plumiInduction: matrices, recurrences and inequalities: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on A.3 Induction: matrices, recurrences and inequalities, 2019–2025, 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 6 questions on Induction: matrices, recurrences and inequalities, as a list
- June 2025, AS Paper 1, Q14 (8 marks): (a) The matrices A and B are given by A = [ 4 –3] –1 1 and B = [ 5 4 ] –3 –2 14 (a) (i) Find the matrices A–1 and B–1 [2 marks] 14 (a) (ii) Hence verify that (A
- June 2024, Paper 1, Q6 (4 marks): The sequence u1, u2, u3, ... is defined by _ u1 = 1 _ un+1 = un + 3n Prove by induction that for all integers n ≥ 1 _ un = 3 2 n2 – 3 2 n + 1 [4 marks]
- June 2022, AS Paper 1, Q11 (4 marks): Prove by induction that, for all integers n × 1 , (ABA−1)n = ABnA−1 where A and B are square matrices of equal dimensions, and A is non-singular. [4 marks]
- November 2021, Paper 1, Q5 (5 marks): The matrix M is defined by M = 3 2 −2 0 1 0 0 0 1 2 64 3 75 Prove by induction that Mn = 3n 3n − 1 −3n + 1 0 1 0 0 0 1 2 64 3 75 for all integers n × 1 [5 marks
- November 2020, Paper 2, Q10 (6 marks): The sequence u1, u2, u3, ... is defined by u1 = 0 un+1 = 5 6 × un Prove by induction that, for all integers n ≤ 1 , un = 5n × 5 5n × 1 [6 marks]
- June 2019, AS Paper 1, Q12 (12 marks): The matrix A is given by A = 1 2 0 3 12 (a) Prove by induction that, for all integers n ≤ 1, An = 1 3n − 1 0 3n [4 marks] 12 (b) Find all invariant lines under
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