plumiProof by deduction and exhaustion: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.01.1 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 13 questions on Proof by deduction and exhaustion, as a list
- June 2024, Paper 1, Q3 (8 marks): (a) Find a counterexample to disprove the statement that the product of two prime numbers is always odd. [1] (b) In each of the following cases write one of the
- June 2023, Paper 2, Q7 (5 marks): 7 A student wishes to prove that, for all positive integers a and b, a 4 b 2 . ! - 2 (a) Prove that a & [2] 4 b 2 a is even. - = 2 (b) Hence or otherwise prove
- June 2023, AS Paper 1, Q7 (5 marks): (a) Two real numbers are denoted by a and b. (i) Write down expressions for the following. • The mean of the squares of a and b • The square of the mean of a an
- June 2022, Paper 1, Q2 (6 marks): (a) Given that a and b are real numbers, find a counterexample to disprove the statement that, 2 2 if a 2 b , then a 2 b . [1] (b) A student writes the statemen
- June 2022, Paper 2, Q7 (8 marks): It is given that any integer can be expressed in the form m 3 + , where m is an integer and r r is 0, 1 or 2. Use this fact to answer the following. (a) By cons
- November 2021, Paper 2, Q8 (6 marks): 8 The number K is defined by K n + , where n is an integer greater than 2. 1 = ^h h, find the constants b and c. ^ 3 2 (a) Given that n 1 n 1 n bn c [1] + / + +
- November 2021, AS Paper 1, Q8 (5 marks): (a) Prove that the following statement is not true. 2p 2 p is a positive integer p [1] & H (b) Prove that the following statement is true. m and n are consecuti
- November 2020, Paper 2, Q5 (5 marks): - and n 2 + are positive integers. (a) Determine the set of values of n for which n 1 1 5 [3] 2 2 2 2 2 A ‘Pythagorean triple’ is a set of three positive intege
- June 2019, Paper 2, Q6 (4 marks): Shona makes the following claim. n “n is an even positive integer greater than 2 2 - is not prime” 1 & Prove that Shona’s claim is true. [4]
- June 2019, AS Paper 1, Q5 (5 marks): (a) Prove that the following statement is not true. 2 m is an odd number greater than 1 m + is prime. 4 [1] & (b) By considering separately the case when n is o
- June 2018, AS Paper 1, Q5 (5 marks): N is an integer that is not divisible by 3. Prove that N2 is of the form p 5 3 + , where p is an integer. 1 [5]
- June 2018, AS Paper 1, Q7 (7 marks): OABC is a parallelogram with OA= a and OC = c. P is the midpoint of AC. A B a P O c C (i) Find the following in terms of a and c, simplifying your answers. (a)
- June 2018, AS Paper 2, Q3 (3 marks): In each of the following cases choose one of the statements P & Q P % Q P + Q to describe the relationship between P and Q. 5 2 (i) P: y 3 x 4 x 12 x = - + d y
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