plumiMatrices and transformations: WJEC A‑Level Further Maths questions
Every WJEC A-Level Further Maths exam question on 1.3 Matrices and transformations, 2018–2025, with its mark scheme and examiner’s report.
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All 10 questions on Matrices and transformations, as a list
- Summer 2025, AS Unit 1, Q5 (11 marks): a b 2 M 2 2 M I, show that a d 5. (a) The matrix M is such that . Given that . [4] c d (b) Prove, by mathematical induction, that n 1
- Summer 2025, AS Unit 1, Q7 (11 marks): y x 7. The transformation T in the plane consists of a reflection in the line , followed by a rotation through 180° about the origin, followed by a translatio
- Summer 2024, AS Unit 1, Q8 (12 marks): A point P is reflected in the line y kx 8. , where k is a constant. It is then rotated anticlockwise about O through an acute angle θ, where cos θ = 0.8. The
- Summer 2023, AS Unit 1, Q2 (5 marks): −1 2 2 0 9 ⎡ ⎤ B = ⎡ ⎤ A = 2. The matrices A and B are such that and . ⎣⎢ ⎦⎥ ⎣⎢ ⎦⎥ − 7 4 –20 13 4 (a) Find the inverse of A. [2] (b) Hence, find the matrix X, w
- Summer 2023, AS Unit 1, Q4 (7 marks): 4. The transformation T in the plane consists of a translation in which the point (x, y) is transformed to the point (x + 2, y – 2), followed by a reflection in
- Summer 2022, AS Unit 1, Q2 (11 marks): The matrices A and B are defined by 2. (a) −11 3 4 ⎛ ⎞ ⎛ ⎞ A = B = ⎠⎟ , ⎠⎟ . ⎝⎜ ⎝⎜ −1 − 2 7 Given that AX = B, find the matrix X . [4] Find the 2 × 2 matrix, T,
- Summer 2022, AS Unit 1, Q8 (7 marks): The point (x, y, z) is rotated through 60o anticlockwise around the z-axis. 8. After rotation, the value of the x-coordinate is equal to the value of the y-coor
- Summer 2019, AS Unit 1, Q1 (6 marks): 7 5 1 ⎛ ⎞ ⎛ ⎞ The matrices A and B are given by A = , B = . 1. ⎝⎜ ⎠⎟ ⎝⎜ ⎠⎟ −2 0 0 4 The matrix X is such that AX = B. Showing all your working, find the matrix
- Summer 2018, AS Unit 1, Q1 (6 marks): ⎡ 4 2 ⎤ ⎡ 4 2 ⎤ The matrices A and B are such that A = and B = . 1. ⎣⎢ ⎦⎥ ⎣⎢ ⎦⎥ −1 −3 2 1 Explain why B has no inverse. (a) [1] Find the inverse of A. (b) (i) [
- Summer 2018, AS Unit 1, Q8 (9 marks): The transformation T in the plane consists of a translation in which the point (x, y) is transformed 8. to the point (x – 1, y + 1), followed by a reflection in
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