plumiDisproof by counter-example: OCR MEI A‑Level Maths questions
OCR MEI A-Level Maths past-paper questions on 1.2 Disproof by counter-example, 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.
Questions from
Paper
All papers
Exam
All years
Loading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDF
All 7 questions on Disproof by counter-example, as a list
- June 2024, Paper 1, Q1 (2 marks): 2 1 A student states that 1 x 1 ( 1 x ) for all values of x. + + Using a counter example, show that the student is wrong. [2]
- June 2023, AS Paper 2, Q3 (2 marks): A student makes the following conjecture. For all positive integers n, n 6 - is always prime. 1 Use a counter example to disprove this conjecture. [2]
- June 2022, Paper 2, Q5 (3 marks): n - is prime. 5 Tom conjectures that if n is an odd number greater than 1, then 2 1 Find a counter example to disprove Tom’s conjecture. [3]
- November 2021, Paper 1, Q1 (2 marks): 2 1 Beth states that for all real numbers p and q, if p 2 q then p 2 q . Prove that Beth is not correct. [2]
- November 2021, AS Paper 1, Q4 (4 marks): 4 (a) Show that ! 4 1 . [2] nn (b) Nina believes that the statement ! n 1 is true for all positive integers n. Prove that Nina is not correct. [2]
- November 2020, Paper 3, Q9 (3 marks): b a 9 (a) Show that if a = 1 and b 2 1 then a 1 b . [2] (b) Find integer values of a and b with b 2 a 2 1 and ab not greater than ba (a counter example to the c
- November 2020, AS Paper 1, Q1 (2 marks): + 1 Celia states that n 2 n 10 is always odd when n is a prime number. + Prove that Celia’s statement is false. [2]
Questions, mark schemes and examiner’s reports are © OCR, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? OCR MEI A-Level Maths past papers.
The Plumi iPad app also offers exam-style questions with AI feedback on your handwritten working.