plumiMatrix arithmetic: OCR A‑Level Further Maths questions
OCR A-Level Further Maths past-paper questions on 3.1 Matrix arithmetic, 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.
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All 12 questions on Matrix arithmetic, as a list
- June 2025, Pure Core 2, Q3 (9 marks): J N J N 1 3 3 3 - = - - KKK OOO and B KKK OOO. 3 Matrices A and B are given by A = 4 8 1 2 L P L P (a) Find the matrix AB. [1] (b) Verify that det ( AB ) det (
- 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, Pure Core 2, Q3 (7 marks): J N J N 4 3 3 5 - - KKK OOO and B KKK OOO. 3 Matrices A and B are given by A = - = 2 2 0 1 L P L P (a) Find 2A - 4B. [2] (b) Write down the matrix C such that A
- June 2023, Pure Core 2, Q1 (8 marks): J N 1 0 2 2 - KK OO. 1 (a) The matrix P is given by P = 4 2 2 3 - L P (i) Write down the dimensions of P. [1] (ii) Write down the transpose of P. [1] J N = ^ h,
- 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, Pure Core 1, Q2 (9 marks): J N 2 2 - KK OO. 2 The matrix A is given by A = 1 3 L P (a) Calculate det A. [1] - . (b) Write down A 1 [1] J N J N (c) Hence solve the equation A x 1 = - KK OO
- June 2022, AS Pure Core, Q2 (7 marks): J N J N a 1 2 5 - KK OO and B KK OO where a is a constant. 2 Matrices A and B are given by A = - = - 1 3 1 0 L P L P (a) Find the following matrices. • A + B •
- November 2021, Pure Core 2, Q1 (3 marks): K O K O 1 Two matrices, A and B, are given by A 2 3 1 OO and B 1 6 4 OO where a is a constant. = KK - = KK - - a 1 1 8 8 1 - - L P L P Find the value of a for w
- 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
- June 2019, AS Pure Core, Q2 (4 marks): f 1 k 0 p and ^ h where k is a constant. 2 Matrices P and Q are given by P Q ( 1 k ) 1 = - = + - 2 1 3 Exactly one of statements A and B is true. Statement A: P
- June 2018, AS Pure Core, Q6 (7 marks): f t 6 p and f 2 t 4 p where t is a constant. 6 The matrices A and B are given by A B = = t 2 t 2 - - (i) Show that A B . [2] = (ii) Verify that AB A B . [3] = (
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