- 11+ Hints and Tips
Lincolnshire is one of the counties that still offer students in year 6 the opportunity to attend a grammar school. To get into these schools students need to sit and achieve the 11+. Although some counties use an English and a Maths paper in these tests, Lincolnshire is not one of them. In Lincolnshire, the 11+ consists of a verbal reasoning paper and a non-verbal reasoning paper.
These are areas not taught in primary and involve logic, vocabulary skills, pattern solving
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…!
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! 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.
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 VWUDZ.
Normally, you just have to move a number of letters forwards or backwards in the alphabet (in this case, it’s +3), 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. These questions 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!
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 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 whether the missing letter is a vowel or a consonant and it’s also helpful 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! 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 (noun, verb, adjective etc). 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.
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 choices by getting rid 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.
To check words mean the same thing you could think of a phrase or sentence containing one of them and then try substituting all the other options. For example, if the words are:
(cook, meal, room) and (oven, space, eat),
start with ‘I like to cook dinner’ and then try all three of the other words. Does ‘I like to oven dinner’ mean the same? What about ‘I like to space dinner’ or ‘I like to eat dinner’? If none of the words fits exactly, then move on to the next word in the left-hand bracket and then the last one, if necessary. In the end, you should find the answer, which in this case is ‘room’ and ‘space’.
You can also narrow down the options by checking the parts of speech. If you’re looking for a word that means the same, it will have to be the same part of speech as the other word, eg a noun, verb or adjective.
These questions ask you to find ‘hidden’ four-letter words between two other words in a sentence, using the last few letters from one word and the first few from the next:
eg ‘The bird sat on the roof’. 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 choices by getting rid pairs of words that definitely don’t mean the opposite to each other. Once you’ve done that, feel free to guess which one of the leftover pairs is the answer.
Complete the Calculation
This is another number question, and it again means you need to know BIDMAS/BODMAS. You’ll be given an equation (or number sentence), and you just have to fill in the missing number to make sure it balances:
eg 24 – 10 + 6 = 8 + 7 + ( ).
First of all, work out what the complete side of the equation equals, and then add, subtract, divide or multiply by the numbers in the other side to work out the answer (in this case, 24 – 10 + 6 = 20, and 20 – 8 – 7 = 5, so 5 is the answer). Don’t forget you’re working backwards to the answer, so you have to use the opposite operators!
Rearrange to make two new words
In these questions, you’re given two words, and you have to take a letter from the first word and put it in any position in the second word to leave two new words:
eg STOOP and FLAT.
Again, check first to see if the answer’s obvious, but then work through systematically, picking letters from the first word one by one and trying to fit it into each position in the second word. (In this case, the answer is STOP and FLOAT.) Remember that both the new words must make sense!
This is another Maths question in which you’ll be given three sets of numbers in brackets with the middle one in square brackets. The middle number in the final set is missing, though, so you have to calculate it using the two on either side, based on what happens in the first two sets:
eg (3  5) (2  4) (7 [ ] 3).
The calculation will only involve the four basic operations (addition, subtraction, multiplication and division), it gets much harder when the numbers appear more than once! In this example, all you need to do is multiply the outside numbers to get the answer (3 x 5 = 15 and 2 x 4 = 8, so 7 x 3 = 21), but you might get more complicated questions like this one:
(16  8) (11  5) (4 [ ] 11).
Here, you have to add the first number to itself and then add the other one (16 + 16 + 8 = 40 and 11 + 11 + 5 = 27, so 4 + 4 + 11 = 19). These kinds of questions can be very difficult, so try not to spend too long on them. If it takes more than a minute or so to answer a question, it’s time to move on. You can always come back later if you have time at the end of the test.
These questions are a variation on number sequences in Maths – except using letters – and you answer them in the same way. You’re presented with several pairs of letters, and you have to fill in the blanks by working out what the patterns are:
eg AB BD CF ??.
