plumiInduction: divisibility: OCR A‑Level Further Maths questions
OCR A-Level Further Maths past-paper questions on 1.2 Induction: divisibility, 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 8 questions on Induction: divisibility, as a list
- June 2025, AS Additional Pure Mathematics, Q5 (5 marks): n n 5 f n for all positive integers n. Let ( ) 3 4 = + f n is a multiple of 7 for all odd integers n [5] Prove by induction that ( ) H . 1
- June 2024, Pure Core 1, Q8 (5 marks): n n 8 - is divisible by 3, for all integers n [5] Prove by induction that 11 7 13 1 0 . - # H
- June 2024, AS Additional Pure Mathematics, Q4 (5 marks): " ,, where n 4 The first five terms of the Fibonacci sequence, Fn H , are 1 F 1 , F 1 , F 2 , F = and F 3 5 = . 5 = = = 1 2 3 4 (a) Use the recurrence definitio
- June 2023, AS Pure Core, Q6 (6 marks): n 6 Prove by induction that 4 8 66 is divisible by 14 for all integers n 0 . [6] + H #
- November 2021, AS Pure Core, Q7 (5 marks): - n n 7 Prove that 2 3 is divisible by 5 for all integers n H . 1 [5]
- November 2021, AS Additional Pure Mathematics, Q3 (6 marks): For positive integers n, the sequence of Fibonacci numbers, { Fn , starts with the terms } F 1 = , F 1 2 = , F 1 2 , … and is given by the recurrence relation F
- November 2020, Pure Core 1, Q7 (5 marks): Prove by induction that the sum of the cubes of three consecutive positive integers is divisible by 9. [5]
- June 2018, AS Pure Core, Q7 (6 marks): n 1 n 7 Prove by induction that 2 + 5 9 is divisible by 7 for all integers n H 1. [6] + #
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