type of question, you’re given a sentence that includes three possibilities for two of the words. You have to use logic and common sense to work out what the two other words should be, eg Teacher is to (bus, school, kitchen) as doctor is to (office, train, hospital).

This is known as an analogy: you have to work out the relationship of the first word to one of the words in the first set of brackets in order to find the same relationship in the second half of the sentence.

Again, the best way to do it is to have a quick scan to see if the answer’s obvious. If it is, write it down. If it’s not, go through the possibilities one by one, making sure to put the relationship into words. In this example, a teacher ‘works in a’ school, and a doctor ‘works in a’ hospital, so ‘school’ and ‘hospital’ are the answer.

Word Codes

These are complicated! You are given four words and three codes, and you have to find the code for a particular word or the word for a particular code, eg TRIP PORT PAST TEST and 2741 1462 1851.

Unfortunately, there’s no set way of doing these kinds of questions, so you just have to use a bit of logic and common sense. It’s useful to remember that each letter is always represented by the same number, so you can look for patterns in the letters that match patterns in the numbers, eg a double T in one of the words might be matched by a double 3 in one of the codes, so that means T = 3, and you can also find out the numbers for all the other letters in that word.

In this example, TEST starts and finishes with the same letter, and 1851 starts and finishes with the same number, so TEST = 1851, which means T = 1, E = 8 and S = 5. You can then fill in those numbers for each of the remaining words, so TRIP = 1???, PORT = ???1 and PAST = ??51.

Next, you should be able to see that the letter R is the second letter in TRIP and the third in PORT, and that’s matched by the number 4, which is the second number in 1462 and the third in 2741.

That means R = 4, which means TRIP = 14??, PORT = ??41 and PAST = ??51. The only code starting with 14 is 1462, so TRIP = 1462, and the only code ending with 41 is 2741, so PORT = 2741 and the only code ending with 51 is 2351, so PAST = 2351. If PAST = 2351, that also tells us that A must equal 3, so you now know what each letter stands for, and you can answer any possible question they might throw at you. Phew!

Complete Word Pairs

These questions are similar to word codes but, fortunately, much easier! You are given three pairs of words in brackets, and you have to work out the missing word at the end by what has gone before, eg (SHOUT, SHOT) (SOLDER, SOLE) (FLUTED, ).

The best way to go about it is to write down the position of the letters in the second word of the first two sets of brackets as they appear in the first.

In other words, the letters from SHOT appear in positions 1, 2, 3 and 5 in the first word, and the letters from SOLE also appear in positions 1, 2, 3 and 5 in the first word, so the missing word must consist of the same letters from FLUTED, which means it must be FLUE.

Now, you may not know that a flue is a kind of chimney, but don’t let that put you off. Just make sure you’ve got the right letters, and the answer must be right – even if you’ve never heard of it!

Another variation on this type of question contains a string of letters that appears in both words of each pair, just with a different letter or letters to start, eg (BLOAT, COAT) (CLING, DING) (SHOUT).

The easy bit is to find the repeated set of letters (in this case OAT) and to see that the second letter is dropped each time, but you still need to work out why the first letter changes (from B to C and then C to D).

That shouldn’t be too hard to work out, though, if you just go through the alphabet to find how many positions forwards or backwards you have to go (in this case, it’s +1, so the answer is TOUT).

Number Series/Sequences

These questions provide you with a series of numbers and ask you to fill in the blanks, which might be anywhere in the sequence, eg 1, 3, 5, 7, ?, ?. As with alphabet series, the best way to find the answer is to draw a loop between each pair of numbers and write down the change in value.

In this case, it’s simple (+2 each time), so the answer is 9 and 11, but look out for more complicated sequences. It’s worth knowing the most common sequences, just so you can recognise them at once and don’t have to work them out. Here are a few of the commonest ones:

Even numbers: 2, 4, 6, 8 etc… Rule: 2n
Odd numbers: 1, 3, 5, 7 etc… Rule: 2n – 1
Powers of 2: 2, 4, 8, 16 etc… Rule: 2ⁿ
Prime numbers: 2, 3, 5, 7 etc… Rule: n/a (each number is only divisible by itself and one)
Square numbers: 1, 4, 9, 16 etc… Rule: n²
Triangular numbers: 1, 3, 6, 10 etc… Rule: sum of the numbers from 1 to n
Fibonacci sequence
: 1, 1, 2, 3 etc… Rule: n₋₂ + n₋₁ (ie each successive number is produced by adding the previous two numbers together, eg 1 + 1 = 2, 1 + 2 = 3)

Things get trickier when the sequence is actually a mixture of two separate sequences, eg 1, 3, 2, 5, 3, ?, ?. Here, the integers (1, 2, 3 etc) are mixed in with odd numbers starting with 3 (3, 5 etc), so you can’t simply find the difference between one number and the next – you have to look at every other number.

In this example, the first missing number is the next integer after 1, 2 and 3, which is 4, and the second one is the next odd number after 3 and 5, which is 7.

Compound Words (Form New Word)

Here, you’re given two groups of three words, and you have to make a word by adding one from the first group to one from the second, eg (sleek pain seek) (search green killer).

Again, it’s important to be systematic, so you have to start with the first word in the first group and try to match it with each word in the second group. If that doesn’t work, repeat as necessary for the next two words in the first group. In this case, ‘pain’ goes with ‘killer’ to make ‘painkiller’.

Create a Word (from the Letters of Two Others)

These questions give you two groups of three words with the middle one in brackets in the first group and missing in the second, eg arise (rage) gears paste ( ) moans. What you have to do is work out what the missing word is by finding where the letters in the word in brackets in the first group come from.

They are all taken from the words outside the brackets, so it’s just a case of working out which letter in the words outside the brackets matches each letter in the word inside the brackets. Your best bet is to write down the second group of words underneath the first and go through each letter one by one.

Just look out for letters that either appear twice in one of the words or letters that appear in both words outside the brackets. Those will obviously give you two different possible letters for the answer word, so you should probably write both of them one above the other until you’ve worked everything out and then simply choose the one that makes a proper word.

In this example, the R from ‘rage’ might come from ‘arise’ or ‘gears’, so the first letter of the answer word is going to be either the second letter of ‘paste’ (A) or the fourth letter of ‘moans’ (N). The same is true of the A and E in ‘rage’. Once you work it all out, the letters are a or n, p or a, m and e or o, and the only sensible word is ‘name’.

Similar Meaning

These questions are slightly different from the synonym questions in that you have to choose a word out of five that has some similarity to or relationship with two pairs of words in brackets, eg (alter, amend) (coins, money) repair, trial, revue, change, passage.

The two pairs of words in brackets usually have different meanings, so you have to look for a word with a double meaning. Again, have a quick look at all the words to see if the answer’s obvious. If it is, write it down. If it’s not, go through the five words one by one, comparing them to the words in brackets.

It’s important to be open to the possibility of different meanings, so try to think laterally. In this example, for instance, the answer is ‘change’ as it can work as a verb meaning ‘alter’ or ‘amend’ but also as a noun meaning ‘coins’ or ‘money’.

Letter Relationships

For these questions, you’re given a sentence that describes the relationship between two pairs of letters – a little bit like the sentence analogies earlier. The final pair of letters is missing, so you have to work out what they are by finding the relationship between the first two pairs, eg CG is to ED as BW is to ( ).

You should see an alphabet line to help you. The first relationship to look at is between the first letter of the first two pairs. In this case, you get from C to E by moving forward two places in the alphabet.

That means you need to move two places on from B to get the first letter of the missing pair, which is D. Repeat this for the second letters, and you’ll find the other half of the answer. In this case, you get from G to D by going back three places, so you have to go back the same three places from W to get T. The overall answer is therefore DT.

Comprehension

The exact format of comprehension questions differs, but you’ll usually be given a lot of information about different people, and you’ll have to find the missing data. The subject could be people’s heights or ages, or it could be a schedule of events.

For example, three children – Susan, George and Ryan – all left school at 1515 and walked home. Susan arrived home first. George arrived home five minutes later at 1530. It took Ryan 10 minutes longer than Susan to walk home. What time did Ryan get home?

The way to approach any of these questions is to build a complete picture of the situation by starting with something you know and then working from there – a bit like building a jigsaw. Start with the absolute data (about heights, ages or times) and then move on to the relative data (comparing other people’s heights, ages or times).

One thing that often helps is to draw a timeline or simply write down the names of the children in order (of height, age etc). In this example, a timeline is probably your best option, starting at 1515 when the children left school and including George getting home at 1530. You can then add in Susan’s arrival time of 1525 (as she arrived five minutes before George) and finally Ryan’s arrival time of 1535 (as he arrived 10 minutes after Susan.

 

 

 

 

If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.

 

Non-verbal Reasoning

Non-verbal reasoning tests are commonly found in Common Entrance exams at 11+ and 13+ level, and they’re designed to test pupils’ logical reasoning skills using series of shapes or patterns. It’s been said that they were intended to be ‘tutor-proof’, but, of course, every kind of test can be made easier through proper preparation and coaching.

Bond produces a lot of useful books of past papers, and there is also a Bond guide on How To Do Non-verbal Reasoning available from Amazon for £8.98. This article is partly a summary of that book, but it’s useful to know how Bond thinks pupils should be doing the questions as they’re the ones producing most of them!

The first thing to do is to describe the kind of questions that are involved. Here is the list taken from the back of one of the Bond papers:

  • Finding the most similar shape
  • Finding a shape within another shape
  • Finding the shape to complete the pair
  • Finding the shape to continue the series
  • Finding the code to match the shape
  • Finding the shape to complete the square
  • Finding the shape that is a reflection of a given shape
  • Finding the shape made when two shapes are combined
  • Finding the cube that cannot be made from a given net

Bond divides the questions into four different types:

  • Identifying shapes
  • Missing shapes
  • Rotating shapes
  • Coded shapes and logic

Each of these types is divided into various subtypes.

Identifying Shapes

Types of question

  • Recognise shapes that are similar and different
  • Identify shapes and patterns
  • Pair up shapes

Sample Questions

  • “Which is the odd one out?”
  • “Find the figure in each row that is most unlike the other figures.”
  • “Which pattern on the right belongs with the two on the left?”
  • “Which pattern on the right belongs in the group on the left?”
  • “Which shape is most similar to the shapes in the group on the left?”

Missing Shapes

Types of Question

  • Find shapes that complete a sequence
  • Find a given part within a shape
  • Find a missing shape from a pattern

Sample Questions

  • “Which one comes next?”
  • “Which pattern completes the sequence?”
  • “Choose the shape or pattern the completes the square given.”
  • “In which larger shape or pattern is the small shape hidden?”
  • “Find the shape or pattern which completes or continues the given series.”

Rotating Shapes

Types of Question

  • Recognise mirror images
  • Link nets to cubes

Sample Questions

  • “Work out which option would look like the figure on the left it it was reflected over the line.”
  • “Work out which of the six cubes can be made from the net.”

Coded Shapes and Logic

Types of Question

  • Code and decode shapes
  • Apply shape logic

Sample Questions

  • “Each of the patterns on the left has a two-letter code. Select the correct code for the shape on the right following the same rules.”
  • “Select the code that matches the shape given at the end of each line.”
  • “Which one comes next? A is to B as C is to ?”
    “Which pattern on the right completes the second pair in the same way as the first pair? A is to B as C is to ?”

Hints and Tips

The Bond book goes into great detail about how to answer each individual type of question, but here we’ll only look at a few key things to look for:

  • Function
  • Location
  • SPANSS
  • Story
  • Symmetry
  • Nets
  • Process of elimination

When looking for similarities between shapes, one thing to think about is the ‘function‘ of the objects shown. In other words, what are they for? If all but one of the drawings show kitchen equipment, then the bedside lamp must be the odd one out.

Another way of looking at it is to think about the ‘location‘ of the objects shown. Where would you usually find them? If there is a rolling pin together with a lot of tools you’d find in the garage, then the tools ‘belong’ together in the same set.

Another useful way of working through a question is to use ‘SPANSS‘, which stands for Shape, Position, Angle, Number, Shading and Size (NOT ‘sides’, as some people have written online!). This is a list of all the possible things that can change in a diagram.

Non-verbal Reasoning questions demand that you’re very disciplined, logical and systematic when working through all the possibilities, so it’s useful to have a mnemonic such as SPANSS to help you tick off all the options.

If none of those works, another thing you can look for is a ‘story‘? For example, do the pictures show the steps you take to get ready for school in the morning, such as getting up, brushing your teeth, getting dressed and having breakfast?

You should also look out for ‘symmetry‘. Could the images be reflections of each other, or could they show rotational symmetry – in other words, has one pattern simply been turned upside-down or turned 90 degrees?

When trying to work out which two-dimensional nets could form which three-dimensional cubes, here are a few tips:

  • If the net has four squares in a row, try to imagine those wrapping round the four sides of a cube with top and bottom flaps that need to be folded over.
  • If the squares on the net share a long edge, they have to share the same edge in the cube (and vice versa).
  • You don’t always need to work out every side. If the question asks which cube can be made from a net (or vice versa), all you need is one side that doesn’t work to cross it off the list.

Finally, it’s a good idea to work by process of elimination. Just cross off all the answers that can’t be right until you’re left with only one. As Sherlock Holmes once said to Doctor Watson, “When you have eliminated the impossible, whatever remains, however improbable, must be the truth.”

I hope this brief outline has been useful. Beyond that, practice makes perfect, and a few lessons with a private tutor wouldn’t go amiss either…!

 

 

 

 

If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.

Creating Off-the-shelf Characters

Common entrance exams have a time limit. If they didn’t, they’d be a lot easier! If you want to save time and improve your story, one thing you can do is to prepare three ‘off-the-shelf’ characters to choose from.

You can work on them beforehand, improving them and memorising them as you go. By the time the exam comes around, it’ll be easy to dash off 8-10 lines about one of your favourite characters without having to spend any time inventing or perfecting them.

Here’s what you need to do.

The first thing to say is that you need your characters to be a little out of the ordinary. Most pupils writing stories tend to write about themselves. In other words, 10-year-old boys living in London tend to write stories about 10-year-old boys living in London!

Now, that’s all very well, and the story might still get a good mark, but what you want to try and do is stand out from the crowd. Why not write a story about an 18-year-old intern at a shark research institute in the Maldives?!

To decide which one you’d rather write about, you just have to ask yourself which one you’d rather read about. One thing you can do to make sure your characters are special is to give them all what I call a ‘speciality’ or USP (Unique Selling Proposition).

It might be a superpower such as X-ray vision or mind-reading, or it might be a special skill such as diving or surfing, or it might be a fascinating back-story such as being descended from the Russian royal family or William Shakespeare – whatever it is, it’s a great way to make your characters – and therefore your stories – just that little bit more interesting.

Secondly, you should also make sure all your characters are different. Try to cover all the bases so that you have one you can use for just about any story. That means having heroes that are male and female, old and young, from different countries and different historical periods and with different looks, personalities and USPs.

For instance, Clara might be the 18-year-old intern at a shark research institute in the Maldives, Pedro might be the 35-year-old Mexican spy during the Texas Revolution of 1835-6, and Kurt might be the 60-year-old Swiss inventor who lives in a laboratory buried deep under the Matterhorn! Who knows? It’s entirely up to you.

Thirdly, creating an off-the-shelf character is a great way to force yourself to use ‘wow words’ and literary techniques such as metaphors and similes. You may have learned what a simile is, but it’s very easy to forget to use them in your stories, so why not describe one of your heroes as having ‘eyes as dark as a murderer’s soul’?

If you use the same characters with similar descriptions over and over again, it’ll become second nature to ‘show off’ your knowledge, and you can do the same with your vocabulary. Again, why say that someone is ‘big’ when you can say he is ‘athletic’, ‘brawny’ or ‘muscular’?

Fourthly, try to stick to what you know. If you’ve never even ridden on a horse, it’s going to be quite tough to write a story about a jockey!

Alternatively, if you’ve regularly been to a particular place on holiday or met someone you found especially interesting, then use what you know to create your characters and their backgrounds. It’s always easier to describe places if you’ve actually been there, and it’s easier to describe people if you know someone similar.

So what goes into creating off-the-shelf characters? The answer is that you have to try and paint a complete picture. It has to cover every major aspect of their lives – even if you can’t remember all the details when you come to write the story. I’d start by using the following categories:

  • Name
  • Age
  • Job or education
  • Looks
  • Home
  • Friends and family
  • Personality
  • USP (or speciality)

Names are sometimes hard to decide on, so you might want to leave this one to last, but you just need to make sure it’s appropriate to the sort of character you’re creating. It wouldn’t be very convincing to have a Japanese scientist called Emily!

Age is fairly easy to decide. Just make sure your three characters are different – and not too close to your own age!

Job or education goes a long way to pigeon-holing someone. You can tell a lot from what someone does for a living or what they are doing in school or at university. You can include as much or as little detail as you like, but the minimum is probably the name and location of the school or college and what your characters’ favourite subjects are. You never know when it might come in handy!

Looks includes hair, eye colour, build, skin colour and favourite clothes. The more you describe your heroes’ looks, the easier it’ll be for the reader to imagine them.

Home can again be as detailed as you like, but the more specific the better. It’s easier to imagine the captain of a nuclear submarine patrolling under the North Pole than someone simply ‘living in London’…

Friends and family are important to most people, and it’s no different for the heroes of your stories. We don’t need to know the names of all their aunts, uncles, cousins and grandparents, but we at least need to know who they live with and who their best friends are.

Personality covers many things, but it should show what your characters are ‘like’ and what their interests are. Again, you don’t have to go into enormous depth, but it’s good to introduce the reader to qualities that might be needed later on in the story, such as athleticism or an ability to sail a boat.

USP stands for Unique Selling Point. It’s used in business to describe what makes products likely to succeed, from cars to Coke. When it comes to characters, the USP can be anything that makes them worth reading about. One of the reasons Superman is so popular is his superpowers: his ability to fly, his X-ray vision and the fact that he’s invulnerable. His greatest weakness is also important: Kryptonite. It’s the same for your characters. What can they do that most people can’t? What qualities can they show off in your stories? What will make them people we admire, respect and even love?

If you wanted to make Superman one of your off-the-shelf characters, this is what your notes might look like:

  • Name: Superman (or Clark Kent, Kal-El, The Man of Steel, The Last Son of Krypton, The Man of Tomorrow)
  • Age: Early 20s (when he first appears)
  • Job or education: News reporter at The Daily Planet in Metropolis
  • Looks: Tall, with a muscular physique, dark-haired, blue eyes
  • Home: Krypton, then the Kents’ farm in Smallville, Kansas, then Metropolis (or a fictionalised New York), where he lives in a rented apartment
  • Friends and family: Jor-El and Lara (biological parents)/Jonathan and Martha Kent (adoptive parents), Lois Lane (colleague, best friend, girlfriend), Jimmy Olsen (colleague), Perry White (boss as editor of The Daily Planet)
  • Personality: Noble, honest, caring, gentle, resolute, decisive
  • USP (or speciality): Superpowers, including invulnerability, super strength, X-ray vision, super hearing, longevity, freezing breath, ability to fly (but vulnerable to Kryptonite!)

Once you’ve created the notes for your three characters, you can write a paragraph of 8-10 lines about each of them. This is your chance to create something that you can easily slot into any of your stories, so use the past tense and stick to what the characters are like, not what they’re doing. That will be different in each story, so you don’t want to tie yourself down.

Here’s an example using Superman again:

Clark Kent led a double life. He wasn’t happy about it, but he needed his secret identity so that no one would find out who he really was. He might have been a mild-mannered reporter for The Daily Planet with a crush on his partner, Lois Lane, but he was also a crime-fighting superhero: he was Kal-El, Superman and The Man of Steel all rolled into one!

His secret was that he’d actually been born on Krypton and sent to Earth as a baby to protect him from the destruction of his home planet. He’d been found by a childless couple living on a farm in Smallville, Kansas, and Jonathan and Martha Kent had adopted him as their own.

They didn’t know where he’d come from, but they’d provided him with a loving home as they watched him grow into a blue-eyed, dark-haired, athletic young man with a passion for ‘truth, justice and the American way’.

And they soon realised he was special when they saw him lifting a tractor with one hand…! He was faster than a speeding bullet, more powerful than a locomotive and able to leap tall buildings in a single bound!
“Look! Up in the sky!”
“It’s a bird!”
“It’s a plane!”
“It’s Superman!”

Try using your characters for stories you’re asked to write by your English teacher (or tutor, if you have one). The more often you use them, the better they’ll get as you change things you don’t like about them, bring in new ideas and polish the wording.

If it helps, you could even do what one or two of my clients did for their sons, which was to feed their descriptions into an AI model to make pictures from them!

Next Steps

Try to create three off-the-shelf characters. Make them different ages, male and female and from different parts of the world. Start with the notes and then create a paragraph of 8-10 lines for each one in the past tense, ready to drop into any story…

If it helps, you could also print out a picture from the internet and put it on your wall, adding notes to it to describe all the details of the character. For example, if you like fantasy tales of ‘swords and sorcery’ and want a hero to match, you could find a warrior from a film such as The Lord of the Rings and scribble down words like ‘helm’, ‘scabbard’ and ‘jerkin’. You could even add poetic devices to describe your hero’s main characteristics, such as his ‘arms of wrought iron’ or his ‘eyes as green as emeralds’.

 

 

 

 

If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.

Children’s Reading List

I’m often asked by parents what books they should try to get their children to read, but I don’t think I’ve been much help so far, so this is my attempt to do better! If you’re still not convinced, there are a number of reading lists on my Useful Links page.

Tastes differ, obviously, so perhaps the best thing I can do is to list all the books that I loved when I was a boy. I can’t remember exactly how old I was when I read them, so you’ll have to use your common sense, but they did at least provide me with happy memories.

Ronald Welch

My favourite series of books when I was a child was the one written by Ronald Welch about the Carey family. He wrote about the men in the family over the course of around 500 years, from 1500 up to the First World War.

Each novel focused on one character in one particular period – rather like Blackadder, and there was a clear formula: whatever the period, he would have to fight a duel, he would do something heroic and he would win the fair lady!

The duels started with a dagger and a sword and then moved on to rapiers and then finally pistols as the years rolled on. I loved the military aspect to the books – as most boys would – and I read just about every single one I could get my hands on.

Unfortunately, they’re almost impossible to find in print nowadays, but it’s always worth a look…

CS Forester

CS Forester wrote the ‘Hornblower’ novels. I was interested in both sailing and military history when I was young, and this sequence of novels about a naval officer called Horatio Hornblower in the Revolutionary and Napoleonic Wars from 1792-1815 was a perfect blend of the two.

Alexander Kent (Douglas Reeman)

Alexander Kent was the pen name of Douglas Reeman, who wrote a series of novels about Richard Bolitho. I first came across him after finishing all the CS Forester novels, and he provided a similar mix of nautical and military history during the same period. They weren’t quite as good as the Hornblower novels, but I still enjoyed them.

Enid Blyton

I didn’t read absolutely all the Enid Blyton books when I was a boy, but the one that I do remember is The Boy Next Door. Among other things, I loved the name of the character (‘Kit’), I loved the bits about climbing trees and I also loved the word ‘grin’, which I never understood but thought was somehow magical!

Roald Dahl

Again, I don’t remember reading all the Roald Dahl novels, but James and the Giant Peach left a big impression. The characters were so interesting, and the idea of escaping from home on an enormous rolling piece of fruit was very exciting to me in those days…!

Sir Arthur Conan Doyle

I read The Complete Adventures of Sherlock Holmes when I was a boy, and it’s probably still the longest book I’ve ever read. I remember vividly that the edition I read was 1,227 pages long! I listened to the whole thing again recently in a very good audiobook edition read by Stephen Fry, and it was just as good second time around.

I loved the mystery of the stories, and I still read a lot of crime fiction even now. I’ve always had a very analytical mind, so Holmes’s brilliant deductions were always enjoyable to read about.

Charlie Higson

The Young Bond novels weren’t around when I was young, but I read the first few as an adult, and I enjoyed them. James Bond is a classic fictional creation that appeals to boys in particular, and I think I would’ve lapped it up as a teenager. The first one is called Silverfin. Once you’ve read it, you’ll be hooked!

Jane Austen

Jane Austen introduced me to irony with the immortal opening line from Pride and Prejudice, but the first of her novels that I read was actually Emma. I had to read it at school as part of my preparation for the Oxford entrance exam, and I didn’t like it at first.

However, that was just because I didn’t understand what was going on. Once my English teacher Mr Finn had explained that the character of Emma is always wrong about everything, I found it very funny and enjoyable. They say that ‘analysing’ a book can sometimes ruin it, but in this case it was quite the opposite.

Ernest Hemingway

“If Henry James is the poodle of American literature, Ernest Hemingway is the bulldog. What do you think?” I was once asked that question in an interview at the University of East Anglia, and I had no idea how to reply!

As it happens, Hemingway was one of my favourite authors. My interviewer called his style ‘macho’, but that wasn’t the appeal for me. I simply liked the stories and the settings. I particularly loved the bull-fighting scenes in The Sun Also Rises, and there was just a glamour to the characters and the period that I really enjoyed.

If you don’t know where to start, try The Old Man and the Sea. It’s very simple and very short, but very, very moving.

 

 

 

 

If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.

John McEnroe

Describing Feelings

In many 11+ and 13+ exams, you have to talk about feelings. Yes, I know that’s hard for most boys that age, but I thought it might help if I wrote down a list of adjectives that describe our emotions. Here we go…

A bloke called Bob (actually Robert Plutchik) thought that people only ever felt eight different emotions:

His list is shown in this ‘wheel of emotions’. The basic eight feelings are:

  • Ecstasy
  • Admiration
  • Terror
  • Amazement
  • Grief
  • Loathing
  • Rage
  • Vigilance

If we had a think about all the adjectives that are associated with these categories (and sub-categories), we might come up with a list like this one:

Ecstasy

crazy
delirious
ecstatic
elated
enthusiastic
euphoric
fervent
glad
happy
joyful
joyous
mad
overjoyed
rapturous
rhapsodic
serene
thrilled
upbeat

Admiration

accepting
admiring
adoring
appreciative
loving
respectful
trustful
trusting

Terror

afraid
aghast
alarmed
apprehensive
awed
frightened
frozen
scared
submissive
terrified

Amazement

amazed
astonished
astounded
awe-struck
bewildered
dazed
distracted
dumbfounded
flabbergasted
impressed
perplexed
shocked
staggered
startled
stunned
surprised
unprepared

Grief

bitter
grief-stricken
grieving
heart-broken
melancholy
mournful
pensive
pessimistic
sad
somber
sorrowful
sorry
unhappy
wistful

Loathing

appalled
bored
disapproving
disgusted
outraged
queasy
tired
weary

Rage

angry
aggressive
annoyed
contemptuous
enraged
exasperated
furious
heated
impassioned
indignant
irate
irritable
irritated
offended
resentful
sullen
uptight

Vigilance

anxious
aware
cautious
circumspect
expectant
interested
keen
observant
optimistic
vigilant
wary

 

 

 

 

If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.

Long Division

Long division is on the syllabus for both 11+ and 13+ exams, so it’s important to know when and how to do it.

The basic idea is that it’s tricky to do short division when the number you’re dividing by (the ‘divisor’) is outside your times tables, ie more than 12. Using long division makes it easier by including a way of calculating the remainder using a proper subtraction sum.

It also makes it neater because you don’t have to try and squeeze two-digit remainders in between the digits underneath the answer line (the ‘dividend’).

So how does it work? Well, the only difference involves the remainder. In normal short division, you work it out in your head and put it above and to the left of the next digit in the dividend.

In long division, you work out the multiple of the divisor, write it down under the dividend and subtract one from the other to get the remainder. You then pull down the next digit of the dividend and put it on the end of the remainder, repeating as necessary.

To take the example at the top of the page, what is 522 divided by 18?

  1. How many 18s in 5?
  2. It doesn’t go
  3. How many 18s in 52?
  4. Two (write 2 on the answer line, and write 36 under the dividend with a line beneath it)
  5. What’s 52 – 36?
  6. 16 (write it on the next line)
  7. Pull down the next digit from the dividend (write it after the 16)
  8. How many 18s in 162?
  9. Nine (write it on the answer line, giving 29 as the answer, or ‘quotient’)

That’s the basic method, but here are a couple of tips to help you out.

The first is that you can make life easier for yourself by guessing round numbers. Working with numbers outside your times tables is tricky, so you can use ‘trial and error’ to come up with the right multiple of the divisor by trying ‘easy’ ones like 5 or 10. If it’s too big or too small, you can simply try again with a smaller or bigger number.

The second is that you can often divide the divisor by two to force it back into your times tables. Why divide by 18 when you can simply divide by nine and halve the result? You just have to be careful that you only deal in even multiples, eg 52 ÷ 18 is tricky, but the nearest even multiple of 9 is 4 (as 5 is an odd number and 6 x 9 = 54, which is too much), so the answer must be 4.

Sample Questions

  1. 391 ÷ 17
  2. 666 ÷ 18
  3. 792 ÷ 24
  4. 2,327 ÷ 13
  5. 2,520 ÷ 15
  6. 2,583 ÷ 21
  7. 48,036 ÷ 12
  8. 10,008 ÷ 36
  9. 41,550 ÷ 25
  10. 38,880 ÷ 120

     

     

     

     

    If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.

How to Write a Letter

Writing a letter is not as easy as it might seem—especially if you have to do it during a Common Entrance exam! In this post, I’d like to explain the traditional format of formal and casual letters and the decisions on wording that you’ll have to make.

(Note that letters can also be written in various other ways, including block format. This involves aligning everything to the left and skipping a line between each paragraph.)

First of all, here’s a quick list of the main parts of a letter that the examiner will be looking at:

  • Sender’s address
  • Date
  • Greeting
  • Text
  • Sign-off
  • Signature

Sender’s Address

It’s important to put the address of the sender (not the recipient!) at the top right of the letter (see above). The postman obviously doesn’t look inside the letter, so the address of the recipient needs to go on the envelope instead!

The only exception is if it’s a business letter intended to be posted in a window envelope. In that case, it needs to have the recipient’s address positioned above the sender’s address at just the right height so that it shows through the window when an A4 sheet is folded in three.

The address should really be aligned right, so you must remember to leave enough space for yourself when you start writing each line. Otherwise, it’ll look a bit of a mess…

Note that you no longer need any punctuation in the address, either after the flat or house number or after each line. 

Date

The date should be placed two or three lines below the sender’s address (again aligned right) in the traditional long format rather than just in numbers, eg 31 May 2023 rather than 31/5/23 (or 5/31/23 if you’re American!). Just make sure you don’t put the month first, which is the style in American English, eg October 7, 2018.

Note that you should write the date using cardinal numbers (1, 2, 3 etc) but read it using ordinal numbers (1st, 2nd, 3rd etc), adding the words ‘the’ and ‘of’, eg what you write is 31 May 2023, but what you read is ‘the 31st of May 2023’.

Including the day of the week is optional, but if you do, you should put a comma after it, eg Monday, 7 October 2018.

Greeting (or Salutation)

Which greeting you use depends on the recipient. If you know the name of the person you’re writing to, then you should use ‘Dear’ rather than ‘To’, eg ‘Dear Mr and Mrs Dursley’. ‘To’ is fine for Christmas cards, but not for letters. You should also put a comma afterwards.

If you’re writing to a company or an organisation and you don’t know the name of the person, you have two options: you can either start the letter off with ‘Dear sir/madam’ or write ‘To whom it may concern’. This works better when it’s a reference for a job or a formal letter that may be circulated among several people.

Body

The body of the letter can obviously be whatever you like, but just make sure you start it underneath the comma after the greeting. You should also use paragraphs if the letter is more than a few lines.

The traditional way to start each paragraph is to ‘indent’ or push in the first word by a centimetre or so, and the traditional way to end each paragraph is to move to the next line—without skipping a line.

Sign-off (or Closing or Complimentary Close)

The sign-off is just the phrase you put at the end of the letter before your signature. If the letter is to a friend or relative, there aren’t any rules. You can say anything from ‘Love’ to ‘Best regards’ or ‘Yours ever’.

Note that they all start with a capital letter (though only for the first word) and should be followed by a comma. If it’s a business letter, the sign-off depends on the greeting: if you’ve used someone’s name, you should use ‘Yours sincerely’, but if you haven’t, it’s ‘Yours faithfully’.

Signature

The signature is very important in letter-writing as it’s a simple way of ‘proving’ who you are, so you should develop one that you’re happy with. It should include your first name or your initial(s) and your surname, eg Nick Dale, N Dale or NW Dale.

Your signature should be special, so it doesn’t need to be ‘neat’ or ‘clear’ like the rest of the letter. In fact, the prettier and the more stylish, the better!

And there you have it. This is only one way of writing a letter, and there are other ways of formatting the information, but these rules will at least give you the best chance of getting full marks in your Common Entrance exam!

 

 

 

 

If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.

Maths Trick

Here’s a Maths trick a friend of mine saw on QI. Who knows? It might make addition and subtraction just a little bit more fun!

  1. Find a book and write down the ninth word on p108, eg ‘becoming’.
  2. Ask someone to write down a number with three different digits in it, eg 321.
  3. Ask him to reverse it and take the smaller number away from the larger, eg 321 – 123 = 198.
  4. Ask him to write down the answer and, again, reverse it, eg 891.
  5. Ask him to add the two new numbers together, eg 198 + 891 = 1089.
  6. Ask him to find the ninth word on p108 of the book, eg ‘becoming’.
  7. Reveal the same word you wrote down earlier!

The trick is that the answer is always going to be 1089, whatever the number you first think of, so it should work every time – unless there’s a problem with the Maths!

 

 

 

 

If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.

The Ones that Got Away

I get nervous before I go on photography trips. Part of that is just worrying about travel arrangements, visas and packing everything I need, but another part of it is worrying that I won’t get the shots I want. Here are a few examples of ‘the ones that got away’.

Taj Mahal

Before I went to the Taj Mahal, I was determined to get the classic ‘Lady Diana’ shot of the building from the end of the reflecting pools. That was the whole point of the trip, and I was really worried about it. I couldn’t face the idea of screwing up what would probably be my only opportunity to visit the world’s most famous building.

When I arrived in India on a G Adventures trip in November 2013, we went to the Taj Mahal early one morning, around 0530. We had to queue for a while and then go through security. At that point, I was about to rush off and take the shot I’d been dreaming about, but our tour leader then introduced us all to a local guide who was about to give us a 15-minute lecture about the building.

What a nightmare!

I knew that the whole place would be crawling with tourists if I didn’t go and take the shot immediately, but it seemed a bit rude just to rush off without hearing the talk. In the end, I was too British about the whole thing and missed the shot of a lifetime. Too bad. On the plus side, I ended up with this image of the Taj Mahal.

It’s the very opposite of the ‘Lady Diana’ shot. One is all symmetry and clarity, the other is misty and mysterious. The higgledy-piggledy minarets and the blue haze make the building seem more like a fairy tale castle. I do like this shot, but I still regret being too polite to get the one I wanted…!

Jumping Impala

The one that got awayNot quite sharp enough…

This would’ve been a great shot. It could’ve been a great shot. It should’ve been a great shot. But it wasn’t. Why? Motion blur. If you look closely, you can see that the whole body is slightly out of focus, and that was simply because I didn’t think to change my shutter speed.

I was parked in a jeep in Botswana when a herd of impala came chasing across the road. They were galloping fast, but there were five or six of them, so I did have time to focus on each of them, one by one, as they crossed the road in turn.

Unfortunately, I was using my default camera settings that were designed to capture animals that were standing still. I was using an 80-400mm lens, so I had my camera on 1/320 and f/8 with auto ISO. That would normally have worked, but not for a jumping impala! What I really needed was a shutter speed of at least 1/1000 of a second. I just didn’t think…

Caracal

Caracal
This is what it looks like on Wikipedia.

A few years ago, I went to a talk given by Paul Goldstein somewhere in London, and one of the slides he showed was a picture of a caracal. I’d never seen one at the time, but Paul was very proud of his shot, which showed a caracal from the side running through long grass.

The image stayed in my mind, and I was very excited when I went to Tanzania in January 2018 and actually saw one for myself! It was quite a way away, but I had my 800mm lens with me, and I was just about to take a shot when the driver told me to wait.

He was going to drive around and get closer. Well, funnily enough, the caracal disappeared, and I never got the shot I wanted…

Polar Bear

Polar bear crossing ice floe in ArcticThe best of a bad bunch

In June 2014, I went on an Exodus trip with Paul Goldstein to Spitsbergen to see the polar bear. It was a last-minute booking, so I got a good deal on the price, and I was lucky enough to share a cabin with a nice French chap called Eric, but the real prize was getting some good shots of a polar bear.

We had 13 or so sightings, but, sadly, they were all too far away for my 500mm lens. That was in the days before I got into the habit of renting the Nikon 800mm monster, and I really wish I’d had it then.

Amongst other sightings, a mother and her two cubs put on a great show for us on the ice, but, when I got back to my cabin to review my shots, I found they were all too soft and too distant. Ah, well, at least I have an excuse to go again now…

The Kill

I’ve been to Africa several times now, visiting Kenya, Uganda, Rwanda, Zambia and Botswana, but I’ve never seen a kill. I’ve seen the chase, and I’ve seen the predator eating its prey, but I’ve never seen the crucial moment of the kill.

Now, I know some people would be a little squeamish about seeing one animal kill another, but I don’t think I’d feel that way. To me, it’s the ultimate expression of ‘the survival of the fittest’, and I’d love to see a lion, leopard or cheetah kill something on the great plains of Africa.

I have many stories of ‘the one that got away’. There was the time when I climbed Mount Kenya and arrived back at the camp, only to find that everyone that morning had spent an hour watching a pride of lions kill a wildebeest 50 yards away from the gate of the national park!

Or there was the time on the same trip when I booked the wrong flight home and had the chance to spend an extra day on my very own personal game drive. We saw a cheetah ‘timing’ (or hunting) an impala, and it was the most exciting thing that’s ever happened to me in Africa – but no kill.

In Antarctica, I watched from a Zodiac as a leopard seal ripped apart a penguin, but I didn’t quite see the initial attack. In the Brazilian Pantanal, I was watching a jaguar on the river bank from a small boat when the call came over the radio that lunch was ready.

No sooner had we met up with the other boat than we had another call, this time to say that the very same jaguar had just killed a caiman! We rushed back and watched as the young jaguar made a mess of the whole thing.

To begin with, he had hold of his prey by the throat rather than the back of the neck. This is fine if you’re a lion, but jaguars prefer to kill caiman (or small crocodiles) by nipping them on the back of the neck.

This jaguar was in a bit of a bind: he didn’t want to kill the caiman the ‘wrong’ way, but he couldn’t change his grip in case it got away. He spent 10 minutes humming and hawing before finally killing the caiman, but that was only the start of his problems.

His next job was to find a safe place to store his prey, but the banks of the river were 8-10ft high and very steep, so he spent another 25 minutes trying to find a way up into the undergrowth, desperately trying to drag the 10ft crocodile with him.

By this stage, around 20 boats had gathered to see the jaguar, and, when he eventually managed to scramble up the bank with his kill, everybody gave him a big round of applause!

NAI’d rather have seen the kill than stopped for lunch! 

Conclusion

All this goes to show exactly how close I’ve come to the elusive kill, but no luck so far. However, I’m off to the Masai Mara in a couple of weeks, so maybe, just maybe I’ll be able to bring back the shot I’ve been dying to get…

Bear Gills

Lightroom Workflow

A few years ago, I started doing all my photographic post-processing in Lightroom. It’s the program used by most professional photographers and is reasonably user-friendly, I got to grips with Lightroom mostly by watching a very useful series of YouTube videos by Anthony Morganti, but this article is just a description of my basic workflow.

I pay around £10 a month for access to Lightroom Classic (which I use almost all the time) and Photoshop (which I rarely use except for model releases that need thumbnail images superimposing on them).

What Does ‘Workflow’ Mean?

Your workflow is simply the steps you go through in order to choose your best shots and make them look as good as possible. You might be on a cruise ship in the Antarctic or in a tent in Chobe National Park or back at home in Blighty, but – wherever you are – you should have a standard approach to cataloguing and post-processing your shots.

This is my system, but feel free to change it or add to it according to what you prefer:

  1. Import to computerI like to keep up-to-date with editing my pictures, so I usually work on them every day after I get back from the game drive (or whatever the shoot happens to be). I’m usually out all day shooting, so I take the first chance I get to go through everything before lunch or dinner back at camp.To do that, I first of all connect my camera to my MacBook Pro and import all the RAW files to a new folder in Pictures using Image Capture. I have two cameras, so I usually have a shower or something while the first one’s chugging away, and then I work on the first batch of images while the second is being copied across from my other camera.

    I usually take over 1,000 images in a day, so this can take a while, and I get very impatient at this point! I’ve done my best to buy Compact Flash (CF) or Secure Digital (SD) cards with the fastest possible read and write speeds just to help speed up the process, and I now have an extra-fast XQD (eXperimental Quality Determination) card for my D850, but it’s never enough.

    I have a Mac, so Image Capture is the default program for importing files, but it will obviously be different if you have a PC. I could import my shots directly using Lightroom, but I’ve had a couple of bad experiences when Lightroom has crashed while trying to import thousands of files, so I use Image Capture just to be on the safe side.

  2. Import to LightroomI then import the files to Lightroom. This doesn’t involve any actual copying of files, so it only takes a few seconds. I usually do it without any of the custom ‘Import’ settings, but you could set this up if you wanted to.It’s a trade-off between speed and convenience. If you always want a vignette, for example, then you could create a preset and import using that preset. That way, every shot has the same vignette. However, it makes the import process last that bit longer, so it’s up to you.

    The other thing you can do is create 1:1 previews. This again is more time-consuming, but it makes a huge difference when it comes to viewing and editing each file in full-screen mode.

    It’s extremely frustrating when Lightroom keeps displaying the ‘Loading…’ message for each new file, particularly when you just want to check sharpness at 1:1, but those messages disappear if you build the previews during the import process. Try it and see for yourself.

  3. Rate imagesI only end up trying to sell about 1% of the shots I take, so rating the images I like is generally much quicker than rejecting the ones I don’t! (If your hit rate is more than 50%, you can always type ‘x’ to reject images and delete them later all in one go.)To rate pictures, you simply type a number between 1 and 5, and the equivalent star rating is added to all the selected images. (You can press 0 to remove the rating or 6 to add the colour red, which I used to do for people shots.)

    In my system, I give 3 stars generally to shots of my friends or fellow guests worth putting on Facebook, 4 stars to shots worth selling and 5 stars to my all-time favourites. (To give you an idea, I currently have over 5,000 shots I’ve rated 4 stars or more, but only 142 5-star shots!)

    During the rating process, I sometimes have to crop an image or do some very basic editing to see if it’s worth keeping, but I try to keep it ‘quick and dirty’ to save time.

  4. Check ratingsOnce I’ve rated all my shots, I go over all the 4- or 5-star images again to check the rating. This crucially includes checking the sharpness at 100% because agencies are very quick to reject images that aren’t quite sharp enough.It also means checking for duplicates. It’s very easy to end up with several shots of the same subject from the same angle, especially if the shots were taken at different times so they don’t end up right next to each other.

    Agencies again tend to reject images that are too similar to each other, so it’s worth going through with a fine-tooth comb at this point. Otherwise, you’ll end up duplicating all your later work for a file that ends up in the trash…!

  5. Post-process images

    Digital images don’t generally look their best straight out of the box, so this is when I spend a bit of time making basic adjustments to my 4- and 5-star images. I make a couple of global changes, but the rest are local.The global changes are Dehaze and Post-crop vignetting. The Dehaze slider in the basic panel of Lightroom can remove haze, but it’s also useful for any shot that just needs a little bit more contrast, clarity, saturation and vibrance.I generally set it to +25, and I’ve created a preset that allows me to apply the change to all of my images at the same time. I do the same with Post-crop vignetting. Vignettes tend to focus the viewer’s eyes on the subject by darkening the corners of the image, so I generally set the slider to +20.

    As most of my pictures are wildlife portraits, that works just fine, but I generally won’t use a vignette when there’s a large expanse of sky as it just looks plain daft!

    The local adjustments I make to each file generally involve using the tools in the basic panel (such as cropping, changing the exposure and choosing different black and white points to avoid clipping of highlights and shadows), so I tend to click the ‘Auto’ button to begin with and then only make further changes where I have to.

  6. Add metadataThe most time-consuming part of this whole process is adding the metadata. If you’re not a serious photographer aiming to sell your shots to stock agencies, then you obviously don’t need to do much at this point, but the more data you add, the easier it is to find files when you need to.For example, if you’ve just come back from Botswana and someone asks to see all your elephant shots, you’ll feel a bit daft if you’ve never even bothered to add any tags! I take all my 4- and 5-star images and add titles, captions and keywords.

    Stock agencies have rules on the type and number of characters in each metadata field, so I avoid apostrophes and give all my images seven-word titles that are no longer than 50 characters. In theory, captions should be different from titles, but I find it too time-consuming to do that for all my files, so I keep them the same except for any 5-star images.

    I put those on my website and tend to enter those in competitions, so it’s worth expending a little extra effort to sell the sizzle! Keywords are essential for Search Engine Optimisation, so I use at least 10 but more often 20 or 30, including tags describing the location, content and theme of the image (plus obvious synonyms).

    After each trip, I set up a metadata preset for Design Pics (my main stock agency) in order to add the data they require, such as city, country and copyright status. I also create a location in the Maps module and drag all my images to it in order to geotag them with GPS data.

    It’s worth noting that I set the time zone, date, time and copyright information on my cameras before I go on a trip so I don’t have to worry about any of that when I get home.

  7. Export imagesLightroom is what they call a ‘non-destructive’ program, which means that the RAW files that you edit aren’t actually changed when you edit them. Instead, Lightroom keeps a list of editing instructions that it follows every time you want to view a file.As a result, it’s essential to export any files that you intend to view outside Lightroom or upload to any stock agencies. I’ve set up presets for all the folders I usually export to, but stock agencies generally want JPEG files no more than 20MB in size, so I’ve used that as my limit.

    Most agencies also have minimum quality thresholds, so I try not to crop so much that the image is less than 6.3 megapixels.

    I initially export all my 4- and 5-star images as 20MB sRGB JPEGs at the highest quality setting to three folders: ‘4*’, ‘5*’ and ‘Favourites’ – which holds both. (These files automatically show up in Lightroom as I’ve set it up that way in Preferences.)

    I then export the same files to my ‘To upload’ folder using a special low-resolution preset that follows the Design Pics guidelines. I have an exclusive agreement with Design Pics, and I give them first refusal on all my photographs.

    However, the metadata requirements for Design Pics are different from those of the other agencies, so I have to be careful to get it right. The main difference is in the Headline and Caption fields.

    Design Pics requires Headline to be ‘NA’, and I write a long description in the Caption field of my 5* images in order to put it on my website, but some agencies take the title of the image from the Headline and Caption fields, so I have to copy and paste the correct data several hundred times!

    (There is a plug-in that copies data from one field to another, but the free version only works on 10 files at a time…)

  8. Upload to agencies

    Once I’ve exported all my 4* and 5* files, I upload them to Design Pics via FTP using Filezilla. It usually takes them a few weeks to decide which ones they want. When I’ve received a list of their ‘selects’, I export high-resolution versions and upload them via FTP again.Sometimes, these files don’t pass QA due to lack of sharpness or some other issue, so I have to wait another week or so before I know exactly which files I can send to the other agencies.Once I have the definitive list, I upload them to all the other agencies using Filezilla, websites or DeepMeta (for Getty Images). Buyers tend to search among the newest images, so I’ve taken to uploading 100 files each month in order to maximise the chances of a sale.

    We’ll see if it works…! I keep track of the whole process on a spreadsheet. Each image has a row, and each agency has a column, and I note the current status by putting ‘u’ for ‘uploaded’, ‘s’ for ‘submitted’ and ‘y’ for accepted.

    I’ve also created quite a few extra columns for continent, country, type of image, exhibitions, online galleries and competitions. Managing over 5,000 images is a complicated process, so I rely on Excel to make sure I know what’s going on!

  9. Delete images

    Once all my images are copied across to my laptop and properly edited and catalogued, I can format the memory cards and delete any unrated files in Lightroom. File management should always be done in Lightroom rather than Finder in order to make sure that the changes are synchronised properly.If you do it the other way round, Lightroom will flag deleted images as ‘missing’. This also applies to any changes you make to the metadata. If you select the right settings in Lightroom, these will automatically be copied to the underlying files in Finder, and that’s a huge time-saver.For example, if you suddenly realise you’ve spelt ‘elephant’ wrong in some of your elephant pictures, you can simply search for the wrong spelling, highlight all the pictures that pop up and correct it globally in the keywords window.
  10. Back up

    Backing up all my pictures and documents is absolutely essential, so I use a cloud storage service called CrashPlan from Code42. It runs in the background and simply copies any changes or deletions to the back-up servers in real time.If I realise I’ve deleted a file by accident, I can search for it on CrashPlan and restore whichever version I want – either the latest version or the version before I made a mistake with my edits.CrashPlan works fine as long as I have a working internet connection, but it did take a few weeks to sync all my files when I first started using it, and it doesn’t help me when I’m in Africa or in the Arctic Circle without any wi-fi!

