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Who or Whom, Who’s or Whose?

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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’.

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

Who’s v Whose

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

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

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

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

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

Circle Theorems

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

Isosceles Triangle

Two Radii and a chord make an isosceles triangle.

Perpendicular Chord Bisection

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

Angles Subtended on the Same Arc

Angles subtended on the same arc

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

Angle in a Semi-Circle

angle in a semi-circle

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

Proof

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

Divide the triangle in two

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

Two isosceles triangles

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

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

Tangents

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

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

angle with a tangent

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

Tangents from an external point are equal in length

Angle at the Centre

Angle at the centre

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

Proof

You might have to be able to prove this fact:

proof diagram 1

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

proof diagram 2

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

Alternate Segment Theorem

Alternate segment theorem

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

Proof

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

proof of alternate segment theorem

We use facts about related angles

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

Cyclic Quadrilaterals

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

A sector

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

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

Verbal Reasoning

Verbal Reasoning

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

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

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

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

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

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

Muddled Words (Anagrams)

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

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

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

     A
S   N    L
      I

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

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

Insert a Letter

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

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

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

Find the Odd Words

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

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

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

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

Alphabet Codes/Code Words

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

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

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

Synonyms (Similar Meaning)

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

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

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

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

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

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

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

Hidden Words

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

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

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

Find the Missing Word

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

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

Algebra (Calculating with Letters)

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

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

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

Antonyms (Opposite Meaning)

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

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

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

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

Complete the Calculation

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

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

Rearrange to Make Two New words

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

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

Number Relationship

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

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

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

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

Alphabet Series/Sequence

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

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

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

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

Analogies (Complete the Sentence)

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

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

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

Word Codes

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

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

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

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

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

Complete Word Pairs

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

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

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

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

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

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

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

Number Series/Sequences

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

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

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

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

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

Compound Words (Form New Word)

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

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

Create a Word (from the Letters of Two Others)

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

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

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

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

Similar Meaning

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

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

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

Letter Relationships

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

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

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

Comprehension

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

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

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

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

 

Non-verbal Reasoning

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

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

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

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

Bond divides the questions into four different types:

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

Each of these types is divided into various subtypes.

Identifying Shapes

Types of question

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

Sample Questions

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

Missing Shapes

Types of Question

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

Sample Questions

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

Rotating Shapes

Types of Question

  • Recognise mirror images
  • Link nets to cubes

Sample Questions

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

Coded Shapes and Logic

Types of Question

  • Code and decode shapes
  • Apply shape logic

Sample Questions

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

Hints and Tips

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

  • Function
  • Location
  • SPANSS
  • Story
  • Symmetry
  • 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…!

Long Division

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

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

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

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

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

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

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

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

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

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

How Do I Make Money from Photography?

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The obvious question for a lot of amateur photographers is ‘How do I make money from photography?’ The answer, unfortunately, is that I don’t know. All I can do is tell you what I’ve done and give you a few ideas.

I’m still learning the business after just four years, but my approach has always been to knock on as many doors as possible, whether it’s microstock, exhibitions, competitions, lessons or even talks. Every source of revenue has its part to play, and it’s just a question of working out where to focus your efforts.

I make just under half my money from microstock/stock agencies and half from exhibitions, but everybody’s different.

Nick Dale Photography

I loved photography when I was a teenager. I bought (or was given) books on Henri Cartier-Bresson, Alfred Eisenstaedt, Ansel Adams and other great photographers, and I even bought myself an old Chinon CE-4 film SLR.

I remember buying two 36-exposure films for it – one colour, one black and white – and using up every single frame in a couple of hours just taking pictures around the house! I took my camera on holiday to Majorca and the United States, developed pictures in a dark room at school and even talked to my mum about becoming a professional photographer.

However, my mother said I could always take it up later – so that was that for 30 years!

Fortunately, I was given a second chance in January 2013 when a friend of a friend invited me to climb Mount Kenya and go on safari with her and a couple of other people. I’d always wanted to go to Africa, but I’d foolishly been saving it for my honeymoon! As that didn’t seem very likely, I jumped at the chance.

My first digital camera was a Sony DSC-HX200V bridge camera, which means it had a good zoom range (both optical and digital), but not a very large sensor. As a result, it was only around £300 and therefore cheap enough for me to buy without worrying too much.

Fortunately or unfortunately, a week in Kenya with people using proper Nikon SLRs gave me camera envy, and I bought a Nikon D800 SLR with a 28-300mm lens as soon as I got home!

And that was how it all started.

I took hundreds of pictures in Kenya of the people, the landscape and especially the wildlife. When I got back, I bought an Apple MacBook Pro to work on them, upgraded the editing program to Aperture and then sent them off to various microstock agencies to see if they would help me sell them.

It was hard at first, but getting the new camera helped, and I had a cash pile from remortgaging my flat in Notting Hill after another property purchase fell through, so I was able to go on plenty of trips to take more and more pictures.

An important breakthrough came when I sold a couple of prints for £100 each at my local tennis club’s Christmas Fair in November 2014, and another photographer told me about a cheap exhibition space called the Norman Plastow Gallery in Wimbledon Village.

I’d always thought it would be very expensive to mount an exhibition, but this place was only £70 for a week, so I booked it as soon as I could! The only problem was that I didn’t have any actual prints to sell, and here I was very fortunate.

I’d recently joined the Putney branch of London Independent Photography (or LIP), and there I’d met a very friendly and helpful chap called James, who’d offered to do all my printing for me at very low cost. After buying a few cheap, black, wooden frames from Amazon, I was all set.

I invited all my friends to the exhibition in May 2015 – especially a group of tennis players from my club – and I ended up selling seven prints. As I was just starting out, I’d priced the small, medium and large framed prints at £80, £100 and £120 and the unframed ones at only £30, but I still managed to make £550 in total.

The gallery hire charge was £200, and there were a few taxis to pay for plus incidental expenses, but the show actually turned a profit – unless you count the thousands of pounds I spent on buying camera equipment and flights to Kenya, Botswana, Antarctica and the Galápagos!

And there’s the rub. It’s relatively easy to generate revenue from photography, but actually making a profit out of it is another matter entirely. As a result, I have nothing but respect for the photographers I meet who have managed to make a career out of it. I’ve been on trips led by Paul Goldstein and Andy Skillen amongst others, and, in a way, that’s where I’d like to end up.

Since that first show in Wimbledon Village, I’ve sold nearly 5,000 downloads through microstock agencies, sold 36 prints at solo exhibitions and art fairs, taught five photography students and given two or three talks to various clubs and societies. Overall, I’ve made around £12,000 from my photography – but that wouldn’t even have paid for my trip to Antarctica!

The problem is that everyone has a camera these days – even if it’s just an iPhone – and it’s almost ‘too easy’ to take pictures now that cameras are digital. The world is also a smaller place these days, with the arrival of cheap flights and a general rise in income and wealth. It takes a special talent to make it as a photographer, and part of that talent is being able to make the most of it.

