11+ Non-Verbal Reasoning 2 — Questions and Answers
Question 1: Four shapes are shown: a large black circle, a small white circle, a large white square, and a small black square. Which shape completes the pattern based on size and colour alternation?
- Large black square
- Small white square (Correct answer)
- Large white circle
- Small black circle
Correct answer: Small white square
The pattern alternates between large/small and black/white. Following the sequence, a small white square completes the pattern.
Question 2: A figure is made of 4 identical right-angled triangles arranged to form a square. If each triangle has legs of 3 cm and 4 cm, what is the side length of the square?
- 3 cm
- 4 cm
- 5 cm (Correct answer)
- 7 cm
Correct answer: 5 cm
When four right-angled triangles with legs 3 and 4 are arranged to form a square, the hypotenuse of each triangle (5 cm, by Pythagoras: 3² + 4² = 5²) forms the side of the square.
Question 3: In a sequence, each figure gains one additional line of symmetry. Figure 1 has 0 lines, Figure 2 has 1 line, Figure 3 has 2 lines. Which shape would be Figure 4?
- Scalene triangle (0 lines)
- Isosceles triangle (1 line)
- Equilateral triangle (3 lines) (Correct answer)
- Rectangle (2 lines)
Correct answer: Equilateral triangle (3 lines)
Figure 4 needs 3 lines of symmetry. An equilateral triangle has exactly 3 lines of symmetry.
Question 4: A shape is translated 3 units right and 2 units up. If it started at position (1, 1), where is it now?
- (4, 3) (Correct answer)
- (3, 2)
- (4, 2)
- (3, 3)
Correct answer: (4, 3)
Starting at (1,1), moving 3 right gives x = 1+3 = 4, and 2 up gives y = 1+2 = 3. The new position is (4, 3).
Question 5: Which 3D shape has 5 faces, 8 edges, and 5 vertices?
- Cube
- Square-based pyramid (Correct answer)
- Triangular prism
- Tetrahedron
Correct answer: Square-based pyramid
A square-based pyramid has 5 faces (4 triangles + 1 square base), 8 edges, and 5 vertices (4 base corners + 1 apex).
Question 6: In a matrix of shapes, the top row shows: circle, triangle, square. The middle row shows: triangle, square, circle. What is the first shape in the bottom row?
- Circle
- Triangle
- Square (Correct answer)
- Pentagon
Correct answer: Square
Each shape appears exactly once in each row and column. Circle and triangle have appeared in column 1, so the bottom-left must be a square.
11+ Non-Verbal Reasoning 2
Four shapes are shown: a large black circle, a small white circle, a large white square, and a small black square.
Which shape completes the pattern based on size and colour alternation?