    My biggest fear is losing all the pictures I’ve taken while I’m on a trip, and I still haven’t worked out a solution to the problem. I guess I could take a spare hard drive or USB stick, but I’ve been too lazy so far. Let’s hope I don’t pay the ultimate price…!

Lightroom is a subject I’m learning all the time, but I hope this will give you a head start!

Simultaneous Equations

Simultaneous equations help you work out two variables at once.

Why do we have simultaneous equations? Well, there are two ways of looking at it.

  1. The first is that it solves a problem that seems insoluble: how do you work out two variables at once? For example, if x + y = 10, what are x and y? That’s an impossible question because x and y could literally be anything. If x was 2, then y would be 8, but if x was 100, then y would be -90, but if x was 0.5, then y would be 9.5 and so on.Simultaneous equations help us solve that problem by providing more data. Yes, we still can’t solve each equation individually, but having both of them allows us to solve for one variable and then the other.
  2. The second way of looking at simultaneous equations is to imagine that they describe two lines that meet. The x and y values are obviously different as you move along both lines, but they are identical at the point where they meet, and that is the answer to the question.

The next question is obviously ‘How do we solve simultaneous equations?’ The answer is simple in theory: you just have to add both equations together to eliminate one of the variables, at which point you can work out the second one and then put it back into one of the original equations to work out the first variable.

However, it gets more and more complicated as the numbers get less and less ‘convenient’, so let’s take three examples to illustrate the three different techniques you need to know.

Simple Addition and Subtraction

The first step in solving simultaneous equations is to try and eliminate one of the variables by adding or subtracting them, but you can only do that if the number of the variable is the same in both. In theory, you could choose the first or the second term, but I find the one in the middle is the easiest, eg

4x + 2y = 10

16x – 2y = 10

Here, the number of the variables in the middle of the equations is the same, so adding them together will make them disappear:

20x = 20

It’s then simple to divide both sides by 20 to work out x:

x = 1

Once you have one variable, you can simply plug it back into one of the original equations to work out the other one, eg

4x + 2y = 10

4 x 1 + 2y = 10

4 + 2y = 10

2y = 6

y = 3

Answer: x = 1, y = 3

Multiplying One Equation

If the number of variables in the middle is not the same, but one is a factor of the other, try multiplying one equation by whatever number is needed to make the number of the variables match, eg

4x + 2y = 10

7x + y = 10

Multiplying the second equation by 2 means the number of the y’s is the same:

4x + 2y = 10

14x + 2y = 20

The rest of the procedure is exactly the same, only this time we have to subtract rather than add the equations to begin with:

10x = 10

x = 1

The next part is exactly the same as the first example as we simply plug in x to find y:

4x + 2y = 10

4 x 1 + 2y = 10

4 + 2y = 10

2y = 6

y = 3

Answer: x = 1, y = 3

Multiplying Both Equations

If the number of variables in the middle is not the same, but neither is a factor of the other, find the lowest common multiple and multiply the two equations by whatever numbers are needed to reach it, eg

4x + 2y = 10

x + 3y = 10

The lowest common multiple of 2 and 3 is 6, which means we need to multiply the first equation by 3:

12x + 6y = 30

…and the second by 2:

2x + 6y = 20

As the number of variables in the middle is now the same, we can carry on as before by subtracting one from the other in order to find x:

10x = 10

x = 1

Again, the final part of the technique is exactly the same as we plug x into the first of the original equations:

4x + 2y = 10

4 x 1 + 2y = 10

4 + 2y = 10

2y = 6

y = 3

Answer: x = 1, y = 3

Practice Questions

Job done! Now, here are a few practice questions to help you learn the rules. Find x and y in the following pairs of simultaneous equations:

  1. 2x + 4y = 16
    4x – 4y = 8
  2. 3x + 2y = 12
    5x + 2y = 16
  3. 12x – 4y = 28
    3x – 2y = 5
  4. 2x – y = 12
    3x – 2y = 17
  5. 4x + 3y = 24
    5x – 2y = 7
  6. 4x + 3y = 31
    5x + 4y = 40
  7. x + 4y = 23
    5x – 2y = 5
  8. 4x + 3y = 37
    2x – 3y = -13
  9. 2x + 4y = 16
    3x – 5y = -9
  10. 2x + 4y = 20
    3x + 3y = 21 

     

     

    If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.

How to Become a Private Tutor

I’ve talked to a few people who wanted to become private tutors, so I thought I’d write down a few tips for anyone who’s interested.

How Did I Start Out?

I started as a private tutor quite by accident. It was 2009, and I was finding it hard to get work as a freelance management consultant when I happened to read an article in the Telegraph called 10 Ways to Beat the Recession.

The author mentioned a few ways of earning some extra cash, including becoming an extra on film sets – which I was already doing – and working as a private tutor. I’d never done any proper teaching before, although I was a golf coach, and I’d coached skiing a few times in the Alps, but I thought I’d sign up with a couple of agencies and see what happened.

Within a week, I had two clients, and I’ve never looked back since!

What Qualifications do I Need?

The first and most important thing to say is that you don’t need any teaching qualifications! Yes, that’s right. You don’t need a PGCE, and you don’t need to have done any training as a teacher. As a private tutor, you are just that – private – so you don’t have to jump through all the Government hoops that a teacher in a state school would have to do.

Obviously, potential clients want the best person to teach their child, so you need to show some sort of academic record, but that can be as little as a degree in English – which is what I had when I started. Admittedly, I went to Oxford, which probably counts for a lot with Russian billionaires (!), but you don’t need to have an Oxbridge degree to become a tutor. Far from it.

However, what you probably will need is a criminal records check. This is just a piece of paper that certifies you haven’t been convicted of a criminal offence and was often known as a ‘CRB check’, although it’s now officially called an Enhanced Certificate from the Disclosure and Barring Service, or ‘DBS check’.

You can’t apply for an ‘enhanced certificate’ yourself, but your tuition agency can help you. In fact, they may require you to have one and even to renew it every year or two. It costs around £18 and can take up to three months to arrive, so it’s worth applying as early as possible.

Some agencies may charge up to £80 to make the application on your behalf, so be careful! You can find further information here.

What Subjects Can I Teach?

You can teach whatever you like! Agencies will just ask you which subjects you offer and at what level, so you have complete freedom to choose. I focus on English and Maths, which are the most popular subjects, but that’s mostly led by demand from clients. They are the main subjects at 11+ level, so that’s what most people are looking for help with.

What Age Children Can I Teach?

Again, the choice is yours. I’ve taught students from as young as five to as old as 75, but the peak demand is at 11+ level, when the children are around 10 years old. I make it a rule that I’ll only teach a subject to a level that I’ve reached myself, such as GCSE or A-level, but clients sometimes take you by surprise.

When I turned up to teach what I thought was going to be English to two boys, the nanny suddenly asked me to do Latin instead. When I said I hadn’t done any Latin since I was 15, she just said, “Oh, you’ll be fine…!”

What Preparation do I Need to do?

Research

One of the big attractions of tutoring for me is that the work is very enjoyable. I like teaching, and I like spending time with children, so it’s the perfect combination! The reason I stopped work as a management consultant was the constant stress, the persistent worry that I wasn’t up to the job, but teaching 10-year-olds never makes me feel like that.

Whether it’s English or Maths, I’m confident in my ability to teach and never worry about being asked an impossible question. However, that doesn’t mean you can walk into your first lesson without doing any preparation at all.

In my case, I wanted to teach English, so I needed to find out what kind of questions cropped up in 11+ and 13+ entrance exams and come up with a good method of answering them. Once I’d done that, I was ready.

Maths was a bit easier, but I still looked through a few papers to make sure there was no risk of being blind-sided by something I’d forgotten how to do or had never studied. Whatever the subject you’re offering, I suggest you do the same.

Past Papers

The other thing I needed to do was to find past papers to give to my pupils. That was a bit tricky in the early days until a kind parent gave me a collection of photocopied exams. After that, I carried a couple around with me to take to lessons, but it wasn’t a great solution, so I decided to create a website – this one.

Over time, I collected dozens of past papers and wrote various articles on how to do different kinds of question in Maths, English and French. Now, I don’t have to carry around anything with me or spend time dictating notes. I can simply ask my pupils to look it up online.

Setting up a website is pretty easy using WordPress or something similar, but you should feel free to use the resources on my past papers tab if you don’t want to go to the trouble yourself, and all my articles are available for free if you need them.

The main ones I use for English are about doing comprehensions and writing stories, but there are plenty more. The website proved unexpectedly popular, and I had over 28,000 visitors last year! The other advantage is that it generated enough business for me not to need agencies any more.

That means I can charge what I like, I don’t have to pay any commission, and I can have a direct relationship with all my clients without anybody acting as an intermediary – and often just getting in the way!

Business Cards

I know it sounds a bit old-fashioned, but having business cards is very useful. If you’re just starting out, nobody knows your name, so paying a few quid to market your services is one of the best investments you can make.

You never know when people will tell you they’re looking for a tutor, and it’s the easiest thing in the world to give them a business card. Even if you don’t have a website, it will at least tell them how to reach you, and you should get a lot more clients out of it.

How Can I Find Work?

Tuition agencies are the best place to start, but there are different kinds. Some are online and simply require you to fill out a form for them to check and vet, but others ask you to go through an interview, either over the phone or in person.

Either way, you need to put together a tailored CV that shows off your academic achievements and highlights any teaching experience you’ve had. This may not be very much at the beginning, but you simply need to show enough potential to get you through the door.

Once you’ve shown enough aptitude and commitment to get accepted by a few agencies, you’ll rapidly build up your experience on the job.

Here is a list of the tuition agencies I’ve been in touch with, together with contact details where available. I’m based in London, so there is obviously a geographical bias there, but some of the agencies such as Fleet Tutors offer national coverage, and you can always search online for others in your local area.

Name

Email

Telephone

Website

A-Star Tuition astartuition@btinternet.com 01772 814739 astartuition.com
Approved Tutors approvedtutors.co.uk
Athena Tuition athenatuition.co.uk/
Beacon Tutors info@beacontutors.co.uk 020 8983 2158 beacontutors.co.uk/
Bespoke Tuition emma@bespoketuition.com 07732 371880 bespoketuition.com
Bigfoot Tutors tutors@bigfoottutors.com 020 7729 9004 bigfoottutors.com
Bright Young Things 07702 019194 brightyoungthingstuition.co.uk
Dulwich Tutors info@dulwichtutors.com 020 8653 3502 dulwichtutors.com
Enjoy Education kate@enjoyeducation.co.uk enjoyeducation.co.uk
Exam Confidence
First Tutors firsttutors.co.uk
Fleet Tutors 0845 644 5452 fleet-tutors.co.uk
Gabbitas gabbitas.com
Greater London Tutors 020 7727 5599 greaterlondontutors.com
Harrison Allen harrisonallen.co.uk
Holland Park Tuition recruitment@hollandparktuition.com 020 7034 0800 hollandparktuition.com
IPS Tutors info@ipstutors.co.uk 01509 265623 ipstutors.co.uk
Ivy Education ivyeducation.co.uk
Kensington & Chelsea Tutors tutors@kctutors.co.uk 020 7584 7987 kctutors.co.uk
Keystone Tutors enquiries@keystonetutors.com 020 7351 5908 keystonetutors.com
Kings Tutors emily@kingstutors.co.uk kingstutors.co.uk
Knightsbridge Tutors 07890 521390 knightsbridgetutors.co.uk
Laidlaw Education laidlaweducation.co.uk
Mentor & Sons andrei@mentorandsons.com 07861 680377 mentorandsons.com
Osborne Cawkwell enquiries@oc-ec.com 020 7584 5355 oc-ec.com
Personal Tutors admin@personal-tutor.co.uk personal-tutors.co.uk
Russell Education Group joe@russelleducationgroup.com n/a
Search Tutors searchtutors.co.uk
Select My Tutor info@selectmytutor.co.uk selectmytutor.co.uk
SGA Education s@sga-education.com sga-education.com
Simply Learning Tuition simplylearningtuition.co.uk
The Tutor Pages thetutorpages.com
Top Tutors 020 8349 2148 toptutors.co.uk
Tutor House info@tutorhouse.co.uk 020 7381 6253 tutorhouse.co.uk/
Tutor Hunt tutorhunt.com
Tutorfair tutorfair.com
Tutors International tutors-international.net
UK Tutors uktutors.com
Westminster Tutors exams@westminstertutors.co.uk 020 7584 1288 westminstertutors.co.uk
William Clarence Education steve@williamclarence.com 020 7412 8988 williamclarence.com
Winterwood winterwoodtutors.co.uk
Youni Tutoring younitutoring.com

That’s obviously a long list, but, to give you an idea, I earned the most from Adrian Beckett (teacher training), Bespoke Tuition, Bonas MacFarlane, Harrison Allen, Keystone Tutors, Mentor & Sons, Personal Tutors and Shawcross Bligh.

Once you’ve been accepted by and started working for a few agencies, you’ll soon see the differences. Some offer higher rates, some the option to set your own rates, some provide a lot of work, some offer the best prospects of jobs abroad. It all depends what you’re looking for.

Where Will the Lessons Take Place?

When I first started tutoring, I had to cycle to all my clients. I put a limit of half an hour on my travel time, but it still took a lot of time and effort to get to my pupils. Fortunately, I’m now able to teach at my home, either in person or online using Skype and an electronic whiteboard, which means my effective hourly rate has gone up enormously.

Travel is still a little bit of a problem for most tutors, though, and I certainly couldn’t have reached my pupils without having a bicycle. I didn’t have a car, and public transport wasn’t really an option in most cases.

You just have to decide how far you’re prepared to go: the further it is, the more business you’ll get, but the longer it’ll take to get there and therefore the lower your effective hourly rate.

The other possibility, of course, is teaching abroad. I’ve been lucky enough to go on teaching assignments in Belarus, Greece, Hong Kong, Kenya, Russia, Switzerland and Turkey, and it’s a great way to see the world.

The clients can sometimes be a little bit difficult, and the children can sometimes behave like spoiled brats (!), but staying with a great client in a sunny getaway overseas can be a wonderful experience.

The only reason I don’t apply for more foreign postings is that I don’t want to let down my existing clients – going away for three weeks just before the 11+ exams in January would NOT go down well!

When Will the Lessons Take Place?

If you’re teaching children, lessons will usually be in the after-school slot between 1600 and 2000 or at weekends. That does limit the amount of hours you can teach, but it’s up to you how much you want to work.

I used to work seven days a week, but I eventually gave myself a day off and then another, so I now work Sundays to Thursdays with Friday and Saturday off.

During the holidays, you lose a lot of regular clients when they disappear to the Maldives or somewhere for six weeks (!), but others might ask for an intensive sequence of lessons to take advantage of the extra time available, and there’s obviously a greater chance of a foreign assignment.

All that means that the work is very seasonal, so you should expect your earnings to go up and down a bit and plan your finances accordingly.

What Should I do During the Lesson?

I generally teach from past papers, so I ask pupils to do a past paper for their homework and then mark it during the following lesson.

‘Marking’ means marking the questions, obviously, but it also means ‘filling in the gaps’ in the pupil’s knowledge. If he or she is obviously struggling with something, it’s worth spending a few minutes explaining the topic and asking a few practice questions.

I’ve written a few articles on common problem areas in English and Maths, such as commas and negative numbers, so I often go through one of those and ask the pupil’s parents to print it out and put it in a binder. After a few weeks, that collection of notes gradually turns into a ready-made revision guide for the exams.

If the parents want you to work on specific topics, that’s also possible. For example, one mother wanted to help her son with ratios, so she printed out dozens of past papers and circled the ratio questions for him to do. He soon got the knack!

I approach English in a slightly different way to begin with. There are two types of question in the 11+, comprehensions and creative writing, so I generally spend the first lesson teaching pupils how to do one of those. I go through my article on the subject online and then ask them to answer a practice question by following the procedure I’ve outlined.

They usually finish it off for their homework. After a few weeks of stories or comprehensions, I’ll switch to the other topic and do the same with that. I also ask pupils to write down any new words or words they get wrong in a vocabulary book because building vocabulary is very important for any type of English exam (and also for Verbal Reasoning).

I ask them to fold the pages over in the middle so that they can put the words on the left and the meanings on the right (if necessary). Every few weeks, I can then give them a spelling test. If they can spell the words correctly and tell me what they mean, they can tick them off in their vocab book.

Once they’ve ticked off a whole page of words, they can tick that off, too! I usually try to reinforce the learning of words by asking pupils to tell me a story using as many words as possible from their spelling test.

It can be a familiar fairy story or something they make up, but it just helps to move the words from the ‘passive’ memory to the ‘active memory’, meaning that they actually know how to use them themselves rather than just understand them when they see them on the page.

What Homework Should I Set?

Most children who have private lessons have pretty busy schedules, so I don’t want to overburden them. I generally set one exercise that takes around 30-45 minutes. That might be a Maths paper or an English comprehension or story, but it obviously depends on the subject and the level.

Just make sure that the student writes down what needs to be done – a lot of them forget! You should also make a note in your diary yourself, just so that you can check at the start of the next lesson if the work has been done.

What Feedback Should I Give the Parents?

I generally have a quick chat with the mother or father (or nanny) after the lesson to report on what we did during the lesson, what problems the child had and what homework I’ve set. This is also a good time to make any changes to the schedule, for instance if the family goes on holiday.

If that’s not possible, I’ll email the client with a ‘lesson report’. Some agencies such as Bonas MacFarlane make this a part of their timesheet system.

How Much Will I Get Paid?

When I first started, I had absolutely no idea how much I was worth, and I ended up charging only £10 an hour, which is not much more than I pay my cleaner! Fortunately, a horrified friend pointed out that it should be ‘at least’ £35 an hour, and I upped my rates immediately.

I now charge £60 an hour for private lessons, whether online or in person. Unfortunately, some agencies such as Fleet Tutors don’t allow you to set your own rates, so that’s one thing to bear in mind when deciding which agencies to work with.

However, they did provide me with quite a bit of work when I first started, so it’s swings and roundabouts. The pay scale often varies depending on the age of the student and the level taught, so you’ll probably earn more for teaching older students at GCSE level or above if the agency sets the prices.

If you have any private clients, you can obviously set whatever rate you like, depending on where you live, the age of your pupils, whether lessons are online or in person and so on. Personally, I only have one rate (although I used to charge an extra £5 for teaching two pupils at the same time), and I raise it by £5 every year to allow for inflation and extra demand.

Tutoring is more and more popular than ever these days, and I read somewhere that over half of pupils in London have private lessons over the course of their school careers, so don’t sell yourself short! You should be able to make around £25,000 a year, which is not bad going for a couple of hours’ work a day!

Foreign jobs are a little different, and there is a ‘standard’ rate of around £800 a week including expenses. That means your flights and accommodation are all covered, and you can even earn a bit more on the side if you decide to rent out your home on Airbnb while you’re away!

When it comes to day-to-day expenses such as taxis and food and drink, it’s important to negotiate that with the agency before accepting the job. It’s no good complaining about having to live in the client’s house and buy your own lunches when you’re in Moscow or Bratislava! It can be a dream job, but just make sure you look at it from every angle:

  • What subjects will I be teaching?
  • How many hours will I have to teach?
  • How many days off will I get per week?
  • Where will the lessons take place?
  • How do I get to and from my accommodation?
  • How long is the assignment? (I refuse anything more than three months.)
  • Where will I be staying? (NEVER at the client’s house!)
  • How old are the children?
  • Will I have any other responsibilities (eg ferrying the children to and from school)?
  • Do I need a visa?
  • What is the weekly rate?
  • What expenses are included (eg flights, accommodation, taxis, food, drink)?

How Do I Get Paid?

Most agencies ask for a timesheet and pay their tutors monthly via BACS payments directly into their bank accounts. That’s a bit annoying from a cash flow point of view, but there’s not much you can do about it – other than using a different agency.

When it comes to private clients, I generally ask for cash after the lesson, but it’s even more convenient if they can pay via standing order – as long as you can trust them! I once let a client rack up over £600 in fees because he tended to pay in big lump sums every few weeks, but then his business folded, and I had to use a Government website to try and chase him up.

Fortunately, his wife saw the email and paid my bill, but it took months to sort out. Normally, though, the worst that happens is that a client just doesn’t have the right change and promises to pay the following week, so you just need to keep track of who owes what.

I hope all this helps. Good luck!

 

 

 

 

If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.

 

How Do I Make Money from Photography?

The obvious question for a lot of amateur photographers is ‘How do I make money from photography?’ The answer, unfortunately, is that I don’t know. All I can do is tell you what I’ve done and give you a few ideas.

I’m still learning the business after just four years, but my approach has always been to knock on as many doors as possible, whether it’s microstock, exhibitions, competitions, lessons or even talks. Every source of revenue has its part to play, and it’s just a question of working out where to focus your efforts.

I make just under half my money from microstock/stock agencies and half from exhibitions, but everybody’s different.

Nick Dale Photography

I loved photography when I was a teenager. I bought (or was given) books on Henri Cartier-Bresson, Alfred Eisenstaedt, Ansel Adams and other great photographers, and I even bought myself an old Chinon CE-4 film SLR.

I remember buying two 36-exposure films for it – one colour, one black and white – and using up every single frame in a couple of hours just taking pictures around the house! I took my camera on holiday to Majorca and the United States, developed pictures in a dark room at school and even talked to my mum about becoming a professional photographer.

However, my mother said I could always take it up later – so that was that for 30 years!

Fortunately, I was given a second chance in January 2013 when a friend of a friend invited me to climb Mount Kenya and go on safari with her and a couple of other people. I’d always wanted to go to Africa, but I’d foolishly been saving it for my honeymoon! As that didn’t seem very likely, I jumped at the chance.

My first digital camera was a Sony DSC-HX200V bridge camera, which means it had a good zoom range (both optical and digital), but not a very large sensor. As a result, it was only around £300 and therefore cheap enough for me to buy without worrying too much.

Fortunately or unfortunately, a week in Kenya with people using proper Nikon SLRs gave me camera envy, and I bought a Nikon D800 SLR with a 28-300mm lens as soon as I got home!

And that was how it all started.

I took hundreds of pictures in Kenya of the people, the landscape and especially the wildlife. When I got back, I bought an Apple MacBook Pro to work on them, upgraded the editing program to Aperture and then sent them off to various microstock agencies to see if they would help me sell them.

It was hard at first, but getting the new camera helped, and I had a cash pile from remortgaging my flat in Notting Hill after another property purchase fell through, so I was able to go on plenty of trips to take more and more pictures.

An important breakthrough came when I sold a couple of prints for £100 each at my local tennis club’s Christmas Fair in November 2014, and another photographer told me about a cheap exhibition space called the Norman Plastow Gallery in Wimbledon Village.

I’d always thought it would be very expensive to mount an exhibition, but this place was only £70 for a week, so I booked it as soon as I could! The only problem was that I didn’t have any actual prints to sell, and here I was very fortunate.

I’d recently joined the Putney branch of London Independent Photography (or LIP), and there I’d met a very friendly and helpful chap called James, who’d offered to do all my printing for me at very low cost. After buying a few cheap, black, wooden frames from Amazon, I was all set.

I invited all my friends to the exhibition in May 2015 – especially a group of tennis players from my club – and I ended up selling seven prints. As I was just starting out, I’d priced the small, medium and large framed prints at £80, £100 and £120 and the unframed ones at only £30, but I still managed to make £550 in total.

The gallery hire charge was £200, and there were a few taxis to pay for plus incidental expenses, but the show actually turned a profit – unless you count the thousands of pounds I spent on buying camera equipment and flights to Kenya, Botswana, Antarctica and the Galápagos!

And there’s the rub. It’s relatively easy to generate revenue from photography, but actually making a profit out of it is another matter entirely. As a result, I have nothing but respect for the photographers I meet who have managed to make a career out of it. I’ve been on trips led by Paul Goldstein and Andy Skillen amongst others, and, in a way, that’s where I’d like to end up.

Since that first show in Wimbledon Village, I’ve sold nearly 5,000 downloads through microstock agencies, sold 36 prints at solo exhibitions and art fairs, taught five photography students and given two or three talks to various clubs and societies. Overall, I’ve made around £12,000 from my photography – but that wouldn’t even have paid for my trip to Antarctica!

The problem is that everyone has a camera these days – even if it’s just an iPhone – and it’s almost ‘too easy’ to take pictures now that cameras are digital. The world is also a smaller place these days, with the arrival of cheap flights and a general rise in income and wealth. It takes a special talent to make it as a photographer, and part of that talent is being able to make the most of it.

What Do I Need to Do First?

  1. Buy a camera
    If you want to make money out of photography, your first job is to get yourself a decent camera, and that means a digital SLR (or DSLR). The easiest way to earn cash is through so-called microstock agencies – which means selling pictures online in exchange for royalty payments – and they usually require shots to be taken with a camera that has at least 12 megapixels, if not more.
    You can obviously try to sell holiday snaps from your ‘back catalogue’, but, as I found out to my cost, it ain’t easy. Once you’ve decided to buy a DSLR, the two main brands to choose from are Nikon and Canon. There isn’t much between them these days, and the only reason I chose Nikon is that I didn’t want a camera from a company that made photocopiers!They both make good lenses, but, unfortunately, they have different mounts, so one you go with one or the other you’re locked in. I have various lenses ranging from an 18-35mm wide angle zoom to a 105mm macro lens for close-up work to an 80-400mm mid-range zoom, but I also rent an 800mm lens from Lenses for Hire whenever I go on a major wildlife photography trip.
  2. Buy a laptop
    If you don’t have one already, buying a decent laptop is great for photography. I take mine with me on all my trips, and it means that I can work on my images every evening after I get back from a shoot or a game drive.I should warn you, though, that the so-called RAW files from digital cameras are very large (in the case of my camera over 40MB each!), so I’d recommend getting as fast a processor as possible and as much memory and hard disk space as you can afford.You should also arrange a back-up system: the last thing you need is for your life’s work to disappear thanks to a software glitch! You could use an external hard drive, but I prefer backing up to the cloud just to be on the safe side.I use CrashPlan, which automatically detects any added, edited or deleted files and backs up the changes in real time, but there are other similar products out there.
  3. Subscribe to Lightroom
    Adobe Lightroom Creative Cloud is the choice of professionals and serious amateurs for organising and editing their photographs. It only costs around £8 a month (including Photoshop), and it’s a very powerful tool, as well as being relatively easy to use once you’ve mastered the basics.Digital photographs never come out of the camera looking perfect, so it’s always a good idea to try and improve the contrast, highlight and shadow areas and anything else you need to. If you’re selling through agencies, you’ll also need to add titles, captions and keywords (plus any other fields you’re asked to fill in), and all that is possible with Lightroom.It’s a pain to do for each individual photograph, but you can ‘synchronise’ any changes you make across a number of pictures, and you only need to do it once. If you’ve never used it before, I suggest you to do what I did and watch Anthony Morganti’s series of free YouTube videos on Lightroom. He takes you through all the functionality, and it’s an easy way to learn.
  4. Start taking pictures
    If you’re a wildlife photographer, this is just a euphemism for ‘spend thousands of pounds on trips to long-haul destinations’! However, you don’t have to travel far to take pictures.Whether you’re a landscape, portrait, Nature, fashion, wildlife, wedding or sports photographer, there’s always something photogenic not far from home, and you simply have to have the enthusiasm (and discipline) to be able to get out there and take more and better shots.Quality and quantity are both important. The quality of your images is ultimately what matters, but even a shot that’ll never win a competition might earn you money on a microstock site. I give my shots three stars if they’re good enough for Facebook, four if they’re good enough to be sold via agencies and five if they’re good enough to go on my website.
  5. Start marketing your work
    As a photographer, you have to learn to talk the talk as well as walk the walk. If you want to be taken seriously, you have to cover the basics, which means building a website, printing out business cards and having an active presence on social media.You can’t expect to win a bid for a photo shoot if you’re still using an old Hotmail address! Personally, I have this website powered by SquareSpace plus a Facebook ‘fan page’, a YouTube page, a LinkedIn account and a Twitter feed, all of which are printed on the back of my business cards.I post articles on my blog about photography trips, exhibitions and useful techniques (which also appear on Facebook, LinkedIn and Twitter), and I tweet and retweet a ‘Shot of the week’ (which gets fed through to my Facebook account as well).

Yes, but how can I make money?

  1. Microstock
    Microstock agencies are online intermediaries that accept work from photographers and then market those images to potential clients such as creative directors of newspapers, magazines and other buyers.The advantage of using them is that it’s ‘making money while you sleep’, in other words, it’s a passive income that you can build over time as you add more and more shots to your portfolio.Some agencies sell a lot of images but with low royalty rates, some the reverse, but here is the list of the ones I’ve used (in descending order of sales):
    Getty Images/iStock
    Shutterstock
    Adobe/fotolia
    DepositPhotos
    123RF
    Bigstock
    PIXTA
    SolidStockArt
    Dreamstime
    EyeEm
    Canstock
    photodune
    ClipDealer
    Panthermedia
    Pixoto
    featurePics
    Mostphotos
    Pond5
    500px
    Redbubble
    Alamy
    Yay Micro
    Stockfresh
    Crestock
    Zoonar
    Lobster MediaI should mention that not all agencies will accept you, and not all your shots will be accepted by any agency that does, but you shouldn’t take it personally. I’ve had over £4,000 in microstock sales in the last four years, but my overall acceptance rate is only 41%!

    Even if your pictures are accepted, of course, that doesn’t mean they’ll sell. I’ve had 5,120 downloads from microstock sites, but only 1,521 individual shots have ever been sold out of a total of 4,389. The rest of them are just sitting there, waiting for a buyer. Every now and then, though, you take a picture that goes viral: I’ve sold my jumping penguin (see above) 705 times!

    The basic process is similar across all agencies. You add titles, captions and keywords to all your pictures and then export them as JPEG files to upload to each individual agency via their websites or an FTP service using a program like Filezilla.

    You then typically add the category, country or other data for each of them and submit them for approval. The agencies then approve the ones they like and reject the ones they don’t. After that, it’s just a question of watching the money rolling in! A useful way of doing that is by downloading an app called Microstockr.

    All you need to do is to set up your various agencies on the accounts page and then check the dashboard every now and then for any sales you’ve made. It’s very addictive! Sales should come quite soon after each batch is uploaded, but you may have to wait a while for payment.

    Most agencies have a ‘payment threshold’ of $50 or $100, which means your first payment (usually through PayPal) might take months to arrive. You’ll also need to keep adding more pictures. Buyers tend to sort images according to what’s most recent, so you definitely get diminishing returns from your shots, however good they are.

    The other thing to say is that, with dozens of agencies and hundreds or even thousands of images, it gets very confusing. As a result, I’ve created a spreadsheet to keep track of the whole thing.

    With filenames down the left and agency names across the top, I know if each file has been uploaded (‘u’), submitted (‘s’) or accepted (‘y’) and how many times it’s been sold. I keep a record of the dollar value of all the image downloads on a separate financial spreadsheet. I suggest you do the same.

  2. Stock agencies
    In the good old days, it was much easier to make a living out of stock photography, mainly because the royalty rates were a lot higher. The difference between ‘stock’ and ‘microstock’ is simply the average price level.Stock agencies want to differentiate themselves from microstock agencies (and everything else out there on the web) in order to charge a higher price, so they generally ask for exclusive agreements over one to five years and set a higher standard for acceptance.I use Design Pics, and you can see that they sell my images for hundreds of dollars rather than just a few dollars for the microstock agencies. My general strategy is to offer Design Pics the first pick of my pictures before sending the leftovers to all the microstock agencies.(I’ve also submitted some flower images to flowerphotos and a few marine wildlife shots to SeaPics, but I haven’t seen any sales from them so far.) Due to the long sales and reporting cycle, I didn’t see my first sale from Design Pics until more than a year after I’d signed up, but sales are starting to trickle in now, so it just takes a bit of patience.

    If you’re looking for a list of stock agencies, I recommend buying a copy of 2017 Photographer’s Market, which is the equivalent of the Writers’ and Artists’ Yearbook. It has comprehensive coverage of the industry, including helpful articles and a wealth of phone numbers and email addresses for magazines, book publishers, greeting card companies, stock agencies, advertising firms, competitions and more.

    I suggest buying the Kindle electronic version, and then you can download everything on to your laptop. I did that and then simply emailed every stock agency on the list – Design Pics was the only one to say yes!

  3. Competitions
    If you just want the ego boost of seeing yourself winning a competition, then I suggest you sign up with Pixoto and enter the contests with the lowest number of entrants. It’s a peer-to-peer site, and you can organise your own competitions, so there’s a very good chance of winning something!That’s exactly what I did, and I ended up with the Judge’s Award in four competitions. However, there isn’t much prestige to something like that, and it certainly doesn’t earn you any money.Alternatively, you can scour the 2017 Photographer’s Market for competitions, bearing in mind your chances of winning, the cost of entry, the potential prizes and the subject matter.The UK national press is a good place to start, too, and I recently won £250 in Wex Photographic vouchers in the weekly Sunday Times/Audley Travel Big Shot competition.
  4. Exhibitions
    Putting on an exhibition may seem like a big deal if you’ve never done it before, but it doesn’t have to be expensive or time-consuming. The Norman Plastow Gallery where I started out is cheap, but it’s slightly off the beaten path, and you have to man the exhibition yourself, which is obviously impossible for most full-time employees.You realise pretty soon as a freelance photographer that the most expensive item on your tab is often the opportunity cost of NOT doing what you usually do when you take time off. As a tutor, for instance, I could easily have earned £1,000 during the two weeks of my first exhibition, but them’s the breaks…If you’re looking for a list of galleries, www.galleries.co.uk is a useful starting point. London is obviously the best place to look, but exhibition spaces there don’t come cheap. I recently looked for galleries to use for an exhibition, and the ones in central London regularly quoted me thousands of pounds for a week! Everything is negotiable, though, so don’t give up.I started out with 15 prints at my first solo show, but I also printed out a few postcards and greetings cards. You might not make as much money out of them, but at least you’ll get something from punters who can’t afford a print.

    There are some who say that cards are just a distraction, but it’s so difficult to tell. I’ve had exhibitions with and without cards on sale, and it doesn’t seem to make much of a difference. However, the main reason for an exhibition is to sell prints, so that should be the focus.

    One of the problems you’ll almost certainly have is knowing how to price your work. Choosing your favourite shots is easy enough – although getting a second opinion from a friend is a useful exercise – but how much should you charge?

    I started off at £80 for an A3 print and ended up three years later at £2,000 for a 53″ x 38″ print, so you’ll just have to suck it and see. Andy Skillen suggested a mark-up of two-and-a-half times your printing and framing costs to make sure your cashflow remained positive, but that’s just a rule of thumb.

  5. Photo shoots
    Proper professional photographers make most of their money from photo shoots, but clients aren’t easy to find.If you’re a wedding photographer, I suppose you can put up flyers at various local venues such as churches and registry offices, but, for the rest of us, it’s just a question of plugging away, taking as many good shots as we can and putting them online so that as many potential clients can see them as possible.It would be a dream to be able to rely on commissions from wealthy clients who called us up whenever they wanted pictures of something. A photographer told me once about a group of directors who asked him for a picture of five hippos in a lake looking at the camera.He sent them all the hippo shots he had, but they weren’t happy. In the end, he told them if they didn’t want to compromise on the picture, then they’d have to send him on an all-expenses-paid trip to Zambia for a week. Which they did!

    He got the shot within a couple of days and then spent the rest of the trip taking pictures for himself!

    That sounds like a nice way to make a living, doesn’t it? However, until we’re well established enough with a good enough reputation to get those kinds of jobs, all we can do is keep on snapping and use the networks that we have.

    I’ve worked for a milliner, a local councillor, a businesswoman and others, but all my photo shoots have come from friends of friends or personal contacts.

    I’m not very good at networking – and it’s certainly not something I enjoy unless it happens naturally – but it’s very important in this business.

  6. Lessons
    I work as a private tutor as well as a photographer, so I guess it was an obvious fit to offer photography lessons. It’s finding the students that’s the real problem, though. One of my tuition agencies provided me with a couple of clients, while the rest came from connections I made at exhibitions and talks.You never know when you might meet just the right person, so it’s important to keep a few cards in your wallet just in case.
  7. Talks
    If you don’t mind public speaking, then giving a slideshow and talk on photography is an enjoyable way to earn some pocket money. Camera clubs and other groups won’t generally pay more than £100 (if anything at all!), but it’s also a useful chance to take along a few prints to sell and to hand out business cards.I got started after meeting a very nice woman on an Antarctic cruise, and I’ve now given talks at her branch of the WI, two camera clubs and a local library. If you want to be proactive about it, I’d simply Google camera clubs (or WI branches!) and email all of them to see what happens.As my mum used to say, you have to cast your bread upon the waters…even if it sometimes comes back a soggy mess!
  8. Photography trips
    One final way of making money is to lead photography trips. A lot of photographers do it to supplement their income, and it’s a good way to reduce your travel budget.I recently put together a list of tour operators and emailed them all one afternoon to find out if it could work, and I soon received a call from the founder of Gane & Marshall, asking me to lead a trip to Tanzania!I offered my services for free in exchange for the chance to go on an all-expenses-paid photographic safari. Now all we have to do is find at least five people to come on the trip and make it economic. Fingers crossed!

I hope all that was useful. If you have any more questions, please drop me a line at nick@nickdalephotography.com. It’s not easy becoming a professional photographer, but we can at least take pictures as a hobby while we wait for our big break.

Here’s to clicking and dreaming…

Nikon D800 diagram

Basics of Photography

When you buy (or borrow), your first digital SLR, everything looks different, and it can be a bit worrying. What are all these buttons and dials for? Why is it so heavy? Where do I start? How do I change the shutter speed? All these are very good questions, and this is the place to find the answers!

Before we start, I should mention that I’m a Nikon user, and I have one D800 and one D810 camera body. The other major camera manufacturer is Canon, and they use slightly different terms for each function, but I’ll try and include both to make life easier.

Our first job is to cover the basics of photography: exposure and focus. Without understanding those two things, nothing else will make sense!

Exposure

Your first job as a photographer is to make sure that your images are well exposed, in other words, not too dark or too bright. Photographers talk about the ‘exposure triangle’, but that’s just a complicated way of saying that how dark or light a photograph is depends on three things: the shutter speed, the aperture and the ISO.

The level of exposure is measured in ‘stops’ or Exposure Values (EV), but what is a ‘stop’? Well, if you increase your exposure by a stop, the light is doubled (and vice versa). For example, if you lengthen your shutter speed from 1/200 of a second to 1/100 of a second, your shot will be twice as bright. They try to use round numbers, though, so the gap from 1/60 to 1/125 is obviously not quite right! The maths gets a bit more complicated when the gap is only 1/3 of a stop, but the idea is the same.

The built-in exposure meter in your camera will work out what the best exposure should be, but it has to make assumptions about the world that may not be true. To judge the ‘best’ exposure, the camera needs a starting point, and that is that the world is, by and large, 18% grey. If it assumes that to be true, then it can set the exposure accordingly.

However, anyone who’s ever taken pictures of polar bears on the ice knows that that’s not always true! In order to make sure the camera is not fooled by very bright or very dark conditions, you need to use exposure compensation.

If the scene is especially bright, you can dial in up to one or two stops of positive compensation. If it’s especially dark, you can do the opposite. It might take a few test shots to get it exactly right, but that’s better than coming home with lots of shots of grey bears!

Shutter Speed (or Time Value if You Have a Canon)

In the old days, cameras used film, and the shutter speed controlled how long it was exposed to the light in order to take the shot. These days, cameras are digital and have electronic sensors at the back, but the principle is still the same.

The longer the shutter speed, the more light reaches the sensor and hence the brighter the image. The shorter the shutter speed, the less light reaches the sensor and hence the darker the image.

The shutter speed is measured in seconds and can be anything from 1/8000 of a second to 30 seconds or more. The amount of camera shake increases with the focal length, so the rule of thumb for general photography is to make sure your shutter speed is no less than the inverse of the length of your lens, eg if you’re using a 400mm lens, you should be using at least 1/400 of a second.

Lens technology such as Nikon’s ‘Vibration Reduction’ or Canon’s ‘Image Stabilisation’ means that you might be able to get away with a couple of stops slower – ie 1/100 of a second – but that’s about it.

The reason why shutter speed is an important setting is that it controls how much (if any) motion blur there is in the image, and that is an artistic decision. Some people like shots of kingfishers catching a fish that look like they’re frozen in time, with every single water droplet sharp as a tack.

Other people prefer shots of waterfalls shown with creamy torrents of water cascading over them. There isn’t a ‘right’ or ‘wrong’ answer. Just try both and see what you think.

Aperture

The aperture is simply the size of the hole in the lens through which light passes on its way to the sensor, and the principle is similar to that of the shutter speed. The bigger the aperture, the more light reaches the sensor and therefore the brighter the image.

The smaller the aperture, the less light reaches the sensor and therefore the darker the image. The only thing difficult about it is the numbers, which often have a decimal point in them like f/5.6 or f/7.1.

The reason the aperture is not always a nice round number is because it is what you get when you divide the focal length of the lens by the diameter of the hole. Neither of those numbers is necessarily going to be a nice round number, so the result of dividing one by the other certainly won’t be!

The aperture is measured in f-stops, which typically start at f/2.8, f/4 or f/5.6 and continue up to f/22 and beyond. A ‘fast’ lens is one that has a wide maximum aperture such as f/1.4. Photographers like fast lenses as they allow pictures to be taken in low light and offer great flexibility.

The reason why the aperture is such an important setting is that it controls the depth of field, which is the amount of the subject that is acceptably sharp.

The human eye is drawn to things it can see clearly, so making sure the subject is sharp and the background is an ideal way to focus the viewer’s attention on an animal, say, but a landscape photographer might want his image to be sharp all the way from the boat in the foreground to the mountains on the horizon.

Again, there is no right answer; the important thing is to experiment and find what works for you.

ISO (or ASA if You’re Still Using a Film Camera!)

The ISO used to measure the sensitivity of the film being used, a ‘fast’ film with a high ISO being more sensitive than a ‘slow’ film with a low ISO. Now that most cameras are digital, we get the same effect, just with an electronic sensor instead of film.

You might think that extra sensitivity is a good thing – and it is – but it comes at a cost. The higher the ISO, the ‘grainier’ or ‘noisier’ the image, in other words, the less smooth it is.

ISO is measured in ISO (funnily enough!), which just stands for International Standards Organisation. The lowest value is usually ISO 100, and the highest might be 12,800 or more, although the image quality at that value wouldn’t be acceptable to most professional photographers.

Focus

Your second job as a photographer is to make sure that the subject of your images is in focus. In the old days of film cameras, there was obviously no such thing as ‘autofocus’, and focusing had to be done by manually turning a ring on the lens, but today’s digital cameras have very good systems for making sure the images are sharp.

In using the autofocus system, your job is first of all to choose the correct settings and secondly to make sure the camera is focusing on the right part of the frame.

There are lots of different focus settings, but the basic choice is between single area, shown as AF-S (or one-shot AF for a Canon), and continuous, shown as AF-C (or AI Servo for a Canon).

Single area looks to focus on the area of the image under the little red square in the viewfinder (which you can move around the frame manually); continuous does the same but follows the actual subject if it moves.

The best version of this on Nikon cameras is called ‘3D’. The other setting you can change is which button actually does the job of focusing. The shutter button does that on most cameras, but the disadvantage of doing it that way is that the camera stops focusing when you take a picture, which is bad news if you’re tracking a cheetah running at 60mph!

The alternative is to use ‘back-button focusing’, which means separating the jobs of focusing and taking pictures. The shutter button still takes the picture, but the focusing is done by pushing a button on the back of the camera. (You have to set this up yourself, but I use the AF-ON button, which I can press with my right thumb.)

Camera Guide (Based on the Nikon D800)

This guide won’t go through every single setting on a DSLR, but it will show how all the main buttons work, not by saying what each one does but by answering the obvious questions. I hope that’s the easier way to learn!

(All the numbers used are taken from the diagram at the top of this article.)

How do I Switch it on?

That’s simple. Just turn the power switch on the top right-hand side (1) to ‘ON’ (and back to ‘OFF’ when you’ve finished). If you turn it to the light bulb symbol, that just lights up the LCD display on top of the camera.

How do I Set it to Manual?

There are lots of exposure modes on a camera, such as aperture-priority, shutter-priority and program, but using anything other than manual is a bit like buying a Ferrari with an automatic gearbox – you just don’t get as much control (or satisfaction).

To select manual, press the ‘Mode’ button (50) and turn the main command dial on the back right of the camera (31). This allows you to set the shutter speed, aperture and ISO yourself, although I usually set the ISO to ‘ISO-AUTO’ by pushing the ‘ISO’ button on the top left of the camera (56) and at the same time turning the sub-command dial (21).

How do I Make Sure I’m Shooting in RAW?

Press the ‘QUAL’ button (47) and turn the main command dial until the word ‘RAW’ appears on its own. The word ‘RAW’ doesn’t actually stand for anything, but everyone writes it that way to show that it’s a file format that contains the ‘raw’ data from the sensor.

The alternative is JPEG (which stands for Joint Photographic Experts Group), but that’s a compressed file format and therefore should not be used. Note that RAW files don’t end in ‘.RAW’. It’s just a generic term, so each manufacturer has its own RAW extension, such as Nikon’s .NEF.

How do I Set the White Balance?

Press the ‘WB’ button 57 and turn the main command dial (31) to whatever is right for the lighting conditions. The icons aren’t very easy to see, but the options are:

  • Incandescent (ie light bulbs)
  • Fluorescent
  • Direct sunlight
  • Flash
  • Cloudy
  • Shade
  • Choose colour temp
  • Preset manual

The white balance tells the camera the colour of the light you’re working with. It’s a bit like working out what colour the curtains are at the cinema.

The camera can’t tell the difference between something white that’s lit by red light and something red that’s lit by white light, so the white balance setting just makes sure it makes the right call.

If you can’t quite see the icons or want to set up a custom white balance or preset, you can always go through the menu system. However, if you’re shooting in RAW, you can always change the white balance later on your computer, so don’t feel bad about sticking with ‘AUTO’!

How do I Set the Focus Mode?

First of all, make sure your lens is not set to ‘M’, or manual focus, and that the focus mode selector (18) is set to ‘AF’, or auto focus. After that, press the AF-mode button (17) and at the same time turn the main command dial (31) to choose single area or – preferably – continuous.

If you want the 3D option, you press the same button but at the same time turn the sub-command dial (21) until the LCD screen shows ‘3D’.

How do I Set up Back Button focusing?

Press the ‘MENU’ button (46), scroll to the menu item with the pencil icon, select ‘a Autofocus’ and then set ‘a4 AF activation’ to ‘AF-ON only’. Half-pressing the shutter-release button won’t work any more, so don’t forget to focus by pressing (and holding) the AF-ON button (30) with your right thumb while you shoot.

How do I Set the Shutter Speed?

Half-press the shutter-release button (3) if the shutter speed is not illuminated in the viewfinder or on the LCD screen and then turn the main command dial (31).

How do I Set the Aperture?

Half-press the shutter-release button (3) if the aperture is not illuminated in the viewfinder or on the LCD screen and then turn the sub-command dial (21).

How do I Set the Shutter-release Button to Continuous Shooting?

Press the release button next to the ‘D800’ symbol and turn the release mode dial (48) to ‘CH’, or Continuous High. The D800 can shoot five frames a second.

How do I Move the Focus Point in the Viewfinder?

Turn the focus selector lock switch (34) to the dot symbol (rather than ‘L’ for lock) and use the multi selector to move the focus point anywhere within the central area of the viewfinder.

How do I Check the Depth-of-field?

Press the depth-of-field preview button (20).

How do I Add Exposure Compensation?

Press the exposure compensation button (52) and at the same time turn the main command dial (31) to add or subtract as many stops of compensation as you need.

How do I Bracket my Shots?

Press the ‘BKT’ bracketing button (55) and at the same time use the main command dial (31) to choose the number of frames (3-9) and/or the sub-command dial (21) to choose the exposure interval (from 0.3 to 1 stop).

How do I Shoot Video?

You have to use the monitor rather than the viewfinder for this, so first of all turn the live view selector (36) to the film camera icon, press the live view button and then, when you’re ready, press the red movie-record button to start (and stop) video recording.

How do I Look at my Pictures?

Just press the playback button (22) and scroll through the images using the multi selector (32). To zoom in, either use the playback zoom in/zoom out buttons (43, 44) or set up the multi selector centre button to zoom immediately to 100%.

This is very useful to check that images are acceptably sharp. To do that, press the ‘MENU’ button (46), select ‘f Controls’, then ‘f2 Multi selector centre button’ and set ‘Playback mode’ to ‘Zoom on/off’ with ‘Medium magnification’.
To play videos, just press the multi selector centre button (32).

How do I Delete my Pictures?

Just press the delete button (23). If you want to delete all the pictures on the memory card, the best way is to format it. Press the ‘MENU’ button, select ‘Format memory card’ and then select the appropriate card, either the small, thin Secure Digital (SD) card or the thicker, bigger Compact Flash (CF) card.

Rules of Composition

As everyone knows, “Those who can, do; those who can’t, teach” – but that doesn’t stop me trying to do both!

Whatever kind of photographer you are and whatever kind of pictures you take, you always need to pay attention to composition. As an introductory guide (or a reminder), here are a few principles of composition to help you take better pictures. Just make sure you break all of them once in a while!

