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A-LevelFurther MathematicsMatrices9231/12 · Oct/Nov 2021 · Q19 Marks

Give full details of the geometrical transformation in the x-y plane represented by the matrix (6 0) (0 6) Let A = (3 4) (2 2)

  1. (a)Give full details of the geometrical transformation in the x-y plane represented by the matrix (6 0) (0 6)[1]
  2. (b)The triangle DEF in the x-y plane is transformed by A onto triangle PQR. Given that the area of triangle DEF is 13 cm², find the area of triangle PQR.[2]
  3. (c)Find the matrix B such that AB = (6 0) (0 6).[2]
  4. (d)Show that the origin is the only invariant point of the transformation in the x-y plane represented by A.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

  1. [1] (a) Enlargement, scale factor 6.
  2. [M1] (b) Finds det A.
  3. [A1] (b) Area = 2 × 13 = 26 cm²
  4. [M1] (c) Finds A⁻¹
  5. [A1] (c) AEF Could be solved by equations.
  6. [B1] (d) Finds (X/Y)
  7. [M1] (d) Uses (X/Y) = (x/y) to form simultaneous equations.
  8. [M1 A1] (d) Solves equations or states that det (2 4 / 2 1) ≠ 0, AG.

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About this question

Topic
Matrices, A-Level Further Mathematics (syllabus 9231). Structured question, 9 marks.
Source
A-Level Further Mathematics, Oct/Nov 2021 Paper 1 Variant 2, question 1.

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