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4024/12 May/Jun 2024, Question 2: Lines of Symmetry

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 2 marks

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The question, in short

On two separate 4 by 4 grids with some squares already shaded, add one shaded square to each grid to give the stated symmetry.

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

Part (a) · 1 mark

Add one shaded square to the 4 by 4 grid so the finished pattern has a single line of symmetry.

  1. 1Mirror line = diagonal from top-left to bottom-right: row 2 col 3 needs its image, row 3 col 2
  2. 2Or mirror line = the other diagonal: row 2 col 2 needs its image, row 3 col 3
  3. 3Shade row 3 column 2 (or row 3 column 3)

AnswerCorrect small square shaded (row 3 column 2 or row 3 column 3)

Part (b) · 1 mark

Add one shaded square to the 4 by 4 grid so the finished pattern has rotational symmetry of order 2.

  1. 1Rotation of order 2 about the centre maps row r, column c to row 5 − r, column 5 − c
  2. 2Row 1 col 4 ↔ row 4 col 1 (both shaded); row 2 col 4 ↔ row 3 col 1
  3. 3Shade row 3 column 1

AnswerCorrect small square shaded

Stuck on a step? Read the free lesson: Lines of Symmetry

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Also searched as: 4024/12/M/J/24 · 4024_s24_qp_12 · 4024 s24 12 · question 2.
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