◈ Oracle PrepSign Up Free
A-LevelFurther MathematicsMatrices9231/12 · Oct/Nov 2024 · Q413 Marks

The matrices A, B and C are given by A = (1 2 3) (2 1 3) (3 2 5) B = (0 -2) (-1 3) (0 0) C = (-2 -1 1) (1 1 3)

  1. (a)Show that CAB = (3 -7) (-9 3)[3]
  2. (b)Find the equations of the invariant lines, through the origin, of the transformation in the x-y plane represented by CAB.[5]
  3. (c)Give full details of the transformation represented by M = (3 0) (0 1).[2]
  4. (d)Find the matrix N such that NM = CAB.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

  1. [M1 A1] Multiplying two matrices correctly, correct dimensions.
  2. [B1] Convincingly completing matrix multiplication, AG.
  3. [B1] Transforms (x, y) to (3x-7y, -9x+3y)
  4. [M1 A1] Uses y=mx and Y=mX.
  5. [A1]
  6. [A1]
  7. [B1] Stretch
  8. [B1] parallel to the x-axis, scale factor 3.
  9. [B1] M⁻¹ = (1/3 0)\n (0 1)
  10. [M1] Correct order
  11. [A1]

Write your answer and get it marked

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Sign up free →

About this question

Topic
Matrices, A-Level Further Mathematics (syllabus 9231). Structured question, 13 marks.
Source
A-Level Further Mathematics, Oct/Nov 2024 Paper 1 Variant 2, question 4.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content

Related Further Mathematics questions

MatricesMay/June 201111m

Find the eigenvalues and corresponding eigenvectors of the matrix \( A = \begin{pmatrix} 4 & -1 & 1 \\ -1 & 0 & -3 \\…

MatricesMay/June 20129m

A matrix A has eigenvalues –1, 1 and 2, with corresponding eigenvectors [1, -1, -2]ᵀ, [-1, -3, 5]ᵀ and [2, 5, -3]ᵀ re…

MatricesMay/June 201210m

The linear transformations T₁ : R⁴ → R⁴ and T₂ : R⁴ → R⁴ are represented by the matrices M₁ = [[1, 1, 1, 4], [2, 1,…

Roots of polynomial equationsMay/June 20116m

The roots of the equation x³ + px² + qx + r = 0 are (β)/k , β , kβ , where p, q, r, k and β are non-zero real constan…

Proof by inductionMay/June 20116m

It is given that \( f(n) = 3^{3n} + 6^{n-1} \).

Polar coordinatesMay/June 20118m

The curve C has polar equation r = 2 cos 2θ . Sketch the curve for 0 ≤ θ < 2π .

← Browse all past-paper questions

© 2026 Oracle Prep