Rule of Thirds

The most common rule in photography is the rule of thirds. The aim of the game here is avoid taking pictures that are too symmetrical. For some reason, the human eye doesn’t like that, so it’s usually best to place the subject off-centre.

The rule of thirds is just one way to do that. Others include the golden ratio or the Fibonacci curve, and you can find them in Lightroom if you really want to, but the rule of thirds is the best and the simplest.

The idea is that you imagine that the viewfinder is divided up into thirds – both horizontally and vertically – and place the subject at the intersection of two of those invisible lines in order to give it more impact.

The lines also help you to place the horizon when you’re taking a landscape shot. If the horizon is in the middle of the frame, it looks a bit static. Instead, try to establish whether most of the interest is in the land or the sky.

If you want people to focus on the land, place the horizon on the lower imaginary line; if you want people to focus on the clouds in the sky, place it on the upper one. Just make sure that it’s straight!

‘The Decisive Moment’

Henri Cartier-Bresson was a French photographer considered a master of candid photography. He pioneered the genre of street photography. The Decisive Moment was the title of a book he wrote, and his idea was that timing is the secret of a good photograph.

This is obviously more important in certain types of photography (such as wildlife) than others (such as landscape), but it is still a useful guide to taking any kind of action shot.

Bear about to catch salmon in mouth

Framing

Every photograph obviously has a frame, but have you ever tried using a ‘frame-within-a-frame’? Photographic frames come in all shapes and sizes, and so do the ones you find in real life. It might be the branches of a tree or a doorway or a window – the point is that it adds depth to a picture and focuses the viewer’s attention.

Negative Space

I don’t know why people call it ‘negative space’ rather than just ‘space’ (!), but the idea is that a picture with a single subject can look more balanced if there is empty space on the other side of the frame.

This is particularly useful for portraits if you want to stop them looking like ‘passport photos’! It’s also a good idea to allow space for a moving subject to move into. It just looks weird if a person appears to be ‘walking out of the frame’, so try to position the subject around a third of the way across in order to draw the eye into the picture rather than out of it.

Leading Lines

Leading lines are supposed to ‘lead’ the eye of the viewer into the frame – and ideally towards the main subject. They don’t have to be straight, but they tend to work best when they are. The obvious examples are railway tracks or a long, straight road stretching into the distance.

S-curves can do the same job as leading lines, but they also add dynamism and visual interest to a photograph, particularly if it’s a landscape. Again, it might be a road or a railway or even a winding river. All that matters is that the line is roughly in the shape of an S, meandering left and right into the distance.

Symmetry

The rule of thirds and others are meant to stop pictures looking too symmetrical, but sometimes symmetry suits the subject matter. If you have a reflection in the water or a human face, for example, you can’t really avoid it, so it’s sometimes best to make the most of it.

That might mean positioning the line where the water meets the line exactly in the centre of the frame or choosing a square aspect ratio for the picture to enhance the symmetry of a face.

Juvenile rufescent tiger heron stretching its wings

Point of View

I’m a wildlife photographer, and the most important rule of wildlife photography is to get down to eye-level with the animals. It makes a huge difference to the composition and elevates a quick snap to an intimate portrait.

Taking pictures at eye level sometimes means getting wet or muddy – especially if you’re taking pictures of insects on the ground! – but it’s the best way to go. The same applies to portraits, which usually look best taken at eye-level or above.

If you get down any lower than that, you take the risk of ending up with a close-up of the model’s nostrils!

Close-up of lion lying in golden light

Motion Blur

A photograph is just a static image, so it’s sometimes difficult to convey a sense of motion. One way to do that is to use a slower shutter speed in order to create motion blur. Different subjects require different shutter speeds, depending on how fast they are moving, so you might need to experiment a little bit to find that sweet spot between too much sharpness and too little.

You could start with 1/4 of a second for a pedestrian walking along the street, but a Formula One car would disappear if you didn’t cut that down to 1/250 or slower. If you want to go the whole hog, you might try the ‘slow pan’.

Panning just means moving the camera from side-to-side to keep a moving subject in the same part of the frame. The ‘slow’ bit relates to the shutter speed. What you get with a ‘slow pan’ should be a recognisable subject with relatively sharp eyes but blurred limbs (or wings) and a blurred background.

I warn you that this is a tricky business – I once took 1,500 slow pan pictures of guillemots in the Arctic and only kept four of them! – but it’s worth it when it works…

Male azure hawker dragonfly flying through undergrowth

Depth of Field

Another crucial element in wildlife and other kinds of photography is depth of field. To make sure the focus is on the subject and separate it from the background, you can use a larger aperture (such as f/4 or f/2.8).

That will blur anything that’s not in the same plane as the subject while keeping the focal point sharp. The eyes are always the most important part of a portrait – whether it’s of an animal or a person – and we will always see something as being ‘in focus’ as long as they look sharp.

Depth of field is just as important in landscapes, but what we generally want now is sharpness all the way through the image, so it’s better to start with a smaller aperture such as f/11 or f/16.

Cobra held by snake charmer

Odd Numbers

One of the funny things about the way people see the world is that we seem to like odd-numbered groups of objects more than even-numbered ones. It doesn’t really matter why, I guess, but it’s an important point to remember when planning something like a still-life shoot. Just make sure you have three or five tomatoes rather than two or four!

Fill the Frame

Everyone has a camera these days because everyone has a mobile phone, but one of the problems with using your mobile to take pictures is that it’s hard to ‘fill the frame’. It’s all very well taking a selfie when you’re only a few inches from the lens, but trying to zoom in on a distant object or animal is difficult when you only have a few megapixels to play with.

It’s important to remember here the difference between ‘optical zoom’ and ‘digital zoom’. The optical version is what you get naturally with a DSLR lens when you zoom in by changing the focal length; the digital version is when a phone or a bridge camera fools you into thinking you’re zooming in by focusing on a smaller and smaller portion of the sensor.

It’s great when you look through the viewfinder or look at the back of the camera, but the image quality is a lot poorer. Anyway, the point is that what you really want to do is to make the subject dominate the image by making it as large as possible.

If you’re taking a picture of a cheetah, you don’t want it to be a dot in the corner of the frame! You can always crop the image later using Lightroom or another editing program, but that means losing pixels, so the quality will suffer.

It’s always better to get it right in camera if you can. You just need to be careful not to chop off body parts in the wrong place when you’re taking a portrait. Generally, it’s fine to crop in on someone’s face so that the top of the model’s head is not shown, but it’s not a good idea to crop people’s bodies at the joints.

It just looks odd if the edge of the frame coincides with the ankles, knees, waist, elbows, wrists or neck.

Close-up of golden eagle head with catchlight

Aspect Ratio

For some reason, taking a picture in landscape format just seems more ‘natural’ than turning the camera 90 degrees for a portrait, but it’s important to choose the ‘right’ aspect ratio for the image.

A photographer once advised me to make sure at least a third of my pictures were in portrait format, but the point is to look at the subject and decide what’s best. If there are a lot of horizontal lines, then landscape is fair enough, but if there are more vertical lines – such as tree trunks in a forest – then you should probably choose portrait instead.

If you really want to emphasise the length (or height) of a subject, why not try a panorama instead? Different cameras have different set-ups, but the average aspect ratio of a DSLR is 3:2, which doesn’t suit all subjects. I’ve set up a 3:1 template in Lightroom to use for images in which nothing much is happening at the bottom and top of the frame.

Pig peeping out from behind wall

Foreground Interest

When we see a beautiful view, most people’s instant reaction is to take a picture, but what we end up with a lot of the time is an image without any focus. Placing an object in the foreground can lead the eye into the frame and give the image balance. A picture taken on the beach, for instance, might be improved by getting down low in front of a weird rock or piece of driftwood.

Balance

Speaking of balance, it can be a good idea to have the main subject on one side of the frame and a smaller subject on the other. Again, it’s just a matter of what looks most satisfying to the human eye.

Juxtaposition

Old and new, blue and orange, large and small – all these are contrasts that a photograph can pick up on and emphasise. This kind of juxtaposition can be made the point of an image. Think of an elephant beside a mouse – it’s not a picture of an elephant or a picture of a mouse, it’s a picture of the contrast between the two.

Patterns, Textures and Colours

Sometimes, you don’t need a traditional ‘subject’ to make an image visually interesting. There are plenty of patterns in Nature or in the man-made environment; the trick is to find them amongst all the surrounding clutter.

Whether it’s the bark of a tree or paint peeling on a wall, you can sometimes get a very effective abstract image out of it. Black and white images tend to emphasise patterns and shapes, as there is no colour to distract the eye, but colours can form patterns as well – it just depends on the subject and your personal preference.

Simplicity

It’s hard to produce a visually striking image if there is no focal point, or if there are too many competing centres of attention. By creating a simple image – in terms of colour and/or composition – you can remove the distractions and focus on what’s important.


Background

To increase the focus on the subject of an image, it’s a good idea to remove any distractions in the background. It’s obviously not a good idea to take a picture of someone with a telegraph pole sticking out of his head (!), but it’s easy to pay too much attention to the subject and not enough to the background unless you consciously check the viewfinder.

One useful way to reduce the chances of an embarrassing blunder is to reduce the depth of field by increasing the size of the aperture. The traditional way of taking portraits of animals or people, for instance, is to use a ‘fast’ lens, which means one that has a very wide maximum aperture, and shoot wide open.

That reduces the depth of field, thus blurring the background and adding to the impact of the main subject. If you have lights in the background, you can even get a nice effect called ‘bokeh’, which works well for something like a bauble with Christmas tree lights in the background.

Malachite kingfisher on dead branch facing camera

Humour

Whatever you’re photographing, there are always odd moments of humour to be found. People and animals are usually the best sources, but it doesn’t really matter what the subject is. If there’s a visual joke to be made, why not have a go?

I laughed when I saw these penguins together on South Georgia. It looked as if the female was confused by the rock. Was it an egg she was supposed to hatch, or was it just a rock? She spent about five minutes looking at it and examining it before the male came up and said something like, “Come on, darling. It’s just a rock…”

King penguin stepping over rock with another

Breaking the Rules

Having said all that, it’s important to break the rules once in a while. Rules tend to set expectations, so breaking them can make an image seem fresh and original. Why should the horizon be straight?

Why should we see the whole face rather than just half of it? Why should the sky start two-thirds of the way up the frame? If you can’t answer these questions, then why not take a risk? It’s a bit like being a painter: you have to be able to follow the rules before you can break them!

If you’d like to know more or want to book a photography lesson with me, then please get in touch.

Good luck…

Getting the Most out of Game Drives

This would’ve been a great shot. It could’ve been a great shot. It should’ve been a great shot. But it wasn’t. Why? Motion blur. If you look closely, you can see that the whole body is slightly out of focus, and that was simply because I didn’t think to change my shutter speed.

I was parked in a jeep in Botswana when a herd of impala came chasing across the road. They were galloping fast, but there were five or six of them, so I did have time to focus on each of them, one by one, as they crossed the road in turn.

Unfortunately, I was using my default camera settings that were designed to capture animals that were standing still. I was using an 80-400mm lens, so I had my camera on 1/320 and f/8 with auto ISO. That would normally have worked, but not for a jumping impala! What I really needed was a shutter speed of at least 1/1000 of a second. I just didn’t think…

In order to avoid moments like that, here are my answers to a few obvious questions:

What Equipment Do I Need?

Good question. It’s obviously too late to do anything once you’re on safari, so it pays to get your equipment sorted out beforehand. People often ask me what camera I use, and it reminds me of a story I heard about Ernest Hemingway. He went to a photography exhibition in New York and was so impressed he asked to meet the photographer.

Hemingway: These pictures are great. What camera do you use?

Photographer: Well, I use a Leica with a 50mm lens for most of my shots. I’m actually a big fan of your work, too, Mr Hemingway. I’ve read all your books. Can I just ask: what typewriter do you use…?

The point is obviously that a good camera doesn’t necessarily make a good picture, and it’s mildly insulting to photographers if you ask about their equipment without complimenting them on their talent!

However, all other things being equal, a good camera can make life a lot easier for wildlife photography. I’d suggest getting a full-frame DSLR with a zoom lens with a maximum focal length of at least 300mm, preferably 400mm or more.

The problem with a bridge or DX camera is that you won’t get the quality you’re after, as they don’t have large enough sensors. I started off with a bridge camera and thought the zoom was great – until I saw the Nikon DSLR one of the other guys had!

I had a severe case of ‘camera envy’, so I emailed a friend of mine who was a professional photographer to ask what he would get. He recommended either Nikon or Canon, but Canon made photocopiers, so that was out of the question!

Instead, I bought myself a Nikon D800 – complete with 36.3 megapixels! – and it’s served me well ever since. I now also have a D810, which is an upgraded version of the D800. Having two cameras means I don’t have to worry about changing lenses.

Instead, I carry them both cameras on a SpiderPro holster that looks a bit like an old Western cowboy’s gun belt. I can take them out and put them back with just one hand, and I can lock them in place if I’m going on a boat ride or clambering over rocks and don’t want to take any chances.

As for lenses, I mainly use an 80-400mm on the D800 and rent an 800mm prime on the D810. They’re both made by Nikon, and for a very good reason. I tried a Sigma 50-500mm and then a Tamron 150-600mm lens, but the images just weren’t sharp enough.

I now manually check the autofocus of all my lenses using Reikan Focal automatic lens calibration software. All you do is print out a ‘target’ and set up your camera on a tripod to take pictures of it from a certain distance away.

Once you load the software, it guides you through the set-up and takes a number of exposures automatically, just asking you to change the manual focus adjustment anywhere from -20 to +20. When the routine is finished, it gives you a PDF report showing the optimal adjustment value – and that’s what persuaded me to use only Nikon lenses.

I’d been on a trip to Svalbard and wasn’t happy with my shots of the polar bears, which were all just a little bit soft. One of the other guys on the trip told me he did a manual focus check, and that’s when I started doing it, too.

It was only when I bought my new 80-400mm lens that I realised the huge difference in sharpness: the Sigma and Tamron were down at around 1400 on the numeric scale, and the Nikon was way up at 2200! In short, check your lenses.

They’re mass-produced items, so there’s always bound to be some slight variation in focus, and you’d rather fix it yourself than have to use it as an excuse when you don’t get the sharpness you want.

I also make sure I always pack a polarising filter together with a lens cleaning kit (with sensor swabs and cleaning fluid), a beanbag (for resting the lens on the windowsill of a jeep) and my laptop (so that I can download and work on my pictures in the evening).

If I’m going to be near a waterfall, like Iguazu or Victoria Falls, I’ll also take my tripod and a ‘Big Stopper’ neutral density filter to give me the chance of taking creamy pictures of the water with a  long shutter speed.

What Else Can I Do Before I Leave?

Getting the right equipment (and changing the time zone on your camera!) is one thing, but you can help yourself out by booking the right holiday in the right location at the right time. Check when the ‘long rains’ are if you’re going to Africa.

Check when the peak season is for wildlife viewing. Check if it’s possible to visit when there’s a full moon or – even better – a harvest moon. You can ask all these questions (and more) to make sure you get the very most out of your trip.

One useful sight for African expeditions is Safari Bookings, which allows you to search for packages by location, duration and price. I also like to travel light. I hate the whole airport experience, so I avoid having to check any bags in by having a roll-aboard camera bag and packing all my clothing into a jacket that has a pocket in the lining that goes all the way round.

It looks a bit funny when you walk through customs – and some people just couldn’t do it – but it saves me an awful lot of time and bother.

What Should I Wear?

When it comes to clothing, I tend to cover up to avoid the sun and the insects. That means I wear green cargo pants (with lots of pockets!), a brown, long-sleeved shirt, a floppy hat and trainers. If I’m going on a walking safari, I’ll put on my hiking boots, and I might bring a jacket for those cool early morning starts. There’s a reason why I don’t wear bright colours. They don’t exactly frighten the animals, but you’ll get some funny looks if you turn up in hot pants and a Day-Glo pink T-shirt…!

What Should I Take With me on the Game Drives?

If you’re a keen photographer, you won’t want to miss anything while you’re out taking pictures from the 4×4, but that doesn’t mean you need to take the entire contents of your camera bag! I would simply take your camera(s) and your longest lens(es) plus a lens cloth, a couple of spare batteries and a bottle of water.

A beanbag might come in handy on certain vehicles, but that’s about it. You can apply sunscreen and/or insect repellent before you leave. When it comes to clothing, I tend to cover up to avoid the sun and the insects.

That means I wear cargo pants (with lots of pockets!), a long-sleeved shirt, a floppy hat and trainers. Oh, and don’t even think about wearing a day-glo orange or pink T-shirt…!

What Camera Settings Should I Use?

There’s an old photographer’s joke:

Fan to photographer: I love your pictures. What settings did you use?

Photographer to fan: f/8 and be there!

The point is that ‘being there’ is more important than any camera settings, but that doesn’t mean they don’t matter at all – as shown by my shot of the leaping impala.

Exposure

The ‘Exposure Triangle’ consists of the aperture, shutter speed and ISO value, and these are the only three ways you can change the brightness of the image: either having a bigger hole, keeping it open for longer or increasing the sensitivity of the sensor.

A lot of beginners stick to automatic as they don’t trust themselves to use manual settings, but they lose a lot of control by doing that. The camera doesn’t know how fast the animal is travelling or how much of it you want to be in focus, so how can it possibly decide the best combination of shutter speed and aperture?

Why not experiment a little and decide for yourself the kind of image you’re going to take? Now, you still have to make sure you get the correct exposure somehow, and I’m not suggesting you use the exposure meter and manually change the settings for each shot!

What I do is start off with a good set of general-purpose settings and set the ISO to automatic. That way, I get exactly the shutter speed and aperture I want, but the camera makes sure it’s correctly exposed.

The general rule is that you need a shutter speed the inverse of your focal length, so, If I’m using my 80-400mm lens at the top end of the zoom range, that means around 1/400th of a second. (Bear in mind, though, that you have to take into account the speed of the animal as well as how steady you can hold the camera!)

I generally like to take ‘portraits’ of the animals, so I want to throw the background out of focus to emphasise the eyes. That means a wide aperture such as f/5.6, but I’ve started using f/8 because my lens tests tell me that both my lenses perform at their sharpest at f/8, and I want the maximum sharpness I can get.

The problem comes, obviously, when there’s not enough light to use your default settings, or the animals are moving too fast. That’s when you need to take charge and make a difficult decision: which is the most important, the shutter speed, the aperture or the ISO?

If it’s a fast-moving animal, the shutter speed obviously takes priority. If the light level is dropping, then you probably want to compromise and change both aperture and shutter speed by 1/3 of a stop (or more). Most stock agencies don’t want pictures taken at high ISO values (640+), so that’s something to bear in mind if you’re trying to sell your work.

Autofocus

Manual focus has its place in macro photography and in low light conditions, but wildlife photography generally demands that we use one of the two methods of autofocus: single point (AF-S on the Nikon) or continuous (AF-C).

I generally keep my D800 with the wide-angle lens on single point, as I’ll be using it to take landscape shots, but I keep my D810 with the long zoom lens on AF-C 3D, as I’ll be using it to take pictures of animals.

In fact, sharpness is so important for wildlife shots that I use what’s called ‘back-button focusing’, which means setting up the camera so that I can focus by pressing the AF-ON button on the back with my right thumb.

The AF-C 3D setting continuously focuses on one particular point on the animal that you select when you first press the AF button, and it magically follows that point even if the animal is moving. It’s not perfect, but what it does mean is that you don’t have to worry about losing focus when you half-press the shutter and then take a picture.

By separating the focusing from releasing the shutter, you get the best chance of getting that all-important sharpness in the animal’s eye.

White Balance

You can always change it in Lightroom later (or another image-processing software package), but I generally still try to update my white balance setting as the light changes. It saves time later, and it follows the general principle of trying to get everything right in camera. Messing around in Lightroom should always be a last resort.

Quality (RAW)

Shoot in RAW. There. Is. No. Alternative.

Other Settings

One of the confusing and frustrating thing about the DSLR is the number of settings there are and the fact that you can’t ‘reset’ everything in one go. It would be wonderful if there were one button that would do everything, but there isn’t.

There are mechanical as well as electronic settings, so it’s impossible to assign one button to change both. As it is, it’s worth having a mental checklist to go through before you go out on the game drive and even while you’re out there. The main settings to monitor are the following:

  • Mode (Manual, unless you’ve never picked up a camera before…)
  • Shutter speed (1/focal length, although Vibration Reduction means you might get away with up to four stops ‘slower’)
  • Aperture (f/5.6 or f/8, depending on where your lens’s sweet spot is)
  • ISO mode (I generally use ‘auto’)
  • Exposure compensation (0 – unless you’re photographing a very bright or dark scene)
  • Autofocus (AF-C 3D for wildlife)
  • White balance (Daylight – if it’s your typical African sunny day!)
  • Active D-lighting (Auto or off unless you’re taking a picture into the sun and want detail in the shot – it’s a kind of in-camera HDR to squeeze the histogram for images that would be too contrasty otherwise)
  • Lens lock (off, obviously – you don’t want to miss a shot because you can’t zoom in!)

What Should I Do While We’re Driving Around?

It’s all very well chatting to the guy next to you and having a laugh, but you’re there to take pictures, so you should follow these guidelines if you don’t want to be disappointed:

  • Always keep an eye out. I try to sit in the front seat so that I get a better view and can let the driver and the rest of the group know if I see something. If it’s not particularly interesting or too far away to get a good shot, I’ll just point or say, “Impala,” but I’m always ready to pat the driver on the shoulder or tell him to stop if there’s the prospect of a good sighting.
    One of the best sightings I had in Botswana came from the cook’s assistant sitting in the back of the jeep. As we were driving along, he suddenly said something in Setswana to our driver, who stopped and then backed up to see what was going on. After another incomprehensible conversation, I was shown a spotted eagle owl sitting on a branch not 10 yards away!
  • Don’t be shy. The guide will often be the one to spot an animal or a bird, and he or she will usually stop without having to be asked. However, if you spot something and want to take a picture, it’s important to stand up for yourself.Just tap the driver on the shoulder or ask him to stop. You always remember the shots you missed more than the shots you made, so be brave!
  • Be prepared. A lot of game drives involve looking at nothing in particular for hours on end, but that doesn’t mean you shouldn’t be ready at all times. You never know when someone will spot a white rhino or a leopard, so you need to make sure you have your camera(s) to hand with the right shutter speed, aperture and other settings dialled in.I tend to use 1/000 of a second at f/8 with auto ISO, but it depends on the light level. In the early mornings, you often have to make some awkward compromises. Just remember, though, that it’s better to get a sharp shot at a high ISO than a blurred one at ISO 100 and 1/60!
  • Keep the noise down. An animal or bird might seem quite far away, but they spook quite easily, so do make sure you don’t speak too loudly – or shout out something in your excitement! The other guests will thank you for it…
  • Keep still. You’re usually in a jeep with three or four other people, all wanting to take the best photographs they can, so you have to be sympathetic with your movements.If someone’s trying to take a picture, try to move as carefully and slowly as you can – or just wait for them to finish. You don’t want to rock the vehicle or jog an elbow and ruin the perfect shot!
  • Be polite. Tempers sometimes fray in the excitement of a game drive, when everyone wants to get the best possible view of the animals, but it’s worth keeping cool and being aware of those around you.If you take too long over a shot or you accidentally get in the way of someone else, just apologise and move on. People go on safari to enjoy themselves and have a good time, not harbour festering grudges over the guy who thought it was all about him…!
  • Take care of your kit. I always cover my lenses with dust- and waterproof covers when I’m shooting. It might not seem necessary in some countries and in some climates, but you never know when you might have a sudden shower or get a cloud of dust in your face from the jeep in front.I also take a lens cloth and/or a dust blower with me on game drives, and it’s worth checking your lens every now and then to make sure it’s not getting dusty. It’s hard to tell sometimes when you have a lens hood on, but it’s very easy for lenses to get dirty during the course of a long game drive.I found Botswana particularly dusty, and there was a lot of dust in the air in Tadoba that gradually stuck to my camera and turned my lens cloth red whenever I used it!

What Makes a Good Photograph?

Dust, air and spume. That’s the Holy Trinity of wildlife photography, according to Paul Goldstein, who is a wildlife photographer and also a great speaker and raconteur.

I’ve been on two trips he’s led to Svalbard to see the polar bear and Tadoba in India to see the tiger, and I’ve seen several of his presentations.

The idea is that ‘dust’ is thrown up by the movement of the animals and gives you a sense of dynamism and energy, ‘air’ means that an animal is in the air and about to land – so we have a sense of anticipation and expectation – and ‘spume’ is the spray that is thrown up by movement in water.

That’s just Paul’s view, and there are obviously other aspects to the question. One thing that he also points out is the difference between a ‘record shot’ and a ‘photograph’. To him, a ‘record shot’ is just a snapshot, a picture that records exactly what’s in front of you, but a ‘photograph’ is something that obeys the rules of composition and has been consciously constructed by the photographer to provoke an emotional reaction.

There aren’t that many rules of composition in wildlife photography, but it’s worth bearing them in mind when you’re out shooting. Here are a few of the common ones:

  • Fill the frame. Robert Capa once said: “If your pictures aren’t good enough, you aren’t close enough.” People don’t want to have to search the image for the animal, so zoom in or ask your driver to get closer so that you can make it the centre of attention!
  • Use leading lines. Where available, they can lead the eye of the viewer into the image, for instance in a picture of an impala on the horizon crossing a road leading into the distance.
  • Use the Rule of Thirds. Human eyes don’t like things that are too symmetrical – unless you can manage a perfect reflection – so try to put the focal point of your shot off-centre. That adds dynamism and a different kind of balance.
  • Focus on the eyes. People don’t care if 99% of an animal is out of focus as long as the eyes are sharp.
  • Wait for ‘the decisive moment’. A guide in the States once compared my shots to those of another guy on the trip. He said that Stefan’s were always technically perfect, very sharp and with gorgeous, saturated colours, but mine were all about the moment.I take that as a compliment. It means you have to wait for the right moment to take the shot. Don’t just keep clicking away like a Japanese tourist by Big Ben. Compose your shot and then wait for the animal to do something to make it more memorable. It could be a sneeze, a yawn – anything! – but it will mark your picture out as special.Here are a couple of examples:
    • If a lion is walking across the road in front of your jeep, don’t take the shot until it steps forward with the leg that’s furthest away from you. That means it will have to turn its body and show more of its chest in the shot, which makes a better shot.
    • Try to capture pictures of birds in flight. Portraits are all very well, but an action shot is usually better. Given how quickly birds take off, the best way to capture them with their wings spread is just before they land. Find a bird on a branch and take a few ‘portrait’ shots, but don’t give up when it flies away.A lot of birds have a ‘favourite’ branch, so it’s worth focusing on it and waiting for the bird to come back. If it does, take a series of shots in continuous mode, starting when the bird is just about to land.That’s the best way to capture the prize, which is a picture of the bird with its wings spread, showing off all its plumage. Just make sure you have reasonable depth of field (at least f/8) and a high enough shutter speed (at least 1/1000).
  • Tell a story. The tagline to this website is ‘Every picture tells a story’, and that’s a goal we should all aspire to when taking pictures. What are we trying to say? What mood are we trying to create? What’s the emotion behind the shot?It’s not always easy, but picking exactly the right composition can create humour, joy, sorrow, horror and any number of other powerful reactions – which is just what we want.
  • Break the rules – selectively! Obeying the rules will give you a nice, balanced image, but Paul for one hates ‘nice’, and I can see his point. Sometimes, the best way of creating a strongly emotional image is to break a rule or two. You have to do it sparingly – and consciously – but it sometimes gives you that much more of a chance of creating a genuinely arresting image.One of his favourite techniques is the ‘slow pan’, which means following a moving animal or bird with a slow shutter speed and taking a number of shots as it goes past.The idea is to create a sense of movement by blurring the background and the legs or wings of the animal or bird while keeping the body and especially the eyes sharp. It’s a technique that’s very difficult to master.

    You have to do a lot of experimentation, and it helps to have a tripod! I once went on a boat trip in Svalbard and took 1,504 pictures of guillemots using the slow pan – but I only kept four of them! It sounds like a lot of effort, but it’s worth it in the end.

A Day in the Life of a Wildlife Photographer

My iPhone just about died yesterday, so I switched it off overnight. Miraculously, it’s now back to 24%!

We saw leopard tracks but no leopard and then a lone impala to start the day. We were out for 90 minutes before collecting the other staff and the trailer. We then drove north towards Chobe NP. At one point, the road ahead was flooded. Contrary to what you may have been told, there’s no bridge on the River Khwai, so we had to take a different route…

“Nkwe!” Makabu suddenly shouted, which I later found out meant ‘leopard’ in Setswana. He had just seen one crossing the road, and he immediately followed it. After a few yards, he stopped, got out and jumped on the roof to work out where it was, then he unhooked the trailer and drove after it off-road.

You’re not supposed to do either of those things, but I like the fact Africans think rules are there to be broken! The leopard escaped, sadly, but that means Makabu now leads 2-1 in big cat sightings…

Fun fact: ‘Nkwe’ means leopard and ‘tau’ means lion in Setswana.

Having said that, our handyman chipped in with a great spot of a spotted eagle owl perched in a tree as we were driving past. It was just hidden by a branch, so I asked if I could get out and walk a bit closer. Makabu said I could, and I took a very rare picture. I’ve never seen a spotted eagle owl before…

We stopped for lunch (and to collect firewood), and I managed to get attacked by very prickly and sticky fertility grass. Not even thick socks are good enough protection against it. Then again,  you can always boil it up and drink the liquid if you’re having problems with your womb!

At around 1400, we dropped off our team to make camp, then we went back out for another game drive. The radio chatter suggested there were lions out there and maybe even a leopard, but it all seemed like a wild goose chase until we saw a pair of young lions asleep under a large fever berry tree. They like it as it has the best shade, and – lo and behold! – you can also boil its leaves in water to cure a fever. Is there any plant out here that doesn’t have medicinal properties?! We even had chance to come back later for some great close-ups.

Shockingly, I had to change my WB setting to cloudy a few times today. Very poor…

Fun fact: You can tell which termite mounds are active by the presence of wet sand deposits on the surface.

Species lists

We saw impala, black-backed jackal, tsessebe, low veld giraffe, hippo, warthog, Burchell’s zebra, blue wildebeest, red lechwe, tree squirrel, chacma baboon, vervet monkey, elephant, waterbuck, lion, wild dog.

We ask saw birds including Burchell’s starling, African darter, blacksmith plover, Swainson’s francolin, helmeted guineafowl, red-billed hornbill, saddle-billed stork, grey hornbill, African fish eagle, spotted eagle owl, long-tailed pied shrike, African jacana, wattled crane, Cape turtle dove, little egret, Egyptian geese, Gabor goshawk.

Enigma machine

Lightroom Settings

In the last year, I’ve started doing all my photographic post-processing in Lightroom. It’s the program used by most professional photographers and is reasonably user-friendly, but the problem is choosing all the right settings.

I shoot in RAW, which captures the maximum amount of information, but it doesn’t necessarily provide a great picture right out of the box. To do that, you need to improve the contrast, clarity, vibrance and various other settings, but what exactly should these settings be?

Enigma had 150 trillion possible combinations of 10 pairs of 26 letters on the plugboard. Lightroom isn’t quite as bad as that (!), but it can be bewildering. Even the experts disagree. I got to grips with Lightroom mostly by watching a very useful series of YouTube videos by Anthony Morganti and an article on KeepSnap, but I’ve now been given conflicting advice by one of my stock agencies!

What to do, what to do…

In the end, I’ve used a combination of the recommended settings as a starting point, but I’ve taken on all the advice from the stock agency, as they pay the bills!

When I’ve taken a batch of pictures, this is my ‘workflow’:

  1. Connect camera to my MacBook Pro (or use my new card reader if it’s quicker!).
  2. Import all the RAW files to a new folder in Pictures using Image Capture.
  3. Import the files to Lightroom using my custom ‘Import’ settings.
  4. Rate the images (3 stars = people shots worth putting on Facebook, 4 stars = shots worth selling, 5 stars = favourite shots).
  5. Check the ratings (which includes checking the sharpness at 100%).
  6. Work on 4- and 5-star images in Lightroom (eg cropping, tagging faces, choosing custom black and white points to avoid clipping of highlights and shadows).
  7. Add metadata to 4- and 5-star images, including titles, captions, keywords, location and copyright.
  8. Export 4- and 5-star images as JPEGs to 4*, 5* and ‘To upload’ folders in Finder.
  9. Import 4- and 5-star JPEGs to 4* and 5* folders in Lightroom.
  10. Upload to stock agencies (and Facebook).
  11. Format the memory card and delete files in the ‘To upload’ folder and any unrated files in Lightroom.

I know that sounds a bit complicated, but I’ve learned from experience which steps work for me! At the end of the day, the most important thing is to keep a copy of the original RAW files. Lightroom is ‘non-destructive’, so, whatever changes you make, you can always start again.

The next thing to cover is what these mysterious ‘Import’ settings actually are. Here are my current user preset settings, shown for each panel in the Develop module:

  • Basic:
    • Contrast +25
    • Highlights -80
    • Shadows +30
    • Whites 0 (edited later for each shot to avoid pure white)
    • Blacks 0 (edited later for each shot to avoid pure black)
    • Clarity +5 (KeepSnap thinks it should be +40!)
    • Vibrance +20
  • Tone Curve
    • Highlights -5
    • Shadows +5
  • Detail:
    • Sharpening – Amount 25  (Anthony Morganti thinks is should be 70!)
    • Noise Reduction – Luminance 10 (Anthony Morganti thinks is should be 40!)
  • Lens Corrections:
    • Enable Profile Corrections ticked
    • Remove Chromatic Aberration ticked

As I say, these settings are only a starting point, and I’ll obviously change them if I think the image would benefit, but it’s important not to push things too far. That will only make the photograph look ‘over-processed’ and unnatural.

The only other thing I add is a vignette to my wildlife ‘portraits’. I do this by setting the Post-Crop Vignetting Amount to -22 in the Effects module. I don’t do it when the background is a perfect blue sky, as I don’t think it looks very good.

I should say a couple of things about export settings and the use of metadata. I’ve set up presets for all the folders I usually export to, but my experience selling via stock agencies has taught me that JPEG files should be no more than 20MB each, so I’ve used that as my file size limit.

Most stock agencies also have minimum quality thresholds, so I try not to crop so much that the image is less than 6.3 megapixels. The agencies also have rules on the type and number of characters in each metadata field, so I avoid apostrophes and give all my images seven-word titles that are no longer than 50 characters.

Finally, keywords are essential for Search Engine Optimisation, so I use at least 10 but more often 20 or 30, including tags describing the location, content and theme of the image (plus obvious synonyms).

Lightroom is a subject I’m learning all the time, but I hope all this will give you a head start!

Red Xmas Tree star with Bokeh Lights

The Idea

I live in an Art Deco mansion block in Putney, and every year the porters put a Christmas tree in the entrance hall. Last year, I took some pictures of some of the baubles, inspired by an email from one of the photographic magazines about how to capture bokeh lighting. This year, the tree and the baubles were different, so I decided to have another go.

The Location

Ormonde Court, Upper Richmond Road, London SW15 6TW, United Kingdom, around 2100 on 12 December 2014.

The Equipment

  • Nikon D800 DSLR camera
  • Nikon AF-S VR Micro-NIKKOR 105mm f/2.8G IF-ED lens
  • Nikon SB-910 Speedlight flash
  • Manfrotto 190XProB tripod with 496RC2 universal joint head
  • Hähnel HRN 280 remote release.

I’ve just managed to remortgage my flat in Notting Hill, so I’ve been investing in a few photographic supplies. Ever since a German called Stefan took a magnificent shot of Old Faithful at night using flash, I’ve wanted a proper flashgun. Well, now I have one. I bought the Nikon SB-910 Speedlight a couple of weeks ago, and it arrived just in time for this shoot. I didn’t know whether I’d need it or not, but I was prepared to experiment.

The Settings

  • Manual ISO 100
  • f/5.6
  • 1 second
  • 105mm
  • Tungsten white balance
  • Single-point auto-focus

The Technique

In the last of these posts, I mentioned how I’d got used to taking a tripod with me in almost all circumstances, and last night was no exception. Last year, I was generally pleased with my shots of the baubles, but the ISO was far too high.

was using my tripod, funnily enough, but to hold the bauble rather than my camera! This year, I decided I would definitely mount the camera on the tripod, but that left me with nothing to hold the baubles.

I thought about using a light stand from my flash kit, but I needed something horizontal rather than vertical so that I could hang the decorations from it. I then had the idea of using my golf clubs. I could stand the bag in the lobby and balance one of the clubs on top, held in place by the other clubs.

As it turned out, I’d forgotten that the bag would be at an angle of 45 degrees, so my original plan didn’t work, but I simply pulled my 4-iron half-way out and hung the first bauble from that. It was a silver reindeer, but the green wire loop wasn’t very long, and I wouldn’t have been able to get the shots I wanted without the golf club getting in the frame.

I needed a piece of string. I thought about going back to my flat, but leaving my golf clubs and my camera unattended in the entrance hall didn’t seem like a sensible idea! Fortunately, I was wearing trainers, so I just used one of the laces.

It took a few gos to get each bauble to point in the right direction and remain still – particularly as there was a stream of curious residents opening the front door on their way home from work! – but I managed in the end. Phew!

I took lots of pictures of the silver reindeer, a red bauble with a spiral pattern on it and the red star shown above, and I played around with the flash settings to try to make the background a bit darker.

Sadly my new flash was so powerful that I couldn’t manage that – even with -3.0EV of exposure compensation! There might’ve been a better way, but it was the first time I’ve ever used a flashgun, so I’m still a newbie.

The main problem I had in taking the shots was actually getting enough depth-of-field. The reindeer was fine, but the round baubles and even the star were proving a nightmare. If I focused on the front of the bauble, the metal cap and wire loop were out of focus, but, if I focused on those, the rest of the bauble was out of focus.

I’m an absolute stickler for sharpness in my images, so I wasn’t sure what to do. In the end, I stopped down a little bit and hoped that f/5.6 would be a small enough aperture to keep everything acceptably sharp. I tried ‘chimping’ (or checking the shots on the LCD screen) a few times, but it was tricky to tell.

My problem was a kind of Catch-22: the three variables controlling depth-of-field are normally the focal length, the aperture and the relative distances of the camera to the subject and the subject to the background.

I couldn’t change to a wide-angle lens, as I needed to limit the background to just the Christmas tree; I couldn’t change to a much smaller aperture without making the bokeh circles of the blurred Christmas lights in the background too small; and I couldn’t change the relative positions of the camera, bauble and tree without changing the composition completely.

Hmm…

As you can see from the shot above, the two arms on the right of the red star didn’t turn out completely sharp, but it was ‘good enough for Government work’. Shutterstock obviously didn’t accept it – they’re very hot on sharpness! – but I did win an award on Pixoto for the sixth best image uploaded to the Christmas category!

The Post-processing

I made three changes to this shot:

  1. I had the camera on ‘Tungsten’ white balance, as I’d just read somewhere that I should use the amber filter on the flashgun when shooting indoors in order to avoid a clash of different light sources. However, it turned out that the shot looked a lot warmer with the ‘Flash’ white balance, and that was just the look I was after at Christmastime.
  2. A lot of my images end up being quite dark, and I’m not sure whether it’s just because I’m lucky to spend a lot of time in very sunny places or whether there’s a problem with my camera! In this case, I actually had to push the exposure up by +2EV in Aperture to make it look like all the others. I have a feeling that’s because I changed from f/2.8 to f/5.6 to get more depth-of-field but forgot to lengthen the shutter speed to compensate. Silly me…
  3. I was desperately trying to frame the shot perfectly so I wouldn’t have to crop, but the balance of the bauble with the ‘negative space’ on the right wasn’t quite right, so I cropped in slightly to position the star a third of the way into the frame.

Close-up of Golden Eagle Head with Catchlight

I’m a photographer (among other things), and this is the first of a series of posts about my favourite photographs. I’ll tell you how I took them and break down the shot into the idea, the location, the equipment, the settings, the technique and any post-processing.

The Idea

When I took this shot, I was at a Battle of Hastings re-enactment at Battle Abbey in Sussex. I was there to take pictures of the battle scenes between enthusiasts dressed up as Normans and Saxons, and I had no idea there was going to be a falconry display until I bought my ticket and was given a flyer with the plan for the day.

The golden eagle is my favourite bird (isn’t it everyone’s?!), so I was very excited to be able to see one in action. The falconers from Raphael Historical Falconry put on a couple of displays with a variety of birds, including a gyrfalcon and a Harris hawk, but the golden eagle was the highlight.

Afterwards, I wandered over to their tent, and I was able to get within just a few feet of all the birds. The falconer was happy to chat with the spectators with a bird on his arm (so to speak!), and later he fed and watered the birds outside. That gave me the chance to set up my tripod and get a few good close-ups, and this was the best of the lot.

The Location

Battle Abbey, High Street, Hastings and Battle, East Sussex TN33 0AD, United Kingdom, around 1500 on 11 October 2014.

The Equipment

  • Nikon D800 DSLR camera
  • Sigma 50-500mm F4.5-6.3 APO DG OS HSM lens
  • Manfrotto 190XProB tripod with 496RC2 universal joint head
  • Hähnel HRN 280 remote release.

I was a bit worried about using my ‘Bigma’ to take this picture, as I hadn’t been very impressed with it on my trip to Spitsbergen to see the polar bears. Admittedly, the bears were usually a few hundred yards away, and no zoom lens is at its best when it’s at its longest focal length, but I was disappointed that my shots were so soft.

As a result, I did a manual focus check and discovered that the calculated auto-focus fine tune setting was a whopping -12! Armed with this new improvement to the sharpest tool in my box, I was ready for anything…

PS They call it the ‘Bigma’ as it’s made by Sigma, and it’s enormous!

The Settings

  • Auto ISO 110
  • f/9
  • 1/250
  • 500mm
  • Daylight white balance
  • Single-point auto-focus

I had the camera on Manual with ISO on Auto, which I thought was appropriate for a day when lots of things would be happening, and I’d be taking candid shots without much opportunity to sit down and check my settings. However, I should probably have set the ISO to its optimum value of 100 for this shot, as I had plenty of time.

The Technique

I’m generally a travel and wildlife photographer, but I normally don’t use a tripod as it gets in the way and doesn’t work too well in a Land-Rover moving at 40mph! However, I learnt a new perspective from a professional photographer called Mark Carwardine.

He happened to be on a cruise to Spitsbergen that I went on a few months ago, and he was always carrying around his tripod with the legs fully extended – even on the Zodiac inflatables that we used to land on the islands.

I thought to myself, If he can do it, so can I! After that, I’ve tried to use a tripod wherever possible. I love really sharp wildlife shots, and a 36.3-megapixel DSLR and a tripod make a winning combination.

Another important thing about wildlife shots is to get down to the level of the animal or bird you’re shooting. You can see from this shot that I’m right at eye-level with the eagle, and that gives the sense of power and intimacy I was looking for.

Finally, I’ve learnt from a couple of portrait shoots the value of the ‘catchlight’. This is the reflection of the light source that you see in the eye of your subject. It’s just as important with wildlife as with people, and I was lucky enough to get a break in the clouds that allowed the sun to provide the perfect catchlight. Lucky me!

The Post-processing

I changed from a PC to a Mac a few years ago, so I do all my post-processing in Aperture. I suppose I should upgrade to Lightroom or Adobe Camera Raw or Photoshop, but iPhoto was the default image-processing software on the Mac, and Aperture was the cheapest upgrade!

I only had two changes to make to this shot:

  1. Even at 500mm, I still wasn’t quite close enough for the bird’s head to fill the frame, so I had to crop in later. I’ve found from experience that 6.3 megapixels is the minimum size that the major online photo libraries accept, so I never go below 6.4 MP (to avoid rounding errors), and that’s the new size of this file.
  2. In the end, the automatic ISO setting was close enough to the optimum of 100, but the shot was slightly overexposed due to the dark colours of the eagle’s feathers and the grassy background, so I had to reduce the exposure by 0.5EV.

Descriptive Writing

Exams at 11+ and 13+ level always let you tell a story in the writing section, but they sometimes provide a picture and simply ask you to describe it or to ‘write about it in any way you like’. Writing a description is obviously different from writing a story, so it’s worthwhile pointing out the differences and the similarities.

When you write a story, the best way of doing it is probably to follow the five-step process that I outline in Story Mountains:

  1. Choose the title
  2. Brainstorm for ideas
  3. Plan your work
  4. Write it
  5. Check it

You can use a similar basic method for doing a description – except the planning stage obviously doesn’t involve creating a story mountain! – but what are the differences? Steps 1, 4 and 5 are pretty much the same, but you might want to have a look at these tips for the brainstorm and planning.

Brainstorm

When you’re brainstorming for a story, you have to think about characters, genre, period, setting and plot, and you also have to make sure there’s a ‘problem’ to solve so that your idea fits into a story mountain. However, descriptions don’t necessarily have all of those things in them, so you have to think about it in a different way.

The simplest form of description would simply involve describing what’s in a picture (or imagining what’s there if you’re just given the title). That might result in some very imaginative creative writing and open up the possibility of using some great vocabulary and all the poetic devices you can think of, including similes and metaphors.

However, the very best descriptions have to have some kind of ‘hook’ to grab the reader’s attention, and that usually means a central character, situation or even a mini ‘plot’. You obviously need to describe exactly what’s in the picture, but what if you want to say more? What if the picture doesn’t have the things in it that you want.

That’s a bit tricky, but you can always ask questions or just ask the narrator to imagine things.

Hal Morey’s picture of New York’s Grand Central Station is a good example. The shot has lots of elements to it, including the architecture, the people and the beams of light from the windows, so you could easily spend your whole time going over the picture in great depth, picking out each detail and thinking up the best words and metaphors to describe it.

One way of doing that is to make sure your paragraphs are Mutually Exclusive and Collectively Exhaustive (or MECE). That just means the things you describe in each one have to be different (like trees and houses), but your whole description has to cover everything in the picture. That means being as observant and descriptive as you can, noting down the ‘male passengers in fedoras and grey, woollen overcoats’ in the station rather than just ‘people’.

Vocabulary is important here, so you might make a list of the words that you planned to use. One good way of organising this is to think about the five senses: sight, hearing, taste, smell and touch. It’s sometimes difficult to get beyond the visual when you’re analysing a picture, so this method just forces you to think of the other aspects of a scene. Try to make separate lists for each of the senses. The visual vocabulary might include the following:

  • columns (not just walls)
  • vaulting (not just roof)
  • passengers (not just people)
  • spotlights (not just light)
  • cathedral (not just station)
  • nave (not just hall)
  • balustrade (not just railing)

It’s not enough to use words like ‘roof’ when more imaginative synonyms exist such as ‘vaulting’, so try to think of the very best words to use. After all, the examiner can’t tell that you know a word unless you use it! And the same goes for metaphors.

Where did the word ‘cathedral’ come from? Well, the shape of the hall and all the windows are similar to what you’d find in a cathedral or a large church, so why not use that in a kind of ‘extended metaphor’?

An extended metaphor takes a comparison and uses it more than once, so the main part of the hall might be the ‘nave’, the two large arched windows might be the ‘west windows’ and the people might be the ‘congregation’.

Even better would be to link the metaphor to the purpose of the other building by saying something like this: “The congregation bustled to find their seats in the pews as they made their daily act of worship to the god of commerce.”

Suddenly, you’ve gone from a bland description of what you can see for yourself to a new and imaginative way of looking at the world.

The other category of words on your checklist should be feelings. Why simply describe what people look like and not examine how they feel? As an example, use the context of Grand Central Station to imagine what’s going through the passengers’ minds? Are they bored, are they reluctant to go to work, or are they happy to be bunking off for a day at the beach?!

So what else can you do to take your writing to the next level?

The answer is to introduce a main character or some kind of situation or miniature plot. You’re hardly ever ‘banned’ from using a plot in this kind of question, so there’s no problem with introducing one, but let’s stick with the idea of doing a description rather than a story.

The Grand Central picture is again a good example. What would be the character or the situation or the plot here? Well, the obvious idea is to pick is a commuter who’s late for his train. You could introduce the description by focusing on one individual in the picture and explaining why he’s in a hurry.

You could then have a kind of countdown clock as you described all the people and objects he sees as he rushes to make his train:

     Lionel Carey was in a hurry. He only had five minutes to make his train to get to the most important meeting of his life! He struggled along with his precious, old, leather briefcase, catching his fedora as it was blown off his head and cursing the long overcoat he had chosen to wear as it made him sweat uncomfortably and almost tripped him over. Now, what platform did he need?
     Four minutes to go…

And so on. This gives the passage a clearer focus and a sense of tension, excitement and mystery. Will Lionel catch his train? Where is he going? What is the meeting about? It just adds another layer to the description – and ideally leads to higher marks!

Alternatively, you can talk about things that are not in the picture by doing one of the following:

  • ask questions, eg if the picture was of the Colosseum in Rome, you could ask questions like Was this where the Roman gladiators stood before they made their way to their deaths in the arena?
  • create a section in which the narrator imagines objects or events, eg It was here that the emperor would stand before giving the thumbs-up or thumbs-down sign that would signal the fate of the gladiators.

Planning

It’s fairly obvious how to plan for a story because it has to have a plot, but how do you plan for a description? Do you just describe what’s in the picture, starting perhaps on the left and working  your way across? Or do you separate your work into five different paragraphs on each of the senses, with perhaps an extra one for the feelings of the travellers? Or can you introduce a timeline, charting the progress of an imaginary character – such as Lionel Carey, hurrying to catch his train?

