plumiProof by induction: CAIE A‑Level Further Maths questions
Every CAIE A-Level Further Maths exam question on 1.7 Proof by induction, June 2024 and the specimen papers, with its mark scheme and examiner’s report.
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![June 2024 Paper 1, question 2: Prove by mathematical induction that 6 4 + n 38 n - is divisible by 74 for all positive integers n. 2 [6]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/923111-jun24-02-qp.webp)
![Specimen Paper 1, question 2: It is given that φ(n) = 5n(4n + 1) – 1, for n = 1, 2, 3, … . Prove, by mathematical induction, that φ(n) is divisible by 8 for every positive integer n. [7]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/923101-spec-02-qp.webp)
All 2 questions on Proof by induction, as a list
- June 2024, Paper 1, Q2 (6 marks): Prove by mathematical induction that 6 4 + n 38 n - is divisible by 74 for all positive integers n. 2 [6]
- Specimen, Paper 1, Q2 (7 marks): It is given that φ(n) = 5n(4n + 1) – 1, for n = 1, 2, 3, … . Prove, by mathematical induction, that φ(n) is divisible by 8 for every positive integer n. [7]
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