What Do I Need to Do First?

  1. Buy a camera
    If you want to make money out of photography, your first job is to get yourself a decent camera, and that means a digital SLR (or DSLR). The easiest way to earn cash is through so-called microstock agencies – which means selling pictures online in exchange for royalty payments – and they usually require shots to be taken with a camera that has at least 12 megapixels, if not more.
    You can obviously try to sell holiday snaps from your ‘back catalogue’, but, as I found out to my cost, it ain’t easy. Once you’ve decided to buy a DSLR, the two main brands to choose from are Nikon and Canon. There isn’t much between them these days, and the only reason I chose Nikon is that I didn’t want a camera from a company that made photocopiers!They both make good lenses, but, unfortunately, they have different mounts, so one you go with one or the other you’re locked in. I have various lenses ranging from an 18-35mm wide angle zoom to a 105mm macro lens for close-up work to an 80-400mm mid-range zoom, but I also rent an 800mm lens from Lenses for Hire whenever I go on a major wildlife photography trip.
  2. Buy a laptop
    If you don’t have one already, buying a decent laptop is great for photography. I take mine with me on all my trips, and it means that I can work on my images every evening after I get back from a shoot or a game drive.I should warn you, though, that the so-called RAW files from digital cameras are very large (in the case of my camera over 40MB each!), so I’d recommend getting as fast a processor as possible and as much memory and hard disk space as you can afford.You should also arrange a back-up system: the last thing you need is for your life’s work to disappear thanks to a software glitch! You could use an external hard drive, but I prefer backing up to the cloud just to be on the safe side.I use CrashPlan, which automatically detects any added, edited or deleted files and backs up the changes in real time, but there are other similar products out there.
  3. Subscribe to Lightroom
    Adobe Lightroom Creative Cloud is the choice of professionals and serious amateurs for organising and editing their photographs. It only costs around £8 a month (including Photoshop), and it’s a very powerful tool, as well as being relatively easy to use once you’ve mastered the basics.Digital photographs never come out of the camera looking perfect, so it’s always a good idea to try and improve the contrast, highlight and shadow areas and anything else you need to. If you’re selling through agencies, you’ll also need to add titles, captions and keywords (plus any other fields you’re asked to fill in), and all that is possible with Lightroom.It’s a pain to do for each individual photograph, but you can ‘synchronise’ any changes you make across a number of pictures, and you only need to do it once. If you’ve never used it before, I suggest you to do what I did and watch Anthony Morganti’s series of free YouTube videos on Lightroom. He takes you through all the functionality, and it’s an easy way to learn.
  4. Start taking pictures
    If you’re a wildlife photographer, this is just a euphemism for ‘spend thousands of pounds on trips to long-haul destinations’! However, you don’t have to travel far to take pictures.Whether you’re a landscape, portrait, Nature, fashion, wildlife, wedding or sports photographer, there’s always something photogenic not far from home, and you simply have to have the enthusiasm (and discipline) to be able to get out there and take more and better shots.Quality and quantity are both important. The quality of your images is ultimately what matters, but even a shot that’ll never win a competition might earn you money on a microstock site. I give my shots three stars if they’re good enough for Facebook, four if they’re good enough to be sold via agencies and five if they’re good enough to go on my website.
  5. Start marketing your work
    As a photographer, you have to learn to talk the talk as well as walk the walk. If you want to be taken seriously, you have to cover the basics, which means building a website, printing out business cards and having an active presence on social media.You can’t expect to win a bid for a photo shoot if you’re still using an old Hotmail address! Personally, I have this website powered by SquareSpace plus a Facebook ‘fan page’, a YouTube page, a LinkedIn account and a Twitter feed, all of which are printed on the back of my business cards.I post articles on my blog about photography trips, exhibitions and useful techniques (which also appear on Facebook, LinkedIn and Twitter), and I tweet and retweet a ‘Shot of the week’ (which gets fed through to my Facebook account as well).

Yes, but how can I make money?

  1. Microstock
    Microstock agencies are online intermediaries that accept work from photographers and then market those images to potential clients such as creative directors of newspapers, magazines and other buyers.The advantage of using them is that it’s ‘making money while you sleep’, in other words, it’s a passive income that you can build over time as you add more and more shots to your portfolio.Some agencies sell a lot of images but with low royalty rates, some the reverse, but here is the list of the ones I’ve used (in descending order of sales):
    Getty Images/iStock
    Shutterstock
    Adobe/fotolia
    DepositPhotos
    123RF
    Bigstock
    PIXTA
    SolidStockArt
    Dreamstime
    EyeEm
    Canstock
    photodune
    ClipDealer
    Panthermedia
    Pixoto
    featurePics
    Mostphotos
    Pond5
    500px
    Redbubble
    Alamy
    Yay Micro
    Stockfresh
    Crestock
    Zoonar
    Lobster MediaI should mention that not all agencies will accept you, and not all your shots will be accepted by any agency that does, but you shouldn’t take it personally. I’ve had over £4,000 in microstock sales in the last four years, but my overall acceptance rate is only 41%!

    Even if your pictures are accepted, of course, that doesn’t mean they’ll sell. I’ve had 5,120 downloads from microstock sites, but only 1,521 individual shots have ever been sold out of a total of 4,389. The rest of them are just sitting there, waiting for a buyer. Every now and then, though, you take a picture that goes viral: I’ve sold my jumping penguin (see above) 705 times!

    The basic process is similar across all agencies. You add titles, captions and keywords to all your pictures and then export them as JPEG files to upload to each individual agency via their websites or an FTP service using a program like Filezilla.

    You then typically add the category, country or other data for each of them and submit them for approval. The agencies then approve the ones they like and reject the ones they don’t. After that, it’s just a question of watching the money rolling in! A useful way of doing that is by downloading an app called Microstockr.

    All you need to do is to set up your various agencies on the accounts page and then check the dashboard every now and then for any sales you’ve made. It’s very addictive! Sales should come quite soon after each batch is uploaded, but you may have to wait a while for payment.

    Most agencies have a ‘payment threshold’ of $50 or $100, which means your first payment (usually through PayPal) might take months to arrive. You’ll also need to keep adding more pictures. Buyers tend to sort images according to what’s most recent, so you definitely get diminishing returns from your shots, however good they are.

    The other thing to say is that, with dozens of agencies and hundreds or even thousands of images, it gets very confusing. As a result, I’ve created a spreadsheet to keep track of the whole thing.

    With filenames down the left and agency names across the top, I know if each file has been uploaded (‘u’), submitted (‘s’) or accepted (‘y’) and how many times it’s been sold. I keep a record of the dollar value of all the image downloads on a separate financial spreadsheet. I suggest you do the same.

