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4024/21 Oct/Nov 2022, Question 7: Removed from the 2025–27 syllabuses (parked)

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 11 marks

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The question, in short

Using the grid with shapes A and B, carry out transformations: describe the mapping from A to B, reflect A, enlarge A, and work with matrix P mapping A to C.

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

Part (a) · 2 marks

Describe fully the single transformation that takes shape A onto shape B.

  1. 1(1, 3) → (3, −2): x + 2, y − 5
  2. 2Translation by column vector (2, −5)

AnswerTranslation column vector (2, −5)

Part (b) · 1 mark

Reflect shape A in the x-axis.

  1. 1Reflect in the x-axis: (x, y) → (x, −y)
  2. 2Vertices (1, −3), (2, −4), (3, −4), (3, −3)

AnswerCorrect reflection (3, −3), (3, −4), (2, −4), (1, −3)

Part (c) · 2 marks

Enlarge shape A by scale factor 2 with centre (5, 4).

  1. 1Each vertex: image = centre + 2 × (vertex − centre)
  2. 2(1, 3) → (5, 4) + 2(−4, −1) = (−3, 2); (2, 4) → (−1, 4)
  3. 3(3, 4) → (1, 4); (3, 3) → (1, 2)

AnswerCorrect enlargement (1, 2), (1, 4), (−1, 4), (−3, 2)

Part (di) · 2 marks

Draw and label shape C, the image of A under matrix P.

  1. 1Matrix (0 −1 / 1 0) maps (x, y) to (−y, x)
  2. 2(1, 3) → (−3, 1); (2, 4) → (−4, 2); (3, 4) → (−4, 3); (3, 3) → (−3, 3)
  3. 3Draw and label shape C

AnswerCorrect transformation (−3, 3), (−3, 1), (−4, 2), (−4, 3)

Part (dii) · 3 marks

Describe fully the single transformation mapping shape A onto shape C.

  1. 1(x, y) → (−y, x) turns each point 90° anticlockwise about the origin
  2. 2Rotation, 90° anticlockwise, centre (0, 0)

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

Part (diii) · 1 mark

Find the matrix for the transformation mapping shape C back onto shape A.

  1. 1C onto A is the inverse: rotation 90° clockwise about (0, 0), (x, y) → (y, −x)
  2. 2Matrix (0 1 / −1 0)

Answermatrix (0 1 / −1 0)

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Also searched as: 4024/21/O/N/22 · 4024_w22_qp_21 · 4024 w22 21 · question 7.
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