EDPT Spatial Reasoning and Patterns 5 — Questions and Answers
Question 1: In a pattern sequence, each frame adds two more identical shapes than the previous frame. Frame 1 has 1 shape, Frame 2 has 3 shapes. How many shapes are in Frame 6?
- 11 (Correct answer)
- 13
- 15
- 17
Correct answer: 11
Frame n has 2n − 1 shapes; Frame 6 = 2(6) − 1 = 11 shapes.
Question 2: A square is divided into 4 smaller squares. Each small square is then divided into 4 even smaller squares. How many smallest squares are there in total?
- 8
- 12
- 16 (Correct answer)
- 20
Correct answer: 16
Dividing each of 4 squares into 4 gives 4 × 4 = 16 smallest squares.
Question 3: A figure has rotational symmetry of order 6. Through how many degrees must it be rotated (minimum) to look identical to its original position?
- 30°
- 45°
- 60° (Correct answer)
- 72°
Correct answer: 60°
Order-6 symmetry means the figure maps onto itself 6 times per full rotation; 360° ÷ 6 = 60°.
Question 4: A staircase pattern is built with blocks: Step 1 uses 1 block, Step 2 uses 3 blocks, Step 3 uses 6 blocks. How many blocks does Step 5 use?
- 10
- 12
- 15 (Correct answer)
- 21
Correct answer: 15
The pattern follows triangular numbers: Step n uses n(n+1)/2 blocks; Step 5 = 5×6/2 = 15.
Question 5: Two identical right triangles are placed together along their hypotenuses. What shape is always formed?
- A rectangle (Correct answer)
- A square
- A parallelogram
- A trapezoid
Correct answer: A rectangle
Two congruent right triangles joined at their hypotenuses always form a rectangle.
Question 6: A pattern shows circles of increasing size: diameter 1, 2, 4, 8. What is the diameter of the 6th circle?
- 16
- 24
- 32 (Correct answer)
- 64
Correct answer: 32
The diameters double each step: 1, 2, 4, 8, 16, 32; the 6th circle has diameter 32.
Question 7: A shape has exactly 4 sides, opposite sides are parallel, all angles are equal, but the sides are NOT all equal. What shape is it?
- Rhombus
- Rectangle (Correct answer)
- Square
- Trapezoid
Correct answer: Rectangle
A rectangle has 4 equal right angles, parallel opposite sides, but sides are only equal in pairs — not all four equal.
EDPT Spatial Reasoning and Patterns 5
In a pattern sequence, each frame adds two more identical shapes than the previous frame.
Frame 1 has 1 shape, Frame 2 has 3 shapes.
How many shapes are in Frame 6?