  2. Stock agencies
    In the good old days, it was much easier to make a living out of stock photography, mainly because the royalty rates were a lot higher. The difference between ‘stock’ and ‘microstock’ is simply the average price level.Stock agencies want to differentiate themselves from microstock agencies (and everything else out there on the web) in order to charge a higher price, so they generally ask for exclusive agreements over one to five years and set a higher standard for acceptance.I use Design Pics, and you can see that they sell my images for hundreds of dollars rather than just a few dollars for the microstock agencies. My general strategy is to offer Design Pics the first pick of my pictures before sending the leftovers to all the microstock agencies.(I’ve also submitted some flower images to flowerphotos and a few marine wildlife shots to SeaPics, but I haven’t seen any sales from them so far.) Due to the long sales and reporting cycle, I didn’t see my first sale from Design Pics until more than a year after I’d signed up, but sales are starting to trickle in now, so it just takes a bit of patience.

    If you’re looking for a list of stock agencies, I recommend buying a copy of 2017 Photographer’s Market, which is the equivalent of the Writers’ and Artists’ Yearbook. It has comprehensive coverage of the industry, including helpful articles and a wealth of phone numbers and email addresses for magazines, book publishers, greeting card companies, stock agencies, advertising firms, competitions and more.

    I suggest buying the Kindle electronic version, and then you can download everything on to your laptop. I did that and then simply emailed every stock agency on the list – Design Pics was the only one to say yes!

  3. Competitions
    If you just want the ego boost of seeing yourself winning a competition, then I suggest you sign up with Pixoto and enter the contests with the lowest number of entrants. It’s a peer-to-peer site, and you can organise your own competitions, so there’s a very good chance of winning something!That’s exactly what I did, and I ended up with the Judge’s Award in four competitions. However, there isn’t much prestige to something like that, and it certainly doesn’t earn you any money.Alternatively, you can scour the 2017 Photographer’s Market for competitions, bearing in mind your chances of winning, the cost of entry, the potential prizes and the subject matter.The UK national press is a good place to start, too, and I recently won £250 in Wex Photographic vouchers in the weekly Sunday Times/Audley Travel Big Shot competition.
  4. Exhibitions
    Putting on an exhibition may seem like a big deal if you’ve never done it before, but it doesn’t have to be expensive or time-consuming. The Norman Plastow Gallery where I started out is cheap, but it’s slightly off the beaten path, and you have to man the exhibition yourself, which is obviously impossible for most full-time employees.You realise pretty soon as a freelance photographer that the most expensive item on your tab is often the opportunity cost of NOT doing what you usually do when you take time off. As a tutor, for instance, I could easily have earned £1,000 during the two weeks of my first exhibition, but them’s the breaks…If you’re looking for a list of galleries, www.galleries.co.uk is a useful starting point. London is obviously the best place to look, but exhibition spaces there don’t come cheap. I recently looked for galleries to use for an exhibition, and the ones in central London regularly quoted me thousands of pounds for a week! Everything is negotiable, though, so don’t give up.I started out with 15 prints at my first solo show, but I also printed out a few postcards and greetings cards. You might not make as much money out of them, but at least you’ll get something from punters who can’t afford a print.

    There are some who say that cards are just a distraction, but it’s so difficult to tell. I’ve had exhibitions with and without cards on sale, and it doesn’t seem to make much of a difference. However, the main reason for an exhibition is to sell prints, so that should be the focus.

    One of the problems you’ll almost certainly have is knowing how to price your work. Choosing your favourite shots is easy enough – although getting a second opinion from a friend is a useful exercise – but how much should you charge?

    I started off at £80 for an A3 print and ended up three years later at £2,000 for a 53″ x 38″ print, so you’ll just have to suck it and see. Andy Skillen suggested a mark-up of two-and-a-half times your printing and framing costs to make sure your cashflow remained positive, but that’s just a rule of thumb.

  5. Photo shoots
    Proper professional photographers make most of their money from photo shoots, but clients aren’t easy to find.If you’re a wedding photographer, I suppose you can put up flyers at various local venues such as churches and registry offices, but, for the rest of us, it’s just a question of plugging away, taking as many good shots as we can and putting them online so that as many potential clients can see them as possible.It would be a dream to be able to rely on commissions from wealthy clients who called us up whenever they wanted pictures of something. A photographer told me once about a group of directors who asked him for a picture of five hippos in a lake looking at the camera.He sent them all the hippo shots he had, but they weren’t happy. In the end, he told them if they didn’t want to compromise on the picture, then they’d have to send him on an all-expenses-paid trip to Zambia for a week. Which they did!

    He got the shot within a couple of days and then spent the rest of the trip taking pictures for himself!

    That sounds like a nice way to make a living, doesn’t it? However, until we’re well established enough with a good enough reputation to get those kinds of jobs, all we can do is keep on snapping and use the networks that we have.

    I’ve worked for a milliner, a local councillor, a businesswoman and others, but all my photo shoots have come from friends of friends or personal contacts.

    I’m not very good at networking – and it’s certainly not something I enjoy unless it happens naturally – but it’s very important in this business.

  6. Lessons
    I work as a private tutor as well as a photographer, so I guess it was an obvious fit to offer photography lessons. It’s finding the students that’s the real problem, though. One of my tuition agencies provided me with a couple of clients, while the rest came from connections I made at exhibitions and talks.You never know when you might meet just the right person, so it’s important to keep a few cards in your wallet just in case.
  7. Talks
    If you don’t mind public speaking, then giving a slideshow and talk on photography is an enjoyable way to earn some pocket money. Camera clubs and other groups won’t generally pay more than £100 (if anything at all!), but it’s also a useful chance to take along a few prints to sell and to hand out business cards.I got started after meeting a very nice woman on an Antarctic cruise, and I’ve now given talks at her branch of the WI, two camera clubs and a local library. If you want to be proactive about it, I’d simply Google camera clubs (or WI branches!) and email all of them to see what happens.As my mum used to say, you have to cast your bread upon the waters…even if it sometimes comes back a soggy mess!
  8. Photography trips
    One final way of making money is to lead photography trips. A lot of photographers do it to supplement their income, and it’s a good way to reduce your travel budget.I recently put together a list of tour operators and emailed them all one afternoon to find out if it could work, and I soon received a call from the founder of Gane & Marshall, asking me to lead a trip to Tanzania!I offered my services for free in exchange for the chance to go on an all-expenses-paid photographic safari. Now all we have to do is find at least five people to come on the trip and make it economic. Fingers crossed!

I hope all that was useful. If you have any more questions, please drop me a line at nick@nickdalephotography.com. It’s not easy becoming a professional photographer, but we can at least take pictures as a hobby while we wait for our big break.

Here’s to clicking and dreaming…

Red Xmas Tree star with Bokeh Lights

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The Idea

I live in an Art Deco mansion block in Putney, and every year the porters put a Christmas tree in the entrance hall. Last year, I took some pictures of some of the baubles, inspired by an email from one of the photographic magazines about how to capture bokeh lighting. This year, the tree and the baubles were different, so I decided to have another go.

