plumiProof by deduction and exhaustion: OCR MEI A‑Level Maths questions
OCR MEI A-Level Maths past-paper questions on 1.1 Proof by deduction and exhaustion, 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 10 questions on Proof by deduction and exhaustion, as a list
- June 2025, Paper 2, Q5 (3 marks): Prove that the sum of the first n positive odd numbers is a square number. [3]
- June 2025, AS Paper 2, Q9 (3 marks): n n A triangular number is any number of the form ( 1 ), + 9 where n is a positive integer. 2 Prove that the sum of any two consecutive triangular numbers is a
- June 2024, AS Paper 1, Q3 (3 marks): + is a multiple of 4 but not a multiple of 8. 3 Prove that, when n is an even number, n 4 [3]
- June 2023, Paper 3, Q13 (4 marks): n =/ 2 13 Prove that Euler’s approximate formula, as given in line 13, when applied to r gives exactly r 1 n n ( 1 2 )( n 1 ) + + . [4] 6 n
- June 2019, AS Paper 2, Q3 (3 marks): Without using a calculator, prove that 3 2 [3] 2 2 3 .
- June 2018, Paper 3, Q11 (2 marks): Line 8 states that a b + 11 ab for a, b 0 . Explain why the result cannot be extended to apply in each of H H 2 the following cases. (i) One of the numbers a an
- June 2018, Paper 3, Q12 (3 marks): a b + 2 H 12 ab a b Lines 5 and 6 outline the stages in a proof that . Starting from ( ) 0 , give a detailed H - 2 [3] proof of the inequality of arithmetic and
- June 2018, Paper 3, Q13 (3 marks): Consider a geometric sequence in which all the terms are positive real numbers. Show that, for any three [3] consecutive terms of this sequence, the middle one
- June 2018, Paper 3, Q14 (4 marks): (i) In Fig. C1.3, angle CBD = i. Show that angle CDA is also i, as given in line 23. [2] (ii) Prove that h ab [2] , as given in line 24. =
- June 2018, AS Paper 2, Q3 (3 marks): P and Q are consecutive odd positive integers such that P > Q. Prove that P 2 ‒ Q 2 is a multiple of 8. [3]
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