Determinants and inverses: Edexcel A‑Level Further Maths questions

Edexcel 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 15 questions on Determinants and inverses, as a list

June 2025, Core Pure 1, Q1 (6 marks): M 3 6 0 3 1 2 a a a where a is a constant (a) Determine the values of a for which the matrix M is singular. (3) Given that matrix M is non-singular and
June 2025, AS Core Pure, Q3 (6 marks): 1 1 a b M where a and b are real constants and a ≠ b (a) Determine M –1 in terms of a and b (3) Given that M + M –1 = I, where I is the 2 × 2 identity
June 2024, Core Pure 2, Q8 (7 marks): A 1 1 1 3 6 0 k k (a) Find, in terms of k, A –1 (4) (b) Determine, in simplest form in terms of k, the coordinates of the point where the follow
June 2024, AS Core Pure, Q4 (8 marks): A B 1 2 7 3 2 1 1 4 4 2 1 7 4 10 3 19 3 1 6 k k k k k where k is a constant. (a) Determine the value of the constant c for which AB
June 2023, Core Pure 1, Q8 (13 marks): A colony of small mammals is being studied. In the study, the mammals are divided into 3 categories N (newborns) 0 to less than 1 month old J (juveniles) 1 to 3
June 2023, AS Core Pure, Q9 (9 marks): (i) P k k k k 3 2 5 7 2 4 where is a constant Show that P is non-singular for all real values of k. (4) (ii) Q 2 1 3 0 The matrix Q represe
June 2022, Core Pure 1, Q5 (6 marks): M = −         a a 2 3 2 3 0 4 2 where a is a constant (a) Show that M is non-singular for all values of a. (2) (b) Determine, in terms of a, M–1 (4)
June 2022, Core Pure 2, Q2 (8 marks): In this question you must show all stages of your working. A college offers only three courses: Construction, Design and Hospitality. Each student enrols on jus
June 2022, Further Pure 2, Q2 (8 marks): Matrix M is given by M = 1 3 0 0 1 1 b a a where a and b are integers, such that a < b Given that the characteristic equation for M is λ3 – 7λ2 + 13λ +
November 2021, Core Pure 1, Q4 (9 marks): (i) A is a 2 by 2 matrix and B is a 2 by 3 matrix. Giving a reason for your answer, explain whether it is possible to evaluate (a) AB (b) A + B (2) (ii) Given t
November 2020, Core Pure 2, Q6 (14 marks): M = −         k 5 7 1 1 1 2 1 1 where k is a constant (a) Given that k ≠ 4, find, in terms of k, the inverse of the matrix M. (4) (b) Find, in terms of
November 2020, Further Pure 2, Q3 (10 marks): M = 1 2 2 4 1 1 2 3 k − −         where k is a constant. (a) Show that, in terms of k, a characteristic equation for M is given by λ3 – (2k + 13)λ + 5(k
June 2019, Core Pure 2, Q7 (11 marks): M = 2 1 1 3 4 3 2 1 − − ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ k where k is a constant (a) Find the values of k for which the matrix M has an inverse. (2) (b) Find, in terms of p, the
June 2019, AS Further Pure 2, Q1 (5 marks): Given that A = ⎛ ⎝⎜ ⎞ ⎠⎟ 3 2 2 2 (a) find the characteristic equation for the matrix A, simplifying your answer. (2) (b) Hence find an expression for the matrix
June 2018, AS Core Pure, Q1 (5 marks): M = − − −         2 1 3 4 2 1 3 5 2 (a) Find M–1 giving each element in exact form. (2) (b) Solve the simultaneous equations 2x + y – 3z = –4 4x – 2y +

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