The Location

Ormonde Court, Upper Richmond Road, London SW15 6TW, United Kingdom, around 2100 on 12 December 2014.

The Equipment

  • Nikon D800 DSLR camera
  • Nikon AF-S VR Micro-NIKKOR 105mm f/2.8G IF-ED lens
  • Nikon SB-910 Speedlight flash
  • Manfrotto 190XProB tripod with 496RC2 universal joint head
  • Hähnel HRN 280 remote release.

I’ve just managed to remortgage my flat in Notting Hill, so I’ve been investing in a few photographic supplies. Ever since a German called Stefan took a magnificent shot of Old Faithful at night using flash, I’ve wanted a proper flashgun. Well, now I have one. I bought the Nikon SB-910 Speedlight a couple of weeks ago, and it arrived just in time for this shoot. I didn’t know whether I’d need it or not, but I was prepared to experiment.

The Settings

  • Manual ISO 100
  • f/5.6
  • 1 second
  • 105mm
  • Tungsten white balance
  • Single-point auto-focus

The Technique

In the last of these posts, I mentioned how I’d got used to taking a tripod with me in almost all circumstances, and last night was no exception. Last year, I was generally pleased with my shots of the baubles, but the ISO was far too high.

I was using my tripod, funnily enough, but to hold the bauble rather than my camera! This year, I decided I would definitely mount the camera on the tripod, but that left me with nothing to hold the baubles.

I thought about using a light stand from my flash kit, but I needed something horizontal rather than vertical so that I could hang the decorations from it. I then had the idea of using my golf clubs. I could stand the bag in the lobby and balance one of the clubs on top, held in place by the other clubs.

As it turned out, I’d forgotten that the bag would be at an angle of 45 degrees, so my original plan didn’t work, but I simply pulled my 4-iron half-way out and hung the first bauble from that. It was a silver reindeer, but the green wire loop wasn’t very long, and I wouldn’t have been able to get the shots I wanted without the golf club getting in the frame.

I needed a piece of string. I thought about going back to my flat, but leaving my golf clubs and my camera unattended in the entrance hall didn’t seem like a sensible idea! Fortunately, I was wearing trainers, so I just used one of the laces.

It took a few gos to get each bauble to point in the right direction and remain still – particularly as there was a stream of curious residents opening the front door on their way home from work! – but I managed in the end. Phew!

I took lots of pictures of the silver reindeer, a red bauble with a spiral pattern on it and the red star shown above, and I played around with the flash settings to try to make the background a bit darker.

Sadly my new flash was so powerful that I couldn’t manage that – even with -3.0EV of exposure compensation! There might’ve been a better way, but it was the first time I’ve ever used a flashgun, so I’m still a newbie.

The main problem I had in taking the shots was actually getting enough depth-of-field. The reindeer was fine, but the round baubles and even the star were proving a nightmare. If I focused on the front of the bauble, the metal cap and wire loop were out of focus, but, if I focused on those, the rest of the bauble was out of focus.

I’m an absolute stickler for sharpness in my images, so I wasn’t sure what to do. In the end, I stopped down a little bit and hoped that f/5.6 would be a small enough aperture to keep everything acceptably sharp. I tried ‘chimping’ (or checking the shots on the LCD screen) a few times, but it was tricky to tell.

My problem was a kind of Catch-22: the three variables controlling depth-of-field are normally the focal length, the aperture and the relative distances of the camera to the subject and the subject to the background.

I couldn’t change to a wide-angle lens, as I needed to limit the background to just the Christmas tree; I couldn’t change to a much smaller aperture without making the bokeh circles of the blurred Christmas lights in the background too small; and I couldn’t change the relative positions of the camera, bauble and tree without changing the composition completely.

Hmm…

As you can see from the shot above, the two arms on the right of the red star didn’t turn out completely sharp, but it was ‘good enough for Government work’. Shutterstock obviously didn’t accept it – they’re very hot on sharpness! – but I did win an award on Pixoto for the sixth best image uploaded to the Christmas category!

The Post-processing

I made three changes to this shot:

  1. I had the camera on ‘Tungsten’ white balance, as I’d just read somewhere that I should use the amber filter on the flashgun when shooting indoors in order to avoid a clash of different light sources. However, it turned out that the shot looked a lot warmer with the ‘Flash’ white balance, and that was just the look I was after at Christmastime.
  2. A lot of my images end up being quite dark, and I’m not sure whether it’s just because I’m lucky to spend a lot of time in very sunny places or whether there’s a problem with my camera! In this case, I actually had to push the exposure up by +2EV in Aperture to make it look like all the others. I have a feeling that’s because I changed from f/2.8 to f/5.6 to get more depth-of-field but forgot to lengthen the shutter speed to compensate. Silly me…
  3. I was desperately trying to frame the shot perfectly so I wouldn’t have to crop, but the balance of the bauble with the ‘negative space’ on the right wasn’t quite right, so I cropped in slightly to position the star a third of the way into the frame.

Close-up of Golden Eagle Head with Catchlight

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I’m a photographer (among other things), and this is the first of a series of posts about my favourite photographs. I’ll tell you how I took them and break down the shot into the idea, the location, the equipment, the settings, the technique and any post-processing.

The Idea

When I took this shot, I was at a Battle of Hastings re-enactment at Battle Abbey in Sussex. I was there to take pictures of the battle scenes between enthusiasts dressed up as Normans and Saxons, and I had no idea there was going to be a falconry display until I bought my ticket and was given a flyer with the plan for the day.

The golden eagle is my favourite bird (isn’t it everyone’s?!), so I was very excited to be able to see one in action. The falconers from Raphael Historical Falconry put on a couple of displays with a variety of birds, including a gyrfalcon and a Harris hawk, but the golden eagle was the highlight.

Afterwards, I wandered over to their tent, and I was able to get within just a few feet of all the birds. The falconer was happy to chat with the spectators with a bird on his arm (so to speak!), and later he fed and watered the birds outside. That gave me the chance to set up my tripod and get a few good close-ups, and this was the best of the lot.

The Location

Battle Abbey, High Street, Hastings and Battle, East Sussex TN33 0AD, United Kingdom, around 1500 on 11 October 2014.

The Equipment

  • Nikon D800 DSLR camera
  • Sigma 50-500mm F4.5-6.3 APO DG OS HSM lens
  • Manfrotto 190XProB tripod with 496RC2 universal joint head
  • Hähnel HRN 280 remote release.

I was a bit worried about using my ‘Bigma’ to take this picture, as I hadn’t been very impressed with it on my trip to Spitsbergen to see the polar bears. Admittedly, the bears were usually a few hundred yards away, and no zoom lens is at its best when it’s at its longest focal length, but I was disappointed that my shots were so soft.

As a result, I did a manual focus check and discovered that the calculated auto-focus fine tune setting was a whopping -12! Armed with this new improvement to the sharpest tool in my box, I was ready for anything…

PS They call it the ‘Bigma’ as it’s made by Sigma, and it’s enormous!

