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:
Plot the ‘vertices’ (or corners) of the reflected shape one by one by drawing a small cross in pencil.
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.
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’.
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!
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.
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!
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.
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!
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.
I love chocolate biscuits and milkshakes.
He said “I always go the gym on Wednesdays.”
There were three items on her shopping list flour, sugar and eggs.
He prized only one quality in his players teamwork.
He stayed in his room it was far too hot to go outside.
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.
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.
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.
I love chocolate biscuits and milkshakes I used to have them all the time as a kid.
She said, “I always go the pool on Saturdays it’s the only day I get enough time.”
There was only one thing she wanted to do go and get her hair cut.
His team always scored great goals the other team just scored more.
I never cook chicken I’m afraid of making myself sick.
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
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
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 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
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
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
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
‘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
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
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
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.”
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
How would you explain the humour in these lines?
“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
“There’s a door,” he whispered. “Where does it go?” “It stays where it is, I think,” said Rincewind. Eric, by Terry Pratchett
“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
“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
“A word to the wise ain’t necessary. It’s the stupid ones who need advice.” Bill Cosby
“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
“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
“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
“There are moments, Jeeves, when one asks oneself, ‘Do trousers matter?'” “The mood will pass, sir.” The Code of the Woosters, by PG Wodehouse
“There was a boy called Eustace Clarence Scrubb, and he almost deserved it.” The Voyage of the Dawn Treader, by CS Lewis
“I write this sitting in the kitchen sink.” I Capture the Castle, by Dodie Smith
“You can lead a horticulture, but you can’t make her think.” Dorothy Parker
“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
“For the better part of my childhood, my professional aspirations were simple – I wanted to be an intergalactic princess.” Seven Up, by Janet Evanovich
“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
“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
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 the sides of 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 of those two sides.
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°.
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 of those two sides.
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°.
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 of those two sides.
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 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°.
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°.
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.
Multiply the top number by the last digit of the bottom number as you would normally.
Write a zero at the end of the next answer line (to show that you’re multiplying by tens now rather than units).
Multiply the top number by the next digit of the bottom number, starting to the left of the zero you’ve just added.
Add the two answer lines together to get the final answer.
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.
Have a go at these questions. Make sure you show your working – just as you’d have to do in an exam.
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:
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.
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.
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.
8 + 5
17 + 12
23 + 19
77 + 88
127 + 899
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.
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.
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.
8 – 5
17 – 12
43 – 19
770 – 681
107 – 89
Multiplication (or short multiplication)
This is short multiplication, which is meant for multiplying one number by another that’s in our 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.
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.
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.
21 x 3
17 x 4
23 x 6
77 x 8
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.
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.
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!
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.
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.
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’.
They talked to Jim, who/whom lived in Stoke.
He played football with the boy who/whom had red hair.
She was friends with the girl who/whom played volleyball.
Who/whom do you think will win the egg and spoon race?
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’.
Who’s/whose in charge of the tennis rackets?
Who’s/whose bag is this?
He speaks to the woman who’s/whose behind the counter.
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 tonight.”
“I could go to the cinema tonight.”
The first sentence means there is a possibility the speaker will go to the cinema that night. 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 either means “I was able to go to the cinema tonight” or “I would be able to go to the cinema tonight.” Neither of those is the same as the first sentence. Adults might get away with confusing ability with possibility, but if you’re taking an English exam any time soon, it’s probably a good idea learn the difference!
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 is a selection of over 5,000 past papers sorted by age group, subject, school and year, together with around 1,000 mark schemes. You’ll find links to over 100 other sources of past papers at the foot of the page.
The first few KS1 SATs papers are available free of charge. To join nearly 2,000 other subscribers in gaining access to the rest, please sign up on the Subscribe page or click the button below. A 12-month plan costs just £12.99 with no automatic renewal.
Long-time user of your priceless past paper collection here. Just wanted to say thank you for putting this all together — it truly is a phenomenal resource for assessment. And as a tutor/teacher/human myself, I’ve used the past papers as a fall-back more times than I’d necessarily like to admit!
If you have specific needs and want to know in advance if papers will be available from a certain school in a certain year for a certain subject, then feel free to leave a comment or email me at email@example.com, and I’ll check for you.
