plumiDeterminants and inverses: OCR A‑Level Further Maths questions
OCR 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.
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All 20 questions on Determinants and inverses, 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 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, 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 2024, AS Pure Core, Q1 (4 marks): Use a matrix method to determine the solution of the following simultaneous equations. [4] 2 x 3 y z 1 - + = x 2 y 4 z 40 - - = x 5 6 y z 61 + - =
- 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, AS Pure Core, Q7 (6 marks): In this question you must show detailed reasoning. J N a 6 a 3 - - K O Matrix A is given by A a 9 a 4 OO where a is a constant. = + KK a 0 13 1 - - L P Find all
- 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, Pure Core 2, Q7 (13 marks): You are given that a is a parameter which can take only real values. J N 2 4 6 - K O The matrix A is given by A 3 10 4 a 9 OO. = - KK - 7 4 4 L P (a) Find an ex
- 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, AS Pure Core, Q8 (6 marks): K O 8 The matrix A is given by A 1 t 6 t OO . = KK - 2 2 t 2 2 t 1 - - L P (a) Find, in fully factorised form, an expression for det A in terms of t. [3] (b) St
- 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, Q4 (6 marks): You are given the system of equations 2 a x 2 y 1 - = 2 x b y 3 + = where a and b are real numbers. (a) Use a matrix method to find x and y in terms of a and b.
- June 2019, Pure Core 1, Q10 (11 marks): K O 10 You are given the matrix A where A 0 a 2 . = KK OO 4 5 1 L P (a) Find, in terms of a, the determinant of A, simplifying your answer. [2] (b) Hence find t
- 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, Q4 (7 marks): f p. 4 The matrix A is given by A 1 1 1 = - 2 2 a (i) Show that detA = 6 - 3a. [2] (ii) State the value of a for which A is singular. [1] (iii) Given that A is
- 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] = (
- 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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