Each one might work, but you’ll probably get the best marks for something that engages the reader, and the best way of doing that is to have a central character and a carefully selected situation to place him in:

Lionel Carey in a hurry – needs to catch train for meeting, looks for platform

4 mins

Describe Lionel – importance of what’s in briefcase, mysterious ‘she’ he’s meeting
Describe station – architecture, light, people

3 mins

Describe people he sees
Bumps into coffee cart
Argues with staff
Will he ever see ‘her’?

2 mins

Describe trains – steam, smoke, whistle
Wrong platform – needs to run to Platform 16

1 min

Describe running, bumping into people, curses

Time’s up!
Too late – but wait! Train is delayed. He can give daughter Xmas present after all!

Whatever the picture or title, try giving this method a try. If you brainstorm and plan correctly, focusing on all five senses and people’s feelings and using a central character to add excitement and mystery, I’m sure you’ll do a good job.

Sample Questions

Write a description based on one of the following images.

Useful links

Interview preparation

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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What is a Full Sentence?

Teachers often tell pupils to use a ‘full sentence’ in their answers, but what is a full sentence?

Parts of a Sentence

First of all, it’s important to know what all the words in the picture mean. (Note that the parts of a sentence are not always individual words, though they can be. For example, ‘she’ is the subject, but ‘a hot dog’ is the direct object even though it is three words.)

Subject

The subject of the sentence performs the action of the verb, in other words, “who’s doing the doing”. The girl in the picture is obviously the one doing the eating, not the hot dog!

Verb

The verb is often called the ‘doing word’, although some verbs like ‘being’ and ‘having’ don’t really involve much ‘doing’! Again, what’s being done is obviously shown by the word ‘ate’. There are two kinds of verb:

  • Transitive verbs need a direct object, like the word ‘ate’ in the picture
  • Intransitive verbs don’t need an object, like the word ‘swim’ in ‘They swim’.

Object

There are two kinds of object:

  • Direct objects are directly affected because they ‘suffer the action of the verb’. In other words, they have something done to them, like the hot dog in the picture.
  • Indirect objects are only indirectly affected, for example if they benefit from the verb like the teacher receiving an apple in the picture below.

Types of Sentence

Now we know what the parts of a sentence are, we can talk about all the possible kinds of full sentence.

  1. Verb only
    Strictly speaking, all you really need to make a full sentence is a verb. For example, ‘Sit!’ is a full sentence, even though it only has one word in it. That only works when you’re telling a dog – or a person! – what to do. Most of the time, you need a subject as well.
  2. Subject-Verb
    ‘He swims’ is a full sentence because it has a subject and a verb, but this only works because the verb is intransitive, which means it doesn’t need an object.
  3. Subject-Verb-Object
    The picture above shows the main parts of a simple sentence, which are the subject (S), the verb (V) and the object (O). The initial letters give us a typical pattern for a sentence, which is SVO. In this case, the object is a direct object, which means it’s directly affected but it can also be an indirect object, which may benefit indirectly. Here, the hot dog is the one that has to suffer being eaten – not the girl! – but it’s slightly different in the next picture. _
  4. Subject-Verb-Indirect Object-Direct Object (or Subject-Verb-Direct Object-Indirect Object)
    Here, the apple is being ‘given’, so the apple is the direct object, but the teacher also benefits indirectly, so she is the indirect object.

Common Mistakes

  1. Punctuation
    Every sentence should end with either a full-stop, a question mark or an exclamation mark, but one common mistake is to put a comma in between sentences instead, eg He loved pizza, he always chose pepperoni. This is called the ‘comma splice’.
  2. Fragments
    A sentence that doesn’t have a subject, verb or object when it needs one is called a ‘sentence fragment’, eg Gave his teacher an apple. It’s obvious that it doesn’t make sense without the word ‘He’, but it’s easily done.
  3. Starting with conjunctions
    Teachers often tell their pupils not to start a sentence with ‘because’. When asked a question like ‘Why is Jack sad?‘, it’s easy to write ‘Because his dog died‘. That’s all right when you’re speaking in class – when people don’t care as much about their grammar – but not when you’re doing your homework. It’s not always wrong to do it, though. If you use ‘because’ to link two sentences together, that’s fine, eg Because it was so sunny, I had to wear sun cream.

If you think you’re ready, here are a few sample questions. Which of these is a full sentence?

  1. Because I’m cold.
  2. From front to back.
  3. Ran down the road.
  4. The girl brushed.
  5. He always did.
  6. Yes.
  7. Hello.
  8. Why is the sky blue?
  9. Shut the door!
  10. He tapped. 

     

     

     

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You Must be Crazy!

Teachers and tutors ask pupils to check their work, but how can you do that in Maths without doing the whole sum all over again? Well, you can’t! So how are you supposed to check your work?

What you have to understand first of all is that checking everything is right is very different from checking nothing is obviously wrong. To check everything is right means doing the whole paper twice, but you obviously don’t have time to do that.

Checking nothing is obviously wrong is much easier because it just means doing a ‘quick and dirty’ calculation in your head. It doesn’t guarantee that the answer is right, but it’s a good compromise.

I call it ‘sanity checking’, which means making sure your answers are not crazy! Unfortunately, there isn’t one method that works for every question – it depends on what type of question it is – but here are a few examples:

Algebra

If you have to ‘solve for 𝑥’ and it’s a difficult question, try putting your answer back into the original equation and seeing if one side equals the other, eg if you think 𝑥 = 5, then that works for 2𝑥 + 6 = 16, but not for 3𝑥 + 2 = 5. That would be crazy!

Multiplication

Every multiplication sum starts with multiplying the last digit of each number together, so try doing that when you’ve got your answer and checking if the last digit of the result is equal to the last digit of the answer, eg 176 x 467 is going to end in a 2 because 6 x 7 = 42, which also ends with a 2. Your answer couldn’t end in any other number. That would be crazy!

Rounding

If you have any kind of sum that involves adding, subtracting, multiplication or division, an easy way to check it is to round the numbers to one or two significant figures (eg to the nearest hundred) and work out the answer in your head. If it’s close enough, then your answer is not obviously wrong. If it’s nowhere near, then you’ll have to do it again, eg 1.7 x 3.4 is close to 2 x 3, so the answer might be 5.78, but it wouldn’t be 57.8. That would be crazy!

Units

Most answers in Maths tests need some kind of unit, such as kg, m, cm or ml. Sometimes, the units are provided, but sometimes they’re not. If they’re not, you just need to make sure that you use the right ones, eg if the scale of a map is 1:100,000, the distance represented by 9.8cm is 9.8km, not 9.8m. That would be crazy!

 

 

 

 

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“The Incident”, by Nick Dale

Here is an example of a story I’ve written to illustrate how to use a story mountain as part of my five-step process for creative writing:

  1. Choose your title
  2. Brainstorm for ideas
  3. Create a story mountain
  4. Write the story
  5. Check your work

The title I chose was The Incident. Normally, I’d suggest drawing a triangle to represent a ‘mountain’ and putting your notes at evenly spaced intervals, but that’s a bit difficult with a blog post, so here’s my version of the story mountain:

  • Introduction (grab the reader’s attention)

A busy day in York (describe spontaneous combustion)

  • Introduction (describe the characters)

Frank and Martha driving along

  • Build-up (what the main characters are trying to do)

Christmas shopping, but have to see police at Frank’s tennis club first

  • Problem (what stops them)

Interviewed about ‘incident’ but Frank refuses to sign gagging order

  • Solution (how do they fix the problem)

Escape as Frank knows code to gate

  • Outcome (whether it’s a happy ending or not)

Go to car, but policeman follows

The Incident

xxxIt was just before Christmas, so it was a busy day in the Shambles area of York, with lots of tourists milling around, window-shopping and occasionally going into one of the olde worlde shops to find a scented candle for Aunt Doris or a packet of joss sticks for a grandson who was ‘into that kind of thing’. One man looked a little lost in all the traffic. He was tall and slim, bareheaded but wearing a grey overcoat and trousers with shiny black shoes. What made him look particularly weird was that he was walking around trying desperately to talk to passers-by and shake their hands . Most people thought he was some sort of lunatic and avoided him like the plague, tutting in that very English way before moving on hurriedly, but one man did stop to help.
xxx“Hello, are you lost or something?” said Frank.
xxx“Hello,” said the stranger, offering his hand.
xxx“Oh, er…” said Frank, awkwardly offering his hand in return. He wasn’t in the habit of shaking hands with random people in the street, but he went along with it. However, just as the two men’s hands touched, the stranger disappeared in a burst of flame, leaving only a pile of sooty ashes on the pavement. Frank jumped back in shock, looking at his hand to check he hadn’t been burned. What on Earth had just happened? It was like spontaneous combustion. Or something…
xxxA week later, Frank and his wife were driving through York on their way to their local tennis club. Progress was slow because of all the tourists, and Frank was chuntering under his breath and honking his horn occasionally – even when he didn’t need to. They were a couple in their mid-sixties. Frank was a little taller than his wife, but both were carrying a few extra pounds and had brown eyes and thinning grey hair. Frank was wearing brown trousers, a check shirt and blazer, while Martha had on a knitted dress and an overcoat with low-heeled shoes.
xxx“I thought we were going Christmas shopping?” said Martha.
xxx“We are, but the police want to interview us about that thing in the Shambles. They called it ‘the incident’.”
xxx“Yes, but why aren’t we going to the police station?”
xxx“Well, apparently, they don’t have the space…”
xxxWhen they arrived at the tennis club, there was a policeman at the gate. He checked their names on a list and pointed them towards the clubhouse. The whole place had been taken over. Frank was used to seeing the members playing tennis or lounging at the bar in their sometimes garish tennis gear, but now the courts were empty, and some of the people waiting inside were wearing leather jackets and smoking. Smoking! It was very busy, and they had to wait over an hour to be interviewed. As time went on, the atmosphere got more and more tense. Some of the people who had been seen just walked out quietly, but one man shouted, “I didn’t see a bloody thing!” in a broad Yorkshire accent on his way out of the manager’s office and was forced to sit down in the members’ lounge by one of the constables.
xxx“Mr and Mrs Marshall?”
xxxFrank and Martha got up and went into the office. The policeman at the manager’s desk looked a bit odd surrounded by tennis racquets and balls, but he gave Frank a serious look.
xxx“Hello, I’m Detective McGregor, and I’d just like to talk to you about the incident last week in the Shambles. It was you who shook the man’s hand, wasn’t it, Mr Marshall? Could you just give us an account of what happened, please?”
xxx“Well, the man just disappeared in a puff of smoke as soon as I touched his hand. That’s all there is to say, really. I don’t know anything else.”
xxxMcGregor asked a few more questions before finally giving up and pushing a form across his desk.
xxx“Well, if that’s really all you’ve got to say, I just need you to sign this form.”
xxx“What for?
xxx“Well, it’s a kind of non-disclosure agreement. Just routine. Just to make sure you don’t talk to anyone about the incident. I’m sure you understand.”
xxxFrank didn’t understand at all. If there was one thing that made him angry, it was being told what to do by pettifogging bureaucrats sitting on their fat backsides behind a desk.
xxx“We haven’t done anything wrong, and there’s no way you can force us to sign this. I have rights, you know? Freedom of speech and all that.”
xxx“Oh, Frank! Just sign the form,” sighed Martha.
xxx“No, I’m not signing this bloody form or any other. We’re leaving.”
xxx“Now, Mr Marshall. I’m afraid I can’t allow that. Everyone who comes in today as a witness must sign the form before leaving.”
xxx“So I’m going to be kept prisoner in my own bloody tennis club, am I? Not on your life, mate.”
xxxAs Frank tried to get up and leave, a constable standing beside the door put his hand on his shoulder to stop him, but, just then, there came the sound of a fierce argument from the members’ lounge. Frank could hear the sounds of a scuffle and a young man shouting, “You can’t keep me here!” McGregor and the constable ran out to see what was happening, leaving Frank and Martha alone in the room.
xxx“Come on, love. Let’s make a run for it,” whispered Frank.
xxx“But how are we going to get out?”
xxx“This is my tennis club, remember, and I know the code to the gate!”
xxxQuietly, Frank and Martha opened the door to the lounge and peeked out. Most people were still sitting down, but four or five policemen were trying to stop a couple of youths from escaping. The boys were kicking and punching anyone in uniform, and everyone was watching the fight. That allowed the Marshalls to sneak out of the door without anyone spotting them. Frank turned left instead of right and led Martha to the back gate, where he entered the numeric code on the keypad.
xxx“Here we go. 1-4-6-3. And we’re free!”
xxx“Oh, Frank! You are dreadful.”
xxx“What do you mean? I got us out of there, didn’t I? And now you can do all the Christmas shopping you want.”
xxxAs they walked back to the car, a policeman appeared at the gate and followed them down the street. And it didn’t look like he had Christmas on his mind…

Preceding Direct Objects in French

Forming the perfect (or pluperfect) tense in French is sometimes made harder than necessary by what’s called a Preceding Direct Object (or PDO). The object of a sentence is whatever ‘suffers the action of the verb’, eg the nail in ‘he hit the nail on the head’.

If the object is a pronoun and the perfect (or pluperfect) tense is being used, the French put it before the auxiliary rather than at the end of the sentence as in English, eg ‘il l‘a frappé’ or ‘he it has hit’!

You might think that’s bad enough, but the real problem is that the past participle has to agree in number and gender with the PDO, eg ‘il les a frappés‘ or ‘he’s hit them’.

When it comes to reflexive verbs, it gets even worse. By definition, every reflexive verb has a PDO, so that means you have to watch what you write when a female character is speaking, eg ‘Je me suis lavé’ for a boy, but ‘Je me suis lavée’ for a girl.

Having said that, one of my male pupils once told me that the best way to get a good mark in his French prose was to tell a story in the first person and pretend to be a girl – that way, he’d get a tick every time he used a PDO!

 

 

 

 

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Prime Factors

Prime factors have nothing to do with Optimus Prime – sadly – but they often crop up in Maths tests and can be used to find the Lowest Common Multiple or Highest Common Factor of two numbers.

Prime factors are the lowest prime numbers that can be multiplied together to make a given number. There are two methods of finding out what they are: the ladder method and the factor tree. I prefer the ladder method.

Ladder Method

  1. Write down the number for which you want to find the prime factors.
  2. Find the lowest prime number that goes into it exactly and write it down next to it on the same line.
  3. Divide one number by the other and write down the result under the original number on the next line.
  4. Repeat steps 2 and 3 until you reach the number 1.
  5. Draw a line between the two columns and lines after the first row and before the last.
  6. Write down the prime factors from the column you have just created, using powers to simplify the expression, eg the factors of 12 are 2² x 3, not 2 x 2 x 3.

Prime factors

Sample Questions

  1. What are the prime factors of 72?
  2. What are the prime factors of 96?
  3. What are the prime factors of 104?
  4. What are the prime factors of 37?
  5. What are the prime factors of 51?

Lowest Common Multiple (LCM)

Prime factors are useful in working out the Lowest Common Multiple (LCM) of two numbers, in other words the lowest number that is divisible by both numbers.

  1. Work out the prime factors of the two numbers and write them down one below the other, eg the prime factors of 30 are 2 x 3 x 5, and the prime factors of 45 are 3 x 3 x 5.
  2. Make a new list by writing down each factor the greatest number of times it appears in either list, eg there are two 3s in one list and one in the other, so the new list is 2 x 3 x 3 x 5.
  3. Multiply together the new list of factors, eg the LCM of 30 and 45 is 2 x 3 x 3 x 5 = 90.

Sample Questions

  1. What is the lowest common multiple of 8 and 12?
  2. What is the LCM of 18 and 24?
  3. What is the lowest common multiple of 72 and 96?
  4. What is the lowest common multiple of 14 and 49?
  5. What is the lowest common multiple of 26 and 39?

Highest Common Factor (HCF)

Prime factors can be used to work out the Highest Common Factor (HCF) of two numbers, in other words the highest number that both numbers can be divided by exactly.

  1. Work out the prime factors of the two numbers and write them down one below the other, eg the prime factors of 30 are 2 x 3 x 5, and the prime factors of 45 are 3 x 3 x 5.
  2. Make a new list by writing down each factor that appears in both lists, eg 3 and 5 appear in both lists, so the new list is 3 x 5.
  3. Multiply together the new list of factors, eg the HCF of 30 and 45 is 3 x 5 = 15.

Sample Questions

  1. What is the highest common factor of 8 and 12?
  2. What is the highest common factor of 72 and 56?
  3. What is the highest common factor of 52 and 104?
  4. What is the highest common factor of 72 and 108?
  5. What is the highest common factor of 132 and 44? 

     

     

     

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French Regular Verbs – Conditional Tense

The conditional tense in French is used to show that someone ‘would do’ or ‘would be doing’ something. All verbs end in -er, -re or -ir, and the endings are different (as shown here in red):

Verbs Ending in -er, eg Donner (to Give)

Je donnerais          (I would give)
Tu donnerais          (You would give – informal)
Il/elle donnerait          (He/she would give)
Nous donnerions          (We would give)
Vous donneriez          (You would give – formal and/or plural)
Ils/elles donneraient          (They would give – masculine or masculine and feminine/feminine only)

Verbs Ending in -re, eg Vendre (to Sell)

Je vendrais          (I would give)
Tu vendrais          (You would give – informal)
Il/elle vendrait          (He/she would give)
Nous vendrions          (We would give)
Vous vendriez          (You would give – formal and/or plural)
Ils/elles vendraient          (They would give – masculine or masculine and feminine/feminine only)

Verbs Ending in -ir, eg Finir (to Finish)

Je finirais          (I would finish)
Tu finirais          (You would finish – informal)
Il/elle finirait          (He/she would finish)
Nous finirions          (We would finish)
Vous finiriez          (You would finish – formal and/or plural)
Ils/elles finiraient          (They would finish – masculine or masculine and feminine/feminine only)

 

 

 

 

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French Regular Verbs – Future Tense

There is only one future tense in French, and it’s used to show that someone ‘will do’ or ‘will be doing’ something. Verbs end in -er, -re or -ir, but the endings are the same (as shown here in red):

Verbs Ending in -er, eg Donner (to Give)

Je donnerai          (I will give)
Tu donneras          (You will give – informal)
Il/elle donnera          (He/she will give)
Nous donnerons          (We will give)
Vous donnerez          (You will give – formal and/or plural)
Ils/elles donneront          (They will give – masculine or masculine and feminine/feminine only)

Verbs Ending in -re, eg Vendre (to Sell)

Je vendrai          (I will sell)
Tu vendras          (You will sell – informal)
Il/elle vendra          (He/she will sell)
Nous vendrons          (We will sell)
Vous vendrez          (You will sell – formal and/or plural)
Ils/elles vendront          (They will sell – masculine or masculine and feminine/feminine only)

Verbs Ending in -ir, eg Finir (to Finish)

Je finirai          (I will finish)
Tu finiras          (You will finish – informal)
Il/elle finira          (He/she will finish)
Nous finirons          (We will finish)
Vous finirez          (You will finish – formal and/or plural)
Ils/elles finiront          (They will finish – masculine or masculine and feminine/feminine only)

 

 

 

 

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French Regular Verbs – Past Tense

Here are the basic forms of French regular verbs in the past tense, which include the perfect (or passé composé), pluperfect, imperfect and past historic (or passé simple). All verbs end in -er, -re or -ir, and there are different endings for each that are shown here in red.

Perfect (or passé composé)

The perfect tense is used in formal written French to say someone ‘has done’ something, but they sometimes use it in conversation and casual writing in the same way we use the simple past tense (or ‘preterite’), eg ‘j’ai donné’ might mean ‘I gave’ rather than ‘I have given’ – you just need to look at the context to help you decide which is the right translation.

Verbs Ending in -er, eg Donner (to Give)

J’ai donné          (I have given or I gave)
Tu as donné          (You have given or you gave – informal)
Il/elle a donné          (He/she has given or he/she gave)
Nous avons donné          (We have given or we gave)
Vous avez donné          (You have given or you gave – formal and/or plural)
Ils/elles ont donné          (They have given or they gave – masculine or masculine and feminine/feminine only)

Verbs Ending in -re, eg Vendre (to Sell)

J’ai vendu          (I have sold or I sold)
Tu as vendu          (You have sold or you sold – informal)
Il/elle a vendu          (He/she has sold or he/she sold)
Nous avons vendu          (We have sold or we sold)
Vous avez vendu          (You have sold or you sold – formal and/or plural)
Ils/elles ont vendu          (They have sold or they sold – masculine or masculine and feminine/feminine only)

Verbs Ending in -ir, eg Finir (to Finish)

J’ai fini          (I have finished or I finished)
Tu as fini          (You have finished or you finished – informal)
Il/elle a fini          (He/she has finished or he/she finished)
Nous avons fini          (We have finished or we finished)
Vous avez fini          (You have finished or you finished – formal and/or plural)
Ils/elles ont fini          (They have finished or they finished – masculine or masculine and feminine/feminine only)

Pluperfect

The pluperfect tense is used to say someone ‘had done’ something. This is common in story-writing when an event is described that happened before that particular moment in the story, eg ‘j’avais donné’ means ‘I had given’.

Verbs Ending in -er, eg Donner (to Give)

J’avais donné          (I had given)
Tu avais donné          (You had given – informal)
Il/elle avait donné          (He/she had given)
Nous avions donné          (We had given)
Vous aviez donné          (You had given – formal and/or plural)
Ils/elles avaient donné         (They had given – masculine or masculine and feminine/feminine only)

Verbs Ending in -re, eg Vendre (to Sell)

J’avais vendu          (I had sold)
Tu avais vendu          (You had sold – informal)
Il/elle avait vendu          (He/she had sold)
Nous avions vendu          (We had sold)
Vous aviez vendu          (You had sold – formal and/or plural)
Ils/elles avaient vendu         (They had sold – masculine or masculine and feminine/feminine only)

Verbs Ending in -ir, eg Finir (to Finish)

J’avais fini          (I had finished)
Tu avais fini          (You had finished – informal)
Il/elle avait fini          (He/she had finished)
Nous avions fini          (We had finished)
Vous aviez fini          (You had finished – formal and/or plural)
Ils/elles avaient fini         (They had finished – masculine or masculine and feminine/feminine only)

Imperfect

The imperfect tense is used to say someone ‘was doing’ or ‘used to do’ something, eg ‘je donnais’ means ‘I was giving’ or ‘I used to give’.

Verbs Ending in -er, eg Donner (to Give)

Je donnais          (I was giving)
Tu donnais          (You were giving – informal)
Il/elle donnait          (He/she was giving)
Nous donnions          (We were giving)
Vous donniez          (You were giving – formal and/or plural)
Ils/elles donnaient          (They were giving – masculine or masculine and feminine/feminine only)

Verbs Ending in -re, eg Vendre (to Sell)

Je vendais          (I was selling)
Tu vendais          (You were selling – informal)
Il/elle vendait          (He/she was selling)
Nous vendions          (We were selling)
Vous vendiez          (You were selling – formal and/or plural)
Ils/elles vendaient          (They were selling – masculine or masculine and feminine/feminine only)

Verbs Ending in -ir, eg Finir (to Finish)

Je finissais          (I was finishing)
Tu finissais          (You were finishing – informal)
Il/elle finissait          (He/she was finishing)
Nous finissions          (We were finishing)
Vous finissiez          (You were finishing – formal and/or plural)
Ils/elles finissaient          (They were finishing – masculine or masculine and feminine/feminine only)

Past Historic (or Passé Simple)

The past historic is the equivalent of the simple past tense (or preterite) in English and is used in novels and other formal writing to say someone ‘did’ something, eg ‘je donnai’ means ‘I gave’ or ‘I used to give’. It is never used in conversation, where it is replaced by the perfect tense.

Verbs Ending in -er, eg Donner (to Give)

Je donnai          (I gave)
Tu donnas          (you gave – informal)
Il/elle donna          (he/she gave)
Nous donnâmes          (we gave)
Vous donnâtes          (you gave – formal and/or plural)
Ils/elles donnèrent          (they gave – masculine or masculine and feminine/feminine only)

Verbs Ending in -re, eg Vendre (to Sell)

Je vendis          (I sold)
Tu vendis          (you sold – informal)
Il/elle vendit          (he/she sold)
Nous vendîmes          (we sold)
Vous vendîtes          (you sold – formal and/or plural)
Ils/elles vendirent          (they sold – masculine or masculine and feminine/feminine only)

Verbs Ending in -ir, eg Finir (to Finish)

Je finis          (I finished)
Tu finis          (you finished – informal)
Il/elle finit          (he/she finished)
Nous finîmes          (we finished)
Vous finîtes          (you finished – formal and/or plural)
Ils/elles finirent          (they finished – masculine or masculine and feminine/feminine only)

 

 

 

 

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Common French Verbs – Present Tense

Language changes over time because people are lazy. They’d rather say something that’s easy than something that’s correct. That means the most common words change the most, and the verbs become ‘irregular’. In French, the ten most common verbs are ‘être’, ‘avoir’, ‘pouvoir’, ‘faire’, ‘mettre’, ‘dire’, ‘devoir’, ‘prendre’, ‘donner’ and ‘aller’, and they’re all irregular apart from ‘donner’. Here are their forms in the present tense.

Note: the irregular forms are shown in red.

Etre (to Be)

Je suis          (I am)
Tu es          (You are – informal)
Il/elle est          (He/she is)
Nous sommes          (We are)
Vous êtes          (You are – formal and/or plural)
Ils/elles sont          (They are – masculine or masculine and feminine/feminine only)

Avoir (to Have)

J’ai          (I have)
Tu as          (You have – informal)
Il/elle as          (He/she has)
Nous avons          (We have – formal and/or plural)
Vous avez          (You have – formal and/or plural)
Ils/elles ont          (They have – masculine or masculine and feminine/feminine only)

Pouvoir (to be Able to, ‘Can’)

Je peux          (I can)
Tu peux          (You can – informal)
Il/elle peut          (He/she can)
Nous pouvons          (We can – formal and/or plural)
Vous pouvez          (You can – formal and/or plural)
Ils/elles peuvent          (They can – masculine or masculine and feminine/feminine only)

Faire (to Do, to Make)

Je fais          (I do or make)
Tu fais          (You do or make – informal)
Il/elle fait          (He/she does or makes)
Nous faisons          (We do or make – formal and/or plural)
Vous faites          (You do or make – formal and/or plural)
Ils/elles font          (They do or make – masculine or masculine and feminine/feminine only)

Mettre (to Put)

Je mets          (I put)
Tu mets          (You put – informal)
Il/elle met          (He/she puts)
Nous mettons          (You put – formal and/or plural)
Vous mettez          (You put – formal and/or plural)
Ils/elles mettent          (They put – masculine or masculine and feminine/feminine only)

Dire (to Say, to Tell)

Je dis          (I say or tell)
Tu dis          (You say or tell – informal)
Il/elle dit          (He/she says or tells)
Nous disons          (We say or tell – formal and/or plural)
Vous disez          (You say or tell – formal and/or plural)
Ils/elles disent          (They say or tell – masculine or masculine and feminine/feminine only)

Devoir (to Have to, ‘Must’)

Je dois          (I have to or must)
Tu dois          (You have to or must – informal)
Il/elle doit          (He/she has to or must)
Nous devons          (We have to or must – formal and/or plural)
Vous devez          (You have to or must – formal and/or plural)
Ils/elles doivent          (They have to or must – masculine or masculine and feminine/feminine only)

Prendre (to Take)

Je prends          (I take)
Tu prends          (You take – informal)
Il/elle prend          (He/she takes)
Nous prenons          (We take – formal and/or plural)
Vous prenez          (You take – formal and/or plural)
Ils/elles prennent          (They take – masculine or masculine and feminine/feminine only)

Aller (to Go)

Je vais          (I have)
Tu vas          (You have – informal)
Il/elle va          (He/she has)
Nous allons          (We have – formal and/or plural)
Vous allez          (You have – formal and/or plural)
Ils/elles vont          (They have – masculine or masculine and feminine/feminine only)

 

 

 

 

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French Regular Verbs – Present Tense

Nobody likes French verbs – not even the French! – but I thought I’d start by listing the most basic forms of the regular verbs in the present tense. All French verbs end in -er, -re or -ir, and there are different endings for each that are shown here in red:

Verbs Ending in -er, eg Donner (to Give)

Je donne          (I give)
Tu donnes          (You give – informal)
Il/elle donne          (He/she gives)
Nous donnons          (We give)
Vous donnez          (You give – formal and/or plural)
Ils/elles donnent          (They give – masculine or masculine and feminine/feminine only)

Verbs Ending in -re, eg Vendre (to Sell)

Je vends          (I sell)
Tu vends          (You sell – informal)
Il/elle vend          (He/she sell)
Nous vendons          (We sell)
Vous vendez          (You sell – formal and/or plural)
Ils/elles vendent          (They sell – masculine or masculine and feminine/feminine only)

Verbs Ending in -ir, eg Finir (to Finish)

Je finis          (I finish)
Tu finis          (You finish – informal)
Il/elle finit          (He/she finish)
Nous finissons          (We finish)
Vous finissez          (You finish – formal and/or plural)
Ils/elles finissent          (They finish – masculine or masculine and feminine/feminine only)

If you’re learning French and have to memorise the present tense, it helps if you can spot the patterns:

  • The je, tu, il/elle and ils/elles forms all sound the same for -er and -re verbs (and the same is true of the je, tu and il/elle forms of -ir verbs)
  • The nous and vous forms always end in -ons and -ez (although -ir verbs have an extra -ss- in the middle)

People learn things in different ways, but the best way I’ve found is to make a recording on my phone and try to repeat the words at the same time as I listened to them on my headphones. I did a lot of acting at Oxford and in the Edinburgh Fringe, and that was the way I learned my lines.

If I made a mistake or forgot something, the recording prompted me with the right words, and I could carry on repeating the exercise until I was word-perfect. It meant I could learn my lines any time, anywhere – whether I was watching sport, making dinner or cycling around town!

Good luck…

 

 

 

 

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Negative Numbers

Working with negative numbers can be confusing, but a few simple rules can help you add, subtract, multiply and divide successfully:

Adding and Subtracting

If the operator and the sign are the same, then you must add the number, eg 4 – -3 = 4 + 3 = 7 or 4 + +3 = 7.

If the operator and the sign are different, then you must subtract the number, eg 4 + -3 = 4 – 3 = 1 or 4 – +3 = 1.

Here are a few practice questions:

  1. 14 – -3
  2. -4 + -7
  3. 21 – +8
  4. -8 + -7
  5. 6 – -4

Multiplication and Division

If the signs of the two numbers are the same, then you must make the answer positive, eg -4 x -3 = 4 x 3 = 12 or +4 x +3 = 4 x 3 = 12.

If the signs of the two numbers are different, then you must make the answer negative, eg -4 x +3 = -12 or +4 x -3 = -12.

Here are a few practice questions:

  1. 1 × -3
  2. -8 ÷ -4
  3. 2 × -7
  4. -14 ÷ -7
  5. 6 × -4 

     

     

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Useful Terms in Maths

 

Maths is complicated, but a good first step on the road to understanding it is to get to know the most useful terms. There are lists in the front of the Bond books, but here’s my own contribution. I hope it helps!

Algebra: expressions using letters to represent unknown values, eg 2(x + 3) = 16.

Angles: there are three types of angle, depending on the number of degrees.

  • acute angles are between 0 and 90 degrees.
  • obtuse angles are between 90 and 180 degrees.
  • reflex angles are between 180 and 360 degrees.

Arc: part of the circumference of a circle.

Averages: there are three types of average, and they are all useful in different ways.

  • The mean is found by adding up all the values and dividing the total by how many there are, eg the mean of the numbers 1-10 is 5.5, as 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55, and 55 ÷ 10 = 5.5.
  • The mode is the most common value (or values), eg the mode of 1, 2, 2, 3, 4, 5 is 2.
  • The median of an odd number of values sorted by size is the one in the middle, eg the median of the numbers 1-5 is 3. The median of an even number of values is the mean of the two numbers in the middle, eg the median of the numbers 1-10 is 5.5, as 5 and 6 are the numbers in the middle, and 11 ÷ 2 = 5.5.

Chord: a straight line drawn between two points on the circumference of a circle.

Circumference: the distance all the way around the edge of a circle.

Congruent: triangles are congruent if they are the same shape and size, eg two right-angled triangles with sides of 3cm, 4cm and 5cm would be ‘congruent’, even if one is the mirror image of the other. You can prove that two triangles are congruent by using any of the following methods: SAS (Side-Angle-Side), SSS (Side-Side-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side) and RHS or HL (Right-angle-Hypotenuse-Side or Hypotenuse-Leg). If all three measurements of the angles and/or sides are equal, the triangles are congruent. You can only create a congruent copy of a triangle by translation, reflection or rotation. (Note: congruence is the same as similarity, except that the triangles have to be the same size.)

Cube: the result of multiplying any number by itself twice, eg 8 is the cube of 2, as 2 x 2 x 2 = 8.

Cube root: the number that has to be multiplied by itself twice to make another number, eg 2 is the cube root of 8, as 2 x 2 x 2 = 8.

Cuboid: a solid with a rectangle for each of the six sides, eg a shoe box.

Denominator: the number on the bottom of a fraction, eg 2 is the denominator of ½.

Diameter: the length of a line drawn across a circle passing through the centre.

Dividend: the number being divided in a division sum, eg in 24 ÷ 4 = 6, the dividend is 24.

Divisor: the number to divide by in a division sum, eg in 18 ÷ 6 = 3, the divisor is 6.

Equation: any line of numbers and operators with an equals sign in the middle, showing that the two sides balance, eg 4x + 12 = 34.

Factor: a number that goes into another number evenly, eg 6 is a factor or 12.

Fibonacci series: a sequence of numbers created by adding the previous two numbers together to get the next one, eg 1, 1, 2, 3, 5, 8, 13…

Formula: a way of calculating the answer to a common problem using letters or words, eg the formula for distance is speed x time (or D = S x T).

Frequency density: the frequency per unit for the data in each class of values, defined as frequency ➗ class width, eg if 10 people were between 180 cm and 190 cm tall (180 ≤ x < 190), the frequency density would be 10 ➗ (190 – 180) = 10 ➗ 10 = 1.

Highest Common Factor (HCF): the highest number that goes into two other numbers evenly, eg the HCF of 12 and 18 is 6.

Improper fraction: a fraction that is greater than one (in other words, the numerator is greater than the denominator), eg 9/5.

Irrational number: a number that can’t be written as a fraction and has an infinite number of decimal places without any repeating sequences, eg pi (or π).

Lowest Common Multiple (LCM) or Lowest/Least Common Denominator (LCD): the lowest number that is divisible by two other numbers, eg the LCM of 6 and 8 is 24.

Multiple: a number that can be divided evenly by another number, eg 12 is a multiple of 6.

Natural number (or counting number): a positive whole number, eg 1. (Some people include zero, some don’t.)

Numerator: the number on the top of a fraction, eg 3 is the numerator of ¾.

Order of operations: the sequence of doing basic mathematical sums when you have a mixture of, say, addition and multiplication. BIDMAS (or BODMAS or PEMDAS) is a good way of remembering it, as it stands for:

  • Brackets/Parentheses
  • Indices/Order/Exponents
  • (in other words, squares, cubes and so on)
  • Division
  • Multiplication
  • Addition
  • Subtraction

Note that division doesn’t come ‘before’ multiplication and addition doesn’t come ‘before’ subtraction. These operations have to be done in the order in which they occur in the sum, and it can make a difference to the answer, eg 4 – 3 + 2 = 3 if you do the calculations from left to right, which is correct, but if you did 3 + 2 first, you’d get -1, which is the wrong answer.

Operator: the sign telling you which mathematical operation to do. The most common ones are +, -, x and ÷.

Parallel: two lines are parallel if they will never meet, eg the rails on a railway line. On diagrams, parallel lines are shown with matching arrows—one for the first pair, two for the second etc.

Perimeter: the distance all the way round the outside of a shape.

Perpendicular: at 90 degrees to each other.

Pi (or π): a constant used to work out the circumference and area of circles, often shown as 22/7 or 3.14 although it’s actually an ‘irrational’ number, which means it goes on for ever.

Prime factors: the lowest prime numbers that can be multiplied together to make a given number, eg the prime factors of 12 are 2² x 3.

Prime numbers: a number that can only be divided by itself and one, eg 2, 3, 5, 7, 11, 13…

Probability: the chance of something happening, calculated as the number of ways of getting what you want divided by the total number of possible outcomes, eg the chance of a coin toss being heads is ½ as there is one ‘heads’ side but two sides in total. To work out the probability of a sequence of events, you have to multiply the individual probabilities together, eg the chance of a coin toss being heads twice in a row is ½ x ½ = ¼

Product: the result of multiplying two numbers together, eg 35 is the product of 5 and 7.

Quadrilateral: a four-sided shape such as the following:

  • Kite: a quadrilateral with two pairs of equal sides next to each other (or ‘adjacent’ to each other).
  • Parallelogram: a quadrilateral with opposite sides parallel to each other.
  • Rectangle: a quadrilateral with two opposite pairs of equal sides and four right angles.
  • Rhombus: a quadrilateral with equal sides.
  • Square: a quadrilateral with equal sides and four right angles.
  • Trapezium (or Trapezoid): a quadrilateral with one pair of parallel sides. (Note: an isosceles trapezium is symmetrical.)

Quotient: the answer to a division sum, eg in 12 ÷ 4 = 3, the quotient is 3.

Radius: the distance from the centre of a circle to the circumference.

Range: the highest minus the lowest value in a list, eg the range of the numbers 1-10 is 9.

Rational number: a positive or negative number that can be written as a fraction, including zero and all whole numbers, eg 1 or ½.

Regular: a shape is regular if all its sides and angles are equal, eg a 50p piece is a regular (-ish!) heptagon.

Right angle: an angle of 90 degrees.

Sector: a ‘slice’ of a circle in between two radii.

Segment: a part of a circle separated from the rest by a chord.

Shapes: the name of each shape depends on the number of sides. Here are the most common ones.

  • Triangles have three sides.
  • Quadrilaterals have four sides.
  • Pentagons have five sides.
  • Hexagons have six sides.
  • Heptagons have seven sides.
  • Octagons have eight sides.
  • Nonagons have nine sides.
  • Decagons have 10 sides.
  • Hendecagons have 11 sides.
  • Dodecagons have 12 sides.

Similar: triangles are similar if they are the same shape, but not necessarily the same size, eg a right-angled triangle with sides of 3cm, 4cm and 5cm is ‘similar’ to a right-angled triangle with sides of 6cm, 8cm and 10cm. (Note: similarity is the same as congruence, except that the triangles don’t have to be the same size.)

Square number: the result of multiplying any number by itself, eg 49 is a square number, as 7 x 7 = 49.

Square root: the number that has to be multiplied by itself to make another number, eg 6 is the square root of 36, as 6 x 6 = 36.

Sum: the result of adding two numbers together, eg 17 is the sum of 8 and 9.

Tangent: either a straight line that touches the circumference of a circle OR the length of the opposite side of a triangle divided by the length of the adjacent side

Transformations: there are three main kinds of transformation: reflection, rotation and translation.

  • With reflection, you need to state the formula of the mirror line, eg the shape has been reflected in the line y = 4.
  • With rotation, you need to state the number of degrees, the direction and the centre of rotation, eg the shape has been rotated 90 degrees clockwise around the point (4, 3).
  • With translation, you need to state the change in the x and y values, eg the shape has been translated four units up and three units to the right.

Triangles: there are four main types, each with different properties.

  • equilateral triangles have all three sides the same length and all three angles the same. On diagrams, lines of similar length are shown with matching tick marks going across them—one for the first pair, two for the second etc.
  • isosceles triangles have two sides the same length and two angles the same.
  • scalene triangles have three sides of different lengths with three different angles.
  • right-angled triangles have one 90-degree angle.

Variable: an unknown in algebra, eg x or y.

Vinculum: the line between the numerator and denominator in a fraction (also called the fraction bar).

 

 

 

 

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Algebra

Nothing makes the heart of a reluctant mathematician sink like an algebra question.

Algebra is supposed to make life easier. By learning a formula or an equation, you can solve any similar type of problem—whatever the numbers involved. However, an awful lot of students find it difficult, because letters just don’t seem to ‘mean’ as much as numbers. Here, we’ll try to make life a bit easier…

Before we start, there are three words that you need to know if you want to learn algebra:

  • variable or unknown is a letter that stands for a number, eg a, b, c, x, y or z.
  • A term is either a number, a letter or a combination of a letter and a number or two or more letters, eg 7, y, 7y or xy.
  • An expression is a sum involving two or more terms, eg 7y + x or 5 + xy.
  • An equation is an expression that equals something, eg 7y = 14 or xy = 4x.

In addition, there are a couple of other tips that make life easier:

  • When you write the letter ‘x’, you should always use the ‘curly x’, ie a backwards and forwards ‘c’, to avoid confusion with the times operator.
  • You should never use the times symbol in algebra. You should put letters and numbers side-by-side to show that they need to be multiplied together, eg 7y means ‘7 times y’ and yz means ‘y times z’.
  • You should never put a 1 before a letter, eg 1a is just written as a.
  • You should generally put your variables in alphabetical order in the final answer, eg ab not ba and 2a + 3b not 3b + 2a.
  • The squared symbol only relates to the number or letter immediately before it, eg 3m² means 3 x m x m, NOT (3 x m) x (3 x m).

Great! Now we can go over the main kinds of algebra questions.

Gathering Terms

X’s and y’s look a bit meaningless, but that’s the point. They can stand for anything. The simplest form of question you’ll have to answer is one that involves gathering your terms. That just means counting how many variables or unknowns you have (like x and y). I like to think of them as pieces of fruit, so an expression like…

2x + 3y – x + y

…just means ‘take away one apple from two apples and add one banana to three more bananas’. That leaves you with one apple and four bananas, or x + 4y.

If it helps, you can arrange the expression with the first kind of variables (in alphabetical order) on the left and the second kind on the right like this:

2x – x + 3y + y

x + 4y

Just make sure you bring the operators with the variables that come after them so that you keep exactly the same operators, eg two plus signs and a minus sign in this case.

Here are a few practice questions:

  1. 3x + 4y – 2x + y
  2. 2m + 3n – m + 3n
  3. p + 2q + 3p – 3q
  4. 2a – 4b + a + 4b
  5. x + y – 2x + 2y

Multiplying out Brackets

This is one of the commonest types of question. All you need to do is write down the same expression without the brackets. To take a simple example:

2(x + 3)

In this case, all you need to do is multiply everything inside the brackets by the number outside, which is 2, but what do we do about the ‘+’ sign? We could just multiply 2 by x, write down ‘+’ and then multiply 2 by 3:

2x + 6

However, that gets us into trouble if we have to subtract one expression in brackets from another (see below for explanation) – so it’s better to think of the ‘+’ sign as belonging to the 3. In other words, you multiply 2 by x and then 2 by +3. Once you’ve done that, you just convert the ‘+’ sign back to an operator. It gives exactly the same result, but it will work ALL the time rather than just with simple sums!

Here are a few practice questions:

  1. 2(a + 5)
  2. 3(y + 2)
  3. 6(3 + b)
  4. 3(a – 3)
  5. 4(3 – p)

Solving for x

Another common type of question involves finding out what x stands for (or y or z or any other letter). The easiest way to look at this kind of equation is using fruit again. In the old days, scales in a grocery shop sometimes had a bowl on one side and a place to put weights on the other.

To weigh fruit, you just needed to make sure that the weights and the fruit balanced and then add up all the weights. The point is that every equation always has to balance – the very word ‘equation’ comes from ‘equal’ – so you have to make sure that anything you do to one side you also have to do to the other. Just remember the magic words: BOTH SIDES!

There are three main types of operations you need to do in the following order:

  1. Multiplying out any brackets
  2. Adding or subtracting from BOTH SIDES
  3. Multiplying or dividing BOTH SIDES by the x coefficient (ie the number next to the variable)

Once you’ve multiplied out any brackets (see above), what you want to do is to simplify the equation by removing one expression at a time until you end up with something that says x = The Answer. It’s easier to start with adding and subtracting and then multiply or divide afterwards (followed by any square roots). To take the same example as before:

2(x + 3) = 8

Multiplying out the brackets gives us:

2x + 6 = 8

Subtracting 6 from BOTH SIDES gives us:

2x = 2

Dividing BOTH SIDES by 2 gives us the final answer:

x = 1

Simple!

Here are a few practice questions:

  1. b + 5 = 9
  2. 3y = 9
  3. 6(4 + c) = 36
  4. 3(a – 2) = 24
  5. 4(3 – p) = -8

Number Triangles

Number triangles (see article) are a helpful way of rearranging the relationship between three terms involving multiplication or division. To take a simple example:

  • speed = distance ÷ time
  • time = distance ÷ speed
  • distance = speed x time

That’s a lot to remember! However, if you use a number triangle, you can put distance (d) at the top and speed (s) and time (t) at the bottom. If you then put your finger over the one you need, you get the formula, eg if you put your finger over speed (s), you get distance (d) over time (t).

You can use number triangles to rearrange complicated equations when solving for x, eg 2 / (x – 2) = 7 becomes x – 2 = 2/7, which means x = 2 2/7.

Fractions

Some algebraic expressions look complicated when they’re really just fractions. As long as you know how to add, subtract, multiply and divide fractions, you can do the same with algebraic fractions, eg to solve (2x – 1) / 4 – (x + 1) / 5 = 2, you can just take the second fraction away from the first using cross-multiplication or a similar method.

Linear Inequalities

If the equation has no powers (eg b²) and contains a ‘less than’ or ‘more than’ operator (<, >, ≤ or ≥) instead of an equals sign (=), it’s called a ‘linear inequality’. Here, the rules are a little bit different.

  1. If you have to multiply or divide both sides of a linear inequality by a negative number to get rid of the number next to the variable (the ‘x coefficient’), you need to reverse the inequality, eg if you divide both sides by -5, -5x < 25 becomes x > -5 (not x < -5).
  2. If the variable ends up on the ‘wrong’ side of the inequality, you have to reverse the direction of the inequality when you flip it, eg 3 < x becomes x > 3 (not x < 3).

Multiplying Two Expressions in Brackets (‘FOIL’ Method)

When you have to multiply something in brackets by something else in brackets, you should use what’s called the ‘FOIL’ method. FOIL is an acronym that stands for:

First
Outside
Inside
Last

This is simply a good way to remember the order in which to multiply the terms, so we start with the first terms in each bracket, then move on to the outside terms in the whole expression, then the terms in the middle and finally the last terms in each bracket.

Just make sure that you use the same trick we saw earlier, combining the operators with the numbers and letters before multiplying them together. For example:

(a + 1)(a + 2)

First we multiply the first terms in each bracket:

a x a

…then the outside terms:

a x +2

…then the inside terms:

+1 x a

…and finally the last terms in each bracket:

+1 x +2

Put it all together and simplify:

(a + 1)(a + 2)

= a² + 2a + a + 2

=a² + 3a + 2

Here are a few practice questions:

  1. (a + 1)(b + 2)
  2. (a – 1)(a + 2)
  3. (b + 1)(a – 2)
  4. (p – 1)(q + 2)
  5. (y + 1)(y – 3)

Factorising Quadratics (‘Product and Sum’ Method)

This is just the opposite of multiplying two expressions in brackets. Normally, factorisation involves finding the Highest Common Factor (or HCF) and putting that outside a set of brackets containing the rest of the terms, but some expressions can’t be solved that way, eg a² + 3a + 2 (from the previous example).

There is no combination of numbers and/or letters that goes evenly into a², 3a and 2, so we have to factorise using two sets of brackets. To do this, we use the ‘product and sum’ method.

This simply means that we need to find a pair of numbers whose product equals the last number and whose sum equals the multiple of a. In this case, it’s 1 and 2 as +1 x +2 = +2 and +1 + +2 = +3.

The first term in each bracket is just going to be a as a x a = a². Hence, factorising a² + 3a + 2 gives (a + 1)(a + 2). You can check it by using the FOIL method (see above) to multiply out the brackets:

(a + 1)(a + 2)

= a² + 2a + a + 2

=a² + 3a + 2

Note that some questions may not have a term in the middle, but that’s just because the two terms you get when you use the FOIL method cancel each other out, eg x² – 25 becomes (x – 5)(x + 5) because x² + 5x – 5x – 25 = x² + 0 – 25.

Here are a few practice questions:

  1. y² + 9y + 20
  2. y² + 10y + 9
  3. p² + 5p – 24
  4. p² + 8p + 16
  5. z² – 121

Subtracting One Expression from Another*

Here’s the reason why we don’t just write down operators as we come across them. Here’s a simple expression we need to simplify:

20 – 4(x – 3) = 16

If we use the ‘wrong’ method, then we get the following answer:

20 – 4(x – 3) = 16

20 – 4x – 12 = 16

8 – 4x = 16

4x = -8

x = -2

Now, if we plug our answer for x back into the original equation, it doesn’t balance:

20 – 4(-2 – 3) = 16

20 – 4 x -5 = 16

20 – -20 = 16

40 = 16!!

