plumiProof: Edexcel International A Level Maths questions
Every Edexcel International A Level Maths exam question on P4.1 Proof, 2019–2025, with its mark scheme and examiner’s report.
Paper
All papers
Exam
All years
All 16 questions on Proof, as a list
- June 2025, Pure 4 (P4), Q10 (4 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. Use proof by contradiction to show tha
- June 2025 (A), Pure 4 (P4), Q10 (5 marks): [In this question you may assume that if n is an integer and n 2 is even, then n is even.] Given that p and q are integers, use proof by contradiction to show t
- January 2025, Pure 4 (P4), Q6 (4 marks): Given that n ∈ , use algebra to prove by contradiction that “ if n 2 – 4n + 5 is even then n is odd”
- October 2024, Pure 4 (P4), Q2 (4 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. The curve C1 has equation y x x 4 2 10
- June 2024, Pure 4 (P4), Q8 (8 marks): f(x) = ( ) 8 3 0 8 3 4 3 x x (a) Show that the binomial expansion of f(x) in ascending powers of x up to and including the term in x 3 is A x x Bx 8 2 2 3 ... w
- January 2024, Pure 4 (P4), Q8 (4 marks): Use proof by contradiction to prove that the curve with equation y = 2x + x 3 + cos x has no stationary points.
- October 2023, Pure 4 (P4), Q4 (5 marks): (a) Prove by contradiction that for all positive numbers k k k + 9 6 (b) Show that the result in part (a) is not true for all real numbers.
- June 2023, Pure 4 (P4), Q7 (4 marks): Use proof by contradiction to prove that 7 is irrational. (You may assume that if k is an integer and k 2 is a multiple of 7 then k is a multiple of 7)
- January 2023, Pure 4 (P4), Q9 (8 marks): A student was asked to prove, for p ∈ , that “if p3 is a multiple of 3, then p must be a multiple of 3” The start of the student’s proof by contradiction is sh
- October 2022, Pure 4 (P4), Q8 (4 marks): A student was asked to prove by contradiction that “there are no positive integers x and y such that 3x2 + 2xy – y2 = 25” The start of the student’s proof is sh
- June 2022, Pure 4 (P4), Q9 (4 marks): Use proof by contradiction to show that, when n is an integer, n 2 – 2 is never divisible by 4
- January 2022, Pure 4 (P4), Q6 (5 marks): Three consecutive terms in a sequence of real numbers are given by k, 1 + 2k and 3 + 3k where k is a constant. Use proof by contradiction to show that this sequ
- October 2021, Pure 4 (P4), Q10 (6 marks): (a) A studentʼs attempt to answer the question ‟Prove by contradiction that if n3 is even, then n is even” is shown below. Line 5 of the proof is missing. Assum
- June 2021, Pure 4 (P4), Q9 (8 marks): (i) Relative to a fixed origin O, the points A, B and C have position vectors a, b and c respectively. Points A, B and C lie in a straight line, with B lying be
- January 2021, Pure 4 (P4), Q3 (2 marks): Prove by contradiction that there is no greatest odd integer.
- October 2020, Pure 4 (P4), Q1 (4 marks): Given that n is an integer, use algebra, to prove by contradiction, that if n3 is even then n is even.
Questions, mark schemes and examiner’s reports are © Pearson Edexcel, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? Every Edexcel International A Level Maths paper.
Rather write your answers by hand on iPad? Plumi marks them against the same mark schemes.