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4024/22 May/Jun 2024, Question 5: Removed from the 2025–27 syllabuses (parked)

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 11 marks

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The question, in short

Using a grid with shapes A and B, identify the single transformation linking A to B, then work with an enlargement of A by scale factor 3 to find a centre and area, and apply a given matrix to A.

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

Part (a) · 2 marks

State the one transformation that takes shape A onto shape B, giving its type and full details.

  1. 1(x, y) → (−y, −x): (−2, 6) → (−6, 2), (−1, 4) → (−4, 1)
  2. 2Reflection in the line y = −x

AnswerReflection in y = −x

Part (bi) · 2 marks

Given two vertices of shape C at (2, 5) and (5, 2), determine the centre of the scale factor 3 enlargement.

  1. 1From the grid, A's vertex (−2, 5) maps to (2, 5) and (−1, 4) maps to (5, 2)
  2. 2Draw lines through each vertex and its image; they meet at the centre
  3. 3Check x: from −4, A's point is 2 right and C's point is 6 right (3 times)
  4. 4Check y: both points are on y = 5, so the centre is (−4, 5)

Answer(−4, 5)

Part (bii) · 2 marks

Calculate the area of shape C after shape A is enlarged by scale factor 3.

  1. 1A is a trapezium: parallel sides 1 and 2, a distance 1 apart.
  2. 2Area of A = 1/2 × (1 + 2) × 1 = 1.5
  3. 3Enlarging by 3 multiplies area by 3² = 9
  4. 4Area of C = 9 × 1.5 = 13.5

Answer13.5 or 13 1/2

Part (ci) · 2 marks

Draw shape D on the grid, where D is the image of A under the matrix with rows 0, −1 and 1, 0.

  1. 1(x, y) → (−y, x)
  2. 2(−2, 6) → (−6, −2), (−1, 6) → (−6, −1), (−1, 4) → (−4, −1), (−2, 5) → (−5, −2)

AnswerShape D at (−6, −1), (−4, −1), (−5, −2), (−6, −2)

Part (cii) · 3 marks

Give a complete description of the single transformation defined by the matrix with rows 0, −1 and 1, 0.

  1. 1(1, 0) → (0, 1) and (0, 1) → (−1, 0)
  2. 2Rotation, 90° anticlockwise, centre (0, 0)

AnswerRotation, 90° anticlockwise, centre (0, 0)

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