That’s why we have to use the other method, treating the operator as a negative or positive sign to be added to the number before we multiply it by whatever’s outside the brackets:

20 – 4(x – 3) = 16

20 – 4x + 12 = 16

32 – 4x = 16

4x = 16

x = 4

That makes much more sense, as we can see:

20 – 4(4 – 3) = 16

20 – 4 x 1 = 16

20 – 4 = 16

16 = 16

Thank Goodness for that!

Here are a few practice questions:

  1. 30 – 3(p – 1) = 0
  2. 20 – 3(a – 3) = 5
  3. 12 – 4(x – 2) = 4
  4. 24 – 6(x – 3) = 6
  5. 0 – 6(x – 2) = -12

 

 

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It’s All About the Apostrophe

Apostrophes. The difference between feeling you’re nuts and feeling your nuts.

The apostrophe is tricky. It means different things at different times. This article is meant to clear up any confusion and help you use apostrophes, which might mean you get straight As in your exams – or should that be A’s?!

  1. The main reason for using apostrophes is to show a contraction, which is a word made up of two other words shunted together – the apostrophe just stands for the missing letter(s), eg didn’t = did not, could’ve = could have and won’t = will not.
  2. The second most common usage is in showing the possessive, in other words showing that something belongs to someone (or something). This is where it gets tricky, because where you put the apostrophe depends on how many things you’re talking about. If the noun is plural and ends with -s, you just need to put an apostrophe on the end of the word. In all other cases,  you should put ‘s, eg two horses’ hooves, BUT a horse’s hooves or the children’s books or St James’s Palace.
  3. The other occasion when you might find an apostrophe is in the plural of individual letters or numbers. Somehow, it just looks better, eg he got three A’s at O-level back in the 1980’s.

If you think you’ve mastered the rules, try taking this quiz! Alternatively, here are a few sample questions. Just choose the correct option.

  1. He stole James’s/James’/Jameses book.
  2. She marked the childrens/children’s/childrens’ homework.
  3. He didnt/didn’t/did’nt mind at all.
  4. They wont/wo’nt/won’t be back in time.
  5. The two girls/girl’s/girls’ bags were next to each other.
  6. You need to get three As/As’/A’s to get into Oxford.
  7. I love the clothes we used to wear in the 1970s/1970’s/1970s’.
  8. He stroked the cats/cat’s/cats’ back.
  9. The Smiths/Smith’s/Smiths’ house was gorgeous.
  10. Diana was the peoples/peoples’/people’s princess. 

     

     

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Spelling Rules

The problem with the English is that we’ve invaded (and been invaded by) so many countries that our language has ended up with a mish-mash of spelling rules.

English is among the easiest languages to learn but among the most difficult to master. One of the problems is spelling. We have so many loan words from so many different languages that we’ve been left with a huge number of spelling rules – and all of them have exceptions!

Contrast that with Spanish, for example, where what you see is generally what you get. The problem for students of English, then, is that it’s very difficult to find shortcuts to improve your spelling, and an awful lot of words just have to be learned off-by-heart. Considering that there are over a million words in English, that’s a big ask!

There are lots of lists of spelling rules on the web, but I thought I’d put down what I think are the most useful ones.

  1. I before E except after C when the sound is /ee/.
    This is the most famous rule of English spelling, but there are still exceptions! Hence, we write achieve with -ie- in the middle but also ceiling, with -ei- in the middle, as the /ee/ sound comes after the letter c. The most common exceptions are weird and seize.
  2. If you want to know whether to double the consonant, ask yourself if the word is like dinner or diner.
    One of the most common problems in spelling is knowing when to double a consonant. A simple rule that helps with a lot of words is to ask yourself whether the word is more like dinner or diner. Diner has a long vowel sound before a consonant and then another vowel (ie vowel-consonant-vowel, or VCV). Words with this long vowel sound only need one consonant before the second vowel, eg  shinerfiver and whiner. However, dinner has a short first vowel and needs two consonants to ‘protect’ it (ie vowel-consonant-consonant-vowel, or VCCV). If the word is like dinner, you need to double the consonant, eg winnerbitter or glimmer. Just bear in mind that this rule doesn’t work with words that start with a prefix (or a group of letters added to the front of a word), so it’s disappoint and not dissapoint.
  3. If the word has more than one syllable and has the stress on the first syllable, don’t double any final consonant, eg focusing, not focussing.
    This rule sounds a bit complicated, but it’s still very useful—as long as you know how to pronounce the word! Which syllable is stressed often changes if the word is used differently. Progress, for instance, has the stress on the first syllable if it’s a noun but on the second if it’s a verb!
    We generally double the final consonant when we add a suffix starting with a vowel, such as -ing, but this rule means we shouldn’t do that as long as a) the word has more than one syllable and b) the stress is on the first syllable, eg focusing and targeted, but progressing and regretting. The main exceptions to this are words ending in -l and -y, hence barrelling and disobeying, but another one is formatting.
  4. When adding a suffix starting with a consonant, you don’t need to change the root word unless it ends in -y. This is among the easiest and most useful rules. There are loads of words ending in suffixes like -less-ment or -ness, but spelling them should be easy as long as you know how to spell the root word, eg shoe becomes shoelesscontain becomes containment and green becomes greenness. However, there are exceptions! Judge becomes judgment (in British English), and words ending in -y need the y changing to an i, so happy becomes happiness.
  5. When adding a suffix starting with a vowel to a word ending in a silent -e, the must be dropped unless it softens a or a g.
    An at the end of a word is often called a ‘Magic E’, as it lengthens the vowel before the final consonant, eg fat becomes fate. However, that job is done by the vowel at the start of the suffix when it is added to the word, so it needs to be dropped, eg race becomes racing and code becomes coded. The main exceptions come when the word ends with a soft or g, which need to be followed by an -e, an -i or a -y to sound like /j/ and /s/ rather than /g/ and /k/. If the suffix doesn’t begin with an e- or an i-, we still need the to make sure the word sounds right, eg managing  is fine without the -e, as the in -ing keeps the soft, but manageable needs to keep the -e to avoid a hard /g/ sound that wouldn’t sound right.
  6. The only word ending in -full is full!
    There are lots of words ending in what sounds like -full, but the only one that has two ls at the end is full. All the other words – and there are thankfully no exceptions! – end in -ful, eg skilfulbeautiful and wonderful.
  7. Words ending in -f or -fe always change the f to a v in the plural, eg leaf becomes leaves, and knife becomes knives. The only exceptions are chief, dwarf and roof. You can remember them all by memorising this sentence: “The chief dwarf sat on the roof.”
    PS I know Tolkien writes about ‘dwarves’ rather than ‘dwarfs’ in The Lord of the Rings, but that’s just because he thought ‘dwarves’ sounded better! 

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Parts of Speech

When is a verb not a verb? When it’s a part of speech.

English exams often ask questions about the ‘parts of speech’. This is just a fancy term for all the different kinds of words, but they’re worth knowing just in case. Just watch out for words such as ‘jump’, which can be more than one part of speech!

If you struggle to remember what they all mean, think about the words themselves. Sometimes, there’s a clue in the way they sound, eg adverbs describe verbs, pronoun sounds like noun, preposition contains the word position and a conjunction is the ‘junction’ between two sentences.

Noun

A noun is a word for a person, place or thing

  • abstract noun: a word to describe an idea, eg peace
  • common (or concrete) noun: a word for a thing or object, eg table
  • proper noun: the name of a person, place etc, eg Nick, London
  • collective noun: the name of a group of animals, eg herd or flock

Tip: Make up a phrase or a sentence with ‘the’ in front of the word. If it makes sense, it’s probably a noun, eg He looked at the ______.

Adjective

An adjective is a word that describes a noun or pronoun, eg green or young

Tip: Make up a phrase or a sentence putting the word between ‘the’ and a noun. If it makes sense, it’s probably an adjective, eg The ______ book lay on the table.

Verb

A verb is a doing word, eg jumped, was, pays

Tip: Make up a phrase or a sentence putting the word after a pronoun such as ‘he’. If it makes sense, it’s probably a verb, eg He ______ it or He ______ in the garden.

Pronoun

A pronoun is a word that stands in for a noun

  • personal pronoun: a word that shows a person or thing, eg he, she, them
  • possessive pronoun: a word that shows the owner of an object, eg his, their
  • relative pronoun: a word that ‘relates’ to the subject just mentioned, eg who, that, which

Tip: Make up a phrase or a sentence with a verb after the word (but without ‘the’ or ‘a’ in front of it). If it makes sense, it’s probably a pronoun, eg ______ looked at the wall.

Article

An article is a word that introduces a noun, ie aan or the.

Strictly speaking, an article is just one kind of ‘determiner’, a word that introduces a noun:

  • Articles (indefinite article: a/an, definite article: the)
  • Demonstratives (thisthatthesethose)
  • Quantifiers (manymuchmoremostsome etc)

Tip: Make up a phrase or a sentence with the word in front of a noun. If it makes sense, it’s probably an article, eg ______ book lay on the table.

Adverb

An adverb is a word that describes an adjective, adverb or verb, usually ending in -ly, eg really or quickly

Tip: Make up a phrase or a sentence with the word after a verb. If it makes sense, it’s probably an adverb, eg He ran ______ around the garden.

Preposition

A preposition is a word that shows the position in time or space, eg in, at or after

Tip: Make up a phrase or a sentence about placing something somewhere, putting the word before the location. If it makes sense, it’s probably a preposition, eg She put the book ______ the table.

Conjunction

A conjunction is a word that connects two sentences together (sometimes called a connective), eg and, but or because.

    • Coordinating conjunctions‘ are used to make a ‘compound’ sentence when the clauses are equally important, and the two ‘main clauses’ should always be separated by a comma, eg ‘The sun was warm, but it was cooler in the shade’.
      There is a useful way of remembering the coordinating conjunctions, which is to use ‘FANBOYS’. This consists of the first letter of ‘for’, ‘and’, ‘nor’, ‘but’, ‘or’, ‘yet’ and ‘so’.
    • Subordinating conjunctions‘ are used to make a ‘complex’ sentence when there is a main clause and a subordinate clause. (Subordinate just means less important.) If the sentence starts with a subordinating conjunction, the clauses need a comma between them, eg ‘Even though it was very hot, he wasn’t thirsty’.
      However, if the subordinate clause comes at the end, there is no need for a comma, eg ‘He wasn’t thirsty even though it was very hot’. There are lots of subordinating conjunctions, such as ‘after’, ‘although’ and ‘because’, but the easy way to remember it is to ask yourself if the conjunction is in FANBOYS. If it is, it’s a coordinating conjunction; if it’s not, it’s a subordinating conjunction.
      Alternatively, subordinating conjunctions are sometimes known as ‘WABBITS’ because some of the commonest ones start with those letters (when, where, while, after, although, before, because, if, though and since).

Tip: Make up a phrase or a sentence with two clauses joined by the word. If it makes sense, it’s probably a conjunction, eg He looked at the problem ______ decided to do something about it.

Interjection

An interjection is either an outburst like hey or a word people say when they’re playing for time, eg well or now.

Tip: Make up a phrase or a sentence that someone might say, putting the word at the start, followed by a comma. If it makes sense, it’s probably an interjection, eg ______, can we go to the mall?

Quiz

Here’s a useful online worksheet on parts of speech with 25 questions and answers.

You can also test yourself by reading any passage in English and going through it word by word, asking yourself what parts of speech they all are.

Why not start with this article? See how fast you can go. If you’re not sure, ask yourself the questions in each of the tips shown above, eg if you think it’s a noun, can you put it into a sentence with ‘the’ in front of it?

If you want a fun way to practise using different parts of speech, try the word game Mad Libs!

Here’s a quick quiz…

  1. What are the nine parts of speech? (9 marks)
  2. What do they all mean? (9 marks)
  3. What are the four different kinds of noun (4 marks)
  4. What are the three different kinds of pronoun (3 marks)
  5. What are the two kinds of article? (2 marks)
  6. What are the two kinds of conjunction? (2 marks)
  7. What are the two words that help you remember the different kinds of conjunction? (2 marks)

Total: 31 marks

 

 

 

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Capital!

I always sign Christmas and birthday cards with a capital ‘N’. It makes me feel like Napoleon…

The three main things to check after writing anything are spelling, punctuation and capital letters, so when do you use capitals?

  • For the important words in titles, either of individuals or pieces of writing, eg Chief Inspector of Schools or This Blog Post is Great! Using title case or headline case for a newspaper article can get complicated, but there are two main ways to do it. You can either capitalise every word that has at least three or four letters or use these principles:
    • Capitalise the first and last words.
    • Capitalise adverbs, nouns, pronouns and verbs.
    • Capitalise prepositions if they’re in a phrasal verb, eg Look Out.
    • Capitalise prepositions if they’re in a Latin phrase, eg Ad Lib.
  • For proper nouns (except the seasons), eg Peter, Tuesday, Blue Tit or Chelsea (but autumn)
  • For adjectives that describe nationality, eg British or French
  • For titles (‘honorifics’) and words we use to address people (‘vocatives’), eg Sir or Mum (but ‘his mum’ not ‘his Mum’ as there are many possible mums)
  • For abbreviations, eg BBC (although acronyms you can actually pronounce only need one at the start, eg Nato, not NATO).
  • For the first word in a sentence, eg This is a sentence.
  • For the first word in direct speech, eg he said, “Hello.”
  • For special words such as government, eg ‘the Government’ but ‘the UK government’
  • The word “I”. 

     

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Speech Marks

Speech marks, inverted commas, quotation marks, quote marks, quotes, 66 and 99 – does any other punctuation mark have so many names or cause so much confusion…?!

Writing a story means striking a balance between what I call The Three Ds: Drama, Description and Dialogue. I’ve read quite a few stories from my pupils in which nobody talks to anyone – which is a bit odd! – but you need to know the rules of punctuation before you start.

  • Start a new paragraph whenever the speaker changes or someone stops talking.
  • Put speech marks before and after the actual words spoken, eg Hello, he said, NOT “Hello, he said.”
  • Start the first spoken word with a capital letter, eg she said, “This needs a capital letter,” NOT she said, “this needs a capital letter.”
  • Put either a comma, question mark, exclamation mark or colon between the speech and the ‘he said/she said’, eg “Don’t forget the comma,” he said, NOT “Don’t forget the comma” he said.
  • Put punctuation that belongs to the speech inside the speech marks, eg “The exclamation mark belongs inside!“, NOT “The exclamation mark belongs inside”! (The only exception comes with inverted commas, which look the same but are used with quotations rather than speech.)
  • Put a full-stop after the ‘he said/she said’ if it comes in the middle of the speech and the first part is a full sentence; otherwise, just put a comma, eg “This is a full sentence,” she said. “This is, too.” BUT “This is not a full sentence,” she said, “and nor is this.”
  • Don’t start the ‘he said/she said’ with a capital letter, even if it comes after a question mark or exclamation mark, eg “Don’t use a capital letter!” he shouted, NOT “Don’t use a capital letter!” He shouted.
  • If a speech lasts more than one paragraph, put speech marks before each paragraph and after the last one but NOT after the ones before.
  • Don’t put ‘he said/she said’ after every single line of dialogue in a long conversation if it’s obvious who is speaking.
  • Finally, put the name of the person speaking after the verb, eg “Hello,” said Mrs Rogers, NOT “Hello,” Mrs Rogers said. It sounds better, and it helps put the emphasis where it belongs—on the person’s name.

Sample Questions

Format and put the correct punctuation and capital letters into the following lines of speech, changing the word order if necessary:

  1. I say john what time is it mr jones asked
  2. hello she said my name is tara
  3. what are you talking about he cried I never said that
  4. hello he said whats your name Sarah she said Im Alan Nice to meet you you too
  5. I hate chocolate she said I only really eat chocolate ice-cream 

     

     

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Divisibility Rules OK!

And, no, this is nothing to do with Harry Potter’s invisibility cloak…

Times tables can be tricky, and there’s no substitute for learning them by heart. However, the divisibility rules can at least tell you whether an answer is definitely wrong. I’m a great believer in ‘sanity checking’ your work. Just ask yourself, “Is this crazy?” If it is, you’ll have to do the question again!

The divisibility rules are quite simple (except for the ones for 7 and 8). They tell you whether a number can be divided by any number from 1 to 10. They’re most useful when simplifying fractions…or when you’re struggling to remember your times tables!

  1. Must be a whole number, eg 2, but not 2.5.
  2. Must be an even number ending in 0, 2, 4, 6 or 8, eg 22, but not 23.
  3. The sum of the digits must be divisible by 3, eg 66, but not 67.
  4. The number formed by the last two digits must be ’00’ or divisible by 4, eg 500 or 504, but not 503.
  5. Must end in 5 or 0, eg 60, but not 61.
  6. Must be divisible by both 2 and 3, eg 18, but not 23.
  7. If you double the last digit and take this away from the number formed by the rest of the digits, the result must be 0 or divisible by 7, eg 672 (2 x 2 = 4, and 67 – 4 = 63, which is divisible by 7), but not 674.
  8. The number formed by the last three digits must be ‘000’ or divisible by 8, eg 5,000 or 5,008, but not 5,003.
  9. The sum of the digits must be divisible by 9, eg 666, but not 667.
  10. Must end in 0, eg 110, but not 111. 

     

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Tips for the QTS Numeracy Test

“If I’d known I’d have to go back to school, I’d never have become a teacher!”

The QTS numeracy and literacy tests are not very popular, but trainee teachers still have to pass them before they can start teaching in the state sector, so I thought I’d try and help out. There is always more than one way of doing a Maths question, but I hope I’ll demonstrate a few useful shortcuts and describe when and how they should be used.

The point of shortcuts is that, even though you may have to do more sums, they’ll be easier sums that can be done faster and more accurately. The numeracy test consists of two sections – mental Maths and interpreting charts – and I’m going to focus on the first of these.

Fractions to Percentages – Type 1

There are a number of typical types of questions in the numeracy test, and a lot of them involve multiplication – so knowing your times tables is an absolute must! One of the most common kinds of questions involves converting fractions to percentages.

These are just two ways of showing the same thing, but to answer these questions, you’ll need to try different approaches. First of all, have a look to see if the denominator (or the number on the bottom of the fraction) is a factor or a multiple of 100.

If it is, you can simply multiply or divide the numerator (the number on the top) and the denominator by whatever it takes to leave 100 on the bottom. Any fraction over 100 is just a percentage in disguise, so you just need to put the percentage sign after the numerator, eg what is the percentage mark if:

  1. a pupil scores 7 out of a possible 20?
    Answer: 20 x 5 = 100, so 7 x 5 = 35%.
  2. a pupil scores 18 out of a possible 25?
  3. a pupil scores 7 out of a possible 10?
  4. a pupil scores 9 out of a possible 20?
  5. a pupil scores 130 out of a possible 200?

Fractions to Percentages – Type 2

If the denominator is not a factor of 100, check if it’s a multiple of 10. If it is, you can convert the fraction into tenths and then multiply the top and bottom by 10 to get a fraction over 100, which, again, is just a percentage in disguise, eg what is the percentage mark if:

  1. A pupil scores 24 marks out of a possible 40?
    Answer: 40 ÷ 4 = 10, so 24 ÷ 4 = 6 and 6 x 10 = 60%.
  2. A pupil scores 12 marks out of a possible 30?
  3. A pupil scores 32 marks out of a possible 80?
  4. A pupil scores 49 marks out of a possible 70?
  5. A pupil scores 24 marks out of a possible 60?

Fractions to Percentages – Type 3

If neither of the first two methods works, that means you have to simplify the fraction. Once you’ve done that, you should be able to convert any common fraction into a percentage in your head. The most commonly used fractions are halves, quarters, fifths and eighths, so it’s worth learning the decimal and percentage equivalents off-by-heart, ie

  • ½ = 0.5 = 50%
  • ¼ = 0.25 = 25%
  • ¾ = 0.75 = 75%
  • ⅕ = 0.2 = 20%
  • ⅖ = 0.4 = 40%
  • ⅗ = 0.6 = 60%
  • ⅘ = 0.8 = 80%
  • ⅛ = 0.125 = 12.5%
  • ⅜ = 0.375 = 37.5%
  • ⅝ = 0.625 = 62.5%
  • ⅞ = 0.875 = 87.5%

To simplify the fractions, check first to see if the numerator goes into the denominator. If it does, you can simply divide both numbers by the numerator to get what’s called a ‘unit fraction’, in other words, a fraction with a one on top, eg 4/8 divided by four top and bottom is ½.

By definition, a unit fraction can’t be simplified, so then you just have to convert it into a percentage.

If the numerator doesn’t go exactly, divide it by the first prime number (two) and then try to divide the denominator by the result, eg 6 ÷ 2 = 3, so 6/9 divided by three top and bottom is 2/3.

If that doesn’t work, try dividing the numerator by the next prime number (three) and so on and so on…

This will guarantee that the fraction ends up in the lowest possible terms, at which point it should be in the list above, which means you can easily convert it into the correct percentage, eg what is the percentage mark if:

  1. a pupil scores 7 out of a possible 28?
    Answer: 7 goes into 28 four times, so the fraction is 1/4, which is 25%.
  2. a pupil scores 27 out of a possible 36?
    Answer: 27 doesn’t go into 36, but 27 ÷ 3 = 9, so 27/36 divided by 9 top and bottom makes 3/4, which is 75%.
  3. a pupil scores 24 out of a possible 48?
  4. a pupil scores 8 out of possible 32?
  5. a pupil scores 9 out of a possible 24?

Multiplying Three Numbers Involving Money

There is often a ‘real world’ money problem in the QTS numeracy test. That usually means multiplying three numbers together. The first thing to say is that it doesn’t matter in which order you do it, eg 1 x 2 x 3 is the same as 3 x 2 x 1.

The next thing to bear in mind is that you will usually have to convert from pence to pounds. You could do this at the end by simply dividing the answer by 100, but a better way is to divide one of the numbers by 100 (or two of the numbers by 10) at the beginning and then multiply the remaining three numbers together, eg a number of pupils in a class took part in a sponsored spell to raise money for charity. The pupils were expected to get a certain number of correct spellings, and the average amount of sponsorship is shown for each.

How many pounds would the class expect to raise for charity if the basic sum is:

  1. 20 x 30 x 5p?
    Answer: 2 x 3 x 5 = 6 x 5 = £30.
  2. 40 x 500 x 7p?
  3. 30 x 400 x 6p?
  4. 50 x 40 x 8p?
  5. 60 x 20 x 9p?

Division by Single-digit Numbers

This is what I call the ‘wedding planner problem’. There are three ways of doing this type of question:

  • Method A: Use the ‘bus stop’ method to divide the total number of guests by the number of seats per table – remembering to add one if there is a remainder.
  • Method B: Go straight to the end of your times tables by multiplying the number of seats by 12, then calculating the remainder and dividing by the number of seats per table, again remembering to add one if there is another remainder.
  • Method C: Use trial and error by estimating the number of tables needed using a nice, round number such as 5, 10 or 20 and working out the remainder as before.
  1. Dining tables seat 7 children. How many tables are needed to seat 100 children?
    Answer:
    Method A) 100 ÷ 7 = 14 r 2, so 14 + 1 = 15 tables are needed.

    Method B) 7 x 12 = 84, 100 – 84 = 16, 16 ÷ 7 = 2 remainder 2, 12 + 2 + 1 = 15 tables.
    Method C) 10 x 7 = 70, which is too small, 20 x 7 = 140, which is too big, 15 x 7 = 70 + 35 = 105, which is just right as there are only 5 seats to spare.
  2. Dining tables seat 6 children. How many tables are needed to seat 92 children?
  3. Dining tables seat 5 children. How many tables are need to seat 78 children?
  4. Dining tables seat 9 children. How many tables are needed to seat 120 children?
  5. Dining tables seat 6 children. How many tables are needed to seat 75 children?

Division by Two-digit Numbers

If the number of seats is outside your times tables, the best option is just to use trial and error, starting with 5, 10 or 20, eg

  1. It is possible to seat 40 people in a row across the hall. How many rows are needed to seat 432 people?
    Answer: 40 x 10 = 400, 432 – 400 = 32, so one more row is needed, making a total of 10 + 1 = 11 rows.
  2. It is possible to seat 32 people in a row across the hall. How many rows are needed to seat 340 people?
  3. It is possible to seat 64 people in a row across the hall. How many rows are needed to 663 people?
  4. It is possible to seat 28 people in a row across the hall. How many rows are needed to seat 438 people?
  5. It is possible to seat 42 people in a row across the hall. How many rows are needed to seat 379 people?

Percentages to Fractions

This is a type of question that looks hard at first but becomes dead easy with the right shortcut. All you need to do is to work out 10% first and then multiply by the number of tens in the percentage.

Another way of saying that is just to knock one zero off each number and multiply them together, eg a test has a certain number of questions, each worth one mark. For the stated pass mark, how many questions had to be answered correctly to pass the test?

  1. ?/30 = 40%
    Answer: 3 x 4 = 12 questions (ie 10% of 30 is 3 questions, but we need 40%, which is 4 x 10%, so we need four lots of three, which is the same as 3 x 4).
  2. ?/40 = 70%
  3. ?/50 = 90%
  4. ?/80 = 70%
  5. ?/300 = 60%

Ratio – Distance

There are two ways of converting between different units of distance from the metric and imperial systems:

  • Method A: Make the ratio into a fraction and multiply the distance you need to find out by that same fraction, ie multiply it by the numerator and divide it by the denominator. (Start with multiplication if doing the division first wouldn’t give you a whole number.)
  • Method B: Draw the numbers in a little 2 x 2 table, with the figures in the ratio in the top row and the distance you need to find out in the column with the appropriate units, then find out what you need to multiply by to get from the top row to the bottom row and multiply the distance you have to find out by that number to fill in the final box.
  1. 8km is about 5 miles. How many kilometres is 40 miles?
    Answer:
    Method A) 8:5 becomes 8/5, and 40 x 8/5 = 40 ÷ 5 x 8 = 8 x 8 = 64km.
    Method B)
    Miles                 km
    5                          8
    x 8
    40               8 x 8 = 64km
  2. 6km is about 4 miles. How many kilometres is 36 miles?
  3. 4km is about 3 miles. How many kilometres is 27 miles?
  4. 9km is about 7 miles. How many miles is 63 kilometres?
  5. 7km is about 4 miles. How many kilometres is 32 miles?

Ratio – Money

You can use the same methods when converting money, except that the exchange rate is now a decimal rather than a fraction. Just remember that the pound is stronger than any other major currency, so there will always be fewer of them. It’s easy to get things the wrong way round, so it’s worth spending a couple of seconds checking, eg

  1. £1 = €1.70. How much is £100 in euros?
    Method A) 100 x 1.70 = €170.
    Method B)
    £                                      €
    1.00                              1.70
    x 100
    100                    1.70 x 100 = €170
  2. £1 = €1.60. How much is £200 in euros?
  3. £1 = €1.50. How much is €150 in pounds?
  4. £1 = €1.80. How much is €90 in pounds?
  5. £2 = €3.20. How much is £400 in euros?

Time – Find the End time

The most useful trick to use here is rounding. If the length of a lesson is 45 minutes or more, then just round up to the full hour and take the extra minutes off at the end. This avoids having to add or subtract ‘through the hour’, which is more difficult.

If the lessons are less than 45 minutes long, just work out the total number of minutes, then convert into hours and minutes and add to the start time, eg

  1. A class starts at 9:35. The class lasts 45 minutes. What time does the class finish?
    Answer: 9:35 + 1 hour – 15 minutes = 10:35 – 15 minutes = 10:20.
  2. A class starts at 11:45. There are three consecutive classes each lasting 25 minutes and then half an hour for lunch. What time does lunch finish?
    Answer: 11:45 + 3 x 25 + 30 = 11:45 + 75 + 30 = 11:45 + 1 hour and 15 minutes + 30 minutes = 13:30.
  3. Lessons start at 11:15. There are two classes each lasting 40 minutes and then lunch. What time does lunch start?
  4. Lessons start at 2:00 in the afternoon. There are four 50-minute classes with a 15-minute break in the middle. What time does the day finish?
  5. Lessons start at 9:40. There are two classes of 50 minutes each with a break of 15 minutes in between. What time do the classes finish?

Time – Find the Start Time

It’s even more important to use rounding when working backwards from the end of an event, as subtraction is that bit more difficult, eg

  1. A school day finishes at 3:15. There are two classes of 50 minutes each after lunch with a break of 15 minutes in the middle. What time does lunch end?
    Answer: 3:15 – 2 hours + 2 x 10 minutes – 15 minutes = 1:15 + 20 minutes -15 minutes = 1:20.
  2. A school day finishes at 4:30. There are two classes of 40 minutes each after lunch. What time does lunch finish?
    Answer: 4:30 – 2 x 40 = 4:30 – 80 minutes = 4:30 – 1 hour and 20 minutes = 3:10.
  3. Lunch starts at 1:05. There are two classes before lunch of 55 minutes each. What time do the classes start?
  4. Lunch starts at 1:15. There are three classes before lunch of 45 minutes each. What time do the classes start?
  5. A school bus arrives at school at 8:45. It picks up 20 children, and it takes an average of four minutes to pick up each child. What time is the first child picked up?

Percentage to Decimal

A decimal is a fraction of one unit, but a percentage is a fraction of 100 units, so, to convert from a percentage to a decimal, you just need to divide by 100, eg

  1. What is 20% as a decimal?
    Answer: 20 ÷ 100 = 0.2.
  2. What is 30% as a decimal?
  3. What is 17% as a decimal?
  4. What is 6% as a decimal?
  5. What is 48% as a decimal?

Multiplying Decimals

Decimal points can be confusing, so the best way to do these sums is to take out the decimal point and put it back at the end. You just need to remember to make sure there are the same number of decimal places in the answer as in both numbers in the question, eg

  1. 1.5 x 1.5
    Answer: 15 x 15 = 10 x 15 + 5 x 15 = 150 + 75 = 225, but there are two decimal places in the numbers you’re multiplying together, so the answer must be 2.25.
  2. 3 x 4.5
  3. 4.7 x 8
  4. 7.5 x 7.5
  5. 2.5 x 6.5

Multiplying Decimals by a Power of 10

Because we have 10 fingers, we’ve ended up with a ‘decimal’ number system based on the number 10.

That makes it really easy to multiply by powers of 10, because all you have to do is to move the decimal point to the right by a suitable number of places, eg one place when multiplying by 10, two when multiplying by 100 etc. (You can also think of it as moving the digits in the opposite direction.)

This type of question is therefore one of the easiest, eg

  1. 4.5 x 10
    Answer: 45.
  2. 3.8 x 100
  3. 7.6 x 1000
  4. 4.6 x 100
  5. 3.5 x 10

Percentage of Quantity

Finding a percentage is easy if it ends with a zero, as you can start by finding 10% (Method A). If you happen to know what the fraction is, you can also divide by the numerator of that fraction (Method B), so 20% is 1/5, so you just need to divide by five, eg

  1. Find 20% of 360
    Answer:
    Method A) 360/10 x 2 = 36 x 2 = 72.
    Method B) 360 ÷ 5 = 72 (or 360 x 2 ÷ 10 = 720 ÷ 10 = 72).
  2. Find 20% of 45
  3. Find 30% of 320
  4. Find 60% of 60
  5. Find 80% of 120

Multiplication

Just because this is the ‘mental Maths’ section of the test doesn’t mean that you can’t work things out on paper, and these simple multiplication sums can be done like that.

Alternatively, you can use ‘chunking’, which means multiplying the tens and units separately and adding the results together, and the shortcut for multiplying by five is to multiply by 10 and then divide by two, eg

  1. 23 x 7
    Answer: 20 x 7 + 3 x 7 = 140 + 21 = 161.
  2. 42 x 5
    Answer: 42 x 10 ÷ 2 = 420 ÷ 2 = 210
  3. 34 x 6
  4. 56 x 8
  5. 34 x 8

Short Division

Again, working these sums out on paper is probably quicker (and more reliable), although the easiest way to divide by four is probably to halve the number twice, and the shortcut for dividing by five is to multiply by two and then divide by 10.

  1. 292 ÷ 4
    Answer: 292 ÷ 2 ÷ 2 = 146 ÷ 2 = 73.
  2. 345 ÷ 5
    Answer: 345 x 2 ÷ 10 = 690 ÷ 10 = 69.
  3. 282 ÷ 3
  4. 565 ÷ 5
  5. 432 ÷ 4 

     

     

     

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Ratios

Hundreds of years ago, it was traditional to put dragons on maps in places that were unknown, dangerous or poorly mapped. Ratios are one of those places…!

A ratio is just a model of the real world, shown in the lowest terms, but answering ratio questions can be just as scary as meeting dragons if you don’t know what you’re doing. The key to understanding ratios is to work out the scale factor.

This is just like the scale on a map. If a map is drawn to a scale of 1:100,000, for instance, you know that 1cm on the map is the same as 100,000cm (or 1km) in the real world. To convert distances on the map into distances in the real world, you just need to multiply by the scale factor, which is 100,000 in this case.

(You can also go the other way – from the real world to the map – by dividing by the scale factor instead.)

To work out the scale factor in a Maths question, you need to know the matching quantities in the real world and in the model (or ratio). Once you know those two numbers, you can simply divide the one in the real world by the one in the ratio to get the scale factor. For example:

If Tom and Katie have 32 marbles between them in the ratio 3:1, how many marbles does Tom have?

To answer this question, here are the steps to take:

  1. Work out the scale factor. The total number of marbles in the real world is 32, and the total in the ratio can be found by adding the amounts for both Tom and Katie, which means 3 + 1 = 4. Dividing the real world total by the ratio total gives 32 ÷ 4 = 8, so the scale factor is 8.
  2. Multiply the number you want in the ratio by the scale factor. If Tom’s share of the marbles in the ratio is 3, then he has 3 x 8 = 24 marbles.

The matching numbers in the real world and the ratio are sometimes the totals and sometimes the individual shares, but it doesn’t matter what they are. All you need to do is find the same quantity in both places and divide the real world version by the ratio version to get the scale factor.

Once you’ve done that, you can multiply any of the ratio numbers to get to the real world number (or divide any real world number to get to the ratio number). Different questions might put the problem in different ways, but the principle is the same.

One complication might be having two ratios that overlap. In that case you need to turn them into just one ratio that includes all three quantities and answer the question as you normally would. For example:

If there are 30 black sheep, and the ratio of black to brown sheep is 3:2, and the ratio of brown to white sheep is 5:4, how many white sheep are there?

This is a bit more complicated, but the basic steps are the same once you’ve found out the ratio for all three kinds of sheep. To do this, we need to link the two ratios together somehow, but all the numbers are different, so how do we do it?

The answer is the same as for adding fractions with different denominators (or for solving the harder types of simultaneous equations, for that matter): we just need to multiply them together. If we were adding fifths and halves, we would multiply the denominators together to convert them both into tenths.

Here, the type of sheep that is in both ratios is the brown one, so we simply have to make sure the numbers of brown sheep in each ratio (2 and 5) are the same by multiplying them together (to give 10). Once we’ve done that, we can combine the two ratios into one and answer the question. Here goes:

  • Ratio of black sheep to brown sheep = 3:2

Multiply by 5

  • Ratio of black sheep to brown sheep = 15:10
  • Ratio of brown to white sheep = 5:4

Multiply by 2

  • Ratio of brown to white sheep = 10:8
  • Therefore, ratio of black sheep to brown sheep to white sheep = 15:10:8

Now that we have just one ratio, we can answer the question by following exactly the same steps as before:

  1. Work out the scale factor. The total number of black sheep in the real world is 30, and the total in the ratio is 15. Dividing the real world total by the ratio total gives 30 ÷ 15 = 2, so the scale factor is 2.
  2. Multiply the number you want in the ratio by the scale factor. If the number of white sheep in the ratio is 8, then there are 8 x 2 = 16 white sheep.

Simple!

Sample Questions

  1. One hundred paintings have to be selected for an art exhibition. If the ratio of amateur paintings to professional paintings has to be 2:3, how many amateur paintings and professional paintings have to be selected?
  2. The ratio of brown rats to black rats is 3:2. If there are 16 black rats, how many brown rats are there?
  3. Peter has 20 blue pens. How many red pens must he buy if the ratio of blue to red pens has to be 2:3?
  4. There are 35 children in a class and 15 are boys. What is the ratio of boys to girls?
  5. There are 15 girls and 12 boys in a class. What is the ratio of girls to boys? Give your answer in its simplest form.
  6. A newspaper includes 12 pages of sport and 8 pages of TV. What is the ratio of sport to TV? Give your answer in its simplest form.
  7. Anna has 75p, and Fiona has £1.20. What is the ratio of Anna’s money to Fiona’s money in its simplest form?
  8. Sam does a scale drawing of his kitchen. He uses a scale of 1:100. He measures the length of the kitchen as 5.9m. How long is the kitchen on the scale drawing? Give your answer in mm.
  9. A recipe to make lasagne for 6 people uses 300 grams of minced beef. How much minced beef would be needed to serve 8 people?
  10. A recipe for flapjacks requires 240g of oats. This makes 18 flapjacks. What quantity of oats is needed to make 24 flapjacks?
  11. Amit is 12 years old. His brother, Arun, is 9. Their grandfather gives them £140, which is to be divided between them in the ratio of their ages. How much does each of them get?
  12. The angles in a triangle are in the ratio 1:2:9. Find the size of the largest angle.
  13. In a certain town, the ratio of left-handed people to right-handed people is 2:9. How many right-handed people would you expect to find in a group of 132 people?
  14. Twelve pencils cost 72p. Find the cost of 30 pencils.
  15. Jenny buys 15 felt-tip pens. It costs her £2.85. How much would 20 pens have cost?
  16. If three apples cost 45p, how much would five apples cost?
  17. Sam is 16 years old. His sister is 24 years old. What’s the ratio of Sam’s age to his sister’s age? Give your answer in its simplest form.
  18. A map scale is 1:20000. A distance on the map is measured to be 5.6cm. What’s the actual distance in real life? Give your answer in metres.
  19. A recipe for vegetable curry needs 300 grams of rice, and it feeds 4 people. How much rice would be needed for 7 people?
  20. £60 is to be divided between Brian and Kate in the ratio 2:3. How much does Kate get? 

     

     

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Athens

Teaching Greek children is like watching France play rugby: you never know what you’re going to get…

I just spent two weeks in Greece preparing a Greek boy and his twin sisters for 10+ and 12+ entrance examinations at a school in England. Highlights included spending a long, sunny weekend at a holiday home in Lagonissi, spending another long, sunny weekend skiing near Delphi – I wonder if the oracle saw that one coming! – and seeing the Parthenon every day from my hotel balcony.

Political refugees take many forms, but, personally, I prefer shipping magnates fleeing with their adorable (if strong-willed) families from Communist governments in the Mediterranean…

What a Turkey!

When it comes to incest, folk dancing and teaching kids who burst into tears every few minutes, my advice is: “Just say no.”

I was due to spend nine weeks in Turkey early in 2015, teaching a 12-year-old boy Maths and English, but all I ended up with was a two-week holiday in the Ankara Sheraton and a client who refused to pay! I only managed to do four lessons before it became clear that things weren’t going to work out, so all I could do was take pictures of the food in the restaurant and the view out of my hotel window.

Given the circumstances, all I can do now is publish a few of the pictures I took. And learn an important lesson: if everything about a job from the very beginning seems wrong, it’s probably better just to say no…

 

 

Red Xmas Tree Star with Bokeh Lights

Christmas is a time for baubles, lights, golf clubs and a Nikon D800…

The Idea

I live in an Art Deco mansion block in Putney, and every year the porters put up a tree in the entrance hall. Last year, I took some pictures of some of the baubles, inspired by an email from one of the photographic magazines about how to capture bokeh lighting. This year, the tree and the baubles were different, so I decided to have another go.

The Location

Ormonde Court, Upper Richmond Road, London SW15 6TW, United Kingdom, around 2100 on 12 December 2014.

The Equipment

  • Nikon D800 DSLR camera
  • Nikon AF-S VR Micro-NIKKOR 105mm f/2.8G IF-ED lens
  • Nikon SB-910 Speedlight flash
  • Manfrotto 190XProB tripod with 496RC2 universal joint head
  • Hähnel HRN 280 remote release.

I’ve just managed to remortgage my flat in Notting Hill, so I’ve been investing in a few photographic supplies. Ever since a German called Stefan took a magnificent shot of Old Faithful at night using flash, I’ve wanted a proper flashgun. Well, now I have one. I bought the Nikon SB-910 Speedlight a couple of weeks ago, and it arrived just in time for this shoot. I didn’t know whether I’d need it or not, but I was prepared to experiment.

The Settings

  • Manual ISO 100
  • f/5.6
  • 1 second
  • 105mm
  • Tungsten white balance
  • Single-point auto-focus

The Technique

In the last of these posts, I mentioned how I’d got used to taking a tripod with me in almost all circumstances, and last night was no exception. Last year, I was generally pleased with my shots of the baubles, but the ISO was far too high.

I was using my tripod, funnily enough, but to hold the bauble rather than my camera! This year, I decided I would definitely mount the camera on the tripod, but that left me with nothing to hold the baubles.

I thought about using a light stand from my flash kit, but I needed something horizontal rather than vertical so that I could hang the decorations from it. I then had the idea of using my golf clubs. I could stand the bag in the lobby and balance one of the clubs on top, held in place by the other clubs.

As it turned out, I’d forgotten that the bag would be at an angle of 45 degrees, so my original plan didn’t work, but I simply pulled my 4-iron half-way out and hung the first bauble from that. It was a silver reindeer, but the green wire loop wasn’t very long, and I wouldn’t have been able to get the shots I wanted without the golf club getting in the frame.

I needed a piece of string. I thought about going back to my flat, but leaving my golf clubs and my camera unattended in the entrance hall didn’t seem like a sensible idea! Fortunately, I was wearing trainers, so I just used one of the laces.

It took a few gos to get each bauble to point in the right direction and remain still – particularly as there was a stream of curious residents opening the front door on their way home from work! – but I managed in the end. Phew!

I took lots of pictures of the silver reindeer, a red bauble with a spiral pattern on it and the red star shown above, and I played around with the flash settings to try to make the background a bit darker.

Sadly my new flash was so powerful that I couldn’t manage that – even with -3.0EV of exposure compensation! There might’ve been a better way, but it was the first time I’ve ever used a flashgun, so I’m still a newbie.

The main problem I had in taking the shots was actually getting enough depth-of-field. The reindeer was fine, but the round baubles and even the star were proving a nightmare. If I focused on the front of the bauble, the metal cap and wire loop were out of focus, but, if I focused on those, the rest of the bauble was out of focus.

I’m an absolute stickler for sharpness in my images, so I wasn’t sure what to do. In the end, I stopped down a little bit and hoped that f/5.6 would be a small enough aperture to keep everything acceptably sharp.

I tried ‘chimping’ (or checking the shots on the LCD screen) a few times, but it was tricky to tell. My problem was a kind of Catch-22: the three variables controlling depth-of-field are normally the focal length, the aperture and the relative distances of the camera to the subject and the subject to the background.

I couldn’t change to a wide-angle lens, as I needed to limit the background to just the Christmas tree; I couldn’t change to a much smaller aperture without making the bokeh circles of the blurred Christmas lights in the background too small; and I couldn’t change the relative positions of the camera, bauble and tree without changing the composition completely.

Hmm…

As you can see from the shot above, the two arms on the right of the red star didn’t turn out completely sharp, but it was ‘good enough for Government work’. Shutterstock obviously didn’t accept it – they’re very hot on sharpness! – but I did win an award on Pixoto for the sixth best image uploaded to the Christmas category yesterday!

Post-processing

I made three changes to this shot:

  1. I had the camera on ‘Tungsten’ white balance, as I’d just read somewhere that I should use the amber filter on the flashgun when shooting indoors in order to avoid a clash of different light sources. However, it turned out that the shot looked a lot warmer with the ‘Flash’ white balance, and that was just the look I was after at Christmastime.
  2. A lot of my images end up being quite dark, and I’m not sure whether it’s just because I’m lucky to spend a lot of time in very sunny places or whether there’s a problem with my camera! In this case, I actually had to push the exposure up by +2EV in Aperture to make it look like all the others. I have a feeling that’s because I changed from f/2.8 to f/5.6 to get more depth-of-field but forgot to lengthen the shutter speed to compensate. Silly me…
  3. I was desperately trying to frame the shot perfectly so I wouldn’t have to crop, but the balance of the bauble with the ‘negative space’ on the right wasn’t quite right, so I cropped in slightly to position the star a third of the way into the frame.

Close-up of Golden Eagle Head with Catchlight

I’m a photographer (among other things), and this is the first of a series of posts about my favourite photographs. I’ll tell you how I took them and break down the shot into the idea, the location, the equipment, the settings, the technique and any post-processing.

The Idea

When I took this shot, I was at a Battle of Hastings re-enactment at Battle Abbey in Sussex. I was there to take pictures of the battle scenes between enthusiasts dressed up as Normans and Saxons, and I had no idea there was going to be a falconry display until I bought my ticket and was given a flyer with the plan for the day.

The golden eagle is my favourite bird (isn’t it everyone’s?!), so I was very excited to be able to see one in action. The falconers from Raphael Historical Falconry put on a couple of displays with a variety of birds, including a gyrfalcon and a Harris hawk, but the golden eagle was the highlight.

Afterwards, I wandered over to their tent, and I was able to get within just a few feet of all the birds. The falconer was happy to chat with the spectators with a bird on his arm (so to speak!), and later he fed and watered the birds outside. That gave me the chance to set up my tripod and get a few good close-ups, and this was the best of the lot.

The Location

Battle Abbey, High Street, Hastings and Battle, East Sussex TN33 0AD, United Kingdom, around 1500 on 11 October 2014.

The Equipment

  • Nikon D800 DSLR camera
  • Sigma 50-500mm F4.5-6.3 APO DG OS HSM lens
  • Manfrotto 190XProB tripod with 496RC2 universal joint head
  • Hähnel HRN 280 remote release.

I was a bit worried about using my ‘Bigma’ to take this picture, as I hadn’t been very impressed with it on my trip to Spitsbergen to see the polar bears. Admittedly, the bears were usually a few hundred yards away, and no zoom lens is at its best when it’s at its longest focal length, but I was disappointed that my shots were so soft.

As a result, I did a manual focus check and discovered that the calculated auto-focus fine tune setting was a whopping -12! Armed with this new improvement to the sharpest tool in my box, I was ready for anything…

PS They call it the ‘Bigma’ as it’s made by Sigma, and it’s enormous!

The Settings

  • Auto ISO 110
  • f/9
  • 1/250
  • 500mm
  • Daylight white balance
  • Single-point auto-focus

I had the camera on Manual with ISO on Auto, which I thought was appropriate for a day when lots of things would be happening, and I’d be taking candid shots without much opportunity to sit down and check my settings. However, I should probably have set the ISO to its optimum value of 100 for this shot, as I had plenty of time.

The Technique

I’m generally a travel and wildlife photographer, but I normally don’t use a tripod as it gets in the way and doesn’t work too well in a Land-Rover moving at 40mph! However, I learnt a new perspective from a professional photographer called Mark Carwardine.

He happened to be on a cruise to Spitsbergen that I went on a few months ago, and he was always carrying around his tripod with the legs fully extended – even on the Zodiac inflatables that we used to land on the islands.

I thought to myself, If he can do it, so can I! After that, I’ve tried to use a tripod wherever possible. I love really sharp wildlife shots, and a 36.3-megapixel DSLR and a tripod make a winning combination.

Another important thing about wildlife shots is to get down to the level of the animal or bird you’re shooting. You can see from this shot that I’m right at eye-level with the eagle, and that gives the sense of power and intimacy I was looking for.

Finally, I’ve learnt from a couple of portrait shoots the value of the ‘catchlight’. This is the reflection of the light source that you see in the eye of your subject. It’s just as important with wildlife as with people, and I was lucky enough to get a break in the clouds that allowed the sun to provide the perfect catchlight. Lucky me!

Post-processing

I changed from a PC to a Mac a few years ago, so I do all my post-processing in Aperture. I suppose I should upgrade to Lightroom or Adobe Camera Raw or Photoshop, but iPhoto was the default image-processing software on the Mac, and Aperture was the cheapest upgrade!

I only had two changes to make to this shot:

  1. Even at 500mm, I still wasn’t quite close enough for the bird’s head to fill the frame, so I had to crop in later. I’ve found from experience that 6.3 megapixels is the minimum size that the major online photo libraries accept, so I never go below 6.4 MP (to avoid rounding errors), and that’s the new size of this file.
  2. In the end, the automatic ISO setting was close enough to the optimum of 100, but the shot was slightly overexposed due to the dark colours of the eagle’s feathers and the grassy background, so I had to reduce the exposure by 0.5EV.
Fractions, decimals and percentages

Working with Fractions

People don’t like fractions. I don’t know why. They’re difficult to begin with, I know, but a few simple rules will help you add, subtract, multiply and divide.

Adding and Subtracting Fractions

Adding and subtracting are usually the easiest sums, but not when it comes to fractions. If fractions have the same denominator (the number on the bottom), then you can simply add or subtract the second numerator from the first, eg 4/5 – 3/5 = 1/5. If not, it would be like adding apples and oranges.

They’re just not the same, so you first have to convert them into ‘pieces of fruit’ – or a common unit. The easiest way of doing that is by multiplying the denominators together. That guarantees that the new denominator is a multiple of both the others.

