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4024/23 May/Jun 2025, Question 4: Rotational Symmetry

Cambridge O Level Mathematics 4024 · Paper 23 (Calculator) · Calculator · 2 marks

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The question, in short

Shade one extra small square in each 4 by 4 grid so that the first pattern gains rotational symmetry of order 2 and the second gains exactly one line of symmetry.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 1 mark

On the 4 by 4 grid with shaded squares at (1,1), (1,2), (1,4), (2,2), (2,4), (3,3), (4,1), (4,3), (4,4), shade one more square to give rotational symmetry of order 2.

  1. 1Order 2: each shaded square must have a shaded partner after a half turn about the centre
  2. 2Row 2, column 4 is shaded but its partner, row 3, column 1, is not
  3. 3Shade row 3, column 1

AnswerShade the square in row 3, column 1 (counting from the top left)

Part (b) · 1 mark

On the 4 by 4 grid with shaded squares at (1,1), (1,3), (2,2), (2,4), (3,2), (3,4), (4,1), (4,3), (4,4), shade one more square to give exactly 1 line of symmetry.

  1. 1Rows 2 and 3 are the same, and row 4 is S W S S
  2. 2Shade row 1, column 4 so row 1 matches row 4
  3. 3Line of symmetry: horizontal line through the middle of the grid

AnswerShade the square in row 1, column 4 (counting from the top left)

Stuck on a step? Read the free lesson: Rotational Symmetry

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Also searched as: 4024/23/M/J/25 · 4024_s25_qp_23 · 4024 s25 23 · question 4.
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