The Settings

  • Auto ISO 110
  • f/9
  • 1/250
  • 500mm
  • Daylight white balance
  • Single-point auto-focus

I had the camera on Manual with ISO on Auto, which I thought was appropriate for a day when lots of things would be happening, and I’d be taking candid shots without much opportunity to sit down and check my settings. However, I should probably have set the ISO to its optimum value of 100 for this shot, as I had plenty of time.

The Technique

I’m generally a travel and wildlife photographer, but I normally don’t use a tripod as it gets in the way and doesn’t work too well in a Land-Rover moving at 40mph! However, I learnt a new perspective from a professional photographer called Mark Carwardine.

He happened to be on a cruise to Spitsbergen that I went on a few months ago, and he was always carrying around his tripod with the legs fully extended – even on the Zodiac inflatables that we used to land on the islands.

I thought to myself, If he can do it, so can I! After that, I’ve tried to use a tripod wherever possible. I love really sharp wildlife shots, and a 36.3-megapixel DSLR and a tripod make a winning combination.

Another important thing about wildlife shots is to get down to the level of the animal or bird you’re shooting. You can see from this shot that I’m right at eye-level with the eagle, and that gives the sense of power and intimacy I was looking for.

Finally, I’ve learnt from a couple of portrait shoots the value of the ‘catchlight’. This is the reflection of the light source that you see in the eye of your subject. It’s just as important with wildlife as with people, and I was lucky enough to get a break in the clouds that allowed the sun to provide the perfect catchlight. Lucky me!

The Post-processing

I changed from a PC to a Mac a few years ago, so I do all my post-processing in Aperture. I suppose I should upgrade to Lightroom or Adobe Camera Raw or Photoshop, but iPhoto was the default image-processing software on the Mac, and Aperture was the cheapest upgrade!

I only had two changes to make to this shot:

  1. Even at 500mm, I still wasn’t quite close enough for the bird’s head to fill the frame, so I had to crop in later. I’ve found from experience that 6.3 megapixels is the minimum size that the major online photo libraries accept, so I never go below 6.4 MP (to avoid rounding errors), and that’s the new size of this file.
  2. In the end, the automatic ISO setting was close enough to the optimum of 100, but the shot was slightly overexposed due to the dark colours of the eagle’s feathers and the grassy background, so I had to reduce the exposure by 0.5EV.

Tips for the QTS Numeracy Test

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“If I’d known I’d have to go back to school, I’d never have become a teacher!”

The QTS numeracy and literacy tests are not very popular, but trainee teachers still have to pass them before they can start teaching in the state sector, so I thought I’d try and help out. There is always more than one way of doing a Maths question, but I hope I’ll demonstrate a few useful short cuts and describe when and how they should be used.

The point of short cuts is that, even though you may have to do more sums, they’ll be easier sums that can be done faster and more accurately. The numeracy test consists of two sections – mental Maths and interpreting charts – and I’m going to focus on the first of these.

Fractions to Percentages – Type 1

There are a number of typical types of questions in the numeracy test, and a lot of them involve multiplication – so knowing your times tables is an absolute must! One of the most common kinds of question involves converting fractions to percentages.

These are just two ways of showing the same thing, but to answer these questions you’ll need to try different approaches. First of all, have a look to see if the denominator (or the number on the bottom of the fraction) is a factor or a multiple of 100.

If it is, you can simply multiply or divide the numerator (the number on the top) and the denominator by whatever it takes to leave 100 on the bottom. Any fraction over 100 is just a percentage in disguise, so you just need to put the percentage sign after the numerator, eg what is the percentage mark if:

  1. a pupil scores 7 out of a possible 20?
    Answer: 20 x 5 = 100, so 7 x 5 = 35%.
  2. a pupil scores 18 out of a possible 25?
  3. a pupil scores 7 out of a possible 10?
  4. a pupil scores 9 out of a possible 20?
  5. a pupil scores 130 out of a possible 200?

Fractions to Percentages – Type 2

If the denominator is not a factor of 100, check if it’s a multiple of 10. If it is, you can convert the fraction into tenths and then multiply the top and bottom by 10 to get a fraction over 100, which, again, is just a percentage in disguise, eg what is the percentage mark if:

  1. A pupil scores 24 marks out of a possible 40?
    Answer: 40 ÷ 4 = 10, so 24 ÷ 4 = 6 and 6 x 10 = 60%.
  2. A pupil scores 12 marks out of a possible 30?
  3. A pupil scores 32 marks out of a possible 80?
  4. A pupil scores 49 marks out of a possible 70?
  5. A pupil scores 24 marks out of a possible 60?

Fractions to Percentages – Type 3

If neither of the first two methods works, that means you have to simplify the fraction. Once you’ve done that, you should be able to convert any common fraction into a percentage in your head. The most commonly used fractions are halves, quarters, fifths and eighths, so it’s worth learning the decimal and percentage equivalents off-by-heart, ie

  • ½ = 0.5 = 50%
  • ¼ = 0.25 = 25%
  • ¾ = 0.75 = 75%
  • ⅕ = 0.2 = 20%
  • ⅖ = 0.4 = 40%
  • ⅗ = 0.6 = 60%
  • ⅘ = 0.8 = 80%
  • ⅛ = 0.125 = 12.5%
  • ⅜ = 0.375 = 37.5%
  • ⅝ = 0.625 = 62.5%
  • ⅞ = 0.875 = 87.5%

To simplify the fractions, check first to see if the numerator goes into the denominator. If it does, you can simply divide both numbers by the numerator to get what’s called a ‘unit fraction’, in other words, a fraction with a one on top, eg 4/8 divided by four top and bottom is ½.

By definition, a unit fraction can’t be simplified, so then you just have to convert it into a percentage.

If the numerator doesn’t go exactly, divide it by the first prime number (two) and then try to divide the denominator by the result, eg 6 ÷ 2 = 3, so 6/9 divided by three top and bottom is 2/3.

If that doesn’t work, try dividing the numerator by the next prime number (three) and so on and so on…

This will guarantee that the fraction ends up in the lowest possible terms, at which point it should be in the list above, which means you can easily convert it into the correct percentage, eg what is the percentage mark if:

  1. a pupil scores 7 out of a possible 28?
    Answer: 7 goes into 28 four times, so the fraction is 1/4, which is 25%.
  2. a pupil scores 27 out of a possible 36?
    Answer: 27 doesn’t go into 36, but 27 ÷ 3 = 9, so 27/36 divided by 9 top and bottom makes 3/4, which is 75%.
  3. a pupil scores 24 out of a possible 48?
  4. a pupil scores 8 out of possible 32?
  5. a pupil scores 9 out of a possible 24?

Multiplying Three Numbers Involving Money

There is often a ‘real world’ money problem in the QTS numeracy test. That usually means multiplying three numbers together. The first thing to say is that it doesn’t matter in which order you do it, eg 1 x 2 x 3 is the same as 3 x 2 x 1.