Once you’ve found the right denominator, you can multiply each numerator by the denominator from the other fraction (because whatever you do to the bottom of the fraction you have to do to the top), add or subtract them and then simplify and/or convert into a mixed number if necessary, eg 2/3 + 4/5 = (2 x 5 + 4 x 3) / (3 x 5) = (10 + 12) / 15 = 22/15 = 1 7/15.

  1. Multiply the denominators together and write the answer down as the new denominator
  2. Multiply the numerator of the first fraction by the denominator of the second and write the answer above the new denominator
  3. Multiply the numerator of the second fraction by the denominator of the first and write the answer above the new denominator (after a plus or minus sign)
  4. Add or subtract the numerators and write the answer over the new denominator
  5. Simplify and/or turn into a mixed number if necessary

Note that you can often use a simpler method. If one of the denominators is a factor of the other, you can simply multiply the numerator and denominator of that fraction by 2, say, so that you get matching denominators, eg 1/5 + 7/10 = 2/10 + 7/10 = 9/10. This means fewer steps in the calculation and lower numbers, and that probably means less chance of getting it wrong.

Sample Questions

  1. 1/5 + 2/3
  2. 3/8 + 11/12
  3. 13/24 – 5/12
  4. 7/8 – 3/4
  5. 5/8 – 2/3

Multiplication

This is the easiest thing to do with fractions. You simply have to multiply the numerators together, multiply the denominators together and then put one over the other, simplifying and/or converting into a mixed number if necessary, eg 2/3 x 4/5 = (2 x 4) / (3 x 5) = 8/15.

  1. Multiply the numerators together
  2. Multiply the denominators together
  3. Put the result of Step 1 over the result of Step 2 in a fraction
  4. Simplify and/or turn into a mixed number if necessary

Sample questions

  1. 1/5 x 2/3
  2. 7/12 x 3/8
  3. 4/5 x 2/3
  4. 4/9 x 3/4
  5. 5/8 x 2/3

Division

Dividing by a fraction must have seemed like a nightmare to early mathematicians, because nobody ever does it! That’s right. Nobody divides by a fraction, because it’s so much easier to multiply.

That’s because dividing by a fraction is the same as multiplying by the same fraction once it’s turned upside down, eg 2/3 ÷ 4/5 = 2/3 x 5/4 = (2 x 5) / (3 x 4) = 10/12 = 5/6. You can even cut out the middle step and simply multiply each numerator by the denominator from the other fraction, eg 2/3 ÷ 4/5 = (2 x 5) / (3 x 4) = 10/12 = 5/6.

  1. Multiply the numerator of the first fraction by the denominator of the second
  2. Multiply the numerator of the second fraction by the denominator of the first
  3. Put the result of Step 1 over the result of Step 2 in a fraction
  4. Simplify and/or turn into a mixed number if necessary

Note: In some cases, it’s possible to divide one numerator by the other and one denominator by the other, but the answers must both be whole numbers for it to work, eg 8/9 ÷ 2/3 = (8 ÷ 2) / (9 ÷ 3) = 4/3 or 1 1/3, but 7/9 ÷ 4/5 doesn’t work because 4 doesn’t go into 7 evenly and 5 doesn’t go into 9 evenly.

The advantage of the second method is that you don’t have to spend so much time simplifying the resulting fraction as the numbers are divided rather than multiplied, which makes them smaller. If we cross-multiplied using the standard method, we’d end up with 24/18 rather than 4/3. However, the benefit of the standard method is that it always works!

Sample Questions

  1. 1/5 ÷ 2/3
  2. 2/7 ÷ 3/5
  3. 4/7 ÷ 2/3
  4. 7/8 ÷ 3/4
  5. 5/6 ÷ 2/3

Simplifying Fractions

One way of simplifying fractions is to divide by the lowest possible prime number over and over again, but that takes forever! It’s much simpler to divide by the Highest Common Factor (or HCF), which is either the numerator itself or half of it or a third of it etc:

  1. If possible, divide both the numerator and the denominator by the numerator. If that works, you’ll end up with a ‘unit fraction’ (in other words, 1 over something) that can’t be simplified any more, eg 7/14 = 1/2 because 7 ÷ 7 = 1 and 14 ÷ 7 = 2.
  2. If the numerator doesn’t go into the denominator, try the smallest fraction of the numerator (usually a half or a third) and then try to divide the denominator by the result, eg 24/36 = 2/3 because half of 24 is 12, and 36 ÷ 12 = 3.
  3. If that doesn’t work, keep repeating Step 2 until you find the answer, eg 24/30 = 4/5 because a quarter of 24 is 6, and 30 ÷ 6 = 5 (and a half and a third of 24 don’t go into 30).

Sample Questions

  1. Simplify 14/28
  2. Simplify 8/24
  3. Simplify 30/50
  4. Simplify 27/36
  5. Simplify 45/72

Turning Improper Fractions into Mixed Numbers

To turn an improper fraction into a mixed number, simply divide the numerator by the denominator to find the whole number and then put the remainder over the original denominator and simplify if necessary, eg 9/6 = 1 3/6 = 1 1/2.

  1. Divide the numerator by the denominator
  2. Write down the answer to Step 1 as a whole number
  3. Put any remainder into a new fraction as the numerator, using the original denominator
  4. Simplify the fraction if necessary

Sample Questions

  1. What is 22/7 as a mixed number?
  2. What is 16/5 as a mixed number?
  3. What is 8/3 as a mixed number?
  4. What is 18/8 as a mixed number?
  5. What is 13/6 as a mixed number?

Turning Mixed Numbers into Improper Fractions

To turn a mixed number into an improper fraction, multiply the whole number by the denominator of the fraction and add the existing numerator to get the new numerator while keeping the same denominator, eg 2 2/5 = (10 + 2)/5 = 12/5.

  1. Multiply the whole number by the denominator of the fraction
  2. Add the answer to the existing numerator to get the new numerator
  3. Write the answer over the original numerator
  4. Simplify if necessary

Sample Questions

  1. What is 2 2/7 as an improper fraction?
  2. What is 3 2/3 as an improper fraction?
  3. What is 4 1/4 as an improper fraction?
  4. What is 5 1/5 as an improper fraction?
  5. What is 3 2/9 as an improper fraction?

There you go. Easy peasy lemon squeezy!

 

 

 

 

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Cold Turkey

Pool, beach or hammock? Hammock, beach or pool? Hmm…

That was the decision that faced me every day during my teaching assignment in Turkey. I was staying at Club Isil in Torba, near Bodrum, for six weeks to teach three Kazakh brothers and their cousin.

They were seven, seven, 11 and 14 years old, and I was there to teach each of them English or Maths for an hour a day. I only worked a maximum of five days a week, and the cousin was only there for a month, so I had plenty of time to do my own thing.

Sometimes that can be a bit difficult on a residential assignment, as you don’t know anyone apart from your clients, and there’s no guarantee of where you’ll be staying or what facilities or transport will be available.

Fortunately, my Kazakh clients put me up at a five-star all-inclusive beach resort called the Isil Club, so I had the choice of pool, beach or hammock every afternoon, plus the use of wi-fi throughout the grounds and the opportunity to participate in a host of sporting activities, including tennis, volleyball and Flyboarding.

Stairway to heaven

Stairway to heaven

Every weekday morning, I would have breakfast from the buffet on the terrace and walk to the front of the hotel, where I’d get picked up at 0845 by a chap in a golf cart and dropped off at my clients’ pair of luxury houses in the grounds of the next door Vogue Hotel.

The first time I walked down the steps to the villas, I thought I’d walked on to the set of Beverly Hills 90210. Each villa had an infinity pool on the terrace, with a view looking out over a sweeping sunlit Mediterranean bay dotted with the odd luxury schooner or motor yacht.

Inside, the houses were both chock full of marble and gold leaf, and there was a constant stream of staff to keep the place looking immaculate and look after our every need. I’d teach for three or four hours and then hitch a lift back to my hotel with one of the staff or even one of the boys. It’s not often I get driven home by an 11-year-old pupil, but that’s what happens when he’s given a Renault Twizy for his birthday…!

I got along pretty well with the boys, although they were rather reluctant students, and their mothers generally left me to my own devices. I’m told that’s fairly typical of clients from the old Soviet Union, but it’s just a bit disconcerting when nobody comes to pick you up and you think you’ve been sacked until you get a belated text to say it’s just someone’s birthday!

I quickly settled into a routine of teaching in the morning and then reading the paper online, sunbathing and watching sport and movies on my laptop for the rest of the day. My main problem was trying to do too many things at once.

It would’ve been nice to be able to sunbathe with my laptop out on the terrace or alongside the various incarnations of Bambi and Thumper on the dock, but it was too hot and bright. It was two weeks before I saw my first cloud, so I didn’t even have the excuse of bad weather to stay indoors. Everywhere I go these days, it always seems to be 35° – either in Centigrade or Fahrenheit!

The Isil Club wasn’t quite so luxurious as the Vogue – where I was greeted by a couple of beautiful girls and offered a free cocktail when I arrived from the airport – but it still offered everything I could possibly want.

I had to switch rooms initially, but that was only because of a glitch in the wi-fi signal, and I ended up in the ideal spot. My front door opened on to the main bar and reception area, but I also had French windows giving access to a grassy lawn at the back (where I found the hammock!), and the restaurant and water sports centre were within easy walking distance.

Breakfast, lunch and dinner were all available from a buffet out on the terrace, and there was a wide selection of salads, hot dishes, deserts and anything else you might fancy. The hotel was run on an all-inclusive basis, so I never had to pay for anything, and it was very tempting to eat far too much. After a couple of weeks, though, I decided to eat what I actually liked rather than everything in sight!

All you can eat...

All you can eat…

The facilities were fabulously comprehensive, including a huge swimming pool, volleyball and tennis courts, artificial five-a-side pitches, table tennis and pool tables, a sauna and spa and a water sports centre down by the dock equipped with catamarans, Jet Skis, banana boats and Flyboards.

(There was even a zoo next door, although it was even smaller than the one in Hong Kong!)

I hardly ever go on beach holidays, so it should’ve come as no surprise when I swam two lengths of the pool with my iPhone in my pocket! That put me off swimming for the rest of the trip, and I didn’t even do many of the other activities – even though I used to love sailing when I was a boy.

However, I’d always wanted to try Flyboarding, and I booked a lesson in the final week. I was strapped into boots attached to what looks a bit like a snowboard, except with two nozzles for the water jet on the underside.

There was also a red hose or pipe hooked up to a Jet Ski, and that was what provided the power. It was pretty difficult to get the hang of it, but I did manage to hover around ten feet off the water a couple of times for a few seconds. I asked Yusuf to take some pictures, but the memory card in my camera stopped working, so I don’t have anything to show for it! Typical…

Fortunately, I did manage to take a few shots myself. I recently took up photography fairly seriously, so I’m always looking for great photo ops, and I was very excited about the idea of getting pictures of the instructors.

I ended up getting to know one of the instructors quite well, and he was an expert Flyboarder. The first time I saw him, he was soaring 20 feet into the air then diving into the water, only to shoot up into the air again and dive again.

It was spectacular!

The only problem was trying to work out when he was due to go out. I asked Yusuf to let me know by text, but he never did, so I ended up camping out on the terrace with my laptop, checking the dock every few minutes to see whether the Flyboard had moved from its usual spot. At least it got me out of the house – and the photos were worth waiting for…

Flyboarder diving in perfect high backlit arc

(This is not me)

Dive! Dive!

Dive! Dive!

I took lots of shots of Yusuf, a couple of the other instructors and a few holidaymakers trying it for the first time. If you want to sell pictures of people online (as I do), you have to get a model release from everybody in the shot, so I did a deal with everyone: you sign the model release, and I’ll give you all the photos for free.

Yusuf was particularly chuffed. “Many photographers ask to take my picture,” he told me once, “but it would not be the same as you.”

The other big chance I had to take pictures came when the American singer/songwriter Akon gave a concert at the Vogue Hotel. One of my pupils told me about it, and I went along to check it out. It turned out to be a very professional gig – just like something you’d expect to see in a big outdoor arena – and it was a great chance to take some good close-up shots.

The grounds were so big that there was plenty of room, even quite near to the stage, so I was lucky to be there. The good thing about going to a private concert at a five-star hotel is that you don’t find any of the usual drawbacks of live music. You don’t have to queue up to get in, you can get as close as you like, and you don’t even need a ticket!

Akon

Akon

When I wasn’t taking pictures or staring at a laptop screen, I tried to meet a few people in the resort, but it was always difficult. I asked a couple of girls to dance and complimented another couple on their dresses, but it never got me anywhere.

Eventually, I gave up and started taking my lunch and dinner plates back to my room rather than eating out on the terrace beside the buffet. However, I did go along to the regular scheduled volleyball and tennis tournaments, and that paid off during the last couple of weeks of my stay, when I met a group of Belgians who were very keen on volleyball.

They played every morning and evening and invited me to join them, so I went along and got to know them pretty well. There were Goodness knows how many Belgians and other Francophone tourists in the resort, so I’m glad I could speak French.

The social ostracism is the worst part of any residential assignment abroad, so it was good to be able to have a chat with a few people over the age of 14!

All in all, I had a very good trip. The clients were happy, I came back with a proper tan for the first time since I ‘retired’ at 29, and I tried out something I’ve always wanted to do. I also managed to take hundreds of pictures.

What could be better? The only disappointment hit me when I got back home to the UK and found that all the sunny beaches and beautiful girls in bikinis had disappeared. My turkey was cold after all…

 

 

Tweets from Turkey

Sunbathing

Sunbathing in Bodrum is like watching French films – you end up thinking breasts aren’t special at all. I need someone to set me straight…

I saw a dolphin playing in the sea and someone having sun cream rubbed in by two beautiful Thai girls. I’m not sure which impressed me more…

When a woman spends 5 mins putting on her bikini top, should you a) ignore her, b) offer your help or c) ask the topless woman next to you?!

The area around the swimming pool here is like a walrus haul-out in the Arctic, except the creatures are 700lbs lighter (in most cases)…

They may not be as glamorous as polar bears in the Arctic, but there’s still a place for French blondes in bikinis called Aurélie…

Food

I’m the least observant person in the world. It’s taken me a week to find the muesli! Now, where’s the champagne and caviare…

One day, I’ll get bored of dining on the terrace while watching the sun set over the Mediterranean, but it won’t be this week…

This hotel is so posh they put soy sauce in a sherry glass. Impractical, but classy.

I’m going to write a book called The All-You-Can-Eat Buffet Diet. It’ll have the same hundred recipes on every page…

For dinner tonight, I was tempted by the ‘turkey chest’ with ‘potetoes’ or ‘fish from the owen’, but I chose pizza instead. Easier to spell…

The French/Belgians

We almost had a Casablanca moment today. When a hundred Germans are singing German drinking songs around the pool, it can only end badly.

It’s a sad day when a pretty French girl in a bikini asks if she can lie next to you on the sun lounger but then calls you ‘vous’. Sigh…

I just heard a French woman say, “Un, deux, trois – cheese!” to her children. Photography, the universal language…

It’s hard to be one of the lads when you’re playing volleyball with Frenchmen. I call them ‘tu’, but I’m so old they have to call me ‘vous’!

“Due to the Belgium National Feast, the 21st. of July, we would like to invite you to a cocktail at the pool, today at 19:30pm. Isil Club”

TV

I’m in the middle of a Transformers marathon, and I’m feeling more and more admiration for director Michael Bay (and Megan Fox, obviously)…

Living abroad means watching every sporting event live, so I now have three windows open for the cricket, the golf and the motor racing…

Great to see Jon Favreau’s Chef. I haven’t seen such a fine feel-good foodie film since Tampopo and Babette’s Feast!

Internet

Why don’t web pages from The Daily Telegraph load properly in Turkey? Is the paper still being punished for its Gallipoli coverage…?

When your profile is being viewed by 63-year-old women, you know you’ve reached the bottom of the online dating pool…

Sport

Middle-aged guys should be banned from water parks. I think I’ve broken my ankle…!

I just lost an air rifle competition by 14 points to 10. If we’d been using AK-47s, it would’ve been a different story…

When I won the singles and doubles matches to win the tennis today, everyone just walked off. It’s the opposite of ‘all must have prizes’…!

That’s the first time I’ve ever had to score a tennis match in French. I suppose it’s better than volleyball in Russian.

Flyboarding is just like snowboarding, except you have 20 feet further to fall! Ouch…

Photography

I went to the zoo today – if you can call it that. The Vogue Hotel is having a competition with Hong Kong for the world’s smallest zoo…

I spent last night on the beach with three cats named Hobie, shooting the stars and watching shooting stars.

I’ve just realised from my photographs which way the stars rotate in the northern hemisphere. Any guesses…?

I just offered to send someone a few photos, and he told me he didn’t have an email address! I didn’t know what to say…

Here I am, watching Lois & Clark and the US PGA on my laptop, sitting on the terrace at midnight while my camera takes photos of the stars…

Thank God that’s over. No more sunshine, no more beaches, no more pretty girls in bikinis. I’m really, really happy to be home. Really…

Other

Turkey’s the only place I know where storms don’t involve either rain or even clouds…

I just saw Akon perform last night at the Vogue. I think in future I’ll only go to private concerts at five-star hotels…

Does anyone want an iPhone? I have one that swam two lengths of the pool with me this afternoon…

I was shaken awake by an earthquake this morning…

 

Hong Kong? Phooey!

When they built Hong Kong, they put the sun in the wrong place. It’s always either behind a building, hidden by a cloud or on the wrong side of the island to see a decent sunset.

Having said that, I did arrive during the monsoon season, which didn’t help! I was there for six weeks from April to June 2014, teaching four families various subjects including English, Maths, Science and tennis.

All the families were very hospitable, lending me iPhones, chauffeuring me around and inviting me regularly for lunch and dinner.

They also had a few diary issues, so I ended up teaching twice as many students as I was supposed to… The tuition agent who had arranged the job had given me a handy introductory guide to Hong Kong, but it took a while to get used to the place.

I felt like Alice in Wonderland in my bathroom, where everything was six inches lower than I was used to, and the bottle labelled ‘Drink me’ was replaced by a dispenser of ‘horse oil! The water also left me feeling queasy, but the worst part was finding my way around.

The apartment block was right next to the Grand Hyatt and Renaissance hotels, and there were two different entrances, north and south. The client who was putting me up in her flat had kindly sorted out a SIM card, wi-fi dongle and an Octopus card for the MTR, but I felt like Captain Oates whenever I left the building.

Would I ever find my way home again…?!

I had two objectives in Hong Kong. First of all, I was obviously there to keep my clients happy. After that, I saw it as a great opportunity to take photographs. I deliberately limited my lessons to around four or five hours a day in an effort to maximise my chances of picture-taking.

The only problem was the weather. I had one sunny day on my first day off, which I used to go up to the Peak, which has spectacular views of Victoria Harbour, but I didn’t see blue skies again until my last week.

As a result, my daily routine revolved around anything I could do within the confines of my apartment block. Fortunately, one of my clients had lent me the use of a very nice one-bed flat in Wan Chai, complete with golf driving range, two tennis courts and three outdoor and indoor swimming pools, but none of that was very appealing when my iPhone predicted thunderstorms every day of the week!

Instead, I generally stayed at home during the morning and early afternoon. I read the papers online (using a very handy 4G dongle a client lent me), watched British sport when I could (thank Goodness for www.vipboxasia.co!) and spent a lot of time taking and processing my photographs before taking one of the cheap and cheerful taxis in the early evening to take me to my first lesson.

The main ideas I’d gleaned from the travel guide and a quick trawl on the web were: climbing up to Victoria Peak to see the panoramic views of the harbour; going on an open-top bus ride; catching the Star Ferry to Kowloon to watch the Symphony of Lights (a regular son et lumière show put on by most of the office blocks around the harbour); going to Happy Valley to see the regular Wednesday night horse races; wandering around one of the ‘wet markets’ that sell fish, meat and other goods on the street; visiting one or two of the outlying islands; and perhaps going over to the Chinese mainland.

I never made it to China proper, as a meeting with another agency was cancelled, but I did do all the rest. My first photographic excursion was a trip to the Peak. I was very lucky to have sunshine on my first day off, and I ended up spending all day up there. There are two buildings at the top, which both look a bit like alien space ships: the Peak Galleria and the Peak Tower.

Victoria Harbour from the Peak

Victoria Harbour from the Peak

The views from both during the day were spectacular, but it got better and better as night fell. My only mistake was in leaving 20 minutes before the Symphony of Lights was due to start! The open-top bus ride was a great way to see all the extraordinary architecture in Hong Kong.

The island is a strange mixture of Gibraltar, New York and Monaco – very hilly, full of skyscrapers and offering several switchbacks akin to Loew’s Corner for the wannabe Formula 1 driver. As I drove around with an audio guide pointing out all the landmarks in my ear, I was constantly taking pictures left, right and centre. It took hours to transfer them to my laptop and edit them all, but I was happy with one or two of the more abstract shots.

Grey skyscraper on a grey day

Grey skyscraper on a grey day

The Symphony of Lights happens every evening at around eight o’clock on both sides of Victoria Harbour. Dozens of skyscrapers switch on their lights in time to a musical soundtrack that gets piped through speakers on the shoreline, and there are even lasers fired from some of the rooftops.

I caught the Star Ferry to Kowloon and watched it from the Avenue of Stars, which is just a posh name for the concrete waterfront. I chose that side of the harbour deliberately, as most of the iconic buildings are on the other side of the water on Hong Kong island, including the distinctive M Pei-designed China Bank Tower.

Hong Kong Symphony of Lights from Kowloon

Hong Kong Symphony of Lights from Kowloon

I thought getting a night off to go to Happy Valley was going to be a problem, but one of my clients helpfully cancelled a lesson one Wednesday, which allowed me to spend the whole evening there.

Happy Valley must be one of the few racecourses in the world that’s located slap bang in the middle of a city, but it certainly makes for a unique backdrop. There were thousands of people in the floodlit arena, most of them dressed up in their glad rags as if they were about to quaff a bottle of champagne in the Royal Enclosure at Ascot, but the fare on offer wasn’t always so classy.

I took a few shots of one very attractive woman in a red dress having an Ed Miliband moment with a cheeseburger and a packet of ketchup! The racing itself was as you’d imagine, but it was still rather strange to see Chinese jockeys wearing the traditional silks.

Jockey in purple and white riding racehorse

Jockey in purple and white riding racehorse

A ‘wet market’ in Hong Kong is just a food market on the street that ends up having to be hosed down to get rid of all the detritus at the end of the day. I went to the one on Bowrington Road and benefited from the delightful insouciance of the locals when it comes to having their pictures taken.

There are so many cameras and iPhones being used over there that the last thing people worry about is some random bloke taking yet another picture! Some of the items on sale were certainly interesting, and the live fish flapping about on the slabs were a magnetic draw.

Once food becomes waste at the end of the day, though, it undergoes an ugly transformation, and I was reminded of a Jonathan Swift poem, A Description of a City Shower, that compares the cleansing effect of the rain to the Old Testament flood:

“Sweepings from butchers’ stalls, dung, guts, and blood,
Drown’d puppies, stinking sprats, all drench’d in mud,
Dead cats, and turnip-tops, come tumbling down the flood.”

Smiling Chinese fishmonger

Smiling Chinese fishmonger

I was keen to get to some of the outlying islands in Hong Kong, but the weather rather limited my options. However, I had a friend over there who lived with his family on Lantau, and we arranged to have lunch with a few of his friends. We went for dim sum, which is rather a local tradition on a Sunday, and then spent the rest of the day together.

A few weeks later, his wife organised a 40th birthday party at a beach bar at Pui O, so I decided to use that as an excuse to explore the island properly.  I’d cancelled all my lessons to go to the party, and I decided to make a day of it.

The big attraction – literally! – on Lantau is the Tian Tan or Big Buddha, and I reached it by taking the cable car from the MTR stop in Tung Chung. The ride up wasn’t that spectacular, but I had a personal reason for going.

A girlfriend once sent me a postcard of the Big Buddha when she was in Hong Kong, and she said it reminded her of me because I close my eyes when I laugh! I wasn’t convinced when I saw it with my own eyes, but I took plenty of pictures just in case.

Big Buddha in profile

Big Buddha in profile

Lantau has changed a lot in the last few years, and it’s very difficult to find any indigenous peasant culture – everyone seems far too well off! However, I’d heard about the stilted houses in Tai O, and I wanted to see them for myself, so I took a taxi there from the Big Buddha.

Tai O used to be a busy fishing village, but it’s turned into a bit of a tourist trap. When I went, it was just gearing up for a dragon boat race, and there were dozens of little stalls by the river selling seaside delicacies such as ‘super fish balls’, ‘fresh cuttlefish’ and ‘crisp fried fish skin’!

Pleasure boat passing moorings of stilted houses

Pleasure boat passing moorings of stilted houses

After wandering round the village and stopping off for a quick ‘lime and salt’ drink (when in Rome…!), I took the bus to Pui O for the party. At the bus stop, I met an American art student and had a good chat with her while we were waiting for the bus and then on the bus itself.

It was nice to have a ‘normal’ conversation with someone for a change, but I had to jump off pretty quickly when I realised I was close to the resort. I had plenty of time on my hands, but it was quite a stroke of luck that I went down there early, as there were three or four kite surfers out in the bay.

They were all very good, and I was happy to spend an hour and a half just taking pictures of their jumps and tricks as the sun went down over the headland.

Close-up of female kite surfer getting air

Close-up of female kite surfer getting air

Mavericks was a pretty good venue, and the party went off well enough, but that marked the end of my stay in Hong Kong. All in all, I enjoyed my six weeks over there. It was not too long and not too short.

My clients were very kind and friendly, and I got along very well with them and their families. Hong Kong is to China as Goa is to India: if you can’t face the real thing, it will ease you gently into the local culture while providing all the trappings of Western civilisation to keep you sane.

You may see the occasional amusing sign, such as ‘Please wrap spittle’, or see the odd Ferrari burst into flames when you’re on the bus, but it’s definitely worth a visit.

Lost in Translation

My best experience in Moscow could easily have been my worst.

“Would you like to come to dinner with us at Café Pushkin and then see the Spasskaya Tower international military music festival in Red Square?”

“Yes, I’d be delighted.”

“Shall we meet you at the restaurant at six thirty?”

Oh, dear. My heart sank. It was my first time in Moscow, and I had only one hour to make sense of the Moscow Metro system all on my own. My clients had kindly given me the equivalent of an Oyster card and an iPhone with a local SIM card in it, but I had to get to the station first.

The nearest one was more than 15 minutes’ walk away, so I decided to try and get the bus. The only problem was that I didn’t know whether my smart card would work. Fortunately, it did. The next problem was knowing which platform to use in the Metro.

I don’t speak Russian, and all the signs and the names of the stations were in Cyrillic, so it was no easy task! Even when I got on the right train, it was very difficult to know where I was. There are so few signs on the Metro stations that it was almost impossible to see one and decipher the station name as the train flew past.

Even the announcements over the PA system were no help, as I didn’t even know how to pronounce the names of the stations en route! I eventually had to make do with counting them. That worked out fine, and I got off at the right one, only to get lost again.

I thought I’d be safe with Google maps, but the network was so slow that my phone wasn’t telling me where I was but where I’d been five minutes earlier!

The weather was so poor that I couldn’t navigate by the sun, and there were so many major roads and sliproads that it was impossible to cross them without taking the underground subway – which was even more confusing!

When I finally reached the restaurant, I was lucky enough to see my clients on the steps.

Phew! Never again…

The food at Café Pushkin was delicious, and my clients Dimitri and Yana encouraged me to try the local specialities and generously paid for my meal. Before we left for the festival, their son Boris showed me round the gorgeous antique interior.

He was 12 years old, and I had come to Moscow for three weeks in September 2013 to help him prepare for his entrance exams at various private schools in England. Everything had happened very quickly. From being told about the job to getting on the plane had only been seven days!

During that time, the only real obstacle had been getting a visa. In return for a couple of hours online and a visit to the Embassy (involving an obligatory lie about being in full-time employment), I was given my Russian visa name. This is similar to your pornstar name, except it’s decided by the Russian Embassy. Mine was NIKOLAS UILLIAM ДЭИЛ, by the way…

Despite the travel nightmares, that evening with Dimitri, Yana and Boris turned out to be the highlight of my trip to Moscow. After dinner, we walked to Red Square from the restaurant and spent the next couple of hours watching a succession of international marching bands play music and go through their parade ground drills in front of the spectacular backdrop of a floodlit St Basil’s Cathedral.

Better Red than dead

Better Red than dead

It was my first ever visit to Red Square, and it was quite an introduction! I was keen to take as many photos and videos of the event as I could, and Boris was doing the same sitting next to me.

By a freakish coincidence, he had almost exactly the same camera as I did (the Nikon D800E), so we had plenty to discuss that night and for the rest of the trip when it came to photography. This might give you some idea of the spectacle…

 

The only disappointing thing about the evening was that the family decided to leave early. I only discovered this later, but there was a firework display at the end of the show. How spectacular would that have been to see fireworks over St Basil’s?! Sadly, I missed out, and I don’t think I’ll ever have the chance again…

The bad news continued on the photography front when the weather stayed cloudy, misty, rainy and miserable for the entire trip. I had been keen to see St Petersburg and the onion-domed churches of Zagorsk and elsewhere, but there was no point in those conditions.

One result of that was that I didn’t have very much to occupy my time. There were a couple of people that I’d planned to see, but it wasn’t possible in the end, so I spent a lot of time in my hotel room. I got on with Boris and his parents reasonably well, and Yana very kindly provided me with lunch most days (although I could have wished for something other than borscht and black bread almost every day!), but it was a bit lonely sometimes.

I’d have been pulling my hair out if I hadn’t found a free VPN service that gave me 24/7 access to Sky Sports! My agent Andrei was also just a quick Skype call away to sort out any problems or just to pass the time. I really appreciated that, and we met up for a curry when I got home to cement our friendship.

I did take a few photographs while I was over there. I’d seen a nearby church out of my hotel window, so I walked over there on my day off and captured the onion domes for posterity.

"It's like an onion..."

“It’s like an onion…”

There was another old church just across the road in a residential gated community, but the security guards at the entrance wanted a bribe to let me in!

In the absence of any exciting landscapes or architecture to shoot, I decided to be a bit more creative. I was up on the 23rd floor of the Astrus Hotel, so I got a good view down Leninsky Prospekt. I took a few ‘miniatures’ of the tower blocks first…

Mini Moscow

Mini Moscow

…and then I went a bit ‘arty’ with my zoom!

Trabants and Mercedes as you've never seen them before...

Trabants and Mercedes as you’ve never seen them before…

The only other pictures I took were of one of the receptionists downstairs called Polina. She bizarrely felt she had to ask permission from her colleagues before she would agree, but we ended up having a good chat.

We’re even friends on Facebook now, so perhaps I should’ve plucked up the courage to talk to her a bit earlier. Who knows what might’ve happened? You know what they say about Moscow girls…

I have a few other memories of my trip:

  • the phenomenal upload speed of my hotel’s DSL connection (23.36Mbps!)
  • the water pressure in the shower – which made me feel like a rioter being hosed down by a water cannon
  • seeing a picture of Boris Johnson on his bike on the bedroom wall of my student Boris; finding a Russian medal on the kitchen table that Dimitri had won for his service to the motherland
  • seeing an abandoned car in the middle lane of Leninsky Prospekt; getting through the Moscow traffic honk-a-thon every morning, when my driver would get so close to the other cars that the parking alarm would regularly go off
  • trying to negotiate the return of my laundry in English with an old Russian woman speaking German!

All in all, I’m glad I had the opportunity to go to Moscow. The family were very kind and generous and easy to talk to, and I made a good friend in Andrei. It’s also another place I’ve been able to tick off my bucket list. Now, where next, I wonder…?!

Back in the USSR

Before I went to Belarus, I was warned it would be like going back to the Soviet Union: brutalist architecture, statues of Karl Marx and a hankering after the Communist era.

In fact, I ended up teaching English to a very nice couple called Mikhail and Natasha, who were very generous and hospitable to me and had a far from typically Russian (or Belarusian) attitude to politics and economics.

She ran a chain of pharmacies, he worked in the agriculture business, and neither of them could understand their friends’ passion for Russian imperialism.

I flew out in March 2014 after a last-minute scare when the agency tried to bring forward my flight with only three days’ notice! Fortunately, that was resolved happily enough, and I was met at Warsaw airport by a driver who would take me across the border to Brest (aka Brest-Litovsk).

The city didn’t have its own airport, so it was a choice between driving across the border from Poland or flying to Minsk and facing an even longer trip by car. When we arrived at the border, big men with big guns stopped the car to check our papers, and we waited to be allowed through.

An hour and a half later, we were still waiting! That has to be the worst border crossing I’ve ever had in my life…

My driver took me to the Hermitage, which was the best place in town (I checked: it was €83 a night – or free if you knew the owner!), but I had a shock when I unpacked my bag and tried to boot up my laptop.

LOT Polish Airlines had managed to drop it from a great height, and was so battered and bruised that the only thing it could do was beep forlornly! (In hindsight, I should perhaps have put it in my carry-on rather than my checked luggage, but I had all my photographic equipment in my camera bag, and there wasn’t really enough room…)

I met Mikhail and Natasha in the hotel restaurant and told them what had happened, and Mikhail very kindly offered to ask his IT department to have a look at my laptop and see if it could be fixed. Natasha even lent me her MacBook until eventually I got mine back – minus a memory card slot that was too damaged to fix…

I was in town to teach Mikhail and Natasha, but they generously farmed me out to a couple of friends of theirs and even Natasha’s mother at one point. (Same iPhones, just different brand of luxury German saloon…)

We quickly slipped into a daily rhythm. I’d start the day by having breakfast in the hotel. On the way to the restaurant, I’d always pass an old German shop till that looked rather photogenic. I planned to come down and take a few pictures of it one day, but it wasn’t until my final week that I eventually got round to it.

Unfortunately, I left the ISO rating on 1600 by mistake, so I had to do the shoot all over again, but I was rewarded when the users of Pixoto voted this my best photo ever!

My best photo ever...?

My best photo ever…?

Breakfast was a struggle, not just because of the rather limited Eastern European rations but because of having to listen to Lana del Rey’s latest album on a loop every morning. I asked at reception if they had any other CDs, but I was told that there was an exhibition of paintings in the foyer, and the artist had made it a condition that Lana del Rey would be played all the time to set the right mood!

One day, the barman tried to compete by playing drum ‘n’ bass at full volume to drown out the sound of Miss del Rey, but it didn’t last…

At nine o’clock, I’d leave the musical torture chamber and walk over to my clients’ apartment, where I would teach Mikhail for an hour and a half and then swap to Natasha for a similar period when she got home from work.

I’d then have a couple of hours to myself before meeting them both for a (very) late lunch at Caffè Venezia, which Mikhail always paid for. They knew the owner, and it was right next door to Mikhail’s office, so it was his favourite place.

There would always be someone to talk to, and the Italian owner knew enough English to be able to keep up a good conversation. After lunch, Olga would pick me up for her lesson, and I’d spend an hour and a half at her house before getting dropped off at my hotel again.

In the evenings, Mikhail and Natasha would usually invite me to dinner, either at a restaurant or at their place. Mikhail explained that there were only three decent restaurants in town – Caffè Venezia, Times Café and Jules Verne – and we ate at all of them.

Natasha was also an excellent cook, and Mikhail had a very well stocked wine fridge, so a typical meal would consist of smoked salmon and caviare washed down with champagne followed by salade de magret de canard and lightly grilled sea bass accompanied by a rather nice Puligny-Montrachet!

We also had dinner with Olga and Sergei one evening, and I had the novel experience of helping Olga and Natasha make ‘pierogi’, a kind of semi-circular dumplings similar to tortellini, which we filled and wrapped. I also had the rather dubious honour of nibbling on black bread topped with carpaccio of pig fat! Well, nothing tastes too bad after four glasses of vodka…

Another constant part of our routine was talking about the Crimea. The annexation by Russia was on the news every day, and we inevitably ended up talking about it as part of our lessons and over lunch or dinner. Today, Crimea.

Tomorrow, the Ukraine. The day after that, perhaps Belarus. You don’t quite realise the difference in your countries’ political traditions until you hear stories about living next door to the Russian bear.

Natasha told me a couple about her own family. Once, when Gorbachev was briefly threatened by a palace coup in 1991, she and Mikhail had actually emigrated to Poland for the day – just in case perestroika and glasnost had come to an end and the borders had been closed.

How many times do we feel we have to leave the country before a British General Election?! She also told me about her grandmother, who decided to take her family to Poland back in the 1920s, when it was briefly possible to leave the old Soviet Union.

She was waiting on the station platform, ready to catch the train, when she suddenly realised her wallet had been stolen! With all her money gone, they couldn’t possibly afford to leave home – and their family history was changed beyond recognition for the next 60 years…

Mikhail and Natasha were also very sporty, and they were kind enough to include me in their regular plans. We went for a long (and very energetic!) walk around the city before dinner one night, and I even had games of volleyball and tennis with Mikhail.

I hadn’t played volleyball for about 30 years, so I rather embarrassed myself on court, but at least I beat him at doubles – although that was probably because I was playing with the coach! We also spent the final Saturday cycling in the Białowieża Forest with Olga and Sergei, which is now a National Park and World Heritage site that spans the Belarusian/Polish border a few miles north of Brest.

The forest is great for cycling as it has a grid of roads from which cars are banned. We drove there in an old van that was big enough to hold all the bikes. Once we’d arrived, I was given a mountain bike, and we set off into the woods.

Our first stop was the zoo, which was a series of enclosures containing all the local animals to be found in the forest (and a few others). This was my chance to take a few pictures of my very first Russian bear, together with wolves, ostriches and a family of European bison.

Close-up of a wolf head in profile

Close-up of a wolf head in profile

We then cycled around the forest for a couple of hours and had a picnic lunch at the residence of Father Frost – a kind of Santa’s Grotto but without the snow! I always like a civilised picnic, but this was the first time I’d had one with pancakes, venison and samogon – or Russian moonshine…

I always try to take advantage of my foreign residential jobs to take pictures of the local landscapes, flora and fauna, so it was good to have a chance to use my camera again. There weren’t many photogenic sights to be seen in Brest, apart from a few onion-domed Russian Orthodox churches, but I found inspiration in the animals.

The following day, I went walkabout and visited the Brest fortress, which is where the first battle was fought in Hitler’s 1941 invasion of Russia. To commemorate the occasion, they’ve installed an enormous block of stone with a Russian soldier’s head carved out of it called the Courage Monument.

CNN once ran a story placing it first in a list of the world’s ugliest monuments, but they swiftly had to remove it when the Russians and Belarusians took offence!

Eyes of soldier on Brest fortress monument

Eyes of soldier on Brest fortress monument

That evening, I walked back into town to find St Simeon’s cathedral, which I’d first seen on my walk with Mikhail and Natasha. Russian Orthodox churches all have the distinctive ‘onion domes’, often painted gold, and they can look spectacular under floodlights.

St Simeon cathedral in Brest at night

St Simeon cathedral in Brest at night

I have to say that I really enjoyed my fortnight in Belarus. It was sometimes quite hard work spending so much time with my clients, as I had to concentrate on their English (and my own) even when we were just chatting together, but I was very lucky to be placed with a couple of similar ages with such similar interests and values.

When people come home from holiday, they often say, “The people were very friendly,” but I’m never quite convinced. After my trip to Belarus, I can safely say I’ve changed my mind. Whatever the economic, political and military history of the country, I’ve never been looked after quite so well, and I have to thank Mikhail and Natasha for showing me the best of Belarus.

I’m also even more thankful to have had the English Channel to protect us from invasion. Our history would have looked very different without it…!

 

A Picture is Worth a Thousand Words

Have you ever tried to do a 10,000-piece jigsaw of grey seals on a grey rock in a grey sea under a grey sky?

Tricky, isn’t it?

The key to doing a jigsaw puzzle or writing a description is attention to detail.

Everything matters: the mood, the setting, the period, the action, the characters – everything that our five senses can tell us and more. To try and produce the very best description you can when faced with any English exam that includes a composition question, it’s important to approach it in the right way.

Choose the Right Question

(1 minute, assuming you have 30 minutes for the whole question)

  • Common Entrance exams at either 11+ or 13+ usually offer a choice between a story, an essay or a description, perhaps of a photograph or illustration. If you choose the description, make sure you know something about the subject or at least have a good enough stock of synonyms or specialist vocabulary to describe it properly. If the picture is of a horse in a tack room bit you don’t know anything about horse riding, leave well alone!
  • We always write more imaginatively and at greater length if we’re writing about something we like or enjoy, so try to find a question that gets an emotional reaction out of you. If you like beautiful things, then you might respond better to a photograph of a sunset in the Maldives than a montage of burnt-out cars in Beirut!

Brainstorm Ideas

(5 minutes)

  • This is where attention to detail is most important. Before you take the exam, make sure you have a mental checklist of all the aspects of a scene that you might need to describe. Once you start planning your description, take a sheet of paper and divide it up into sections (or use a mind map with different bubbles for sight, hearing, taste, touch and smell). Make notes based on all five senses. Even if you can’t think of anything to write about one of them, such as ‘taste’, use your imagination. If it’s a seascape, is there the tang of salt on the air? Can the sailors smell land?
  • Think creatively about how to approach the description. A little bit of plot or context goes a long way to creating an appropriate mood, so think about topping and tailing the piece with one or two sentences about the observer. What’s the point of view of the narrator? Is he or she a spy, a pilot, a soldier or a scientist? Is he or she deaf or blind? Would it be better to write in the first or third person?
  • Even if you don’t decide to tell part of a story, think carefully about what the atmosphere of the scene should be. Every situation will demand a different mood or tone. Do you want it to be peaceful, suspenseful or frantic? What’s about to happen? Is it an ambush, an escape plan or a drug deal?
  • The atmosphere should be reflected in the vocabulary you choose to describe the scene. Make a list of the words that have the right associations or connotations, including ‘wow words’ or ‘golden words’ that you think might impress the examiner. Think of as many synonyms as you can. Why ‘destroy’ when you can ‘annihilate’? Why should a tree be plain old ‘green’ when it could be ‘verdant’?
  • Writing descriptively is not the same as writing an essay or doing a comprehension. You don’t need to be brief and matter-of-fact all the time. Think of different poetic devices you can use to make the characters or objects jump off the page. Can you get over the atmosphere or the emotion better with a simile, a metaphor or onomatopoeia? Is the sun in the Sahara desert ‘rather warm’ or ‘as hot as the furnace in the forge of Hell’?

Write a Plan

(5 minutes)

  • Failing to plan means planning to fail. I’ve read hundreds of compositions written by pupils of all ages, and it doesn’t take long to realise when something hasn’t been planned. You don’t need a plot here necessarily, but you do need some sort of structure. Look at the ideas that you came up with during your brainstorming and decide how to group them together.
  • Draw up a brief outline on a clean sheet of paper, listing the different paragraphs and including bullet points for each with the subject matter, key concepts or particular words that you want to use. What needs to go first? How are you going to finish? Are you going to take each sense in turn? Should you describe the different parts of the scene one by one, the lake followed by the mountains and then the village?

Write the Description

(whatever time you have left, less 5 minutes to check at the end)

  • Stick to the plan. It’s all very well having a plan, but getting your head down and writing the whole answer without looking at it is no better than not having one in the first place! If you do have a good idea that you want to include, by all means add it to the plan, but make sure you don’t get carried away and write too much about one topic, leaving too little time for all the others.
  • You don’t get any marks for answering a question that’s not even on the exam paper, so make sure you don’t get tempted to wander off the beaten path. Re-read the question now and again. Are there any special instructions? Are you doing exactly what you’ve been asked to do? Are you covering every part of the question?
  • Write as quickly as you can. I could never write as much as I wanted to, and one of the professors at my Oxford interview actually complained about it! I had to tell him I hoped that I was giving him ‘quality rather than quantity’, but I wish I’d been able to hand in six sides rather than four! You don’t have much time, so don’t spend a whole minute searching for the perfect word when another will do. You can always come back to it later when you check your answer.

Check your Work

(5 minutes)

  • Check for spelling, punctuation and capital letters (as you should for any piece of writing in English).
  • Check you haven’t made any other silly mistakes, either grammatical or stylistic. Make sure you’ve said what you want to say, and feel free to cross out the odd word and replace it with a better one if you can. Just make sure your handwriting is legible!

If you follow all these steps, you may not have the greatest ever description in the history of English literature, but you’ll have given it your best shot! If it helps, challenges or inspires you, here’s one of my favourites. It was written by James Joyce and comes in the final paragraph of his short story The Dead:

“Yes, the news­pa­pers were right: snow was gen­eral all over Ire­land. It was falling softly upon the Bog of Allen and, fur­ther west­wards, softly falling into the dark muti­nous Shan­non waves. It was falling too upon every part of the lonely church­yard where Michael Furey lay buried.

It lay thickly drifted on the crooked crosses and head­stones, on the spears of the lit­tle gate, on the bar­ren thorns. His soul swooned slowly as he heard the snow falling faintly through the universe and faintly falling, like the descent of their last end, upon all the liv­ing and the dead.”

Number Sequences

Number sequences appear in Nature all over the place, from sunflowers to conch shells. They can also crop up either in Maths or Verbal Reasoning, and both are essential parts of 11+ and other school examinations.

The trick is to be able to recognise the most common sequences and, if you find a different one, to work out the pattern so that you can find the missing values (or ‘terms’).

Common Sequences

Here are a few of the commonest number sequences. For each one, I’ve given the rule for working out the nth term, where n stands for its position in the sequence.

Even numbers: 2, 4, 6, 8 etc… Rule: 2n
Odd numbers: 1, 3, 5, 7 etc… Rule: 2n – 1
Powers of 2: 2, 4, 8, 16 etc… Rule: 2ⁿ
Prime numbers: 2, 3, 5, 7 etc… Rule: n/a (each number is only divisible by itself and one)
Square numbers: 1, 4, 9, 16 etc… Rule: n²
Triangular numbers: 1, 3, 6, 10 etc… Rule: sum of the numbers from 1 to n
Fibonacci sequence
: 1, 1, 2, 3 etc… Rule: n₋₂ + n₋₁ (ie each successive number is produced by adding the previous two numbers together, eg 1 + 1 = 2, 1 + 2 = 3)
Factors: 36, 18, 9, 6, 4 etc Rule: Factors from largest to smallest (tricky one, this…!)

Here are a few questions for you to try. What are the next two numbers in each of the following sequences?

  1. 14, 16, 18, 20…
  2. 9, 16, 25, 36…
  3. 3, 6, 12, 24…
  4. 7, 11, 13, 17…
  5. 5, 8, 13, 21…

Working out the Pattern

The best way to approach an unfamiliar sequence is to calculate the gaps between the terms. Most sequences involve adding or subtracting a specific number, eg 4 in the case of 5, 9, 13, 17 etc.

Sometimes, the difference will rise or fall, as in 1, 2, 4, 7 etc. If you draw a loop between each pair of numbers and write down the gaps (eg +1 or -2), the pattern should become obvious, enabling you to work out the missing terms.

  • If the missing terms are in the middle of the sequence, you can still work out the pattern by using whatever terms lie next to each other, eg 1, …, 5, 7, …, 11 etc. You can confirm it by checking that the gap between every other term is double that between the ones next to each other.
  • If the gaps between terms are not the same and don’t go up (or down) by one each time, it may be that you have to multiply or divide each term by a certain number to find the next one, eg 16, 8, 4, 2 etc.
  • If the gaps go up and down, there may be two sequences mixed together, which means you’ll have to look at every other term to spot the pattern, eg 1, 10, 2, 8 etc. Here, every odd term goes up by 1 and every even term falls by two.

Generating a Formula

At more advanced levels, you may be asked to provide the formula for a number sequence.

Arithmetic Sequences

If the gap between the terms is the same, the sequence is ‘arithmetic’. The formula for the nth term of an arithmetic sequence is xn ± k, where x is the gap, n is the position of the term in the sequence and k is a constant that is added or subtracted to make sure the sequence starts with the right number, eg the formula for 5, 8, 11, 14 etc is 3n + 2.

The gap between each term is 3, which means you have to multiply n by 3 each time and add 2 to get the right term, eg for the first term, n = 1, so 3n would be 3, but it should be 5, so you have to add 2 to it. Working out the formula for a sequence is particularly useful at 13+ or GCSE level, when you might be given a drawing of the first few patterns in a sequence and asked to predict, say, the number of squares in the 50th pattern.

You can also work out the position of the pattern in the sequence if you are given the number of elements. You do this by rearranging the formula, ie by adding or subtracting k to the number of elements and dividing by 𝒳. For example, if 3n +2 is the formula for the number of squares in a tiling pattern, and you have 50 squares in a particular pattern, the number of that pattern in the sequence = (50-2) ÷ 3 = 48 ÷ 3 = 16.

Quadratic Sequences

If the gap between the terms changes by the same amount each time, the sequence is ‘quadratic’, which just means there is a square number involved.

The formula for a quadratic sequence is 𝒳n² ± k, where 𝒳 is half the difference between the gaps (or ‘second difference’), n is the position of the term in the sequence and k is a constant that is added or subtracted to make sure the sequence starts with the right number, eg the formula for 3, 9, 19, 33 etc is 2n² + 1.

The differences between the terms are 6, 10, 14, so the second difference is 4, which means you need to multiply the square of n by 4 ÷ 2 = 2 and add 1, eg for the first term, n = 1, so 2n² would be 2, but it should be 3, so you have to add 1 to it.

