Practice Paper: Non-Verbal Reasoning 2

This is your second GL 11+ Non-Verbal Reasoning practice paper. It covers nets and cubes, spatial reasoning, codes with shapes, and more complex pattern work.

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Instructions

• Time allowed: 45 minutes
• Total marks: 40
• Study each pattern carefully before answering
• Eliminate clearly wrong answers to improve your chances
• Answer every question
• Answers are at the end of this paper — do not look until you have finished!

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Section A: Nets and Cubes (10 marks)

A net is a flat shape that folds up into a 3D shape. In the exam, you may be shown a net and asked which 3D shape it makes — or shown a cube with patterns on its faces and asked which net matches.

Key Rules for Cube Nets

Rule	Explanation
A cube net has exactly 6 squares	Any net with more or fewer is wrong
Opposite faces never share an edge in the net	If two squares share an edge, they are adjacent on the cube, not opposite
There are exactly 11 possible cube nets	Learn to recognise the common ones

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Q1. A cube has a star on the top face and a circle on the front face. The net shows the star in the centre square of a cross-shaped net. Which square is opposite the star? (2 marks)

Q2. A net is shaped like a T: three squares in a row on top and three squares in a column below the middle square of the top row. Does this form a valid cube net? (1 mark)

Q3. Two faces of a cube are shaded grey. On the net, the grey squares share an edge. Can these two grey faces be opposite each other on the cube? (1 mark)

Q4. A cube has the number 1 on the top, 2 on the front, and 3 on the right side. If you rotate the cube 90 degrees forward (so the front face becomes the bottom), what number is now on top? (2 marks)

Q5. How many faces of a cube can you see at any one time from a single viewpoint? (1 mark)

Q6. A net has squares labelled A, B, C, D, E, F arranged as a cross: B is above A, C is below A, D is to the left of A, E is to the right of A, and F is below C. Which pairs are opposite on the cube? (3 marks)

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Section B: Spatial Reasoning (10 marks)

Q7. Two right-angled triangles, each with base 4 cm and height 3 cm, are placed together along their longest sides (hypotenuses). What shape do they form? (1 mark)

Q8. A square piece of paper is folded in half diagonally to make a triangle. A semi-circle is cut from the folded edge. When the paper is unfolded, what shape is the hole? (2 marks)

Q9. A square piece of paper is folded in half vertically, then a triangle is cut from the top-right corner. When unfolded, what appears at the top? (2 marks)

Q10. How many small cubes make up a 3 x 3 x 3 cube? (1 mark)

Q11. In a 3 x 3 x 3 cube, how many small cubes have exactly THREE faces painted if the outside of the large cube is painted? (2 marks)

Q12. In the same 3 x 3 x 3 cube, how many small cubes have NO faces painted? (2 marks)

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Section C: Shape Codes (10 marks)

In shape code questions, each feature of a shape is given a code letter or number. You use the code to identify a shape, or work out the code for a given shape.

Here is the code system:

Feature	Option A	Option B	Option C
Shape	Triangle = T	Square = S	Circle = C
Size	Large = L	Small = s	—
Shading	Black = B	Striped = St	White = W
Border	Thick border = Th	Thin border = Tn	No border = N

A shape is coded by listing: Shape, Size, Shading, Border.

Example: A large black triangle with a thick border = T, L, B, Th

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Q13. What is the code for a small white square with a thin border? (1 mark)

Q14. What is the code for a large striped circle with no border? (1 mark)

Q15. The code is T, s, B, Th. Describe the shape. (1 mark)

Q16. The code is S, L, W, N. Describe the shape. (1 mark)

Q17. Two shapes have codes: Shape X = C, L, B, Tn and Shape Y = C, s, B, Tn. What is the ONLY difference between them? (1 mark)

Q18. A shape is coded C, L, St, Th. If the shading changes to white and the border changes to no border, what is the new code? (2 marks)

Q19. How many different shapes can be made using this coding system? (Hint: multiply the number of options for each feature.) (1 mark)

Q20. A mystery shape has the code ?, s, ?, Th. The shape has 4 sides and is not white. What are the possible full codes? (2 marks)

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Section D: Complex Patterns (10 marks)

These questions combine multiple pattern rules. You need to track several changes at once.