plumiProof by induction: Edexcel A‑Level Further Maths questions
Every Edexcel A-Level Further Maths exam question on CP.1 Proof by induction, 2018–2025, with its mark scheme and examiner’s report.
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All 14 questions on Proof by induction, as a list
- June 2025, Core Pure 2, Q3 (12 marks): Given A 1 5 0 2 (a) prove by mathematical induction that, for n ∈ An n n 1 5 2 1 0 2 (6) Given B 1 0 0 1 (b) describe fully the singl
- June 2025, Further Pure 2, Q4 (9 marks): A sequence is defined by un+2 = 6un+1 – 8un n 1 u1 = 399.6 u2 = 798.4 (a) Prove by induction that, for n ∈ un = 200(2 n) – 1 10 (4 n) (6) (b) Hence determin
- June 2025, AS Core Pure, Q6 (6 marks): Prove by induction that for all positive integers n 3 2 2 1 1 ( 1) 4 n r r n n (6)
- June 2024, Core Pure 1, Q6 (6 marks): Prove by induction that, for all positive integers n, 2 1 1 3 4 1 2 1 2 r n n r n (6)
- June 2024, AS Core Pure, Q7 (10 marks): (i) Prove by induction that, for all positive integers n, 1 1 1 1 r r n n r n (5) (ii) Prove by induction that, for all positive integers n, f ( n ) = 3 2n +
- June 2023, Core Pure 1, Q4 (5 marks): Prove by induction that for n ∈ 1 2 0 1 1 2 0 1 n n (5)
- June 2023, Core Pure 2, Q6 (6 marks): Given that y = e 2x sinh x prove by induction that for n ∈ d d e n n x n n y x x x 2 3 1 2 3 1 2 sinh cosh (6)
- June 2022, Core Pure 2, Q3 (11 marks): M = 3 0 1 a where a is a constant (a) Prove by mathematical induction that, for n ∈ M n = 3 2 3 1 0 1 n n a ( ) − (6) Triangle T has
- June 2022, AS Core Pure, Q7 (6 marks): Prove by mathematical induction that, for n ∈ − − = − − + 5 9 4 7 1 6 9 4 1 6 n n n n n (6)
- November 2021, Further Pure 2, Q6 (6 marks): A recurrence system is defined by un+2 = 9(n + 1) 2 un − 3un+1 n 1 u1 = −3, u2 = 18 Prove by induction that, for n ∈ , un = (−3) n n! (6)
- November 2020, Core Pure 1, Q6 (12 marks): (i) Prove by induction that for n ∈ + ( )( ) ( )( ) 3 1 2 2 3 1 r r n n n r n + + = + + =∑ (6) (ii) Prove by induction that for all positive odd integers n f(n
- November 2020, AS Core Pure, Q8 (6 marks): Prove by induction that, for n ∈ + f(n) = 2n + 2 + 32n + 1 is divisible by 7 (6)
- June 2019, Core Pure 1, Q6 (6 marks): 3URYHE\LQGXFWLRQWKDWIRUDOOSRVLWLYHLQWHJHUVn I n 2n + 4í2n LVGLYLVLEOHE\ (6)
- June 2018, AS Core Pure, Q8 (12 marks): (i) Prove by induction that for n + 5 8 2 3 4 1 8 2 1 4 − − = + − − n n n n n (6) (ii) Prove by induction that for n + f (n) = 4n + 1 +
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