Geometric Sequences

If each term is calculated by multiplying the previous term by the same number each time, the sequence is ‘geometric’. The formula for the nth term of a geometric sequence (or progression) is ar(n-1), where a is the first term, r is the multiplier (or ‘common ratio’) and n is the position of the term in the sequence, eg the formula for 2, 8, 32, 128 etc is 2 x 4(n-1). The first term is 2, and each term is a power of 4 multiplied by 2, eg the fourth term = 2 x 4(4-1) = 2 x 43 = 2 x 64 = 128.

Here are a few questions for you to try. What is the formula for the nth term in each of the following sequences?

  1. 14, 16, 18, 20…
  2. -1, 3, 7, 11…
  3. 4, 6, 10, 16…
  4. 9, 7, 5, 3…
  5. 2, 6, 18, 54… 

     

     

     

    If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.

Essay Writing

There comes a point in everyone’s life when you have to undergo the ritual that marks the first, fateful step on the road to becoming an adult. It’s called ‘writing an essay’ and involves long hours of hard work, boredom, and often embarrassment (when you find out your mark).

Pretty soon, your first essay turns into a weekly essay, and the pattern is set for the rest of your educational life. Essays can be stressful, particularly when laziness, the opposite sex or a preference for extra-curricular activities leads to a caffeine-fuelled ‘all-nighter’, but here are a few tips for getting by in the exams…

Choose the Right Question

Sometimes, you won’t be able to choose the question, as your teacher will make one up for you and expect you to answer it whether you like it or not. In most exams, however, you’ll have a range of questions to choose from, and that’s when it’s important to go for a topic that you have studied and might – just possibly – enjoy writing about.

When I was at Oxford, I only revised for the number of essays that I knew I would have to tackle. That caused a bit of a problem in the Examination Schools when I found out I couldn’t do the advertising language question because my tutor had got the sections mixed up (!), but it saves a lot of revision time.

Brainstorm Ideas

I’ve written (and marked) Heaven knows how many essays, and the key to success is almost always the quality of the ideas – but how do you come up with good ideas in the first place? Studies have shown that the best way is to brainstorm.

That means spending five minutes or more doing nothing but thinking up ideas. One idea often leads to another, so the point is to be creative and not worry about which ones are good enough to use.

I’ve led brainstorming sessions for business people, and there are always one or two who spend their time shooting everybody else down in flames, but there is no such thing as a bad idea. The right time to think about which ideas to use is when the list is complete and you can begin to pick out the main themes.

To get the most out of your brainstorming, it’s a good idea to impose some structure, but what works best depends on the nature of the question. If it asks for pros and cons, then it might make sense to draw a line down the middle of a sheet of A4 and come up with separate lists of arguments for and against.

Other questions lend themselves to mind mapping, which involves writing down an idea, drawing a circle around it and linking it with other similar ideas by drawing lines between the bubbles.

Whatever method you choose, it must give you a list of points to make and also the evidence to back them up. ‘Point, Evidence, Explanation’ (or PEE) is a useful tool for structuring your paragraphs in an essay, but there are plenty of variations:

  • PEEE: Point, Evidence, Explanation, Expand
  • PEEL: Point, Evidence, Explanation, Link
  • PETAL: Point, Evidence, Technique, Analysis and Link.

Whichever format you use, just make sure your brainstorming generates enough ‘points’ with supporting ‘evidence’ that you don’t run out of things to say halfway through! You normally won’t have a great deal of time for brainstorming, so you don’t have to write down everything in full sentences.

You just need enough keywords to remember what you meant. That means using abbreviations for characters’ names, leaving out ‘filler’ words like ‘the’ or ‘a’ and generally playing fast and loose with the normal rules of grammar. Your notes don’t have to be neat either – as long as you can read them yourself…!

Write a Plan

Once you have enough ideas, it’s just a matter of putting them in the right order and grouping them together into sensible categories using a standard template. It shouldn’t take more than five minutes, and the right structure will help the reader navigate through the essay, setting up signposts to show what’s going to be discussed:

  • Introduction
  • Main body
  • Conclusion

“Tell ’em what you’re going to tell ’em, tell ’em, then tell ’em what you told ’em!”

That may sound a bit repetitive, but it’s a good way to make your essay clear, readable and well-structured.

Take a clean sheet of A4, draw lines a little way from the top and bottom and label the three sections ‘Introduction’ (or ‘Intro), ‘Main body’ (or ‘MB’) and ‘Conclusion’ (or ‘Conc’).

Introduction

The introduction should sum up the answer to the essay question, list the topics to be covered and – if necessary – explain your approach. For example, if you’re asked whether Macbeth is Shakespeare’s ‘darkest’ play, you might make the following notes:

“Intro
Yes, but…
Literally or metaphorically ‘dark’?
Importance of night scenes
Many evil characters
Pessimistic view of human nature?”

The question is ambiguous. What does ‘darkest’ mean? There are plenty of important scenes set at night, including Macbeth’s encounters with the witches and his murder of Duncan, but the play is also about the evil of ambition and the lengths it drives us to – whether or not Shakespeare himself believed human nature was fundamentally sinful.

Your introduction will make these points, set out your own interpretation and list the areas you’ve decided are within the scope of the question.

Main Body

The main body should sketch out the meat of the essay, with a section for each topic and every point backed up by some sort of evidence, either a quotation, a statistic or an episode in the story. Your notes might include the following:

“Main body

P: Night scenes are important – pathetic fallacy
E: Witches, murder of Duncan

P: There are many evil characters (witches, Lady M, M’s own ambition)
E: ‘oftentimes to win us to our harm/The instruments of darkness tell us truths’
E: ‘Vaulting ambition, which o’erleaps itself’

P: S’s view of human nature is hard to find
E: Keats’s ‘negative capability’

etc…”

Yes, the encounter with the witches takes place at night, but the ideas of literal and metaphorical darkness are deliberately mixed together. This is the pathetic fallacy at work, creating a mood of uncertainty, fear and foreboding through stage lighting and sound effects.

The witches (and Lady Macbeth) do encourage Macbeth to murder Duncan and do whatever he has to do to wear and keep the crown, but Macbeth’s own ambition is the root cause.

This is not a morality tale about human nature in general. In fact, as the poet John Keats pointed out, Shakespeare possesses a kind of ‘negative capability’ that makes it almost impossible to ‘hear’ his voice and opinions in those of his characters.

Conclusion

Finally, the conclusion should mirror the introduction by repeating the answer to the question and recapping the topics discussed or points made, plus any more general comments you may want to make.

Write the Essay

The most important point to make here is that you should stick to the plan. It’s very tempting to go off on a tangent when you have a good idea on the spur of the moment, but it can too often lead you off track. If the idea is good enough, by all means include it, but make sure it fits into your plan first and change the template accordingly.

You should also try to find an appropriate tone of voice. We all use different kinds of words when we’re talking (or writing) to different people, and the language we use for essays should be careful, mature and precise. Hamlet might be ‘gobsmacked’ when he accidentally stabs Polonius through the tapestry, but there’s probably a better word to use…!

In the PEE format, each paragraph should begin with a sentence containing the point you want to make (taken from your plan). After that, you should introduce the evidence to back it up (also from your plan), followed by a more detailed explanation. (This will obviously vary slightly if you use the PEEE, PEEL or PETAL format.)

Quotations should be short and sharp. I understand the temptation to write down a long quotation just to make it look like your essay is longer than it really is, but examiners are wise to that trick! Try to find instead the key word or phrase that best supports your argument and build it into one of your own sentences.

If you want to miss out a few words, use the ellipsis (…). If you want to change the quotation to make it fit grammatically, put your changes in square brackets.

Try to avoid waffle. I know it’s sometimes difficult to think of enough to write, but expressions such as ‘it says in the text that…’ or ‘the author says that he thinks that…’ are just a waste of space. Quality is more important than quantity – at least, that’s what I told the tutor who interviewed me for Oxford when he complained I hadn’t written very much!

Say what you mean and mean what you say. It’s sometimes very tempting to write something because it sounds academic or impressive or professional even though you don’t really mean it. Try to avoid it if possible. The worst sin is to plagiarise a critic whose book you might have read. Copying someone else’s work is bad enough, but copying it when you don’t even agree with it is even worse!

Demonstrate your knowledge. Nobody likes a show-off, but the examiner has to judge you on the basis of your essay alone, so take every opportunity to drop handy pieces of literary trivia into your answer, particularly if they relate to the broader genre or literary period to which the text belongs. If you can show that you know about the historical or cultural context as well as the text itself, then you’ll stand out from the crowd.

One other small point is that essays are generally not written in the first person. It sounds a bit childish to write ‘I think…’ all the time, so you might want to find other ways of expressing an opinion, either by dropping the ‘I think’ altogether or stealing a trick from TS Eliot, whose answer was to (over)use the passive in phrases such as ‘It is thought that…’.

Here’s a model paragraph based on the essay title about Macbeth being Shakespeare’s darkest play:

“The night scenes are important and draw on the pathetic fallacy to link the physical darkness to the moral ‘darkness’ of the lead characters, Macbeth and his wife. (Point) Several key scenes take place at night, including Macbeth’s meetings with the witches, the murder of King Duncan and the appearance of the ghost of Banquo. (Evidence) Darkness is a constant presence throughout the play, and there appears to be a link between what happens at night and the evil thoughts and motives of the main characters. That means darkness comes to be closely associated with the subterfuge of the witches, the evil of Duncan’s murder and the guilt Macbeth feels for having Banquo killed. (Explanation)

Check your Work

The three main points of grammar to check are spelling, punctuation and capital letters, but you should also read your essay through to yourself to make sure it makes sense and says exactly what you want it to say. These are the most important five minutes of the exam, so don’t take the easy way out and claim you don’t have time. Make time!

Good luck!

Quiz

  1. What are the five steps you should take when writing an essay?
  2. What are the two types of ideas you should think of when preparing an essay?
  3. What tool can you use to help structure your ideas?
  4. What are the three sections of an essay?
  5. What goes into the first part?
  6. What goes into the second part?
  7. What goes into the third part?
  8. What are some of the ways of proving your arguments are true?
  9. What should you try and do when writing the essay itself?
  10. What should you check for at the end?

Sample Titles

  1. Electric vs petrol cars: which are better?
  2. Breakfast is the most important meal of the day. Do you agree?
  3. Should children be forced to wear school uniforms?
  4. What children do after school is more important than what they learn in school. Discuss.
  5. Are there too many people in the world?
  6. Why would a mission to Mars be a good thing? 

     

     

     

    If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.

Fractions, decimals and percentages

Fractions, Decimals and Percentages

Pizzas are very useful, mathematically speaking. However much we hate fractions, we all know what half a pizza looks like, and that’s the point. Numbers don’t have any intrinsic meaning, and we can’t picture them unless they relate to something in the real world, so pizzas are just a useful way of illustrating fractions, decimals and percentages.

They all do the same job of showing what share of something you have, and a common question involves converting from one to another, so here are a few tips…

Fractions to Decimals

Calculator

  • Simply divide the numerator by the denominator, eg 3/4 = 3 ÷ 4 = 0.75.

Non-calculator

You can always use the standard ‘bus stop’ method to divide the numerator by the denominator on paper (or in your head), but the numbers may be easy enough for you to use a shortcut.

  • If the denominator is a power of 10 (eg 10 or 100), write the numerator down straight away as a decimal. You just have to make sure you end up with the digits in the right columns, eg a fraction involving hundredths needs to end in the second column after the decimal point, so 29/100 = 0.29.
  • If the denominator ends in zero, you may be able to simplify the fraction into tenths first and then convert it into a decimal, eg 16/20 = 8/10 = 0.8.
  • If you express the fraction in its lowest terms by simplifying it (ie dividing the numerator and denominator by the same numbers until you can’t go any further), you may  recognise a common fraction that you can easily convert, eg 36/45 = 4/5 = 0.8. Just make sure that you learn all these by heart, especially the eighths!

Quiz

  1. What is 5/10 as a decimal?
  2. What is 8/40 as a decimal?
  3. What is 36/60 as a decimal?
  4. What is 27/36 as a decimal?
  5. What is 77/88 as a decimal?

Fractions to Percentages

Calculator

  • Simply divide the numerator by the denominator, multiply by 100 and add the ‘%’ sign, eg 3/4 = 3 ÷ 4 x 100 = 0.75 x 100 = 75%.

Non-calculator

You can always convert the fraction into a decimal (see above) and then multiply by 100 and add the ‘%’ sign. Otherwise, try these short cuts in order.

  • If the denominator is a factor of 100 (eg 10, 20, 25 or 50), multiply the numerator by whatever number will turn the denominator into 100 and add the ‘%’ sign, eg 18/25 = 18 x 4 = 72%.
  • If the denominator is a multiple of 10 (eg 30, 40 or 70), divide the numerator by the first digit(s) of the denominator to turn the fraction into tenths, multiply the numerator by 10 and add the ‘%’ sign, eg 32/80 = 32 ÷ 8 x 10 = 4 x 10 = 40%.
  • If you express the fraction in its lowest terms by simplifying it (ie dividing the numerator and denominator by the same numbers until you can’t go any further), you may  recognise a common fraction that you can easily convert from memory, eg 8/64 = 1/8 = 12.5%.

Quiz

  1. What is 4/10 as a percentage?
  2. What is 6/20 as a percentage?
  3. What is 24/40 as a percentage?
  4. What is 14/70 as a percentage?
  5. What is 40/64 as a percentage?

Decimals to Fractions

Every decimal is really a fraction in disguise, so the method is the same whether you’re allowed a calculator or not.

Calculator/non-calculator

  • Check the final column of the decimal (eg tenths or hundredths) and place all the digits over the relevant power of 10 (eg 100 or 1000) before simplifying if necessary, eg 0.625 = 625/1000 = 5/8.

Quiz

  1. What is 0.4 as a fraction?
  2. What is 0.25 as a fraction?
  3. What is 0.24 as a fraction?
  4. What is 0.875 as a fraction?
  5. What is 0.375 as a fraction?

Decimals to Percentages

Again, this is an easy one, so the method is the same whether you’re allowed a calculator or not.

Calculator/non-calculator

  • Multiply by 100 and add the ‘%’ sign, eg 0.375 x 100 = 37.5%.

Quiz

  1. What is 0.27 as a percentage?
  2. What is 0.1 as a percentage?
  3. What is 0.55 as a percentage?
  4. What is 0.001 as a percentage?
  5. What is 1.5 as a percentage?

Percentages to Fractions

You can think of a percentage as simply a fraction over 100, so the method is easy enough whether you’re allowed a calculator or not.

Calculator/non-calculator

  • If the percentage is a whole number, remove the ‘%’ sign, place the percentage over 100 and simplify if necessary, eg 75% = 75/100 = 3/4.
  • If not, turn the fraction into a whole number as you go by multiplying the numerator and denominator by whatever number you need to (usually 2, 3 or 4), eg 37.5% = (37.5 x 2) / (100 x 2) = 75/200 = 3/8.

Quiz

  1. What is 22% as a fraction?
  2. What is 15% as a fraction?
  3. What is 37.5% as a fraction?
  4. What is 87.5% as a fraction?
  5. What is 6.25% as a fraction?

Percentages to Decimals

This is easy enough, so the method is the same whether you’re allowed a calculator or not.

Calculator/non-calculator

  • Remove the ‘%’ sign and divide by 100, eg 70% ÷ 100 = 0.7.

Quiz

  1. What is 40% as a decimal?
  2. What is 70% as a decimal?
  3. What is 35% as a decimal?
  4. What is 45.5% as a decimal?
  5. What is 62.1% as a decimal?

Ordering Fractions, Decimals and Percentages

A common question in the 11+ or 13+ involves putting a list of fractions, decimals and/or percentages in size order—either from largest to smallest or smallest to largest.

There are a number of ways of doing this, and it depends what kind of numbers are involved. However, a good first step is to start with the first two numbers and ask yourself if one is ‘obviously’ bigger than another. For instance, it might be quite difficult to compare 1/17 and 18/19 by converting them to fractions with the same denominator, but you don’t have to because 1/17 is clearly smaller!

After that, you can look at each number one by one and work out where it fits in your list. To keep track of everything, it’s a good idea to put numbers in pencil next to each value. Once you have the final order, you can write them all down on the answer line.

One simple question you can always ask yourself is whether the two fractions, decimals or percentages are smaller or larger than a half. If one is smaller but the other is larger, then the answer’s obvious.

If that doesn’t work, here are a few more ways to do it.

Ordering Fractions

If two fractions have the same denominator, the larger one will be the one with the larger numerator, eg 2/3 is bigger than 1/3.

If the fractions have different denominators, turn them into fractions with the same denominator and then compare the numerators, eg 5/6 and 7/8 are the same as 40/48 and 42/48, so 7/8 must be larger.

Quiz

  1. Put these numbers in order from largest to smallest: 1/2, 1/4, 2/5, 4/7, 5/8
  2. Put these numbers in order from largest to smallest: 3/4, 1/8, 5/6, 4/9, 3/8
  3. Put these numbers in order from largest to smallest: 4/5, 1/9, 3/4, 7/8, 1/4
  4. Put these numbers in order from largest to smallest: 1/3, 3/4, 2/3, 1/8, 5/6
  5. Put these numbers in order from largest to smallest: 2/5, 1/2, 2/3, 4/5, 3/4

Ordering Decimals

Decimals are easy to sort. It’s a bit like putting words in alphabetical order:

  • Start with the first digit after the decimal point, which is the number of tenths. The number with the bigger first digit is bigger overall, eg 0.2 is bigger than 0.1.
  • If the numbers have the same number of tenths, compare the hundredths, eg 0.12 is bigger than 0.11.
  • Repeat until you find the first digit that’s different. Just remember that if one number ends before you get a different number, it will always be smaller, eg 0.45 is smaller than 0.456.

Quiz

  1. Put these numbers in order from smallest to largest: 0.2, 0.3, 0.11, 0.2, 0.33
  2. Put these numbers in order from smallest to largest: 0.8, 0.6, 0.55, 0.5, 0.555
  3. Put these numbers in order from smallest to largest: 0.9, 0.4, 0.8, 0.11, 0.1
  4. Put these numbers in order from smallest to largest: 0.13, 0.103, 0.301, 0.013
  5. Put these numbers in order from smallest to largest: 0.4444, 0.44444, 0.444, 0.44, 0.4

Ordering Percentages

Percentages are also easy to sort as they’re just values that you can put in numerical order, eg 35% is bigger than 17% because 35 is bigger than 17.

Quiz

  1. Put these numbers in order from largest to smallest: 25%, 12%, 80%, 100%, 4%
  2. Put these numbers in order from largest to smallest: 13%, 103%, 31%, 30%, 30.1%
  3. Put these numbers in order from largest to smallest: 2%, 222%, 22%, 2.2%, 2.22%
  4. Put these numbers in order from largest to smallest: 24%, 4%, 4.4%, 80%, 42%
  5. Put these numbers in order from largest to smallest: 14%, 71%, 3.5%, 5.3%, 4%

Ordering a Mixture

This is where it gets tricky. There’s no single way of comparing fractions, decimals and percentages, so once you’ve numbered the values that are ‘obviously’ bigger and smaller, you’ll have to convert the others into the most common form, eg if there are three fractions, two decimals and a percentage, turn them all into fractions.

This usually saves time, but look out for ‘awkward’ numbers that you can’t easily turn into a different format, eg 0.618 is impossible to turn into a common fraction, and the number π is an ‘irrational number’ that can’t be converted into anything else!

Quiz

  1. Put these numbers in order from smallest to largest: 0.2, 11%, 25%, 1/4, 3/8
  2. Put these numbers in order from smallest to largest: 99.9%, 0.9, 7/8, 8/9, 0.99
  3. Put these numbers in order from smallest to largest: 0.8, 4/5, 5/6, 81%, 90%
  4. Put these numbers in order from smallest to largest: 0.5, 55%, 4/5, 7/8, 77%
  5. Put these numbers in order from smallest to largest: 77%, 0.7, 3/4, 2/3, π 

     

     

     

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Useful Formulas

What is a problem? A problem = a fact + a judgment. That is a simple formula that tells us something about the way the world works. Maths is full of formulas, and that can intimidate some people if they don’t understand them or can’t remember the right one to use.

However, formulas should be our friends as they help us to do complex calculations accurately and repeatably in a consistent and straightforward way. The following is a list of the most useful ones I’ve come across while teaching Maths to a variety of students at a variety of ages and at a variety of stages in their education.

Averages

  • The mean is found by adding up all the values and dividing the total by how many there are, eg the mean of the numbers 1-10 is 5.5, as 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55, and 55 ÷ 10 = 5.5.
  • The mode is the most common value (or values), eg the mode of 1, 2, 2, 3, 4, 5 is 2.
  • The median of an odd number of values sorted by size is the one in the middle, eg the median of the numbers 1-5 is 3. The median of an even number of values is the mean of the two numbers in the middle, eg the median of the numbers 1-10 is 5.5, as 5 and 6 are the numbers in the middle, and 11 ÷ 2 = 5.5.
  • The range is the highest value minus the lowest, eg the range of the numbers 1-10 = 10 – 1 = 9.

Sample Questions

  1. What is the mean of the numbers 6, 5, 8, 2 and 4?
  2. What is the mode of the numbers 1, 5, 5, 12 and 3?
  3. What is the median of the numbers 2, 8, 9, 6 and 5?
  4. What is the median of the numbers 1, 13, 4, 6, 8 and 20?
  5. What is the range of the numbers 15, 2, 3, 8 and 4?

Circle Theorems

  • Alternate segment theorem
    The angle between a tangent and a chord is equal to the angle subtended by the same chord in the alternate segment.
  • Angles at the centre and at the circumference
    The angle formed at the centre of the circle by lines starting from two points on the circumference is double the angle formed on the other side of the circle by lines originating from the same points.
  • Angles in the same segment
    If you create two triangles between the ends of the chord and the side of the circle, the angles in the same segment are equal.
  • Angles in a semicircle
    If you draw a triangle using the diameter and any point on the circumference, the angle at that point is 90°.
  • Perpendicular chord bisection
    The perpendicular from the centre of a circle to a chord will always bisect the chord (divide it into two equal parts).
  • Tangent of a circle
    a) The angle between a tangent and radius is 90°.
    b) Tangents that meet at the same point outside the circle are equal in length.
  • Cyclic quadrilateral
    The opposite angles in a cyclic quadrilateral add up to 180°.
  • Angles subtended on the same arc
    Angles formed from two points on the circumference of a circle are equal to other angles, in the same arc, formed from those two points.
  • Angle in a semi-circle
    Angles created by drawing lines from the ends of the diameter of a circle to the circumference form a right angle.

Geometry

  • Angles around a point add up to 360º
  • Angles on a straight line add up to 180º
  • Vertically opposite angles are equal, ie the two pairs of angles opposite each other when two straight lines bisect (or cross) each other
  • Alternate angles are equal, ie the angles under the arms of a ‘Z’ formed by a line (or ‘transversal’) bisecting two parallel lines
  • Corresponding angles are equal, ie the angles under the arms of an ‘F’ formed by a line (or ‘transversal’) bisecting two parallel lines
  • Complementary angles add up to 90º
  • Any straight line can be drawn using y = mx + c, where m is the gradient and c is the point where the line crosses the y-axis (the ‘y-intercept’)
  • The gradient of a straight line is shown by δy/δx (ie the difference in the y-values divided by the difference in the x-values of any two points on the line, usually found by drawing a triangle underneath it)

Polygons

  • Number of diagonals in a polygon = (n-3)(n÷2) where n is the number of sides
  • The sum of the internal angles of a polygon = (n-2)180º, where n is the number of sides
  • Any internal angle of a regular polygon = (n-2)180º ÷ n, where n is the number of sides

Sample Questions

  1. How many diagonals are there in a square?
  2. How many diagonals are there in an octagon?
  3. What is the sum of the internal angles of a pentagon?
  4. What is the sum of the internal angles of a hexagon?
  5. What are the internal angles of a regular decagon?
  6. What are the internal angles of a regular heptagon?

Probability

  • The probability of something happening = the number of ways of getting what you want divided by the number of possible outcomes, eg the chance of getting heads if you flip a coin is 1/2 (or 0.5 or 50%).
  • The probability of a sequence of events = the probability of all the events multiplied together, eg the chance of getting two heads in a row if you flip a coin is 1/2 x 1/2 = 1/4 (or 0.25 or 25%).

Sample Questions

  1. What is the probability of rolling a six?
  2. If there are two red and three black balls in a bag, what is the probability of taking out a red one?
  3. What is the probability of rolling a number greater than 3?
  4. What is the probability of tossing three heads in a row?
  5. If the chance of hitting treble 20 is 1/10, what is the probability of scoring 180 with three darts?

Rectangles

  • Perimeter of a rectangle = 2(l + w), where l = length and w = width
    Note that this is the same formula for the perimeter of an L-shape, too.
  • Area of a rectangle = lw, where l = length and w = width

Sample Questions

  1. What is the perimeter of a rectangle measuring 5 x 7 cm?
  2. What is the perimeter of a rectangle measuring 13 x 4 cm?
  3. What is the perimeter of an L-shape measuring 12 x 8 m overall with a 4 x 2 m piece missing?
  4. What is the area of a rectangle measuring 3 x 12 cm?
  5. What is the area of a rectangle measuring 6 x 8 cm?

Trapeziums

  • Area of a trapezium = lw, where l = average length and w = width (in other words, you have to add both lengths together and divide by two to find the average length)

Sample Questions

  1. What is the area of a trapezium with a height of 7 cm and horizontal sides of 4 and 8 cm?
  2. What is the area of a trapezium with a height of 10 inches and horizontal sides of 5 and 4 inches?
  3. What is the area of a trapezium with a height of 5 cm and horizontal sides of 2 and 4 cm?
  4. What is the area of a trapezium with a height of 12 m and horizontal sides of 6 and 9 m?
  5. What is the area of a trapezium with a height of 10 cm and horizontal sides of 4 and 5 cm?

Triangles (Trigonometry)

  • Area of a triangle = ½bh, where b = base and h = height
  • Angles in a triangle add up to 180º
  • Pythagoras’s Theorem: in a right-angled triangle, a² + b² = c², ie the area of a square on the hypotenuse (or longest side) is equal to the sum of the areas of squares on the other two sides

 

 

 

 

 

 

Circles

  • Circumference of a circle = 2πr, where r = radius
  • Area of a circle = πr², where r = radius (π = 3.14 to two decimal places and is sometimes given as 22/7)

Sample Questions

  1. What is the area of a triangle with a height of 5 cm and a base of 3 cm?
  2. What is the remaining internal angle of a triangle if the others are 20º and 30º?
  3. What is the length of the remaining side of a right-angled triangle if the others are 4 cm and 3 cm?
  4. What is the circumference of a circle with a radius of 5cm, assuming π = 3.14?
  5. What is the area of a circle with a diameter of 4 m, assuming π = 22/7?

Spheres

  • Surface area of a sphere = 4πr², where r = radius
  • Volume of a sphere = 4/3πr³, where r = radius

Sample Questions

  1. What is the surface area of a sphere with a radius of 15 cm, assuming π = 3.14?
  2. What is the surface area of a sphere with a diameter of 7 cm, assuming π = 3.14?
  3. What is the volume of a sphere with a radius of 1 cm, assuming π = 22/7?
  4. What is the volume of a sphere with a radius of 5 cm, assuming π = 3.14?
  5. What is the volume of a sphere with a diameter of 5 m, assuming π = 22/7?

Cuboids

  • Surface area of a cuboid = 2(lw + lh + wh), where l is length, w is width and h is height
  • Volume of a cuboid = lwh, where l is length, w is width and h is height

Sample Questions

  1. What is the surface area of a cuboid measuring 3 x 4 x 5 cm?
  2. What is the surface area of a cuboid measuring 6 x 2 x 12 cm?
  3. What is the volume of a cuboid measuring 8 x 5 x 6 cm
  4. What is the volume of a cuboid measuring 2 x 15 x 7 cm
  5. What is the volume of a cuboid measuring 18 x 9 x 2 cm

Number Sequences

  • The nth term of any arithmetic sequence (with regular intervals) = xn ± k, where x is the interval (or difference) between the values, n is the value’s place in the sequence and k is a constant that is added or subtracted to make sure the sequence starts at the right number, eg the formula for 5, 8, 11, 14…etc is 3n + 2
    • If you know where the term is in the sequence, you can find it by plugging in n and solving the equation, eg the fourth term of the sequence above = 3n + 2 = 3 x 4 + 2 = 14
    • If you know what the term is, you can find its position in the sequence by adding the number as the result of the formula and solving for n, eg if the term in the sequence above = 14, then 3n + 2 = 14, 3n = 12 and n = 4.
  • The sum of n consecutive numbers is n(n + 1)/2, eg the sum of the numbers 1-10 is 10(10 + 1)/2 = 110/2 = 55

Sample Questions

  1. What is the formula for the nth term of 2, 4, 6, 8…?
  2. What is the formula for the nth term of -5, -3, -1, 1…?
  3. What is the seventh term of the sequence 4, 8, 12, 16…?
  4. What position is 66 in the sequence 3, 6, 9, 12…?
  5. What is the sum of the numbers 12 to 18?

Other

  • Speed = distance ÷ time
  • Time = distance ÷ speed
  • Distance = speed x time
  • Profit = sales – cost of goods sold
  • Profit margin = profit ÷ sales
  • Mark-up = profit ÷ cost of goods sold

Sample Questions

  1. What is the speed of a vehicle that travels 20 miles in two hours?
  2. How long does it take to travel 210 km at 70 km/h?
  3. What profit does a butcher make on three steaks he buys at £2 and sells for £2.50?
  4. What’s his profit margin on those steaks?
  5. What’s his mark-up on those steaks? 

     

     

     

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Commas

If you had the chance to take a contract out on one punctuation mark, most people would probably choose the comma. Unfortunately, that’s not possible although modern journalists are doing their best to make it into an optional extra!

Punctuation should be there to help the writer and the reader, and the comma is no exception. If I know the rules for using commas, I expect one in certain situations and not in others. If there isn’t one when there should be, or there is one where there shouldn’t be, then I end up getting confused.

I may even have to re-read the passage to make sure I understand it. There are certainly ‘grey areas’ when even experts don’t know whether a comma is required or merely optional, but those should be the exception rather than the rule.

You might say that nobody has the right to decide what grammatical rules are ‘correct’ and that the plethora of rules I go by were taught to me back in the 1970s, but clarity comes first in my view, so here goes…

  • Lists are the obvious example of using a comma. In the old days, people used to use what’s called an ‘Oxford comma’ before the word ‘and’, but we don’t any more, eg ‘I went to the market and bought apples, pears and bananas’. There are some circumstances when using the Oxford comma makes the sense of the text clearer, but most people would agree that you don’t need it. The list may also be a list of adjectives before a noun, eg ‘It was a juicy, ripe, delicious peach’.
  • Conjunctions (or connectives) make two sentences into one ‘compound’ or ‘complex’ sentence with two separate clauses.
    • Coordinating conjunctions‘ are used to make a ‘compound’ sentence when the clauses are equally important, and the two ‘main clauses’ should always be separated by a comma, eg ‘The sun was warm, but it was cooler in the shade’. There is a useful way of remembering the coordinating conjunctions, which is to use ‘FANBOYS’. This consists of the first letter of ‘for’, ‘and’, ‘nor’, ‘but’, ‘or’, ‘yet’ and ‘so’. If a FANBOYS word is NOT used to separate two clauses, then you don’t need a comma, eg in lists.
    • Subordinating conjunctions‘ are used to make a ‘complex’ sentence when there is a main clause and a subordinate clause. (Subordinate just means less important.) If the sentence starts with a subordinating conjunction, the clauses need a comma between them, eg ‘Even though it was very hot, he wasn’t thirsty’. However, if the subordinate clause comes at the end, there is no need for a comma, eg ‘He wasn’t thirsty even though it was very hot’. There are lots of subordinating conjunctions, such as ‘after’, ‘although’ and ‘because’, but the easy way to remember it is to ask yourself if the conjunction is in FANBOYS. If it is, it’s a coordinating conjunction; if it’s not, it’s a subordinating conjunction. Alternatively, subordinating conjunctions are sometimes known as ‘WABBITS’ or ‘WABITS’ because some of the commonest ones start with those letters (when, where, while, after, although, before, because, if, though and since).
  • Which (but not that) needs a comma before it when used as a relative pronoun, eg ‘The sky, which was tinged with orange, was getting darker before sunset’ or ‘He looked up at the sky, which was tinged with orange’. If you don’t know whether to use which or that, the word ‘which’ describes something, whereas the word ‘that’ defines it. The rule about commas also applies to ‘who’ when it comes to describing people, although you still use the same word whether you’re defining or describing someone. Relative pronouns such as ‘which’, ‘that’ and ‘who’ all create a relative clause, which is a type of subordinate clause, so the sentence will be a complex sentence.
  • Openers (or sentence starters or fronted adverbials) are a useful way of starting a sentence, usually to specify a particular time, place or manner, eg ‘At half-past three, we go home to tea’, ‘At the end of the road, there is a chip shop’ or ‘With a smile on his face, he went to the ice-cream parlour’. They need a comma after them because the subject of the sentence (ie the noun or pronoun that governs the verb in the main clause) should come first.
  • Direct speech needs something to separate what’s actually said from the description of who said it, and this is normally a comma (although it can sometimes be a question mark or exclamation mark if it’s a question or a command), eg
    “Hello,” he said.
    …or…
    He said, “Hello.”
    The tricky bit comes when the description of the speaker comes in the middle of what’s being said. Here, the rule is that a comma should be used after the ‘he said’/’she said’ if the speaker hasn’t finished the sentence yet, eg
    “On Wednesday evening,” he said, “we’re planning to go to the cinema.”
    When the sentence is over, though, you need a full-stop afterwards, eg
    “I like chocolate biscuits,” she said. “They’re so delicious.”
  • Vocatives (people’s names or titles) and interjections are simply interruptions to a normal sentence – usually when someone is speaking – to include a name or words such as ‘well’ or ‘now’. They should be separated with one or more commas – even if that leads to a long list of words followed by commas, eg “Well, now, Mum,” he said, “let me explain.”
  • Certain adverbs fall into the same boat, such as ‘however’, ‘nevertheless’, ‘furthermore’ and the humble ‘too’, and should be separated by commas, eg ‘She played on the swings and the roundabout, too.’
  • Extra information (or embedded clauses, interrupters or bracketing commas) is sometimes added to a sentence to describe something or someone. If the sentence would still make sense without it, you should put commas before and after the phrase to separate it from the rest of the sentence, eg ‘He stood, cold and alone, before his fate.’
    A tricky example of this is when you introduce people with a description of who they are, for example by saying ‘his best friend, James, is coming for dinner’. This is extra information, so there does need to be a comma before and after the word ‘James’. However, that’s only because the meaning is NOT changed by adding his name: nobody can have more than one ‘best friend’, so it HAS to be James, and including his name therefore makes no difference as to his identity.
    On the other hand, if you said ‘his friend James is coming for dinner’, you shouldn’t put commas around ‘James’ because James is not the man’s only friend – or let’s hope not, anyway!  Adding the name ‘James’ DOES change the meaning of the sentence, so it’s no longer just extra information.
  • Present participles (ie verbs ending in -ing) are often used to describe what someone is doing, and they need to be separated by a comma, eg ‘He stood at the gate, jingling the keys in his pocket.’
  • Eg and ie are useful shorthand to mean ‘for example’ (exempli gratia in Latin) and ‘that is’ (id est) and should be preceded by a comma, eg ‘He knew lots of poetic devices, eg metaphors and similes.’
  • Names and places sometimes need a comma to separate their different parts. If the day comes after the month and before the year, it should have one, eg ‘December 7, 1941′. If someone has a qualification or letters after his or her name, you should use a comma, eg ‘John Smith, PhD’. If a town is followed by a state or country, the state or country should be separated by commas, eg ‘He lived in Lisbon, Portugal, for five years.’
  • Numbers need commas to separate each power of a thousand. Start on the right at the decimal point and work left, simply adding a comma after every three digits, eg 123,456,789.0.
  • Repetition of a word or phrase also demands a comma, eg “Half a league, half a league, half a league onward…”

Quiz

Put the correct punctuation in the following sentences:

  1. I like music shopping and dancing
  2. The food was good but he didn’t like the service
  3. The book arrived after she went to the shops
  4. He put on a jacket that was thick enough to keep out the cold
  5. She called her mother which is what she usually did on Sunday evenings
  6. At the end of the road he saw a fox
  7. These apples are expensive he said
  8. What are you doing she cried I need those biscuits for the charity bake sale
  9. When Im on my own she admitted I watch a lot of daytime TV
  10. Could you help me please David he asked
  11. Fortunately he was experienced enough to avoid capsizing the boat
  12. He stood nervous and bashful in front of the prettiest girl hed ever seen
  13. He loved 19th Century novels eg Emma
  14. She was persona non grata ie she wasnt welcome
  15. He lived in Paris France
  16. The Germans invaded Poland on September 1 1939
  17. He watched 1001 Dalmations
  18. All he could see was rain rain rain 

     

     

     

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Poetic Devices

It’s important to be able to recognise and analyse poetic devices when studying literature at any level. Dylan Thomas is my favourite poet, and he uses so many that I decided to take most of my examples from his writings.

  • A simile is just a comparison using the word ‘like’ or ‘as’, such as ‘I sang in my chains like the sea’ or ‘happy as the grass was green’.
  • A metaphor treats an object or person as if it is something else to make the comparison more vivid, as in ‘the force that through the green fuse drives the flower’. If you prefer Churchill to Thomas, Russia is ‘a riddle, wrapped in a mystery, inside an enigma’.
  • Personification goes one step further and treats an inanimate object as if it were a person with human habits, as in ‘It is night, moving in the streets’.
  • An analogy is sometimes just a simple comparison, such as ‘the heart is like a pump’, but it is more often more complicated than that, for instance when it describes a relationship between two things, eg ‘As a dog returns to its vomit, so a fool returns to his folly’.
  • Tone just means ‘tone of voice’, or the way in which you would read a passage. It could be anything from matter-of-fact to lyrical, but one of the most common moods is irony.
    • Irony takes many forms, but a typical example comes from the famous opening line of Jane Austen’s Pride and Prejudice: ‘It is a truth universally acknowledged that a single man in possession of a good fortune must be in want of a wife.’ The joy of this quotation (and irony in general) is that it can mean whatever you want it to mean! To Mrs Bennett (and any other mother who values marrying off her daughters more than anything else in the world), this is a simple statement of fact. To Mr Bennett (and anyone else who believes there are far more important things in life), it is funny because it is such a ridiculous exaggeration.
    • Dramatic irony is a kind of foreshadowing, when the audience or reader knows more than the characters, usually when we are told something in advance. The classic example of this is in a horror film, when we see the axe murderer in the loft, but the blonde cheerleader still climbs the rickety staircase to see what’s wrong. Shouting at the TV won’t do any good – she’s just a victim of dramatic irony.
    • We also use irony to describe a situation that’s the last thing we would expect, such as ‘Water, water, everywhere, | Nor any drop to drink’. Alanis Morissette even wrote a song about it, although her examples are incongruous rather than ironic. Now that’s irony!
  • Rhyme is fairly easy to spot when the ending of one word matches that of another, eg ‘night’ and ‘light’, but it is useful to be able to map out the rhyme scheme of a poem by giving each different sound at the end of a line a different letter, eg the rhyme scheme of a limerick is aabba. There are also a couple of variations that often introduce a discordant note into a lot of 20th century poetry: an eye-rhyme is a pair of words whose endings look the same but sound different, eg ‘wove’ and ‘love’, and a ‘half-rhyme’ involves two words that don’t quite match, eg ‘frowned’ and ‘friend’.
  • The rhythm of a poem is often not obvious, but it’s worth becoming familiar with the two main types of meter, or rhythmical pattern. The first is based on the number of beats to a line. A beat is simply a syllable that is given extra stress, and the obvious example is again the limerick. It doesn’t matter how many syllables the lines have as long as the number of beats is 3, 3, 2, 2 and 3. The second is more common and is based on the number of syllables. Each line is divided into a number of metrical ‘feet’, each of which has one stressed syllable and one or more unstressed syllables in a particular order. Shakespeare wrote almost all his plays and poetry in iambic pentameter, as he thought that best matched the natural rhythm of English. All it means is that there are five feet in each line, each containing an unstressed syllable followed by a stressed one, eg ‘From fairest creatures we desire increase’. You can also have dactylic, trochaic or anapaestic feet if you so desire! A pause in the middle of a line of poetry is called a caesura. Anglo-Saxon poetry was full of them, and even Shakespeare used one in his most famous line: “To be, or not to be, that is the question”. The second syllable of ‘question’ is also an example of what’s called a feminine ending, which just means it’s unnecessary. (No jokes, please!)
  • An allegory is a story that works on two levels. In the days of William Langland’s Piers Plowman, religion was a far greater part of people’s lives, and priests and their congregations would be more familiar with interpreting texts on many different levels: the literal, the metaphorical, the spiritual, the tropological, the anagogical and the allegorical! Just be thankful times have changed…
  • Alliteration is often the simplest technique to identify but the most difficult to talk about. It is simply the repetition of the first letter in two or more words, usually but not always right next to one another, eg ‘Rage, rage against the dying of the light.’ Yes, we know it’s there, but what can we say about it? I’ll leave that for you to decide…
  • Assonance is similar to alliteration, but it’s the vowel sounds that are repeated. The classic examples are from 19th century elocution lessons, such as ‘The rain in Spain falls mainly on the plain’.
  • Onomatopoeia is the choice of words that sound like the actual sounds they represent, such as ‘crash, bang, wallop’.
  • Enjambment describes a line of poetry that doesn’t end with any punctuation, such as a comma or full-stop, eg ‘Now as I was young and easy under the apple boughs | About the lilting house and happy as the grass was green’. It encourages the smooth flow of the words and is the opposite of the usual end-stopped line, which adds an extra beat to the natural pause at the end of the line (and/or stanza). This emphasises whatever happens to be the last word, particularly if that word is part of a rhyming couplet.
  • Rhetoric used to be taught in school way back in ancient Greece, but most people would only recognise a few examples these days. They often have complicated names that come from ancient Greek, but they’re still useful!
    • An oxymoron is a paradox, or something that appears to be a contradiction, such as ‘military intelligence’! It is usually meant as a joke or a surprising truth, but one or two have now become clichés, such as ‘deafening silence’.
    • Hyperbole is another word for extreme exaggeration. As Dylan Thomas once said, “Our discreditable secret is that we don’t know anything at all.”
    • The tricolon or rule of three appeals to a uniquely human habit of listing things in threes. If you want someone to blame for starting it all off, look no further than Julius Caesar, when he arrived in Britain and said ‘veni, vidi, vici’. Translated into English, it means, “I came, I saw, I conquered.” This repetition of the first element of a sentence is called anaphora and helps emphasise the message. If you repeat the last few words instead, it’s called epistrophe.
    • Rhetorical questions are questions that don’t have to be answered – even in class! In one of Shakespeare’s most famous scenes, Romeo answers his own question: “But, soft! what light from yonder window breaks? | It is the east, and Juliet is the sun.” This is called hypophora. Juliet tragically receives no reply to hers: ” O Romeo, Romeo! wherefore art thou Romeo?”.
    • Metonymy or synecdoche is when a part stands for the whole. There are many variations, but an obvious example is ‘the crown’. It is only something the king or queen wears, but it has come to stand for the monarchy or government in general.
    • An anecdote is a story or account of an event used to illustrate a point. It’s often intended to be funny, so the writers can get the audience on their side.
  • Repetition is easy to spot. It’s simply the repeated use of a word or phrase to add emphasis, eg
    ‘Half a league, half a league,
    Half a league onward,
    All in the valley of Death,
    Rode the six hundred.’
  • Diction is the choice of words that a writer makes. Are they long or short? Where do they come from – Latin, French, Anglo-Saxon or elsewhere? What connotations or associations do they have – pleasant or unpleasant, dreamy and romantic or painful and humiliating? In Do Not Go Gentle Into That Good Night, the words are remarkably straightforward and monosyllabic. ‘Gentle’, ‘against’ and ‘dying’ are the only polysyllabic words in the opening stanza, and the simplicity and spare, conversational style of the language is appropriate to the subject of loss and bereavement. Thomas Hardy adopts a similar approach in The Voice, which at one point has 41 monosyllables in a row!
  • Imagery is the use of pictures or other visual comparisons to make a piece of writing more vivid and appeal to our imagination. Thomas’s Fern Hill seems to have more pictures in it than the National Gallery! In the first stanza alone, we are invited to imagine the poet ‘young and easy under the apple boughs | About the lilting house and happy as the grass was green, | The night above the dingle starry’, and later he recalls having ‘the trees and leaves | Trail with daisies and barley | Down the rivers of the windfall light’. The frequent references to things that are ‘green’ and vibrant and the flood of images conjured up by powerful childhood memories make us long for the innocence of youth and the joy of being at one with Nature.
  • A transposed epithet sounds complicated, but it’s just an adjective that’s used to describe the ‘wrong’ noun. ‘Transposed’ means swapped, and ‘epithet’ means a word or phrase used to describe something (like an adjective). Hence, Dylan Thomas writes about ‘the dogs in the wet-nosed yards’ in Under Milk Wood. Obviously, it’s not the ‘yards’ that have the wet noses, but the ‘dogs’!
  • The pathetic fallacy means using the weather or landscape to create an upbeat or downbeat mood. ‘Pathetic’ means to do with emotions while a ‘fallacy’ is something that people believe even though it’s not true, such as the idea that the Earth is flat. We all know that it’s possible to be happy on a rainy day or unhappy on a sunny day, but that’s not how we feel sometimes, and that’s why the pathetic fallacy can be so powerful. Thomas uses it a lot in Fern Hill, telling us, for example, that ‘All the sun long it was running, it was lovely’ when he was young, but the mood changes in the final verse when he starts talking about death, and that’s emphasised by words such as ‘shadow’ and ‘moon’.
  • Sentence structure is the pattern or frequency of long and short sentences and the use of different types of sentences, either simple, compound or complex. Whereas something like a simile or alliteration is easy enough to spot, this is the kind of device that’s not generally obvious on a first or even a second reading, so it’s worth counting the words in each sentence to see what you find. It might just give you a clue to understanding the rhythmic effects that the writer is aiming for. There are only seven sentences in the 54 lines of Fern Hill, and the first has 76 words in it!

These are just a sample of the most important poetic devices. If you’re looking for a way to remember them all, try ‘SHAMPOO’. This is a mnemonic or acrostic that stands for Simile, Hyperbole, Alliteration, Metaphor, Personification, Onomatopoeia and Oxymoron.

If you want to find examples of literature chock-full of poetic devices, try reading a little Dylan Thomas. If ‘the dogs in the wet-nosed yards’ catch your eye, you can congratulate yourself on spotting a rare example of the transposed epithet!

Enjoy…

Sample questions

Can you spot the poetic devices used in the following examples?

  1. bothersome badgers
  2. as flat as a pancake
  3. faster than a speeding bullet
  4. death stalked the land
  5. it’s an oven in here
  6. the trees danced in the wind
  7. how now, brown cow?
  8. the cat in the hat
  9. hiss
  10. “Why, why, why must you do that?”
  11. “What is the most important question facing our country today?”
  12. He had 12 pens in his pencil case, but not one pencil.
  13. the long arm of the law 

     

     

     

    If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.

Story mountains

Whether you’re doing something as easy as climbing Mount Everest or as hard as writing a story, you always need a plan!

One of the ways of planning a story is to use story mountains, with each stage of the tale labelled on the diagram.

The drawing doesn’t have to be any more than a big triangle, but the five stages help to provide a good structure.

However, the story mountain is only part of the process.

Even before the exam, you could invent two or three interesting characters to use or practise telling a particular story – perhaps an old fairy tale in a modern setting.

It’s always good to be prepared, and it’s too late by the time you sit down in the exam hall.

If you’re taking an 11+ or 13+ combined English entrance exam, you should have around half an hour left for the composition after doing the reading comprehension.

The routine to follow includes the following five steps:

  • Title: choose the right title or question
  • Brainstorm: think of ideas
  • Plan: create the story mountain
  • Write: write the story
  • Check: check your work.

Depending on the total length of the exam, you should plan to leave yourself a set amount of time for each stage (shown in brackets, assuming you have a total of 30 minutes).

1. Choose the Right Title
(Less than 1 minute)

Sometimes you won’t be given a choice, but you will always have different options in a proper 11+ English exam.

One might be a description (often based on a drawing or photograph), and another might be a newspaper story or diary, but there will usually be the chance to write a story, either based on a suggested title or in the form of a continuation of the passage from the reading comprehension.

The important thing here is to try to find a topic you know a bit about and – in an ideal world – something you’d enjoy writing about.

If you’ve never ridden a horse, it would be pointless trying to write a story all about horse racing, and it would probably be pretty boring!

2. Brainstorm Ideas
(5 minutes)

Some pupils go straight into writing the story at this point. Big mistake!

You have to give yourself time to come up with the best possible ideas, and you certainly won’t make it easy for yourself to structure the story if you don’t have a plan to help you.

Whether in business or at school, the best way of coming up with ideas is to spend some time brainstorming.

That means coming up with as many ideas as possible in a limited time.

There’s no such thing as a bad idea, so try to think positively rather than crossing out anything you don’t like.

