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4024/11 Oct/Nov 2021, Question 4: Rotational Symmetry

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 2 marks

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The question, in short

On two 4 by 4 grids, shade extra small squares so each completed diagram has the stated symmetry: order 4 rotational, then 2 lines.

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

Part (a) · 1 mark

Shade one more small square in the 4 by 4 grid so the pattern has rotational symmetry of order 4.

  1. 1A quarter turn about the centre sends the square in row 4, column 3 to row 3, column 1
  2. 2Shade the square in row 3, column 1

AnswerShade the square in row 3, column 1

Part (b) · 1 mark

Shade two more small squares in the tilted 4 by 4 grid so the pattern has 2 lines of symmetry.

  1. 1The lines of symmetry are the two diagonals of the grid (the diamond's vertical and horizontal lines through its centre)
  2. 2Reflecting (row 1, column 2) gives (row 2, column 1); reflecting (row 4, column 3) gives (row 3, column 4)
  3. 3Shade the squares at (row 2, column 1) and (row 3, column 4)

AnswerShade the squares at (row 2, column 1) and (row 3, column 4), giving symmetry about both diagonals of the diamond

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

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Also searched as: 4024/11/O/N/21 · 4024_w21_qp_11 · 4024 w21 11 · question 4.
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