Once you’ve subscribed, finding papers is easy:
If you’re looking for papers for a particular level, subject or school, just search for it by name (using Ctrl-F or Cmd-F), eg 11+, English or Latymer.
If you’re looking for papers with answers, just search for answers or mark scheme.
If you’re looking for multiple choice papers, just search for multiple choice.
If you’re looking for scholarship papers, just search for scholarship.
Papers are available from the following schools, as well as other organisations such as the Independent Schools Examinations Board (ISEB):
Bancroft’s, Bedford School, Benenden
Caterham School, Chigwell School, Christ’s Hospital, City of London Freemen’s School, City of London School, City of London School for Girls, Cheadle Hulme School, Colfe’s School, The Crossley Heath School
Dame Alice Owen’s School, Dulwich College
Eltham College, Emanuel School, Epsom College, Eton College
Felsted School, Forest School London
Godolphin & Latymer, Greenshaw High School
The Haberdashers’ Aske’s Boys’ School, Hereford Cathedral School, Highgate School
Immanuel College, Ipswich School
James Allen’s Girls’ School (JAGS), John Lyon
King Edward VI High School for Girls, King Edward’s School Birmingham, King Henry VIII School, King’s College Junior School Wimbledon, King’s College School Wimbledon, King’s High Warwick, Kingston Grammar School
Latymer Prep School, The Latymer School, Latymer Upper School, Leicester High School for Girls, The Leys
Magdalen College School, The Manchester Grammar School, Manchester High School for Girls, Merchant Taylors’ School
Nonsuch High School for Girls, North Halifax Grammar School, North London Collegiate School
The Perse Prep School, The Perse Upper School
Queen Elizabeth’s School, Queenswood School
Radley, Reigate Grammar School
Sevenoaks School, Shrewsbury School, Solihull, St Albans, St Anselm’s College, St Edward’s, St Faith’s Cambridge, St. Francis’ College, St George’s College Weybridge, St John’s School Leatherhead, St Joseph’s Catholic Primary School, St Mary’s School Cambridge, St Paul’s Girls’ School, Stockport Grammar School, Stowe School, Streatham & Clapham High School, Sutton Grammar School, Sydenham High School
Tonbridge School, Trinity School Croydon
Wallington County Grammar, Wallington High School for Girls, Warwick School, Westminster School, Whitgift, Wilson’s School, Winchester College, Withington Girls’ School, Woldingham School
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)
This article explains circle theorems, including tangents, sectors, angles and proofs (with thanks to Revision Maths).
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 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
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.
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.
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.
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.
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.
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.
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.
You might have to be able to prove this fact:
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
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
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.
You may have to be able to prove the 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
A 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
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
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’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 they can be used. more
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 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
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
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
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
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
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
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
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, 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 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 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 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 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! 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
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 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 (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
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
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
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 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
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 Working with negative numbers can be confusing, but a few simple rules can help you add, subtract, multiply and divide successfully… more
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 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! 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
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
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
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 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 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 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 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 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
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 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 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 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
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 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 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 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
African field guide Find an alphabetical list of the most common animals seen on safari in Africa, including mammals, reptiles and birds. more
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
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
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
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
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
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
Safari pub quiz Challenge your friends and family on their wildlife knowledge with this fun quiz. more
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 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
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.
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.
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!
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  5) (2  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  8) (11  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.
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.
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).
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’.
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’.
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.
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.
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:
Coded shapes and logic
Each of these types is divided into various subtypes.
Types of question
Recognise shapes that are similar and different
Identify shapes and patterns
Pair up shapes
“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?”
Types of question
Find shapes that complete a sequence
Find a given part within a shape
Find a missing shape from a pattern
“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.”
Types of question
Recognise mirror images
Link nets to cubes
“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
“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:
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 is 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?
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…!
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. 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 with different looks, personalities and nationalities. 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:
Job or education
Friends and family
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 (or speciality) covers anything that makes a character worth reading about. One of the reasons Superman is so popular is his super powers: 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)
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.
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…
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.
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 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.
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!
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.
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 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.
“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.