It takes time to come up with well-thought-through ideas for a story, so be patient, and don’t just go for the first one you think of.

That’s like walking into a shop and buying the first pair of trousers you see: they might not be the right size, colour, design or price, so you have to browse through the whole range.

Try to come up with at least two ideas so that you can pick the best one. Just make sure it’s believable!

If you’re having trouble, think about the different elements you can change: the plot, the characters, the setting, the period and the genre.

Those are the basics, and imagining a particularly good character or setting might just provide the clue you’re looking for. You can always change what kind of story it is. A thriller will look a lot different from a romance or a comedy!

3. Create a Story Mountain
(5 minutes)

Once you’ve decided on an idea, you can create your story mountain.
You don’t actually have to draw a mountain or a triangle, but you do need to map out the five main stages of the story.

You don’t need to write full sentences, just notes that are long enough to remind you of your ideas. Try to use five or six words for each section (using your heroes’ initials and missing out ‘filler’ words such as ‘the’ and ‘an’), such as ‘M frees dog from fence’ or ‘Shark bites F in leg’.

Just remember that the opening has two parts to it, so your story will have six main paragraphs, not five—although that doesn’t include any lines of dialogue, which should be in separate paragraphs.

Continuations

If you’re doing an exam paper that includes a comprehension as well as a composition, you might be asked to continue the story from the comprehension passage.

In that case, your story mountain will have to be a bit different. You obviously won’t be able to choose your own main character, so you’ll have to take out your usual description and decide which of the characters in the passage is going to be your hero instead.

In addition, you won’t be able to start with the opening section because you’re supposed to be continuing the story. So what should you do?

It’s probably best to think about the printed text and your continuation as one long story. Try and decide which bits of your story mountain have already been covered in the passage and then plan your own story from there.

For example, you might treat the passage as just the opening, in which case your story mountain would start from the build-up. Alternatively, you might think that the text includes the opening, build-up and problem, in which case you’d start with the solution.

However, this is only a guideline, and you might not always be able to make it work. If the printed text is very long and only contains the opening, for instance, you’d have to write thousands of words to keep all the sections roughly the same length!

The main thing is to use your common sense and come up with the best plan you can. Don’t just wing it!

In addition, it’s important to keep to the style of the original text and make sure the characters behave in the same ways. Your goal is to try and carry on the story just as the author would’ve done, and you’ll be marked on how well you can do that.

A. Opening (or Introduction)

The best way to open a story is probably to start ‘in the middle’.

Most fairy stories start with something like this:

Once upon a time, there lived a beautiful princess with long, golden hair. Esmeralda was madly in love with Prince Charming, but her wicked stepmother kept her locked up in a tower a thousand feet above the valley below…

The trouble with this kind of description of the characters and their situation (‘exposition’) is that it’s just a bit boring!

Nothing actually happens.

Far better to think of the most exciting moment in your story and start from there:

“Aaaaaaagggghhh!!!” screamed Prince Charming as his fingers slipped from Princess Esmeralda’s icy window ledge and he fell a thousand feet to his death…!

Another approach is to create a sense of mystery by keeping something important from the reader, such as the location or the identity of the main character. This is called the ‘delayed drop’.

Once you’ve written a paragraph or so grabbing the reader’s attention, you can then introduce the main characters, where they live, when the story is set and so on.

That means the opening needs two paragraphs:
1. Grab the reader’s attention
2. Describe the main character

Why do you need to describe your heroes?
Well, the more the reader knows about them, the more they can imagine what they look like, how they sound like and how they might behave in certain situations.

That leads to sympathy, and sympathy is important because the reader has to care about the heroes in order for stories to be exciting.

So how should you describe them?

Here’s a quick list of the major details in roughly the right order:
1. Name
2. Age
3. Job or school
4. Looks (including eye colour, hair colour and style, height, build, skin tone and favourite clothes)
5. Home
6. Friends and family
7. Personality and interests
8. USP or ‘Unique Selling Proposition’ – something that makes the characters special and readers want to read about them.

You can be as detailed or as general as you like about some of these things, but giving more detail is usually better as it helps paint a picture in the reader’s mind.

Your hero’s home, for instance, could just be ‘London’, or it could be ‘the famous Blue Cross lighthouse on the promontory overlooking Shark Bay in Antigua’!

Overall, you should probably be writing eight to 10 lines of A4 for the whole description.

You can save yourself time by thinking up, say, three ‘off-the-shelf’ characters and memorising them (see article). One of my clients even helped her son by using AI to turn his characters into pictures!

B. Build-up (or Rising Action)

The build-up should describe what the main character is trying to do.
For instance, is he or she robbing a bank, escaping from prison or fighting off an alien invasion?

C. Problem (or Climax or Dilemma)

Every story needs drama, which is really just conflict.
If you show what the hero’s trying to do in the Build-up, the Problem is just what gets in the way.

It might be guilt at leaving a friend behind, say, or a prison warder spotting the escaping convicts or a searchlight lighting up the yard.

Whatever it is, it’s a problem that needs to be solved.

D. Solution (or Resolution or Falling Action)

The solution to the problem is what the hero tries to do to fix it.
It may not work, but it’s usually the best option available.

E. Ending (or Outcome)

Not many 10-year-old boys like happy endings, so the plan doesn’t always have to come off!
If you want your hero to die in a hail of bullets like Butch and Sundance, that’s up to you.
Another way to end a story is to use a ‘cliffhanger’.

In the old days, that meant the hero of a TV serial might literally be hanging on to the edge of a cliff, and the viewer would obviously have to ‘tune in next week’ to find out if he managed to hold on or not.

These days, it just means adding another mystery or problem that needs to be fixed.

For example, the hero could escape from prison…only to find a police car chasing him!

Finally, you could always have a ‘twist in the tale’, in which the good guy turns out to be a bad guy, for example.

It doesn’t take long to write – just a sentence or two – but it’s a great way to leave readers scratching their heads and thinking, “Wow! I never saw that coming…”

4. Write the Story
(15 minutes or more, depending on the length of the exam)

Now for the important bit!

Stick to the Plan

The most important thing to remember is to stick to the plan!

It’s very tempting to get carried away when you’re writing and follow wherever your imagination leads you, but the downside is that your story probably won’t have a proper beginning, middle and end, and you might run out of time trying to get the plot back on track.

Don’t Leave Loose Ends

A good story will have narrative tension. In other words, it will be exciting.

Part of that involves doubt about whether your heroes will succeed or not, and that’s where the ‘good’ questions come in.

If readers are asking themselves questions like “Will the hero escape?” or “Will the hero survive?”, then you’re doing your job as a writer.

Those are ‘good’ questions because they get to the heart of what the story is all about and keep your readers guessing.

Excitement comes from uncertainty and doubt, so you want your readers to wonder what’s going to happen.

Look at it another way: imagine if they didn’t ask themselves any questions at all. That’s basically the same as saying they’d be bored stiff!

However, you don’t want them to be asking ‘bad’ questions. These are the loose ends that crop up if you don’t give good enough explanations for your characters’ actions or abilities.

For example, if your hero is robbed and tries to solve the crime on his own, the obvious loose end is why he didn’t call the police.

Alternatively, if your hero has a special power like being able to read minds, you either need to explain where it came from (like Spiderman being bitten by a radioactive spider) or admit that it’s somehow ‘mysterious’ so that your readers can stop worrying about it.

Balance the Three Ds

You should also strike a balance between the Three Ds: Drama, Description and Dialogue.

Every story has a plot, so drama will always be there, but a lot of pupils focus so much on what’s happening that there is very little if any description or dialogue.

Readers want to imagine what people look like and how they feel, so you have to give them something to go on.

People also generally have a lot to say when they get emotional or find themselves in tough situations, so you won’t be able to capture that unless they talk to one another in your story.

Show off Your Vocabulary

This is also a chance to show off your vocabulary.

Including a few ‘wow words’ (or ‘golden words’) such as ‘cerulean’ instead of ‘blue’ will impress the examiner no end – as long as you know how to spell them!

Use Energetic Verbs

You can create energy in different ways, but choosing powerful verbs is a good way to appeal to the imagination and show part of someone’s character along the way. For example, if a kid is greedy, you could say ‘he picked up the slice of chocolate cake’, but saying ‘he grabbed the slice of chocolate cake’ suggests he just wants to stuff his face!

Use the Active Voice

You can either use the passive or active voice. The passive voice shows something happening to someone; the active voice shows someone doing something. For example, ‘he was hit by Mark’s shovel’ is passive, but ‘Mark hit him with the shovel’ is active.

As you can probably see from this example, the active voice is better at showing power and intention. Writing that someone ‘was hit’ almost suggests it was an accident, but ‘Mark hit him’ shows exactly what happened and whose fault it was!

Use Poetic Devices

What’s the difference between ‘in the evening’ and ‘on a night as black as a murderer’s soul’?

If you think one of these is a little bit more descriptive and atmospheric than the other, then why not use poetic devices or literary techniques in your own writing?

Just make sure the comparison is appropriate. If you’re telling a story set on the south coast of England, don’t say someone swam ‘as fast as a cheetah’. Cheetahs live in mainland Africa, so they have nothing to do with Britain or the sea. Instead, you could say he swam ‘as fast as a dolphin’.

It’s hard to think of good poetic devices, but you’ll get higher marks if you avoid common clichés like ‘as flat as a pancake’ and use something rarer, like ‘as silent as a shadow’.

I’ve written an article on them if you want to find out more, but the most common ones are these:

  • Simile
  • Metaphor
  • Personification
  • Alliteration
  • Onomatopoeia
  • Repetition
  • Rhetorical questions
  • Imagery
  • Sentence structure (ie long and short sentences or simple, complex and compound sentences)

If you want a handy way of remembering them, you can use SMARPOPS, which stands for Simile, Metaphor, Alliteration, Rhetorical question, Personification, Onomatopoeia, Punctuation and Speech. These are the most common poetic devices (if you ignore the final two items!).

Alternatively, SHAMPOO stands for Simile, Hyperbole, Alliteration, Metaphor, Personification, Onomatopoeia, and Oxymoron.

Show, Don’t Tell

Whether you’re describing characters or the environment, it’s better to show rather than simply tell the reader. Telling is lazy, but showing engages your readers and makes them part of the experience, letting them use their imagination to work out what’s going on rather than spoon-feeding them every detail.

For example, it’s easy to say a character ‘was a keen walker’, but it would be better to say she ‘hiked six miles of the Appalachian Trail every weekend’. Equally, rather than describe someone, you could use dialogue instead. Rather than say ‘he was tired’, his best friend could say, “You look like you were up all night!” Another way is to suggest something and then surprise the reader later in the story. For instance, you could describe a black-and-white poster of an old boat on a girl’s bedroom wall but only reveal she’s an expert yachtswoman when she has to sail across the bay to rescue someone!

One way of looking at it is to imagine that you’re directing a film rather than writing a story. In films, you hardly ever hear a narrator telling you what’s going on. You’re simply shown everything you need to know. You might see someone’s breath on a cold night, for example. If you want to do the same when writing a story, you can make your description much more vivid (and alliterative!) by saying ‘Frank’s breath formed frozen clouds in front of his face’.

A similar trick is to leave out the answers to questions. This is something screenwriters do all the time to keep the audience in suspense! “What are you going to do to get your revenge?” one character asks another, but you’ll have to wait to find out…!

Appeal to the Senses

It’s easy to forget to describe a scene during a story, but that means readers can’t imagine it and so won’t feel as if they were actually there. One way to make your descriptions more vivid and memorable is to appeal to the five senses:

  • Sight
  • Smell
  • Hearing
  • Taste
  • Touch

You don’t have to use them all, but try picking the most important ones. Obviously, you need to show what the setting looks like, but if it’s a coffee shop, for instance, you could say ‘she inhaled the aroma of freshly brewed espressos’.

5. Check Your Work (4-5 minutes)

If there’s one tip that beats all the rest, it’s ‘Check your work’.

However old you are and whatever you’re doing, you should never finish a task before checking what you’ve done.

However boring or annoying it is, you’ll always find at least one mistake and therefore at least one way in which you can make things better.

In the case of 11+ or 13+ exams, the most important thing is to test candidates’ imagination and ability to write an interesting story, but spelling and grammar is still important.

Schools have different marking policies.

Some don’t explicitly mark you down (although a rash of mistakes won’t leave a very good impression!), some create a separate pot of 10 marks for spelling and grammar to add to the overall total and some take marks off the total directly – even if you wrote a good story.

Either way, it pays to make sure you’ve done your best to avoid silly mistakes.

If you think you won’t have time to check, that’s entirely up to you.

You’ll almost certainly gain more marks in the last five minutes by correcting your work than trying to answer one more question, so it makes sense to reserve that time for checking.

If you do that, there are a few simple things to look out for.

You may want to make a quick checklist and tick each item off one by one.

Spelling

This is the main problem that most Common Entrance candidates face, but there are ways in which you can improve your spelling.

Firstly, you can look out for any obvious mistakes and correct them.

It can help to go through each answer backwards a word at a time so that you don’t just see what you expect to see.

Secondly, you can check if a word appears anywhere in the text or in the question.

If it does, you can simply copy it across.

Finally, you can choose another, simpler word.

If you’re not quite sure how to spell something, it’s often better not to take the risk.

Capital Letters

This should be easy, but candidates often forget about checking capitals in the rush to finish.

Proper nouns, sentences and abbreviations should all start with capital letters.

If you know you often miss out capital letters or put them where you don’t belong, you can at least check the beginning of every sentence to make sure it starts with a capital.

Punctuation

This simply means any marks on the page other than letters and numbers, eg full-stops, commas, quotation marks, apostrophes and question marks.

Commas give almost everybody problems, but you can at least check there is a full-stop at the end of every sentence.

Other Grammar

It’s always useful to read through your story to make sure everything makes sense.
It’s very easy to get distracted the first time around, but it’s usually possible to spot silly mistakes like missing letters or missing words on a second reading.

And that’s it! I hope these tips on story mountains will help.

Quiz

Test yourself on what you’ve learned about story mountains from this article!

  1. What are the five steps to writing a story?
  2. What are the five stages of a story mountain?
  3. How many main paragraphs should be in your story?
  4. How do you know which title to pick?
  5. What’s wrong with using the first idea you think of?
  6. What are the Three D’s?
  7. What are five different poetic devices?
  8. What should you check your work for?

Sample Titles

Try going through the whole five-step process to write a story based on the following choice of titles (all but one taken from actual 11+ papers):

Left Behind

A Summer’s Day

Saying Sorry

The Lie

The Race

Lost Boy

A Fresh Start

The Voice in the Darkness

Noah’s Ark

Smoke

Silence

The Hot Afternoon

My Father Was Furious

The Swimming Lesson

Caravanning

The Choice

The Garden

Sleeping

Twins

Junk Food

The Picnic by The Lake

A Gift

Great Things Come from Small Beginnings

Saying Goodbye

The Person in The Queue

Through The Window

The Photograph

The Long Hot Summer

The Joke

The Loner

The Dare

The First Day of Term

Crossing The Line

Weird Habits

Mirror

Show And Tell

Going Underground

Echo

A Visit from Uncle

‘The room was so quiet that I noticed the clock ticking’
(Write a story that opens with this sentence.)

‘Every day, she sat alone by the upstairs window.’
(Write a story that opens with this sentence.)

‘Nobody’s perfect.’
(Write a story that uses this as its final line.)

Model Answer

Here are two stories created by Open AI’s ChatGPT chatbot entitled The Ghost from the Future.

Version 1

The ghost from the future appeared out of nowhere on a dark and stormy night. It was a transparent figure, translucent and ethereal, with eyes that glowed like embers in the night. It drifted silently through the streets, its movements flowing and graceful, as if it were weightless and without substance.

As it moved, the ghost left a trail of frost in its wake, coating everything it touched with a thin layer of ice. People who crossed its path recoiled in fear, feeling a chill run down their spine as the ghost seemed to look straight through them.

No one knew where the ghost had come from, or why it was here. Some whispered that it was a harbinger of death, sent to collect the souls of the doomed. Others believed it was a lost spirit, trapped between worlds and unable to find its way to the afterlife.

Despite the fear it caused, the ghost from the future continued to haunt the town, appearing at random intervals and in unexpected places. No one knew how to stop it, or even if it could be stopped. All they could do was wait and hope that it would eventually move on.

One day, a brave young man named Jack decided to confront the ghost. He gathered his courage and followed it into the woods, determined to discover its true nature and purpose.

As he pursued the ghost, Jack realized that it was moving towards a decrepit old house on the edge of town. He followed it inside, and was shocked to find that the ghost was leading him to a hidden room in the basement.

Inside the room, Jack found a strange and ancient machine. It was covered in dust and cobwebs, and looked as if it had not been used in centuries.

The ghost from the future stood beside the machine, gesturing for Jack to approach. As he drew closer, the ghost spoke in a whispered voice that seemed to come from everywhere and nowhere at once.

“This is a time machine,” the ghost said. “It was built by a madman who sought to change the course of history. But he was stopped before he could use it, and now it lies here, forgotten and abandoned.”

“What does this have to do with me?” Jack asked.

“You have been chosen to travel into the future,” the ghost replied. “You must go and see what has become of the world, and bring back knowledge that will help us to prevent a terrible fate.”

Jack hesitated, unsure if he was ready for such a daunting task. But the ghost from the future was insistent, and in the end, he agreed to go.

He stepped into the time machine, and with a flash of light and a wave of dizziness, he was whisked away into the future.

What he found there was a world unlike any he had ever seen. The cities were filled with towering skyscrapers and flying cars, and the streets were crowded with people of all shapes and sizes.

But there was also a sense of dread and darkness that hung over everything. The air was thick with pollution, and the sky was a sickly shade of green.

Jack soon discovered that the world was on the brink of disaster. Climate change had wreaked havoc on the planet, and the oceans were rising at an alarming rate. Many species of animals and plants had gone extinct, and the air was toxic to breathe.

With the help of a group of rebels who were fighting against the ruling government, Jack set out to uncover the truth about what had happened to the world…

Version 2

The ghost from the future was a strange and eerie presence that no one could explain. It appeared out of nowhere, in the dead of night, and always seemed to be watching. It had a pale, transparent face and cold, dead eyes that seemed to see right through you.

People whispered that it was the ghost of someone who had died in a terrible accident, or perhaps a victim of a crime. Some even said it was a warning from the future, a glimpse of what was to come if things didn’t change.

No one knew for sure, but one thing was certain: the ghost from the future was a chilling reminder that the past was never truly gone, and the future was always lurking just around the corner.

As the ghost continued to haunt the town, people began to fear for their safety. They locked their doors at night and avoided going out after dark. But despite their best efforts, the ghost from the future always seemed to be one step ahead, appearing at the most unexpected times and places.

One day, a young girl named Emily was walking home from school when she saw the ghost from the future standing in the middle of the road. She tried to run, but the ghost was too quick. It reached out with its cold, bony hand and touched her on the shoulder.

In that moment, Emily felt a strange sensation wash over her. She felt as if she was being pulled into the future, and she saw visions of what was to come. She saw wars and disasters, but she also saw moments of great happiness and love.

When the vision ended, Emily was back in the present, but she was different. She had a newfound sense of purpose, and she knew what she had to do. She had to warn the people of her town about the dangers of the future, and do everything she could to help them prepare for what was to come.

With the help of the ghost from the future, Emily began to spread the word. She held meetings and organized events, and slowly but surely, people began to listen. They started to take action, and the town began to change for the better.

Thanks to Emily and the ghost from the future, the people of the town were able to face the future with hope and courage, knowing that they were ready for whatever came their way.

 

 

 

 

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Shortcuts

There is always more than one way of solving a Maths problem. That can be confusing, but it can also be an opportunity – if only you can find the right trade-off between speed and accuracy.

I’ve taught a lot of QTS numeracy candidates recently, and the Maths itself isn’t particularly difficult, particularly in the mental arithmetic section.

The trick is to be familiar with all the possible shortcuts and capable of using the right one at the right time. It may mean having to do more sums, but it will be much simpler and quicker in the long run. You don’t have to use all of these all the time, but it is useful to know what they are just in case you need them.

  • Multiplying and dividing by 5
    The most useful shortcut I’ve come across is very simple. To multiply by 5, try multiplying by 10 and then dividing by 2 (or vice versa), eg
    13 x 5
    = 13 x 10 ÷ 2
    = 130 ÷ 2
    = 65
    You have to do two sums rather than one, but the point is that you should be able to save time and improve the chances of getting the answer right by doing both in your head rather than having to work out a more difficult sum on paper.
    You can divide by 5 in a similar way by multiplying by 2 and dividing by 10 (or vice versa), eg
    65 ÷ 5
    = 65 x 2 ÷ 10
    = 130 ÷ 10
    = 13
    You can do a similar trick with 50, 500 etc simply by multiplying or dividing by a higher power of ten.
  • Chunking
    If you have to multiply by a two-digit number outside your times tables, chunking is an easy way to do the sum in your head. Instead of writing it down on paper and using long multiplication (which would take a long time and is easy to get wrong!), try multiplying by the tens and the units separately and adding up the results, eg 16 x 15 = 10 x 15 + 6 x 15 = 150 + 90 = 240. The numbers might still be too tricky to do it comfortably, but it’s often worth a try.
  • Rounding
    To avoid sums with ‘tricky’ numbers, try rounding them up to the nearest ‘easy’ figure and adjusting at the end. This is particularly useful when working out start and end times, eg
    ‘The morning session in a school began at 09:25. There were three lessons of 50
    minutes each and one break of 20 minutes. At what time did the morning session end? Give your answer using the 24-hour clock.’
    If you assume the lessons last an hour, you can add three hours to 09:25 to get 12:25. You would normally then knock off 3 x 10 = 30 minutes, but the 20-minute break means you only need to subtract 10 minutes, which means the session ended at 12:15.
  • Money problems
    There is often a ‘real-world’ money problem in the QTS numeracy test. That usually means multiplying three numbers together. The first thing to say is that it doesn’t matter in which order you do it – 1 x 2 x 3 is just the same as 3 x 2 x 1. The next thing to bear in mind is that you will usually have to convert from pence to pounds. You could do this at the end by simply dividing the answer by 100, but a better way is to divide one of the numbers by 100 (or two of the numbers by 10) at the beginning or turn multiplication by a fraction of a pound into a division sum, eg
    ‘All 30 pupils in a class took part in a sponsored spell to raise money for charity. The pupils were expected to get an average of 18 spellings correct each. The average amount of sponsorship was 20 pence for each correct spelling. How many pounds would the class expect to raise for charity?’
    The basic sum is 30 x 18 x 20p, and there are a couple of ways you could do this:
    1) Knock off the zeroes in two of the numbers, change the order of the numbers to make it easier and double and halve the last pair to give yourself a sum in your times tables, ie
    30 x 18 x 20p
    = 3 x 18 x 2
    = 3 x 2 x 18
    = 6 x 18
    = 12 x 9
    = £108
    2) Convert pence into pounds, turn it into a fraction, change the order of the numbers, divide by the denominator and, again, double and halve the last pair to give yourself a sum in your times tables, ie
    30 x 18 x 20p
    = 30 x 18 x £0.20
    = 30 x 18 x ⅕
    = 30 x 18 ÷ 5
    = 30 ÷ 5 x 18
    = 6 x 18
    = 12 x 9
    = £108
  • Percentages
    Many students get intimidated by percentages, fractions and decimals, but they are all just different ways of showing what share you have of something. You will often be asked to add or subtract a certain percentage. The percentage will usually end in zero (eg 20%, 30% or 40%), so the easiest way is probably to find 10% first. That just means dividing by 10, which means moving the decimal point one place to the left or, if you can, knocking off a zero. Once you know what 10% is, you can simply multiply by 2, 3 or 4 etc and add or subtract that number to find the answer, eg
    ‘As part of the numeracy work in a lesson, pupils were asked to stretch a spring to extend its length by 40 per cent. The original length of the spring was 45 centimetres. What should be the length of the extended spring? Give your answer in centimetres.’
    You need to find 40% of 45cm, so you can start by finding 10%, which is 45 ÷ 10 or 4.5cm. You can then multiply it by 4 to find 40%, which is best done by doubling twice, ie 4.5 x 2 x 2 = 9 x 2 = 18. Finally, you just add 18cm to the original length of the spring to find the answer, which is 45 + 18 = 63cm.
  • Common fractions
    An awful lot of questions involve converting between fractions, percentages and decimals. There is a proper technique for doing any of those, but it’s very useful if you learn the most common fractions and their decimal and percentage equivalents by heart, eg
    ½ = 0.5 = 50%
    ¼ = 0.25 = 25%
    ¾ = 0.75 = 75%
    ⅕ = 0.2 = 20%
    ⅖ = 0.4 = 40%
    ⅗ = 0.6 = 60%
    ⅘ = 0.8 = 80%
    ⅛ = 0.125 = 12.5%
    ⅜ = 0.375 = 37.5%
    ⅝ = 0.625 = 62.5%
    ⅞ = 0.875 = 87.5%
  • Times tables
    There are far more multiplication questions in the QTS numeracy test than any other kind, so it’s very important to know your times tables inside out. Some pupils are taught to memorise only the results, eg 4, 8, 12… etc. This is catastrophic! If you have to go through the whole table to find the answer, counting off the number of fours on your fingers, you can’t save yourself any time at all. The proper way is to learn the whole sum, eg 1 x 4 is 4, 2 x 4 is 8, etc (or 1 4 is 4, 2 4s are 8, etc). That way, the answer to any question in your times tables will pop into your head as soon as you’ve heard it. One good way of learning your tables is to time yourself using the stopwatch function on your iPhone. If you press ‘Lap’ after you’ve recited each table, you can write down your times and work out which tables you need to practise. Once you’re confident, you can make certain sums fit into your times tables by doubling one number and halving the other, eg
    3 x 24
    = (3 x 2) x (24 ÷ 2)
    = 6 x 12
    = 72
    Alternatively, you can halve just one of the numbers and double the result, eg
    24 x 9
    = 12 x 9 x 2
    = 108 x 2
    = 216
  • Multiplying by 4
    If you have to multiply by 4 and the number is not in your times tables, a simple way to do it is to double it twice, eg
    26 x 4
    = 26 x 2 x 2
    = 52 x 2
    = 104
  • Multiplying by a multiple of 10
    If you have to multiply by a multiple of 10, such as 20 or 30, try knocking the zero off and adding it in again afterwards. That way, you don’t have to do any long multiplication and, with any luck, the sum will be in your times tables, eg
    12 x 30
    = 12 x 3 x 10
    = 36 x 10
    = 360
  • Multiplying decimals
    This can be a bit confusing, so the best way of doing it is probably to ignore any decimal points, multiply the numbers together and then add back the decimal point to the answer so that you end up with the same number of decimal places as you had in the beginning, eg
    0.5 x 0.5
    = 5 x 5 ÷ 100
    = 25 ÷ 100
    = 0.25
  • Using the online calculator
    The second section of the QTS numeracy test consists of on-screen questions that can be answered using an online calculator. This obviously makes working out the answer a lot easier, and shortcuts are therefore less useful. However, just because the calculator’s there doesn’t mean you have to use it, particularly for multiple-choice questions. If you have to add up a column of cash values, for example, and compare it with a number of options, you could simply tot up the number of pence and pick the option with the right amount. Alternatively, the level of accuracy needed in the answer may give you a helping hand if it rules out all but one of the possible answers, eg 6 ÷ 21 to one decimal place is always going to be 0.3. Why? Well, it’s a bit less than 7 ÷ 21, which would be a third or 0.3 recurring. An answer of 0.4 would be more than that, and 0.2 would be a fifth, which is far too small, so it must be 0.3.
  • Don’t do more than you have to!
    There are several types of questions that could tempt you into doing more work than you need to do. If you’re trying to work out how many tables you need at a wedding reception for a given number of guests, the answer is always going to need rounding up to the next whole number, so you don’t need to spend any time working out the exact answer to one or two decimal places. Equally, some numbers are so close to being an ‘easy’ number that you don’t need to add or subtract anything after rounding up or down to make the basic sum easier, eg
    ‘For a science experiment, a teacher needed 95 cubic centimetres of vinegar for each pupil. There were 20 pupils in the class. Vinegar comes in 1000 cubic centimetre
    bottles. How many bottles of vinegar were needed?
    If you round 95cc to 100cc, the answer is 20 x 100 ÷ 1000 or 2 bottles, and the remainder, consisting of 20 lots of 5cc of vinegar, can safely be ignored. 

     

     

     

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Remember the Iceberg!

To pass Common Entrance, you have to remember the iceberg.

Only a small part of any iceberg is visible above the waves, and only a small part of any answer to a question is visible in the text.

To discover the rest, you have to ‘dive in’ deeper like a scuba diver…

There are two main types of English question at 11+ and 13+: reading comprehension and composition.

Most 11+ papers last an hour or an hour and a quarter, and the marks are equally divided between the comprehension and the composition. That means half an hour or so for the comprehension.

The 13+ exam is a little different and may involve two papers, one covering a prose comprehension and the other a poetry comprehension and a story.

Whatever the format, it’s important to read the instructions on the front cover. They will tell you exactly what you have to do and – crucially – how much time to spend on each section.

When it comes to doing a comprehension, I recommend a five-step process:

  1. Read the passage
  2. Read the questions
  3. Read the passage again
  4. Answer the questions
  5. Check your work.

Read the Passage
(5 mins)

The text is usually taken from a short story, a novel or a poem.

Whatever it is, the most important thing to do is to make sure you understand it and remember the main points.

Don’t just read it as fast as you can to get it over and done with, but take your time and read it as if you were reading aloud.

Make sure you read the title and any introduction. They might include important information and background to make it easier to understand what follows.

If you don’t understand any of the words, re-read it first and then look at the context.

For example, it might say there are dozens of ‘delphiniums’ in the garden.

You might not know what delphiniums are, but it’s pretty obvious they must be plants or flowers!

To make sure you’ve got the main points of the story, it’s a good idea to ask yourself the W questions at the end:

  • Who are the characters?
  • What are they doing?
  • Where is the story set?
  • When is it set?
  • Why are they doing what they’re doing?
  • How are they doing it?

It might help to tell yourself the story (very briefly!) – just to make sure everything makes sense.

Read the Questions
(1 min)

Once you’ve read the passage, it’s time to read the questions so that you know what to look out for when you read the passage a second time.

Again, understanding and remembering them are more important than sheer speed.

If it helps, you can ask yourself how many questions you can remember after you’ve read them.

Alternatively, you can underline key words and phrases in the questions to help you focus on what you have to do.

Read the Passage Again
(5 mins)

Reading the text twice is probably a good compromise between speed and memorability.

It also gives you the chance to underline or highlight the answers to any of the questions you happen to find.

Some people suggest only reading the passage once, but that means you wouldn’t know it well enough to answer any questions off the top of your head.

If you can’t do that, you’ll end up having to hunt through the text for the answers, so you’ll have to read most of the passage three or four times anyway!

Answer the Questions
(15-30 mins, depending on the length of the exam)

If it’s a 30-minute exam, you should have around 15 minutes to write down the answers to the questions. (If it’s a 45-minute or hour-long exam, you’ll obviously have a bit longer.)

There are usually 25 marks available, which means around 30 seconds per mark.

The number of marks available for each question will tell you how much time you have to do each one, eg two minutes for a four-mark question.

To get the best possible mark, you clearly need to get the answers right, but you also need to phrase them in the right way and avoid wasting any time.

Here are a few pointers…

Approach Each Question in the Same Way

Try to be consistent in the way you approach each question, and make sure you do all the things you need to do:
a) Read the question carefully.
b) Read it again (and again!) if you don’t understand it.
c) Check the mark scheme to work out how many points and pieces of evidence you need.
d) Scan the text to find the answer, underlining any words you might need.
e) Write down the answer.
f) Read it through to make sure you’ve actually answered the question correctly and you haven’t made any silly mistakes.

Read the Question Carefully

You’re never going to get the right answer to the wrong question, so make sure you understand exactly what you need to do.

If that means reading the question two or three times, then that’s what you’ll have to do.

Use the Mark Scheme as a Guide

Most exam papers will let you know the number of marks for each question, so you should bear that in mind when writing your answers.

There’s no point spending ten minutes on a question that’s only worth one mark, and it would be daft to write only one sentence for a question worth ten marks.

You should also try and work out how many ‘points’ and pieces of ‘evidence’ you’re being asked for:

  • A point is the basic answer to a question, and it might be a fact, a reason or an explanation.
  • A piece of evidence is usually a quotation that backs up whatever point you’re trying to make.

Working out the mark scheme can be a bit tricky as there are three possibilities for the breakdown of marks:

  1. Points only
  2. Evidence only
  3. Points and evidence

You just have to read the question and see what makes the most sense.

Here are a few tips:

  • If the question asks you to ‘refer to the text’ in your answer, that’s code for saying you need evidence.
  • If the question asks you to explain a quotation, that means you’ll just need points because they’ve already given you the evidence. Try making a point for every keyword in the quotation.
  • If there’s an odd number of marks, you probably won’t need to provide a mixture of points and evidence. In that case, you’d end up with a point without any evidence or evidence without any point!

Once you’ve worked out how many points and pieces of evidence you need, it might help to write down the matching number of P’s and E’s and cross them off as you find them in the text and/or include them in your answer.

Follow any Instructions to the Letter

All these hints and tips are useful, but they are only general rules.

Occasionally, examiners will let you off the hook and tell you that you don’t need to use full sentences, eg for the meanings of words.

Just be sure to follow what they say.
If you’re told to answer a question ‘in your own words’, that means you can’t use any of the words in the text.

The only exceptions are ‘filler’ words such as ‘the’ and ‘of’ or words that don’t have any obvious alternative, eg ‘football’ or the names of the characters.

You need to show that you understand the passage, and you’ll actually be marked down for using quotations – even though that’s what’s usually needed.

Look in the Text

Even if you read the text twice, you can’t possibly expect to remember the answers to all the questions and all the quotations to back them up!

The answer is always in the text, so don’t be afraid to spend a few seconds going back over it. That way, you can make sure you get the answer right and support it with the right evidence.

One way of speeding up your search is to work backwards through the text to find the word(s) you’re looking for. Yes, it sounds daft, but if you scan the text forwards, it’s very tempting to read every word properly – which just slows you down.

Answer the Actual Question

I often see pupils writing down facts that are true but don’t actually answer the question.

For instance, if the question asks how Jack feels after losing his dog, it’s no use writing, “He’s crying.” That’s not a feeling.

It’s a bit like writing “2 + 2 = 4”. Yes, that may be true, but it’s completely irrelevant!

Use Full Sentences

Even if a question is as simple as ‘What is Jack’s dog’s name?’, the answer should be ‘His name is Rover’ rather than just ‘Rover’.

The only time you don’t need to use a full sentence is either if it’s the meaning of a word or if the question gives you special permission. It might say something like ‘you don’t need to use full sentences’, or it might just ask for a particular word, such as an adjective or someone’s name. In that case, you shouldn’t have to use a full sentence – but it is a bit of a grey area!

Make Sure any Word Meanings Work in Context

Even the simplest words sometimes have different meanings, so you can’t know which one is the right one just by reading the question. You need to check the context by looking back at the passage. For example, ‘bark’ can be the sound a dog makes or the outside of a tree!

You also need to make sure your answer is the right part of speech, such as a noun or an adjective. Synonyms are always the same part of speech, so the meaning of an adjective will never be a noun or a preposition!

Nouns also vary in number, and verbs vary in tense and person, so it’s easy to lose marks by putting down ‘destroy’ rather than ‘destroys’, say.

The best way to make sure you’ve got exactly the right answer is by putting it back in the original sentence and checking that it means the same thing. For example, if the question asked, “What does annihilated mean in line 13?”, you’d have to think of your answer and put it into the sentence instead of the word annihilated.

Suppose the sentence was, “Alexander the Great annihilated the Persian army.” If you chose ‘destroyed’, that would be fine, because “Alexander the Great destroyed the Persian army” means the same thing. However, it wouldn’t work to say ‘destroy’ or ‘it means to destroy something’ because those wouldn’t fit.

Don’t Use PEE (Point, Evidence, Explanation)

PEE is designed to help you write essays rather than do a comprehension.

At Common Entrance, it’s unlikely a question will ask you for a point, a piece of evidence and an explanation.

That would mean two points and only one piece of evidence, which is unbalanced.

It’s also confusing because it suggests that an ‘explanation’ is somehow different from a ‘point’.

This is not true: points can be explanations as well as facts.

Answer ‘How’ Questions by Talking About Language

Comprehensions often start with a simple one-mark question such as ‘In what country is this passage set?’ This is a ‘what?’ question, a question about content, about facts.

However, there is another kind of question, the ‘how?’ question, which is all about language.

Suppose you’re asked, ‘How does the writer explain how Jack feels after losing his dog?’ What do you have to do?

What you definitely shouldn’t do is just describe how he feels.

The question is not ‘What are Jack’s feelings?’

You’re not being asked for facts but for an analysis of the techniques the author uses.

If it helps, you can keep a mental checklist and look for each technique in the passage:
a) Poetic devices
How has the author used metaphors, similes, diction or sentence structure?
b) Parts of speech
What can you say about the kind of adjectives, verbs or adverbs used in the passage?
c) The Three Ds
Has the writer used Drama, Description or Dialogue to achieve a particular effect?

However difficult the question is, just remember to write about language rather than what happens in the story.

Use the Same Tense as the Question

Most of the time, people use the ‘eternal present’ to talk about works of fiction. Sometimes, though, passages are about historical events, so the past is more appropriate.

For example, if the text comes from The Diary of Anne Frank, it wouldn’t make sense to talk about the Second World War as if it were still going on!

So which tense should you use?

The simple answer is to write in the same tense as the question. That way, you’ll never go wrong.

Sometimes, the question will tell you to do something, which means the verb is in the imperative rather than the past, present, future or conditional tense. If that happens, you just need to look at one or two of the other questions to see which tense they use. You can then use the same tense in your answer.

Don’t Repeat the Question in Your Answer

In primary school, teachers often tell their pupils to do this to make sure they’ve understood the question.

It’s not wrong and you won’t lose a mark for it, but it just takes too long.

I’ve seen children spend a whole minute carefully copying down most of the question before they’ve even thought about the answer!

It’s a bit like the old joke:

Why did the chicken cross the road?
I don’t know. Why did the chicken cross the road?
The chicken crossed the road because it wanted to get to the other side!

If this punchline were your answer in a comprehension, you’d be writing down six words before you’d even started answering the question – or earning any marks! That’s why you should start with the word after ‘because’, which means writing ‘It wanted to get to the other side’ in this case.

This normally means using a pronoun, which is much shorter than a noun phrase like ‘the chicken’. Whatever the question asks about, just turn it into a pronoun and start with that. In this case, you don’t need to say ‘the chicken’ because it’s obvious what you’re talking about, so you can just say ‘it’.

Never Write ‘Because’

Unfortunately, bad things tend to happen when you use the word ‘because’:

  • You might repeat the question in your answer.
  • You might not use a full sentence (if you start with ‘Because…’).
  • You might misspell it.
  • You might waste time (since it’s five letters longer than ‘as’!)

That means you should NEVER write ‘because’. ‘As’ means the same thing and is impossible to get wrong. Even then, you should only use it for two-part, ‘what and why’ questions. For instance, imagine you’re asked, “Does Jack feel sad after losing his dog? Why?” In this case, it’s fine to say, “Yes, as he was his best friend.”

Answer All Parts of the Question

Examiners will sometimes try to catch you out by ‘hiding’ two questions in one.

You should be careful with these questions, eg ‘How do you think Jack feels about losing his dog, and how do you think you’d feel if you lost your favourite pet?’

It would be easy to answer the first part of the question and then forget about the rest!

Don’t Waste Time With Words You Don’t Need

You never have enough time in exams, so it’s pointless trying to pad out your answers by including waffle such as ‘it says in the text that…’ or ‘the author writes that in his opinion…’

Far better to spend the time thinking a bit more about the question and coming up with another quotation or point to make.

Use Quotations

Using quotations is tricky, and there are a lot of things to remember.

  • Make sure you use quotation marks (“…”) or inverted commas (‘…’) for anything you copy from the text.
  • Copy the quotation out accurately.
  • Drop the keywords into a sentence of your own, eg Jack feels ‘devastated’ by the loss of his dog.
  • Quotations are not the same as speech, so the full-stop goes after the quotation marks, not before, eg he felt ‘devastated’. ‘Devastated’ is not a full sentence, so it doesn’t need a full-stop after it. The full-stop belongs to your sentence.
  • Don’t just tag a quotation on the end of an answer, eg Jack is really sad, ‘devastated’.
  • Don’t start with a quotation followed by ‘suggests’ because it won’t make sense, eg ‘Devastated’ suggests Jack is really sad. ‘Devastated’ is not a noun or a pronoun, so it can’t suggest anything!
  • If you really want to use ‘suggests’ or ‘shows’, it’s better to start with ‘The word…’ or ‘The fact…’, eg The word ‘devastated’ suggests Jack’s really sad or The fact Jack is ‘devastated’ suggests he’s really sad.
  • If the quotation is too long, you can always miss words out and use an ellipsis (…), eg Liz went to the supermarket and bought ‘apples…pears and bananas’.
  • If the quotation doesn’t use the right tense, you can always change the verb. Just put the new ending in square brackets, eg Jim ‘love[s] strawberries’ instead of Jim ‘loved strawberries’.

Remember the Iceberg!

As you can see from the picture, the vast majority of an iceberg remains hidden from view.

It’s the same with the answers to questions in a reading comprehension.

Don’t be satisfied by what you can see on the surface – that won’t get you full marks.

Like a scuba diver, you have to dive in deeper to find the rest…!

Multiple-choice

Multiple-choice tests are generally easier than long-format ones because it’s easier to guess.

Because of that, the most important thing to remember is to answer ALL the questions. It only takes a second to guess if you don’t know the answer.

The best method is to work by process of elimination. That just means narrowing down your options by crossing off any answers that simply can’t be true. As Sherlock Holmes once said to Dr Watson, “Once you’ve eliminated the impossible, whatever remains, however improbable, must be the truth!”

You may not be able to cross off all the ‘wrong’ answers, but every one improves your chances. Let’s say there are five options. That means you have a 20% shot at getting the question right by pure guesswork. As you cross off the answers one by one, your chances rise to 25%, then 33%, then 50% and finally 100%!

Just remember that the answer won’t always be black and white. There are often shades of grey in comprehensions, so it’s not a question of finding one single, ‘right’ answer but the one that’s ‘the most right’.

To get the highest possible score, it’s important to understand the marking policy. That depends on the school, but let’s take the Sutton 11+ multiple choice test as an example. There are a few things to bear in mind:

  • The test is split into four sections: Spelling, two Texts (ie comprehensions) and a Comparison of Texts (ie another comprehension)
  • Each question has five possible answers (A to E).
  • There may be one right answer or a combination of answers, but there are never five right answers.
  • If the question asks for one answer, marks will only be awarded if you select the correct option (and no others).
  • If the question asks for two answers, marks will only be awarded if you select the two correct options (no more and no less!).
  • If the question asks for more than one possible answer (1, 2, 3 or 4 options) without saying how many, you should obviously try to pick all the correct ones. You might score a mark if you don’t select them all, but there’s no further explanation.

Check Your work
(5 mins)

If there’s one tip that beats all the rest, it’s ‘Check your work’.

However old you are and whatever the subject, you should never finish a piece of work before checking what you’ve done – and it’s no excuse to say, “I didn’t have time.” You need to make time!

However boring or annoying it is, you’ll always find at least one mistake and therefore at least one way in which you can make things better.

In the case of 11+ or 13+ comprehensions, the most important thing is to test candidates’ understanding of the passage.

However, spelling and grammar is still important.

Schools have different marking policies:

  • Some don’t mark you down for bad grammar (although a lot of mistakes won’t leave a very good impression!)
  • Some use a separate pot of marks for spelling and grammar to add to the overall total
  • Some take marks off for each grammatical mistake – even if you got the answer ‘right’.

Either way, it pays to make sure you’ve done your best to avoid silly mistakes.

If you think you won’t have time to check, make sure you manage your time so that you have a few minutes left at the end.

You’ll probably gain more marks by correcting your work than trying to finish the last question, so it makes sense to keep that time for checking.

If you do that, there are a few simple things to look out for.

Check the Answers are Correct and Complete

This is the most important thing to check, and it takes the longest.

Make sure that each answer is correct (by referring back to the text if necessary) and that each part of the question has been covered.

Quite a few of my students have lost marks by forgetting to look at all the pages, so you should always check you haven’t missed any questions.

Check Spelling

This is the main problem that most Common Entrance candidates face, but there are ways in which you can improve your spelling.

  1. Look out for any obvious mistakes and correct them. It can help to go through each answer backwards a word at a time so that you don’t just see what you expect to see.
  2. Check if a word appears anywhere in the text or in the question. If it does, you can simply copy it out from there.
  3. Choose a simpler word if you’re not quite sure how to spell something. It’s sometimes better not to take the risk.

Check Capital Letters

This should be easy, but candidates often forget about checking capitals in the rush to finish.

Proper nouns, sentences, speech and abbreviations should all start with capital letters.

If you know you often miss out capital letters, you can at least check to make sure all your answers start with a capital.

Check Punctuation

Make sure you’ve put full-stops, commas, quotation marks, apostrophes and question marks in the right places.

Commas give almost everybody problems, but you can at least check there is a full-stop at the end of every sentence.

Check Other Grammar

It’s always useful to check for missing words and to make sure everything makes sense.

Grammar may not be the first thing on your mind when you’re answering the questions. However, you can usually spot most silly mistakes if you read through your answers carefully at the end.

Quiz

If you want to test your knowledge of this article, here are a few questions for you.
You can mark them yourselves!

  1. What are the five steps involved in doing a comprehension? (5 marks)
  2. Name three things you should do when reading the text for the first time. (3 marks)
  3. Why should you read the questions before re-reading the text? (1 mark)
  4. What should you be doing when you read the text for the second time? (1 mark)
  5. What are the six steps to take when answering a question? (6 marks)
  6. What are five hints and tips for answering questions? (5 marks)
  7. What are the two types of things that questions might ask for? (2 marks)
  8. What are the two occasions when you don’t need to answer in a full sentence? (2 marks)
  9. Name five poetic devices. (5 marks)
  10. What five things should you be checking for at the end? (5 marks)

Total: 35 marks

 

 

 

 

If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.

Learning the Right Words

One of the frustrations about learning French is that you’re not given the words you really need to know.

I studied French up to A-level, but I was sometimes at a complete loss when I went out with my French girlfriend and a few of her friends in Lyon.

I was feeling suitably smug about following the whole conversation in French…until everyone started talking about chestnuts!

At the end of almost every story, someone would mention them. Now, it’s not often that chestnuts crop up in conversation (!), so I thought I’d check with Isabelle later on. When I asked her about it, she said her friends hadn’t been talking about chestnuts at all.

When I pressed her, she said they hadn’t been saying ‘marrons’ but ‘marrant’ – which is slang for ‘funny’! The next day, I started a list of all the slang words – or ‘argot’ – I came across, and within a few weeks I had over a hundred.

This is just a trivial example of what anyone knows who has lived and spoken French among French people: the words they use are almost never the ones you find in Longmans Audiovisual French!

More often than not, they are ‘argotique’ or slang. For example, a house is not a ‘maison’ but a ‘baraque’, and a car is not a ‘voiture’ but a ‘caisse’ or a ‘bagnole’. In addition, there are rules about when you can use slang and when you can’t.

I got into real trouble with my girlfriend when I threw a few slang words into my conversation with an old family friend of hers. I was just trying to practise my ‘argot’, but Isabelle told me in no uncertain terms that you NEVER, EVER use slang with someone you address as ‘vous’!

Pupils spend a long time being taught vocabulary for a given set of situations and environments – doing the shopping, going to school, going to the cinema etc – but they are rarely given a simple list of the most common words.

You can easily find such a list online (http://en.wiktionary.org/wiki/Wiktionary:French_frequency_lists/1-2000), and learning those words strikes me as much more useful than wasting time with ‘le muguet’ (or lily-of-the-valley), which I remember cropping up in my own Longmans text book!

French Argot English
une pretexte baroque a bizarre or flimsy pretext
une benne a skip — where you dump things
merde s**t – can mean almost anything you want
le chef boss
la bagnole car
la bite, bitte c**k
cool cool
le pénaliste criminal lawyer
au tapis down (as in dead)
laisse tomber! drop it! Leave it!
stupéfiants, stupes drugs
s**t drugs, such as cannabis resin – as in “cent grams de s**t!”
gagner du fric earn money
une escort girl escort girl
la femme de compagnie escort girl
poilu First World War veteran
magouiller avec f**k with
marrant funny
le gentleman gentleman
le flingue gun
tu as plongé? have you started using [drugs] again?
c’est du bluff he’s bluffing
la baraque house
j’ai des comptes à régler I have scores to settle
je sais ce que vous traversez I know what you’re going through
illico immediately?
embrouillé in a fine mess
mediatique media-friendly, media-savvy
la crise d’angoisse panic attack
le proxénétisme pimping, profiting from prostitution
dégagez! piss off!
le merdeux s**thead
bouché stupid
point final that’s it, end of story
la salope the bitch, the disloyal woman
larguer to dump
fumer to kill
les chiottes toilets
t’as reçu un pain you got punched in the face

 

 

 

 

If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.