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A-LevelFurther MathematicsMatrices9231/12 · Oct/Nov 2025 · Q410 Marks

Let k and m be non-zero constants. The matrices A, B and C are given by A = [[0,1],[-1,1],[1,1]], B = [[k,0],[0,m]], and C = [[2,-1],[1,2]].

  1. (a)(i)Give full details of the geometrical transformation in the x-y plane represented by the matrix B in each of the following cases. m = 1[2]
  2. (a)(ii)Give full details of the geometrical transformation in the x-y plane represented by the matrix B in each of the following cases. m = k[2]
  3. (b)Show that the matrix ABC is singular.[6]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

  1. [B1] Stretch
  2. [B1] parallel to the x-axis, scale factor k.
  3. [B1] Enlargement,
  4. [B1] centre the origin, scale factor k.
  5. [M1 A1] Multiplies two matrices correctly. Allow one error for the M mark.
  6. [A1]
  7. [M1 A1] Finds determinant. Allow two errors for the M mark
  8. [A1] AG. There must be evidence to show that the determinant is equal to zero

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About this question

Topic
Matrices, A-Level Further Mathematics (syllabus 9231). Structured question, 10 marks.
Source
A-Level Further Mathematics, Oct/Nov 2025 Paper 1 Variant 2, question 4.

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