Updated June 2026 · free, no sign-up · facts checked against official sources
Non-verbal reasoning (NVR) tests your child's ability to spot patterns and relationships in shapes, sequences and spatial arrangements - without relying on words. It appears in GL Assessment, CEM and most grammar school 11+ tests. The questions below are written as text-described NVR-logic problems so you can practice the core reasoning skills on any device.
NVR question types in the 11+ (2026)
Series - shapes change in a predictable sequence; find the next shape.
Analogies - Shape A relates to Shape B in the same way Shape C relates to Shape D; find D.
Odd-one-out - four or five shapes; one doesn't share the common property.
Matrices - a 3×3 grid of shapes follows row and column rules; find the missing cell.
Reflections and rotations - identify the correct mirror image or rotated version of a shape.
Nets - which 2D net folds into a given 3D shape (usually a cube)?
Codes - shapes are assigned letter or number codes; work out the code for a new shape.
In the actual test, shapes are shown as images. PipPrep's app renders full image-based NVR questions with tap-to-answer. The questions below use described shapes to practise the same reasoning skills in a text format.
Free NVR-style practice questions
Tap an option to check it; a worked explanation follows every answer.
Question 1 · Series
A shape sequence goes: triangle (3 sides), square (4 sides), pentagon (5 sides), hexagon (6 sides), ___. What comes next?
Answer: Heptagon. Each shape gains one side: 3, 4, 5, 6, so next is 7 sides - a heptagon.
Question 2 · Codes
In a shape code: Circle = code 1, Triangle = code 3, Pentagon = code 5. What shape does code 4 represent?
Answer: Square. The code equals the number of sides (circle = 1, triangle = 3, pentagon = 5), so code 4 = 4 sides = square.
Question 3 · Odd-one-out
Which is the odd one out: equilateral triangle, square, rhombus, scalene triangle?
Answer: Scalene triangle. An equilateral triangle, square and rhombus all have sides of equal length. A scalene triangle has no equal sides - it is the only shape in the group where all sides differ.
Question 4 · Analogy
Shape A is a large dark circle. Shape B is a small dark circle. Shape C is a large dark square. What is Shape D, following the same rule?
Answer: A small dark square. The rule changes large → small while keeping colour (dark) and shape type the same. C is a large dark square, so D is a small dark square.
Question 5 · Matrix
A 3×3 grid has these shapes:
Row 1: star, circle, triangle
Row 2: circle, triangle, star
Row 3: triangle, star, ___
What fills the blank?
Answer: Circle. Each row and each column contains exactly one star, one circle and one triangle. Row 3 already has triangle and star, so the missing shape is circle.
Question 6 · Reflection
A shape is reflected in a vertical mirror line. The original has a dot in its top-left corner and an arrow pointing right. Where is the dot in the reflection, and which way does the arrow point?
Answer: Top-right corner; arrow points left. A vertical mirror swaps left and right only - top stays top, bottom stays bottom. The dot moves from top-left to top-right. The arrow, originally pointing right, now points left.
Question 7 · Codes
In a letter-shape code:
AX = shape with 3 sides (triangle)
BY = shape with 4 sides (square)
CZ = shape with 5 sides (pentagon)
What does DW represent?
Answer: Hexagon (6 sides). The first letter increases (A, B, C, D) and the number of sides increases by 1 each step (3, 4, 5, 6). DW therefore represents a shape with 6 sides - a hexagon.
Question 8 · Nets
Which of these descriptions is a valid net for a cube?
A: Six squares arranged in a straight line (1×6 strip)
B: Six squares in a cross shape (one centre, four arms, one on the end of one arm)
C: Four squares in an L-shape
D: Three squares across the top, three squares down the left side only
Answer: B - cross shape of 6. A cube has 6 faces. A straight line of 6 cannot fold into a cube (opposite faces would overlap). The cross shape (T-cross / plus sign) is one of the 11 valid cube nets and folds correctly.
Question 9 · Series
A number-of-sides sequence goes: 3, 6, 9, 12, ___. What comes next?
Answer: 15. The sequence is multiples of 3 (3×1, 3×2, 3×3, 3×4, 3×5). The next term is 3 × 5 = 15.
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