plumiProof: WJEC A‑Level Maths questions
Every WJEC A-Level Maths exam question on P.1 Proof, 2018–2025, with its mark scheme and examiner’s report.
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![Summer 2025 Unit 3, question 9: Use proof by contradiction to show that there are no integers x and y for which 3 x 15 y 2 9. . [4]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/1300u30-jun25-09-qp.webp)
![Summer 2024 Unit 3, question 5: 5. Prove by contradiction the following proposition: 81 18 When x is real and positive, x . [4] x x](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/1300u30-jun24-05-qp.webp)
![Summer 2024 AS Unit 1, question 4: n 2 4. Given that n is an integer such that 1 X n X 6, use proof by exhaustion to show that is not divisible by 3. [3]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/2300u10-jun24-04-qp.webp)
![Summer 2024 AS Unit 1, question 8: x 10 x 5 x 8. Prove that for all real values of x. [4] !](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/2300u10-jun24-08-qp.webp)
![Summer 2023 AS Unit 1, question 8: Show, by counter example, that the following statement is false. 0 8 2 “For all positive integer values of n, n is a prime number.” 1 [3]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/2300u10-jun23-08-qp.webp)
![Summer 2019 Unit 3, question 15: 1 5 Use proof by contradiction to show that is irrational. [5]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/1300u30-jun19-15-qp.webp)
![Summer 2019 AS Unit 1, question 5: 5 Given that n is an integer such that 1 X n X 4, prove that 2n2 + 5 is a prime number. [3]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/2300u10-jun19-05-qp.webp)
![Summer 2018 Unit 3, question 11: π 1 1 Prove by contradiction that, for every real number x such that 0 X x X , 2 sinx + cosx x 1. [4]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/1300u30-jun18-11-qp.webp)
All 10 questions on Proof, as a list
- Summer 2025, Unit 3, Q9 (4 marks): Use proof by contradiction to show that there are no integers x and y for which 3 x 15 y 2 9. . [4]
- Summer 2024, Unit 3, Q5 (4 marks): 5. Prove by contradiction the following proposition: 81 18 When x is real and positive, x . [4] x x
- Summer 2024, AS Unit 1, Q4 (3 marks): n 2 4. Given that n is an integer such that 1 X n X 6, use proof by exhaustion to show that is not divisible by 3. [3]
- Summer 2024, AS Unit 1, Q8 (4 marks): x 10 x 5 x 8. Prove that for all real values of x. [4] !
- Summer 2023, AS Unit 1, Q8 (3 marks): Show, by counter example, that the following statement is false. 0 8 2 “For all positive integer values of n, n is a prime number.” 1 [3]
- Summer 2022, AS Unit 1, Q6 (5 marks): 6 In each of the two statements below, x and y are real numbers. One of the statements is true while the other is false. x2 + y2 x2xy , for all real values of x
- Summer 2019, Unit 3, Q15 (5 marks): 1 5 Use proof by contradiction to show that is irrational. [5]
- Summer 2019, AS Unit 1, Q5 (3 marks): 5 Given that n is an integer such that 1 X n X 4, prove that 2n2 + 5 is a prime number. [3]
- Summer 2018, Unit 3, Q11 (4 marks): π 1 1 Prove by contradiction that, for every real number x such that 0 X x X , 2 sinx + cosx x 1. [4]
- Summer 2018, AS Unit 1, Q14 (4 marks): 4 In each of the two statements below, c and d are real numbers. One of the statements is true, while the other is false. (2c – d)2 = 4c2 – d 2, for all values
Questions, mark schemes and examiner’s reports are © WJEC CBAC Ltd, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? Every WJEC A-Level Maths paper.
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