All 8 Non-Verbal Reasoning for the 11 Plus syllabus points are listed, with the corresponding 25 11 plus sample paper questions, fully explained answers and helpful tips to smash the 11 plus exam!
1) Odd One Out
Sample 11 Plus Non-Verbal Reasoning Question: One of the tiles is different to the remaining four in some way. Which of the five options is the odd one out?
Answer and Explanation: E. All of the remaining images have a line connecting opposite sides within a square, except for E where the line connects two sides that are next to each other.
Tips: When attempting a question like this, you should first identify all of the possible things that can vary question to question. Here these include: the connecting line, the dot, the rotation of the surrounding square etc. You should then narrow down which of these might be changing but are ‘distractors’, which vary with no obvious pattern (eg. the rotation of the square in this case). The process of doing this should bring about one answer whereby one of these changes just doesn’t quite fit in. Be vigilant!
Now Try These:
Answer and Explanation: C. It’s a long process, but counting the number of sides in each option gives you 24, apart from C where the total is 26.
Answer and Explanation: E. Every tile contains 3 black-lined shapes, each with grey borders. One is on the inside of the shape, one is on the outside of the shape and one is on both sides of the shape. For E, two are on the outside of the shape and one is on both sides.
Answer and Explanation: B. The dots are on the acute angles for every other parallelogram, whereas here they are on the obtuse angles.
2) Folding Nets
Sample 11 Plus Non-Verbal Reasoning Question: The cube below has been formed by folding up a template. Which of the five options could be the net used?
Answer and Explanation: D. The top three sides of the net in D come together to form the three sides of the cube shown.
Tips: You may find these tricky! If you are having difficulty ‘just spotting it’ then try the following approach. Find a net with two shapes that are similar to two shapes on the cube. Try and fold the appropriate parts of the net to see how they fall next to each other – remember that how shapes orientate during the folding process (particularly asymmetrical ones) is very important. If these two sides are compatible with the cube, then repeat the process for another pair of sides (one of which will be the same as one which you picked last time). If these two tests work, then you have found the answer!
Now Try These:
Answer and Explanation: C. The pinhead should point towards the wide part of the heart, and the arrow should point in the same direction as the heart’s tail.
Answer and Explanation: A. The orientation of the registration mark is correct relative to the orientation of the grass. The grid is in the correct location with respect to these two objects. Be careful here, as the grid is symmetrical which means that you cannot use its orientation as a reference point.
Sample 11 Plus Non-Verbal Reasoning Question: In each case, the tile on the left is changed in some way to change the tile on the right, as indicated by the arrows. Which of the five options fills in the blank tile?
Answer and Explanation: B. While in the first tile on the left there is just one loose line in the top right hand corner, it is changed to form a tile with two loose lines. The T in the top right hand corner of the question tile is therefore duplicated similarly.
Tips: It is important that you identify all of the components which could change, be that by duplication, deletion, reflection, rotation, transformation, distortion etc. Carefully compare each of these factors (and any other relevant ones that you have identified) to the tile it gets converted to.
You may notice that the approach you are using is very similar to ‘Odd One Out’, however these questions have a tendency to be a bit more mathematical as an ‘operation’ is being applied, so you may wish to focus more at first on looking for mathematical concepts.
Now Try These:
Answer and Explanation: A. The tile in each case is rotated by 90 degrees clockwise.
Answer and Explanation: B. The four surrounding objects remain unchanged, and the central object is enlarged.
4) Incomplete Array
Sample 11 Plus Non-Verbal Reasoning Question: The nine tiles connected all relate to each other to form a pattern or sequence, however one of the tiles has been removed. Which of the five options completes the array?
Answer and Explanation: A. Each tile contains 4 sub-shapes. Across the entire array, each sub-shape appears 6 times in one particular orientation and 3 times in another particular orientation. All you have to do is complete the chart so that this ‘6 and 3’ theme is maintained. Be warned that array questions can test so many thought processes that they are often the hardest in each paper. They are part of the reason why we allow 1 hour per paper, as we want your child to have time to think about every possible alternative!
Tips: Array questions can test multiple simultaneous thought processes, and so are especially tricky. You should look out for a ‘left to right’ trend and ‘top to bottom’ trend first of all. It is often not useful to begin by looking for a ‘diagonal’ trend as you may well be observing multiple things changing together. If by this point you have not spotted a trend, try other routes, like reading the tiles of the array ‘like a book’ to find any progressive changes, or try spotting if something is happening in the ‘corners only’ for example. If nothing has come to mind, at this point you should look at the problem as a whole, as is the required case in this problem – treat the array as one giant tile and see if there is a running theme, or if you can make a theme given one of the answers.
Now Try These:
Answer and Explanation: C. Going from left to right, the shape on the left gets increasingly large and goes from black to grey to white.
Answer and Explanation: D. If the shape within the tile represents the tile’s position within the array, it will be a tick. If it does not, then it will be a cross. For example, the top left tile has a tick in the top left corner and the middle tile has a tick in the middle of the box, but the bottom left tile has a cross in the top right corner (as this is not represent the tile’s location in the array). The two options for the missing tile are a tick in the bottom right hand corner or a cross in any other corner – only one of these is a given answer, D.
5) Incomplete Sequence
Sample 11 Plus Non-Verbal Reasoning Question: The five tiles below that are connected by arrows progress as a sequence in this direction, however one of the tiles has been removed. Which of the five options is the missing tile?
Answer and Explanation: D. Going from the left to the right, the spoke of the star which is coloured moves clockwise and skips a spoke each time. The ‘distractor’ in this question is the manner in which the spoke is coloured.