Atom Learning is a KS2 online adaptive learning platform, covering English, Maths, Verbal and Non-verbal reasoning and Science. It combines high-quality, teacher-made content with sophisticated technology to keep students on their individual, optimal learning paths.
Atom Learning is designed to consolidate KS2 knowledge and help those preparing for senior school entrance assessments such as the 11+, the ISEB Common Pre-Tests and the London Consortium tests.
You can find the latest Atom Learning marketing video here.
There have also been some exciting new releases happening on the platform that you might appreciate.
Now Launching: Science!
Here’s what’s available in the latest Atom Learning Science module (see video):
Complete curriculum coverage mapped to both the KS2 National Curriculum for Science and the ISEB 11+ Science syllabus
Some curriculum coverage of early KS3 National Curriculum for Science and 13+ Science syllabus
Content for four main topics: Biology, Chemistry, Physics, and Working Scientifically
~8,000 science questions
~100 science videos
~100 science helpsheets
Science mock tests based on either specific exams or a general year group progress test
Weekly live science lessons
Two Science lessons a day over May half-term
Differentiated materials for every topic in KS2: every topic has content from Y3 to Y6+. in schools, a child might only be taught a science topic once or twice in a four year period. On Atom, every science topic is revisited in every year group campaign. We have designed the product this way to maximise long-term learning – we want children to remember what we teach them! We also want to give Atom students the best possible chance to get ahead for KS3! We know how important this is to Atom parents.
Upgraded Videos and Helpsheets for Years 5 & 6
They’re upgrading all of their videos and helpsheets and adding thousands of new questions covering every topic in the syllabus.
Brand New Videos and Helpsheets for Years 3 & 4
To accompany their Years 3 and 4 content, brand new videos and helpsheets will go live focusing on the building blocks for KS2 success!
Launching this Spring 2021…
The highly anticipated Tutor dashboard! This will be designed specifically for tutors to tailor their students’ learning journey.
One More Thing…
Atom Nucleus (the Home Platform) has launched an entirely new learning campaign. Children are now able to work through new highly interactive and fully adaptive ‘worlds’ where they can move from island to island mastering topics. Take a look here at this video to see what we’ve been working on!
Bespoke Tuition is pleased to offer a £200 discount on the Employability Accelerator Programme, designed to offer real, practical support for young adults during this extraordinarily turbulent time – for whatever their next step may be. By creating a programme of invaluable career mentoring from FTSE 500 recognised executive coaches, intensive and focused work experience, and with an award-winning learning platform, Employability Accelerator aims to ensure that participants stand out and accelerate their prospects, whether ensuring their place at university, internship, graduate job or first step on the career ladder. The programme is currently delivered online and is carefully tailored to suit each individual’s goals, aspirations and abilities.
Get Prepared. The pandemic has made career development more difficult. The programme is specifically designed to work in a virtual environment. How students use this summer can significantly change future employability – don’t waste it.
Experience Work. Exposure to real work as early as possible is integral to success. Over a third of recruiters who took part in a Highfliers survey of the graduate market* warned that ‘irrespective of their academic achievements, graduates who have had no previous work experience…have little or no chance of receiving a job offer.’
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2-weeks of work experience and tailored personal development sessions
Ongoing one-to-one feedback from professional Coaches to ensure you master core business skills and personal development
Recommendations, application support and improved confidence to optimise your employability chances
Duration and hours
The programme lasts for 2 weeks and aims to replicate the structure of a working week, running from 9.30am-4.30pm, Monday-Friday. There is social activity too with your managers, coaches and peer group.
Students must typically be a minimum of 18 years of age and currently students or recent graduates. For the work experience project, students will be organised into groups of around 5 peers.
Dates and pricing
The Programmes run throughout the summer and over Christmas 2020. Please click below to be taken to more information about current programme availability and price. More info.
If you quote ‘Bespoke’ on application, you’ll receive a special £200 discount. Apply now.
Boss Box Gives Kids the Gift of Entrepreneurship this Xmas – now with 10% off
2020 has certainly been a strange year, but that doesn’t mean that Christmas is cancelled. If you’re struggling to find the perfect present for your children why not help foster their creative juices with a Boss Box Business Creation Kit.