The next thing to bear in mind is that you will usually have to convert from pence to pounds. You could do this at the end by simply dividing the answer by 100, but a better way is to divide one of the numbers by 100 (or two of the numbers by 10) at the beginning and then multiply the remaining three numbers together, eg a number of pupils in a class took part in a sponsored spell to raise money for charity. The pupils were expected to get a certain number of correct spellings, and the average amount of sponsorship is shown for each.

How many pounds would the class expect to raise for charity if the basic sum is:

  1. 20 x 30 x 5p?
    Answer: 2 x 3 x 5 = 6 x 5 = £30.
  2. 40 x 500 x 7p?
  3. 30 x 400 x 6p?
  4. 50 x 40 x 8p?
  5. 60 x 20 x 9p?

Division by Single-digit Numbers

This is what I call the ‘wedding planner problem’. There are three ways of doing this type of question:

  • Method A: Use the ‘bus stop’ method to divide the total number of guests by the number of seats per table – remembering to add one if there is a remainder.
  • Method B: Go straight to the end of your times tables by multiplying the number of seats by 12, then calculating the remainder and dividing by the number of seats per table, again remembering to add one if there is another remainder.
  • Method C: Use trial and error by estimating the number of tables needed using a nice, round number such as 5, 10 or 20 and working out the remainder as before.
  1. Dining tables seat 7 children. How many tables are needed to seat 100 children?
    Answer:
    Method A) 100 ÷ 7 = 14 r 2, so 14 + 1 = 15 tables are needed.
    Method B) 7 x 12 = 84, 100 – 84 = 16, 16 ÷ 7 = 2 remainder 2, 12 + 2 + 1 = 15 tables.
    Method C) 10 x 7 = 70, which is too small, 20 x 7 = 140, which is too big, 15 x 7 = 70 + 35 = 105, which is just right as there are only 5 seats to spare.
  2. Dining tables seat 6 children. How many tables are needed to seat 92 children?
  3. Dining tables seat 5 children. How many tables are need to seat 78 children?
  4. Dining tables seat 9 children. How many tables are needed to seat 120 children?
  5. Dining tables seat 6 children. How many tables are needed to seat 75 children?

Division by Two-digit Numbers

If the number of seats is outside your times tables, the best option is just to use trial and error, starting with 5, 10 or 20, eg

  1. It is possible to seat 40 people in a row across the hall. How many rows are needed to seat 432 people?
    Answer: 40 x 10 = 400, 432 – 400 = 32, so one more row is needed, making a total of 10 + 1 = 11 rows.
  2. It is possible to seat 32 people in a row across the hall. How many rows are needed to seat 340 people?
  3. It is possible to seat 64 people in a row across the hall. How many rows are needed to 663 people?
  4. It is possible to seat 28 people in a row across the hall. How many rows are needed to seat 438 people?
  5. It is possible to seat 42 people in a row across the hall. How many rows are needed to seat 379 people?

Percentages to Fractions

This is a type of question that looks hard at first but becomes dead easy with the right short cut. All you need to do is to work out 10% first and then multiply by the number of tens in the percentage.

Another way of saying that is just to knock one zero off each number and multiply them together, eg a test has a certain number of questions, each worth one mark. For the stated pass mark, how many questions had to be answered correctly to pass the test?

  1. ?/30 = 40%
    Answer: 3 x 4 = 12 questions (ie 10% of 30 is 3 questions, but we need 40%, which is 4 x 10%, so we need four lots of three, which is the same as 3 x 4).
  2. ?/40 = 70%
  3. ?/50 = 90%
  4. ?/80 = 70%
  5. ?/300 = 60%

Ratio – Distance

There are two ways of converting between different units of distance from the metric and imperial systems:

  • Method A: Make the ratio into a fraction and multiply the distance you need to find out by that same fraction, ie multiply it by the numerator and divide it by the denominator. (Start with multiplication if doing the division first wouldn’t give you a whole number.)
  • Method B: Draw the numbers in a little 2 x 2 table, with the figures in the ratio in the top row and the distance you need to find out in the column with the appropriate units, then find out what you need to multiply by to get from the top row to the bottom row and multiply the distance you have to find out by that number to fill in the final box.
  1. 8km is about 5 miles. How many kilometres is 40 miles?
    Answer:
    Method A) 8:5 becomes 8/5, and 40 x 8/5 = 40 ÷ 5 x 8 = 8 x 8 = 64km.
    Method B)
    Miles                 km
    5                          8
    x 8
    40               8 x 8 = 64km
  2. 6km is about 4 miles. How many kilometres is 36 miles?
  3. 4km is about 3 miles. How many kilometres is 27 miles?
  4. 9km is about 7 miles. How many miles is 63 kilometres?
  5. 7km is about 4 miles. How many kilometres is 32 miles?

Ratio – Money

You can use the same methods when converting money, except that the exchange rate is now a decimal rather than a fraction. Just remember that the pound is stronger than any other major currency, so there will always be fewer of them. It’s easy to get things the wrong way round, so it’s worth spending a couple of seconds checking, eg

  1. £1 = €1.70. How much is £100 in euros?
    Method A) 100 x 1.70 = €170.
    Method B)
    £                                      €
    1.00                              1.70
    x 100
    100                    1.70 x 100 = €170
  2. £1 = €1.60. How much is £200 in euros?
  3. £1 = €1.50. How much is €150 in pounds?
  4. £1 = €1.80. How much is €90 in pounds?
  5. £2 = €3.20. How much is £400 in euros?

Time – Find the End time

The most useful trick to use here is rounding. If the length of a lesson is 45 minutes or more, then just round up to the full hour and take the extra minutes off at the end. This avoids having to add or subtract ‘through the hour’, which is more difficult.

If the lessons are less than 45 minutes long, just work out the total number of minutes, then convert into hours and minutes and add to the start time, eg

  1. A class starts at 9:35. The class lasts 45 minutes. What time does the class finish?
    Answer: 9:35 + 1 hour – 15 minutes = 10:35 – 15 minutes = 10:20.
  2. A class starts at 11:45. There are three consecutive classes each lasting 25 minutes and then half an hour for lunch. What time does lunch finish?
    Answer: 11:45 + 3 x 25 + 30 = 11:45 + 75 + 30 = 11:45 + 1 hour and 15 minutes + 30 minutes = 13:30.
  3. Lessons start at 11:15. There are two classes each lasting 40 minutes and then lunch. What time does lunch start?
  4. Lessons start at 2:00 in the afternoon. There are four 50-minute classes with a 15-minute break in the middle. What time does the day finish?
  5. Lessons start at 9:40. There are two classes of 50 minutes each with a break of 15 minutes in between. What time do the classes finish?

