Transformations with matrices: OCR MEI A‑Level Further Maths questions

OCR MEI A-Level Further Maths past-paper questions on 3.3 Transformations with matrices, 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 20 questions on Transformations with matrices, as a list

June 2025, Core Pure, Q14 (10 marks): - , show that 14 (a) By using the definition of cosh x and sinh x in terms of ex and e x 2 2 x x x [2] cosh sinh cosh 2 . + / J cosh x sinh x N KKK OOO and (b)
June 2025, Extra Pure, Q5 (14 marks): In this question you must show detailed reasoning. J N a b 0 K O 2 2 The matrix A is given by b a 0 OO where a and b are constants with a b = and a 1 1 . KK - +
June 2025, AS Core Pure, Q3 (7 marks): The matrices M and N are given by J N J N a b b a - - KK OO and KK OO where a and b are positive constants. M = N = b a a b L P L P 2 = (a) Given that M N , det
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 2023, Core Pure, Q6 (9 marks): J N J N The matrices M and N are 0 1 OO and 2 0 KK KK OO respectively. 6 1 0 0 1 L P L P (a) In this question you must show detailed reasoning. Determine whethe
June 2023, AS Core Pure, Q1 (3 marks): The transformation R of the plane is reflection in the line x = 0. (a) Write down the matrix M associated with R. [1] (b) Find M2. [1] (c) Interpret the result
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, 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, Q6 (12 marks): J N 1 1 + m KK OO, where m is a non-zero 6 A transformation T of the plane has associated matrix M = 1 1 - - m constant. L P (a) (i) Show that T reverses orient
November 2020, Core Pure, Q9 (8 marks): J N 1 2 - KK OO, where m is a 9 A linear transformation of the plane is represented by the matrix M = 3 m constant. L P (a) Find the set of values of m for whic
November 2020, Extra Pure, Q5 (8 marks): In this question you must show detailed reasoning. J N 1 2 2 - - K O J N 1 3 3 3 K O K O 2 1 2 The matrix A is given by and the vector e is given by OO. You are
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, 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, Q11 (12 marks): (a) Specify fully the transformations represented by the following matrices. J N 3 4 - K O 5 5 • M1 = K O 3 4 5 5 L P J N 1 0 • M KK OO [4] 2 = 0 1 - L P (b) Fi
June 2019, Extra Pure, Q1 (5 marks): J N 0 6 . 0 8 . KK OO. 1 The matrix A is 0 8 . 0 6 . - L P (a) Given that A represents a reflection, write down the eigenvalues of A. [1] (b) Hence find the eig
June 2019, AS Core Pure, Q6 (11 marks): J N k m KK OO, and m 6 A linear transformation T of the x-y plane has an associated matrix M, where M = 1 k - m and k are real constants. L P (a) You are given
June 2018, AS Core Pure, Q5 (7 marks): c cos 2 sin m, where i is a positive acute i i 5 A transformation of the x-y plane is represented by the matrix 2 sin cos i - i angle. (i) Write down the image

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