Tips: These questions tend to be a little easier. Firstly, see which tile is missing. If it is an early or a late one, then focus on the cluster of tiles which you can see in a row. Shortlist a series of things that could be changing from tile to tile, and keep a note of the manner in which they are changing. If you identify that the change and the method of change is consistent, then you have found you answer. Be careful, however, as sometimes multiple things change from tile to tile and you should ensure that you have spotted all of them by going over the other answers and seeing if any fit.
Now Try These:
Answer and Explanation: A. Every two turns, the central grey triangle rotates 90 degrees clockwise, and the circle and the square move around the tile 90 degrees anticlockwise.
Answer and Explanation: E. Every other tile contains 3 shapes black-line shapes with a grey border. One is on the inside of the shape, one is on the outside of the shape and one is on both sides of the shape. For E, two are on the outside of the shape and one is on both sides.
Sample 11 Plus Non-Verbal Reasoning Question: For each tile to the left of the vertical line, there is a corresponding code that is related to its content. This information can be used to decipher the coding system. Which of the five options contains the missing code for the tile to the right of the vertical line.
Answer and Explanation: A. The first letter represents the number of lined circles (3, so ‘B” is first), and the second letter represents whether or not there is a large non-lined circle (there is not, so “S” is second). There are a few things happening in this question that make it a little tricky. The orientation of the lined circles and the variation in the number of lined / non-lined circles throws off the student. When comparing the first tile and code the second tile and code, multiple things can be eliminated (for example, the idea that the second letter may represent the number of non-lined circles present cannot be true as no letters are in common between these two). Comparing all pairs of the given tiles allows us to eliminate many options.
Tips: Many students like to try and jump to the answer, but in codes it is very important that students look for themes letter-by-letter. It is important to go through all likely logic routes first and see which ones are ‘most probable, as it is possible on occasion for students to find contorted reasoning which justifies a code whereas actually it is not correct because of the fact that such a trend cannot be drawn from just a few tiles! Some code questions will have 3 tiles shown, some will have 4. Some will have 2 letters to the code, some will have 3.
What’s interesting to note with ‘codes’ is that there are often multiple logic routes to getting to the correct answer. For example, here it is perfectly fine to think that the second letter represents the total number of circles present in each tile – the student will still get to the correct answer.
Now Try These:
Answer and Explanation: E. The first letter encodes colour of the main central shape (so ‘A’ is dark grey, based on the first tile) and the second letter encodes the number of grey stars surrounding the shape (so ‘L” is one star, based on the third tile).
Answer and Explanation: A. This is a tricky one. The third letter represents the main shape – square or pentagon (which is shared by the first and third tiles, and by the second and fourth tiles), so the last letter must be K. At this point it must be realised that successive letters represent a progression. A to B to C (first letter) represents the progression from 1 line to 1.5 lines to 2 lines. S to T to U (second letter) represents the progression from 1 dot to 2 dots to 3 dots. J to K represents the progression from a 4-sided shape to a 5-sided shape. The answer therefore has to be ASK.
Sample 11 Plus Non-Verbal Reasoning Question: The image in the tile to the right has been rotated to some extent. Which of the five options is the rotated version of the original image?
Answer and Explanation: E. This option is the image in the tile rotated anticlockwise by 80 degrees or so. For the other options, the sub-shapes are either in the incorrect positions with respect to each other, or in the incorrect orientations with respect to each other, or both.
Tips: These questions tend to be reasonably easy and follow two themes. Either there are several sub-shapes all varying with relative to each other (as seen here), or the entire construct will be rotating but most of the other options are mirror images. It is really easy to get caught out by a mirror image shape, so you should always double-check these by identifying two points on the original tile and ensuring that they are still at the same angle and direction (clockwise / anticlockwise) to each other.
Now Try These:
Answer and Explanation: A. Look at the tile with your head rotated such that the lines in the center of the circles are horizontal – you will notice that one circle is to the top-right of the other circle. This is also true for ‘A’, however when you repeat this for all other tiles, you will notice that one circle is to the top-left of the other circle and so each of these are mirror images.
Answer and Explanation:B. There are 4 separate shapes which make up the construct. For the other answers, one or more of the sub-shapes is reflected, rotated or the order of the three objects on the top row is changed.
Sample Question: The two tiles to the right are similar to each other in some way. Which of the five options best fits in with these tiles?
Answer and Explanation: B. The two tiles at the top have the following things in common: they consist of a four sided shape that has a dotted border, inside which there are three small triangles of equal size, of which two are shaded black and one is unshaded. The answer also fits this exact description, but the alternatives vary in some way.
Tips: For these questions you should make a note of any similarities that you spot between the two given tiles, and then see which of the given tiles is most likely to match this description. It is worth noting that the correct tile may not fit every single criteria – you have had to make a trend from two tiles after all, so it is very possible that something you have spotted is not part of the rules.
Now Try These:
Answer and Explanation: B. The number of dots is equal to the number of ‘points’ on the shape, ie. the number of acute, right or obtuse angles. The number of lines is two less than this number. It is possible that some students may interpret that the ‘number of dots’ multiplied by the ‘number of lines minus one’ is equal to the number of sides of the shape, however this logic works for both A and E, so is not correct. While the student may then restrict their answer to A on the merit that the number of dots is equal to the number of ‘points’, this additional logic is a bit too contorted to be realistic, and so the answer they should run with is B.
Answer and Explanation: B. In each case, two chains are present with 12 sides being the total sum of the chains on the left, and 12 sides of the chains on the right. B contains two circles and a decagon on the left, and a triangle, a square and a pentagon on the right.