Time – Find the Start Time

It’s even more important to use rounding when working backwards from the end of an event, as subtraction is that bit more difficult, eg

  1. A school day finishes at 3:15. There are two classes of 50 minutes each after lunch with a break of 15 minutes in the middle. What time does lunch end?
    Answer: 3:15 – 2 hours + 2 x 10 minutes – 15 minutes = 1:15 + 20 minutes -15 minutes = 1:20.
  2. A school day finishes at 4:30. There are two classes of 40 minutes each after lunch. What time does lunch finish?
    Answer: 4:30 – 2 x 40 = 4:30 – 80 minutes = 4:30 – 1 hour and 20 minutes = 3:10.
  3. Lunch starts at 1:05. There are two classes before lunch of 55 minutes each. What time do the classes start?
  4. Lunch starts at 1:15. There are three classes before lunch of 45 minutes each. What time do the classes start?
  5. A school bus arrives at school at 8:45. It picks up 20 children, and it takes an average of four minutes to pick up each child. What time is the first child picked up?

Percentage to Decimal

A decimal is a fraction of one unit, but a percentage is a fraction of 100 units, so, to convert from a percentage to a decimal, you just need to divide by 100, eg

  1. What is 20% as a decimal?
    Answer: 20 ÷ 100 = 0.2.
  2. What is 30% as a decimal?
  3. What is 17% as a decimal?
  4. What is 6% as a decimal?
  5. What is 48% as a decimal?

Multiplying Decimals

Decimal points can be confusing, so the best way to do these sums is to take out the decimal point and put it back at the end. You just need to remember to make sure there are the same number of decimal places in the answer as in both numbers in the question, eg

  1. 1.5 x 1.5
    Answer: 15 x 15 = 10 x 15 + 5 x 15 = 150 + 75 = 225, but there are two decimal places in the numbers you’re multiplying together, so the answer must be 2.25.
  2. 3 x 4.5
  3. 4.7 x 8
  4. 7.5 x 7.5
  5. 2.5 x 6.5

Multiplying Decimals by a Power of 10

Because we have 10 fingers, we’ve ended up with a ‘decimal’ number system based on the number 10.

That makes it really easy to multiply by powers of 10, because all you have to do is to move the decimal point to the right by a suitable number of places, eg one place when multiplying by 10, two when multiplying by 100 etc. (You can also think of it as moving the digits in the opposite direction.)

This type of question is therefore one of the easiest, eg

  1. 4.5 x 10
    Answer: 45.
  2. 3.8 x 100
  3. 7.6 x 1000
  4. 4.6 x 100
  5. 3.5 x 10

Percentage of Quantity

Finding a percentage is easy if it ends with a zero, as you can start by finding 10% (Method A). If you happen to know what the fraction is, you can also divide by the numerator of that fraction (Method B), so 20% is 1/5, so you just need to divide by five, eg

  1. Find 20% of 360
    Answer:
    Method A) 360/10 x 2 = 36 x 2 = 72.
    Method B) 360 ÷ 5 = 72 (or 360 x 2 ÷ 10 = 720 ÷ 10 = 72).
  2. Find 20% of 45
  3. Find 30% of 320
  4. Find 60% of 60
  5. Find 80% of 120

Multiplication

Just because this is the ‘mental Maths’ section of the test doesn’t mean that you can’t work things out on paper, and these simple multiplication sums can be done like that.

Alternatively, you can use ‘chunking’, which means multiplying the tens and units separately and adding the results together, and the short cut for multiplying by five is to multiply by 10 and then divide by two, eg

  1. 23 x 7
    Answer: 20 x 7 + 3 x 7 = 140 + 21 = 161.
  2. 42 x 5
    Answer: 42 x 10 ÷ 2 = 420 ÷ 2 = 210
  3. 34 x 6
  4. 56 x 8
  5. 34 x 8

Short Division

Again, working these sums out on paper is probably quicker (and more reliable), although the easiest way to divide by four is probably to halve the number twice, and the short cut for dividing by five is to multiply by two and then divide by 10.

  1. 292 ÷ 4
    Answer: 292 ÷ 2 ÷ 2 = 146 ÷ 2 = 73.
  2. 345 ÷ 5
    Answer: 345 x 2 ÷ 10 = 690 ÷ 10 = 69.
  3. 282 ÷ 3
  4. 565 ÷ 5
  5. 432 ÷ 4

Red Xmas Tree Star with Bokeh Lights

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Christmas is a time for baubles, lights, golf clubs and a Nikon D800…

The Idea

I live in an Art Deco mansion block in Putney, and every year the porters put up a tree in the entrance hall. Last year, I took some pictures of some of the baubles, inspired by an email from one of the photographic magazines about how to capture bokeh lighting. This year, the tree and the baubles were different, so I decided to have another go.

The Location

Ormonde Court, Upper Richmond Road, London SW15 6TW, United Kingdom, around 2100 on 12 December 2014.

The Equipment

  • Nikon D800 DSLR camera
  • Nikon AF-S VR Micro-NIKKOR 105mm f/2.8G IF-ED lens
  • Nikon SB-910 Speedlight flash
  • Manfrotto 190XProB tripod with 496RC2 universal joint head
  • Hähnel HRN 280 remote release.

I’ve just managed to remortgage my flat in Notting Hill, so I’ve been investing in a few photographic supplies. Ever since a German called Stefan took a magnificent shot of Old Faithful at night using flash, I’ve wanted a proper flashgun. Well, now I have one. I bought the Nikon SB-910 Speedlight a couple of weeks ago, and it arrived just in time for this shoot. I didn’t know whether I’d need it or not, but I was prepared to experiment.

The Settings

  • Manual ISO 100
  • f/5.6
  • 1 second
  • 105mm
  • Tungsten white balance
  • Single-point auto-focus

The Technique

In the last of these posts, I mentioned how I’d got used to taking a tripod with me in almost all circumstances, and last night was no exception. Last year, I was generally pleased with my shots of the baubles, but the ISO was far too high.

I was using my tripod, funnily enough, but to hold the bauble rather than my camera! This year, I decided I would definitely mount the camera on the tripod, but that left me with nothing to hold the baubles.

I thought about using a light stand from my flash kit, but I needed something horizontal rather than vertical so that I could hang the decorations from it. I then had the idea of using my golf clubs. I could stand the bag in the lobby and balance one of the clubs on top, held in place by the other clubs.

As it turned out, I’d forgotten that the bag would be at an angle of 45 degrees, so my original plan didn’t work, but I simply pulled my 4-iron half-way out and hung the first bauble from that. It was a silver reindeer, but the green wire loop wasn’t very long, and I wouldn’t have been able to get the shots I wanted without the golf club getting in the frame.

I needed a piece of string. I thought about going back to my flat, but leaving my golf clubs and my camera unattended in the entrance hall didn’t seem like a sensible idea! Fortunately, I was wearing trainers, so I just used one of the laces.

It took a few gos to get each bauble to point in the right direction and remain still – particularly as there was a stream of curious residents opening the front door on their way home from work! – but I managed in the end. Phew!