A perfect way to entertain the whole family over the Christmas holiday, Boss Box Creation Kits come in three different formats and allow kids to ‘make, package and sell’ either Cake Pops, Dog Treats or Bath Bombs. Playing to children’s love for baking each kit contains an easy step by step instruction manual to guide them every step of the way so they can bake and sell their product in just a few hours.
From detailed instructions on how to make and package their product, naming their company and how to fill in their marketing flyers, each kit contains all the key ingredients to launch a mini business, enabling children to learn the basic skills of entrepreneurship.
By teaching children essential ‘off syllabus’ life lessons through play it provides the creativity, empathy, and passion to improve their ability to become business starters and possible future leaders.
Boss Box Business Creation Kits are available from £34.95 with a 20%discount for Black Friday purchases from the Boss Box website www.bossbox.co. You can get an additional 10% discount by quoting ‘TUTOR10‘ when you check out.
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Types of school
The terminology for schools in the UK can be quite confusing, so here’s a quick guide.
Private schools charge fees and are not run by the Government, although they have to follow certain rules. They are also known as independent schools, and the most famous ones such as Eton and Harrow are- confusingly – known as public schools
Grammar schools are state schools and don’t charge fees, but they are academically selective and have a very good reputation. There are only 164 of them left.
Comprehensive schools make up the vast majority of free state schools and generally have the worst reputation, but there are exceptions.
Faith schools have to follow the national curriculum, but they can choose what they teach in religious studies and may have different admissions criteria and staffing policies to other state schools, although anyone can apply for a place.
Free schools are Government-funded but aren’t run by the local council, which means they have more control over staffing and curriculum. However, they’re ‘all-ability’ schools, so they can’t use academic selection processes like grammar schools.
Academies are state schools that are funded by the Government but run by an academy trust, a charity that controls how funds are spent and how the school is managed.
City technology colleges are independent schools in urban areas that are free for pupils to attend. They’re owned and funded by businesses as well as the Government and specialise in practical and technical skills.
Special schools are schools for children aged 11 and over with special educational needs. They can specialise in one of four areas: communication and interaction, cognition and learning, social, emotional and mental health, or sensory and physical needs. Within each area, they can go further, for instance by catering specifically for children with autism or visual impairments.
The Independent Schools Council has a searchable database of private schools here, but I’ve listed the major ones in the Greater London area and elsewhere.
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:
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:
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?
How many 18s in 5?
It doesn’t go
How many 18s in 52?
Two (write 2 on the answer line, and write 36 under the dividend with a line beneath it)
What’s 52 – 36?
16 (write it on the next line)
Pull down the next digit from the dividend (write it after the 16)
How many 18s in 162?
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.
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.
First of all, here’s a quick list of the main parts of a letter that the examiner will be looking at:
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…
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 7th October 2018 rather than 7/10/18 (or 10/7/18 if you’re American!).
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.
The text can obviously be whatever you like, but 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 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 really any rules. You can say anything from ‘Love’ to ‘Best regards’ or ‘Yours ever’. Note that they all start with a capital letter and should be followed by a comma. If the letter is to someone else, the sign-off depends on the greeting: if you’ve used someone’s name in the greeting, you should use ‘Yours sincerely’, but it’s ‘Yours faithfully’ if you haven’t.
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) plus your surname, eg Nick Dale or 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!
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’.
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.
‘There once lived an exotic princess in a fairy tale castle…’
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…!
Not 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…
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…
The 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…
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!
I’d rather have seen the kill than stopped for lunch!
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…
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:
Import to computer I 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.
Import to Lightroom I 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.
Rate images I 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.
Check ratings Once 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…!
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.
Add metadata The 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.
Export images Lightroom 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…)
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!
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.
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 help you work out two variables at once.
Why do we have simultaneous equations? Well, there are two ways of looking at it.
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.
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
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:
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.
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.
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?
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.
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.
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.
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.
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?
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.
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!
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.
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.
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.
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.
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!
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 email@example.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.
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!
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.
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.
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)
Choose colour temp
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 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 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.
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.
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.
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 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.
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.
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!
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 m