The best way to do this is to focus on the first and second letters of each pair separately as there will always be a pattern that links the first letters of each pair and a pattern that links the second letters of each pair, but there usually won’t be a pattern that links one letter to the next. There’ll be a printed alphabet next to the question, so just do the same as you would for a number sequence question in Maths, drawing loops between the letters and labelling the ‘jump’ forwards or backwards in the alphabet, eg +1 or -2. Once you know what the pattern is, you can use it to work out the missing letters.
Just watch out for sequences with two patterns mixed together:
eg CD TS GH RQ KL PO ?.
Here, the first, third and fifth pairs of letters make up the sequence (with two letters missing between each pair), so the answer is OP.
Analogies (Complete the Sentence)
In this type of question, you’re given a sentence that includes three possibilities for two of the words. You have to use logic and common sense to work out what the two other words should be:
eg Teacher is to (bus, school, kitchen) as doctor is to (office, train, hospital).
This is known as an analogy: you have to work out the relationship of the first word to one of the words in the first set of brackets in order to find the same relationship in the second half of the sentence. Again, the best way to do it is to have a quick scan to see if the answer’s obvious. If it is, write it down. If it’s not, go through the possibilities one by one, making sure to put the relationship into words. In this example, a teacher ‘works in a’ school, and a doctor ‘works in a’ hospital, so ‘school’ and ‘hospital’ are the answer.
These are tricky! Be careful and take it steady! 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 not a single 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 of this type of question contains a string of letters that appears in both words of each pair, just with a different letter or letters to start:
eg (BLOAT, COAT) (CLING, DING) (SHOUT, ).
The easy bit is to find the repeated set of letters (in this case OAT) and to see that the second letter is dropped each time, but you still need to work out why the first letter changes (from B to C and then C to D). That shouldn’t be too hard to work out, though, if you just go through the alphabet to find how many positions forwards or backwards you have to go (in this case, it’s +1, so the answer is TOUT).
These questions provide you with a series of numbers and ask you to fill in the blanks, which might be anywhere in the sequence:
eg 1, 3, 5, 7, ?, ?.
As with alphabet series, the best way to find the answer is to draw a loop between each pair of numbers and write down the change in value. In this case, it’s simple (+2 each time), so the answer is 9 and 11, but look out for more complicated sequences. It’s worth knowing the most common sequences, just so you can recognise them at once and don’t have to work them out. Here are a few of the commonest ones:
- Even numbers: 2, 4, 6, 8 etc… Rule: 2n
- Odd numbers: 1, 3, 5, 7 etc… Rule: 2n – 1
- Powers of 2: 2, 4, 8, 16 etc… Rule: 2ⁿ
- 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
- Prime numbers: 2, 3, 5, 7 etc… Rule: n/a (each number is only divisible by itself and one)
- 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 a 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 (milk pain male) (man green water).
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, ‘milk’ goes with ‘man’ to make ‘milkman’.
Create a Word (from the Letters of Two Others)
These questions give you two groups of three words with the middle one in brackets in the first group and missing in the second,:
eg arise (rage) gears paste ( ) moans.
What you have to do is work out what the missing word is by finding where the letters in the word in brackets in the first group come from. They are all taken from the words outside the brackets, so it’s just a case of working out which letter in the words outside the brackets matches each letter in the word inside the brackets. Your best bet is to write down the second group of words underneath the first and go through each letter one by one. Just look out for letters that either appear twice in one of the words or letters that appear in both words outside the brackets. Those will obviously give you two different possible letters for the answer word, so you should probably write both of them one above the other until you’ve worked everything out and then simply choose the one that makes a proper word. In this example, the R from ‘rage’ might come from ‘arise’ or ‘gears’, so the first letter of the answer word is going to be either the second letter of ‘paste’ (A) or the fourth letter of ‘moans’ (N). The same is true of the A and E in ‘rage’. Once you work it all out, the letters are a or n, p or a, m and e or o, and the only sensible word is ‘name’.
These questions are slightly different from the synonym questions in that you have to choose a word out of five that has some similarity to or relationship with two pairs of words in brackets:
eg (alter, amend) (coins, money) repair, trial, revue, change, passage.