I took lots of pictures of the silver reindeer, a red bauble with a spiral pattern on it and the red star shown above, and I played around with the flash settings to try to make the background a bit darker.

Sadly my new flash was so powerful that I couldn’t manage that – even with -3.0EV of exposure compensation! There might’ve been a better way, but it was the first time I’ve ever used a flashgun, so I’m still a newbie.

The main problem I had in taking the shots was actually getting enough depth-of-field. The reindeer was fine, but the round baubles and even the star were proving a nightmare. If I focused on the front of the bauble, the metal cap and wire loop were out of focus, but, if I focused on those, the rest of the bauble was out of focus.

I’m an absolute stickler for sharpness in my images, so I wasn’t sure what to do. In the end, I stopped down a little bit and hoped that f/5.6 would be a small enough aperture to keep everything acceptably sharp.

I tried ‘chimping’ (or checking the shots on the LCD screen) a few times, but it was tricky to tell. My problem was a kind of Catch-22: the three variables controlling depth-of-field are normally the focal length, the aperture and the relative distances of the camera to the subject and the subject to the background.

I couldn’t change to a wide-angle lens, as I needed to limit the background to just the Christmas tree; I couldn’t change to a much smaller aperture without making the bokeh circles of the blurred Christmas lights in the background too small; and I couldn’t change the relative positions of the camera, bauble and tree without changing the composition completely.

Hmm…

As you can see from the shot above, the two arms on the right of the red star didn’t turn out completely sharp, but it was ‘good enough for Government work’. Shutterstock obviously didn’t accept it – they’re very hot on sharpness! – but I did win an award on Pixoto for the sixth best image uploaded to the Christmas category yesterday!

Post-processing

I made three changes to this shot:

  1. I had the camera on ‘Tungsten’ white balance, as I’d just read somewhere that I should use the amber filter on the flashgun when shooting indoors in order to avoid a clash of different light sources. However, it turned out that the shot looked a lot warmer with the ‘Flash’ white balance, and that was just the look I was after at Christmastime.
  2. A lot of my images end up being quite dark, and I’m not sure whether it’s just because I’m lucky to spend a lot of time in very sunny places or whether there’s a problem with my camera! In this case, I actually had to push the exposure up by +2EV in Aperture to make it look like all the others. I have a feeling that’s because I changed from f/2.8 to f/5.6 to get more depth-of-field but forgot to lengthen the shutter speed to compensate. Silly me…
  3. I was desperately trying to frame the shot perfectly so I wouldn’t have to crop, but the balance of the bauble with the ‘negative space’ on the right wasn’t quite right, so I cropped in slightly to position the star a third of the way into the frame.

Close-up of Golden Eagle Head with Catchlight

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I’m a photographer (among other things), and this is the first of a series of posts about my favourite photographs. I’ll tell you how I took them and break down the shot into the idea, the location, the equipment, the settings, the technique and any post-processing.

The Idea

When I took this shot, I was at a Battle of Hastings re-enactment at Battle Abbey in Sussex. I was there to take pictures of the battle scenes between enthusiasts dressed up as Normans and Saxons, and I had no idea there was going to be a falconry display until I bought my ticket and was given a flyer with the plan for the day.

The golden eagle is my favourite bird (isn’t it everyone’s?!), so I was very excited to be able to see one in action. The falconers from Raphael Historical Falconry put on a couple of displays with a variety of birds, including a gyrfalcon and a Harris hawk, but the golden eagle was the highlight.

Afterwards, I wandered over to their tent, and I was able to get within just a few feet of all the birds. The falconer was happy to chat with the spectators with a bird on his arm (so to speak!), and later he fed and watered the birds outside. That gave me the chance to set up my tripod and get a few good close-ups, and this was the best of the lot.

The Location

Battle Abbey, High Street, Hastings and Battle, East Sussex TN33 0AD, United Kingdom, around 1500 on 11 October 2014.

The Equipment

  • Nikon D800 DSLR camera
  • Sigma 50-500mm F4.5-6.3 APO DG OS HSM lens
  • Manfrotto 190XProB tripod with 496RC2 universal joint head
  • Hähnel HRN 280 remote release.

I was a bit worried about using my ‘Bigma’ to take this picture, as I hadn’t been very impressed with it on my trip to Spitsbergen to see the polar bears. Admittedly, the bears were usually a few hundred yards away, and no zoom lens is at its best when it’s at its longest focal length, but I was disappointed that my shots were so soft.

As a result, I did a manual focus check and discovered that the calculated auto-focus fine tune setting was a whopping -12! Armed with this new improvement to the sharpest tool in my box, I was ready for anything…

PS They call it the ‘Bigma’ as it’s made by Sigma, and it’s enormous!

The Settings

  • Auto ISO 110
  • f/9
  • 1/250
  • 500mm
  • Daylight white balance
  • Single-point auto-focus

I had the camera on Manual with ISO on Auto, which I thought was appropriate for a day when lots of things would be happening, and I’d be taking candid shots without much opportunity to sit down and check my settings. However, I should probably have set the ISO to its optimum value of 100 for this shot, as I had plenty of time.

The Technique

I’m generally a travel and wildlife photographer, but I normally don’t use a tripod as it gets in the way and doesn’t work too well in a Land-Rover moving at 40mph! However, I learnt a new perspective from a professional photographer called Mark Carwardine.

He happened to be on a cruise to Spitsbergen that I went on a few months ago, and he was always carrying around his tripod with the legs fully extended – even on the Zodiac inflatables that we used to land on the islands.

I thought to myself, If he can do it, so can I! After that, I’ve tried to use a tripod wherever possible. I love really sharp wildlife shots, and a 36.3-megapixel DSLR and a tripod make a winning combination.

Another important thing about wildlife shots is to get down to the level of the animal or bird you’re shooting. You can see from this shot that I’m right at eye-level with the eagle, and that gives the sense of power and intimacy I was looking for.

Finally, I’ve learnt from a couple of portrait shoots the value of the ‘catchlight’. This is the reflection of the light source that you see in the eye of your subject. It’s just as important with wildlife as with people, and I was lucky enough to get a break in the clouds that allowed the sun to provide the perfect catchlight. Lucky me!

Post-processing

I changed from a PC to a Mac a few years ago, so I do all my post-processing in Aperture. I suppose I should upgrade to Lightroom or Adobe Camera Raw or Photoshop, but iPhoto was the default image-processing software on the Mac, and Aperture was the cheapest upgrade!

I only had two changes to make to this shot:

  1. Even at 500mm, I still wasn’t quite close enough for the bird’s head to fill the frame, so I had to crop in later. I’ve found from experience that 6.3 megapixels is the minimum size that the major online photo libraries accept, so I never go below 6.4 MP (to avoid rounding errors), and that’s the new size of this file.
  2. In the end, the automatic ISO setting was close enough to the optimum of 100, but the shot was slightly overexposed due to the dark colours of the eagle’s feathers and the grassy background, so I had to reduce the exposure by 0.5EV.