Transformations with matrices: OCR A‑Level Further Maths questions

OCR 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 18 questions on Transformations with matrices, as a list

June 2025, Pure Core 1, Q1 (4 marks): J N 5 0 KK OO. 1 (a) A matrix M is given by M = 0 5 L P Describe the transformation represented by M. [2] (b) Write down the 2 # matrix that represents a rotati
June 2025, AS Pure Core, Q4 (6 marks): Two transformations, TA and TB, are represented by matrices A and B respectively. J N 0 1 KK OO. The matrix A is given by A = 1 0 L P (a) (i) Describe the trans
June 2025, AS Pure Core, Q8 (7 marks): K O 8 Matrix A is given by A a OO where a is a constant and all entries of A are integers. 3 13 6 = KK + a 4 20 9 - - - L P The transformation represented by A
June 2024, Pure Core 1, Q3 (8 marks): K O 3 A transformation T is represented by the matrix N 5 1 0 OO, where a is a constant. = KK 3 6 3 L P (a) Find N2 in terms of a. [3] (b) Find det N in terms o
June 2024, AS Pure Core, Q8 (10 marks): Three transformations, TA, TB and TC, are represented by the matrices A, B and C respectively. J N J N 1 0 1 0 KK OO and B KK OO. You are given that A = = 2 3 0
June 2023, Pure Core 1, Q4 (11 marks): The transformations TA and TB are represented by the matrices A and B respectively, where J N J N 0 1 0 1 - KK OO and B KK OO. A = = 1 0 1 0 L P L P (a) Describ
June 2023, Pure Core 1, Q8 (15 marks): The points P, Q and R have coordinates (0, 2, 3), (2, 0, 1) and (1, 3, 0) respectively. The acute angle between the line segments PQ and PR is i. 2 (a) Show tha
June 2023, AS Pure Core, Q9 (10 marks): K O 9 Matrix R is given by R 0 1 0 OO where a and b are constants. = KK b 0 a L P (a) Find R2 in terms of a and b. [2] ^ h and b ^ h. 2 2 The constants a and b
June 2022, AS Pure Core, Q6 (11 marks): J N 5 12 1 KK OO. 6 The matrix A is given by A = 13 12 5 - L P You are given that A represents the transformation T which is a reflection in a certain straight
November 2021, Pure Core 2, Q6 (6 marks): In this question you must show detailed reasoning. J N 1 2 KK OO. The matrix A is given by A = 0 1 L P (a) Define the transformation represented by A. [1] (b) S
November 2021, AS Pure Core, Q5 (8 marks): J N K O - 1 0 = - 13 13 KK OO and B K O 5 Matrices A and B are given by A . = 12 5 0 1 KK OO L P 13 13 L P (a) Use A and B to disprove the proposition: “Matrix
November 2020, Pure Core 1, Q3 (5 marks): K O 3 You are given the matrix A 0 0 1 . = KK OO 0 1 0 - L P A4 (a) Find . [1] (b) Describe the transformation that A represents. [2] The matrix B represents a
November 2020, Pure Core 2, Q7 (6 marks): 6 . 2 4 . KK OO. 7 The matrix A is given by A = - 0 8 . 1 8 . L P (a) Find det A. [1] The matrix A represents a stretch parallel to one of the coordinate axes f
November 2020, AS Pure Core, Q2 (10 marks): P, Q and T are three transformations in 2-D. P is a reflection in the x-axis. A is the matrix that represents P. (a) Write down the matrix A. [1] J N J N Q is a
June 2019, Pure Core 2, Q4 (5 marks): A 2-D transformation T is a shear which leaves the y-axis invariant and which transforms the object point (2, 1) to the image point (2, 9). A is the matrix whic
June 2019, AS Pure Core, Q6 (5 marks): f x 1 4 p. + - 6 A transformation T is represented by the matrix T where T = 2 2 3 2 x x 5 - + A quadrilateral Q, whose area is 12 units, is transformed by T to
June 2019, AS Pure Core, Q7 (7 marks): f p. 7 A transformation A is represented by the matrix A where A 7 x 6 1 = - - 5 5 x 2 x - The tetrahedron H has vertices at O, P, Q and R. The volume of H is 6
June 2018, AS Pure Core, Q8 (13 marks): The 2 # 2 matrix A represents a transformation T which has the following properties. • The image of the point (0, 1) is the point (3, 4). • An object shape whos

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