The two pairs of words in brackets usually have different meanings, so you have to look for a word with a double meaning. Again, have a quick look at all the words to see if the answer’s obvious. If it is, write it down. If it’s not, go through the five words one by one, comparing them to the words in brackets. It’s important to be open to the possibility of different meanings, so try to think laterally. In this example, for instance, the answer is ‘change’ as it can work as a verb meaning ‘alter’ or ‘amend’ but also as a noun meaning ‘coins’ or ‘money’.
For these questions, you’re given a sentence that describes the relationship between two pairs of letters – a little bit like the sentence analogies earlier. The final pair of letters is missing, so you have to work out what they are by finding the relationship between the first two pairs,
eg DH is to FD as NY 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 D to F by moving forward two places in the alphabet. That means you need to move two places on from N to get the first letter of the missing pair, which is P. Repeat this for the second letters, and you’ll find the other half of the answer. In this case, you get from H to D by going back four places, so you have to go back the same four places from Y to get V. The overall answer is therefore PV.
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 – Talia, George and Ryan – all left school at 1530 and walked home. Talia arrived home first. George arrived home five minutes later at 1545. It took Ryan 10 minutes longer than Talia 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 1530 when the children left school and including George getting home at 1545. You can then add in Talia’s arrival time of 1540 (as she arrived five minutes before George) and finally Ryan’s arrival time of 1550 (as he arrived 10 minutes after Talia.
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, through proper preparation and coaching every kind of test can be made easier.
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 based on advice from the book. (Bond tends to produce most of the non-verbal papers used in the 11+.)
The first thing to do is to describe the kind of questions that are involved. Here is the list from the back of one of the Bond papers:
Finding the most similar shape
Finding a shape within another shape
Finding the shape to complete the pair
Finding the shape to continue the series
Finding the code to match the shape
Finding the shape to complete the square
Finding the shape that is a reflection of a given shape
Finding the shape made when two shapes are combined
Finding the cube that cannot be made from a given net
Bond divides the questions into four different types:
Coded shapes and logic
Each of these types is divided into several variations.
Types of question
Recognise shapes that are similar and different
Identify shapes and patterns
Pair up shapes
“Which is the odd one out?”
“Find the figure in each row that is most unlike the other figures.”
“Which pattern on the right belongs with the two on the left?”
“Which pattern on the right belongs in the group on the left?”
“Which shape is most similar to the shapes in the group on the left?”
Types of question
Find shapes that complete a sequence
Find a given part within a shape
Find a missing shape from a pattern
“Which one comes next?”
“Which pattern completes the sequence?”
“Choose the shape or pattern the completes the square given.” “In which, larger shape or pattern is the small shape hidden?”
“Find the shape or pattern which completes or continues the given series.”
Types of question
Recognise mirror images
Link nets to cubes
“Work out which option would look like the figure on the left it it was reflected over the line.”
“Work out which of the six cubes can be made from the net.”
Coded shapes and logic
Types of question
Code and decode shapes
Apply shape logic
“Each of the patterns on the left has a two-letter code. Select the correct code for the shape on the right following the same rules.”
“Select the code that matches the shape given at the end of each line.”
“Which one comes next? A is to B as C is to ?”
“Which pattern on the right completes the second pair in the same way as the first pair? A is to B as C is to ?”
Hints and tips
The Bond book goes into great detail about how to answer each individual type of question; here we will look at the few key things to look out for in non-verbal reasoning questions.
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 flower pot 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 duvet cover 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 I have sometimes seen online!). This is a list of all the possible things that can change in a diagram. When tackling non-verbal reasoning questions you need to be very disciplined, logical and systematic. So it is useful, when working through the possibilities, to have a mnemonic like SPANSS to help you tick of 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 – meaning, has one image simply been turned upside-down or turned 90 degrees?
Finally, use the 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 article has given you some useful hints and tips.
Remember: practice makes perfect, and a few lessons with a private tutor wouldn’t go amiss either…!