Tag Archives: ratios

Hints and Tips

Here are a few articles to show how to tackle common problems in English, Maths, French, Verbal and Non-verbal Reasoning and photography.

General

Hints and tips

 

 

 

 

 

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…! more

English

 

 

 

 

 

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. more

 

 

 

 

 

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. more

 

 

 

 

 

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 the tick, but if you get it wrong, you’ll get a cross. This article will explain how to use both colons and semicolons so that you can be confident of getting far more ticks than crosses! more

 

 

 

 

 

 

Explaining humour
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 they can be used. more

Who-or-whom

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

Could vs might

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. more

Homophones

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. more

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 that you can choose from. more

Books
Children’s reading list
I’m often asked by parents what books their children should be reading. Here’s a list of my favourite books when I was a boy. Maybe a few of them might be worth ordering online…! more

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… more

Screen Shot 2018-10-07 at 19.37.39
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 typical format of formal and casual letters and the decisions on wording that you’ll have to make… more

Grand Central
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… more

SVO
What is a full sentence?
Teachers often tell pupils to use a ‘full sentence’ in their answers, but what is a full sentence? more

Apostrophe
It’s all about the apostrophe
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?! more

Keep calm and check your spelling
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… more

 

 

 

 

 

 

 

Parts 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! more

Letter N
Capital!
The three main things to check after writing anything are spelling, punctuation and capital letters, so when do you use capitals? more

speech marks
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…?! more

Essay writing
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’… more

Commas
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… more

Poetic devices
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… more

Story mountains
Story mountains
Everyone needs a route map, whether it’s Hillary and Tenzing climbing Mount Everest or an English candidate writing a story. One of the ways of planning a story is to create a story mountain, with each stage of the tale labelled on the diagram… more

Remember the iceberg!
Remember the iceberg!
To pass Common Entrance, you have to be a scuba diver. 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 and deeper… more

Maths

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. more

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. more

SOHCAHTOA
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! more

Screenshot-2020-05-26-at-20.13.54
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. more

Screenshot-2020-05-26-at-14.55.08
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. more

Screen Shot 2018-10-07 at 19.50.29
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… more

maths trick
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! more

download
Simultaneous equations
Why do we have simultaneous equations? Well, there are two ways of looking at it… more

Prime factors
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… more

negative-numbers
Negative numbers
Working with negative numbers can be confusing, but a few simple rules can help you add, subtract, multiply and divide successfully… more

maths
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! more

algebra
Algebra
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… more

Divisibility rules OK
Divisibility rules OK!
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! more

Back-to-school-blackboard-chalk
Tips for the QTS numeracy test
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 short cuts and describe when and how they should be used… more

Here be ratios
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… more

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… more

Number sequences
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… more

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… more

Useful formulas
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… more

Short cuts
Short cuts
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… more

French

French verbs
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 certain verbs that also take the word ‘que’ after them. These are generally the ones that express feelings or doubts (eg craindre, vouloir), 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… more

French verbs
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’… more

French verbs
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)… more

French verbs
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… more

French verbs
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… more

French verbs
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’… more

French verbs
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… more

Learning the right words
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! more

Non-verbal Reasoning

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. more

Photography

Slide01
African field guide
Find an alphabetical list of the most common animals seen on safari in Africa, including mammals, reptiles and birds. more

Slide01
Basics of photography
Learn all about the basic aspects of photography, including types of camera, types of lenses, the Exposure Triangle (shutter speed, aperture and ISO), focus and other settings. more

Slide1
Game drives
Read all about the best gear, equipment to take with you on safari, learn the rules of composition and find out the best workflow for editing your wildlife images. more

Slide01
How to stand out from the herd
Read this quick guide to improve your wildlife shots by setting up something a little bit different, from slow pans to sunny silhouettes. more

Slide01
Introduction to Lightroom
Learn how to import, edit and organise your images in Lightroom, including the main features available in the Library and Develop modules and a summary of keyboard shortcuts. more

Slide1
Making money from photography
Find out how to start making money from your photography with this quick and easy guide to entering competitions, putting on exhibitions, selling through stock (and microstock) agencies and more. more

Slide01
Rules of composition
Find out the rules of composition to help you get the most out of your photography, including the Rule of Thirds, framing, point of view, symmetry and a whole lot more. more

Slide01
Safari pub quiz
Challenge your friends and family on their wildlife knowledge with this fun quiz. more

Slide01
Wildlife photography
Learn how to take great wildlife shots by preparing properly, taking the right equipment and getting to know the rules of composition. more

Verbal Reasoning

VRTypeO

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. Here is a guide to the different kinds of problems and the best ways to approach them. more

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…

Here be ratios...!

Here be ratios…!

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!

Quiz

Here are a few practice 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?