Determinants and inverses: OCR MEI A‑Level Further Maths questions

OCR MEI A-Level Further Maths past-paper questions on 3.2 Determinants and inverses, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.

All 19 questions on Determinants and inverses, as a list

June 2025, Core Pure, Q4 (7 marks): (a) You are given that M and N are non-singular 2 # matrices. 2 Write down the product rule for the inverse matrices of M, N and MN. [1] (b) Verify this rule fo
June 2025, AS Core Pure, Q1 (5 marks): The matrices A and B are given by J N J N 1 3 2 1 KK OO and B KK OO. A = = 0 1 0 1 L P L P (a) Use A and B to show that matrix multiplication is not, in general
June 2025, AS Core Pure, Q4 (8 marks): K O 4 (a) The transformation T is represented by the matrix M 2 1 0 OO. = KK 1 2 1 - L P A shape S1 is mapped to a shape S2 by the transformation T. Show that v
June 2024, Core Pure, Q8 (10 marks): (a) Specify fully the transformation T of the plane associated with the matrix M, where = c 1 m and m is a non-zero constant. m M [2] 0 1 (b) (i) Find det M. [1
June 2024, AS Core Pure, Q5 (6 marks): K O 5 (a) Find the volume scale factor of the transformation with associated matrix 0 3 1 OO. [2] - KK 1 0 2 - L P (b) The transformations S and T of the plane
June 2024, AS Core Pure, Q6 (9 marks): J N 4 9 - KK OO. 6 You are given that M = 1 2 - L P J N n n 1 3 9 + - n = KK OO for all positive integers n. (a) Prove that M [6] n 1 3 n - L P (b) A student th
June 2023, Core Pure, Q14 (13 marks): Three planes have equations kx - z 2 , = x ky 2 z = , 1 - + + 2 kx 2 y 3 z 0 , + + = where k is a constant. (a) By considering a suitable determinant, show that
June 2022, Core Pure, Q4 (7 marks): K O 4 (a) A transformation with associated matrix 0 1 2 OO, where m is a constant, maps the vertices KK - 2 0 3 L P of a cube to points that all lie in a plane.
June 2022, AS Core Pure, Q1 (6 marks): (a) (i) Write the following simultaneous equations as a matrix equation. x y 2 z 7 + + = 2 x 4 y 3 z 5 - - =- [1] 5 x 3 y 5 z 13 - + + = (ii) Hence solve the eq
June 2022, AS Core Pure, Q8 (12 marks): J N cos 2 cos sin - i i i KK OO. 8 A transformation T of the plane has matrix M, where M = sin 2 sin cos + i i i L P (a) Show that T leaves areas unchanged for
November 2021, Core Pure, Q9 (11 marks): J N 1 0 = - KK OO. 9 The transformation T of the plane has associated matrix M, where M 2 1 - L P (a) On the grid in the Printed Answer Booklet, plot the image
November 2021, AS Core Pure, Q4 (5 marks): - . Her attempted 1 1 4 Anika thinks that, for two square matrices A and B, the inverse of AB is A - B proof of this is as follows. 1 1 1 1 ( AB A )( - B - ) A
November 2020, Core Pure, Q2 (6 marks): J N 0 1 a K O KK OO and 2 (a) The matrices M N 1 c OO are such that MN = I. = = - KK 1 b 0 L P 1 1 - L P Find a, b and c. [5] (b) State with a reason whether or
November 2020, AS Core Pure, Q4 (4 marks): K O 4 The matrix M is 1 0 0 OO. KK 0 0 1 L P (a) (i) Calculate det M. [1] (ii) State two geometrical consequences of this value for the transformation associate
November 2020, AS Core Pure, Q6 (8 marks): J N J N 2 1 m n KK OO and 1 KK OO respectively, where m and n are constants. 6 The matrices M and N are 2 m n L P L P (a) Investigate whether M and N are commut
November 2020, AS Core Pure, Q8 (7 marks): J N 0 1 - KK OO. 8 (a) The matrix M is 1 0 - L P (i) Find M2. [1] (ii) Write down the transformation represented by M. [1] (iii) Hence state the geometrical sig
June 2019, Core Pure, Q3 (7 marks): J N J N 3 1 k 1 KK OO and B KK OO, where k is a constant. 3 Matrices A and B are defined by A = = 2 1 2 0 L P L P 1 1 1 (a) Verify the result ( AB ) - B - A - i
June 2019, Extra Pure, Q3 (8 marks): K O 3 The matrix A is 0 1 25 OO. - - KK 3 5 1 - - L P Use the Cayley-Hamilton theorem to find A−1. [8]
June 2019, AS Core Pure, Q3 (6 marks): In this question you must show detailed reasoning. J N 2 1 1 = - KK OO. 1 A and B are matrices such that B - A - 1 1 L P (a) Find AB. [3] J N 1 1 KK OO, find B.

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