Algebraic Proof — Practice Questions
12 exam-style questions (40 marks), building from warm-up to grade 8–9. Show full working: Edexcel gives method marks even when the final answer is wrong.
Section A — Warm-up (grades 4–5)
- (2 marks)Give a counterexample to show that this statement is false: “The sum of two prime numbers is always even.”
- (3 marks)Prove that the sum of any three consecutive integers is a multiple of 3.
- (3 marks)Prove that the difference between the squares of two consecutive integers is always odd.
Section B — Core (grades 5–7)
- (3 marks)Prove that the product of any two odd numbers is odd.
- (3 marks)Prove that the sum of the squares of two consecutive even numbers is a multiple of 4.
- (3 marks)Prove that (x + 2)² − (x − 2)² ≡ 8x.
- (3 marks)Prove that x² − 8x + 19 > 0 for all values of x.
- (4 marks)n is a positive integer. Prove that (n + 1)² + (n − 1)² is always even, and is 2 more than twice a square number.
Section C — Stretch (grades 8–9)
- (4 marks)Prove that the difference between the squares of any two consecutive odd numbers is a multiple of 8.
- (4 marks)Prove that the square of any odd number is one more than a multiple of 8.
Hint
Write the odd number as 2n + 1 and factorise 4n² + 4n. - (4 marks)Prove that n³ − n is a multiple of 6 for all integers n.
- (4 marks)(a) Write 2x² + 4x + 7 in the form a(x + b)² + c.
(b) Hence prove that 2x² + 4x + 7 is always greater than 4.
← Back to the Edexcel Unit 2 resource listThe Vector Academy · thevectoracademy.in
Book a free trial class
Tell us a little about your requirement.