plumiProof: Edexcel International A Level Further Maths questions
Every Edexcel International A Level Further Maths exam question on FP1.8 Proof, 2019–2025, with its mark scheme and examiner’s report.
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All 14 questions on Proof, as a list
- June 2025, Further Pure 1 (FP1), Q8 (13 marks): (a) Using the standard summation formulae show that 2 1 4 3 1 2 1 2 r n n an b r n where a and b are integers to be determined. (b) Prove by induction tha
- January 2025, Further Pure 1 (FP1), Q8 (10 marks): (i) Prove by induction that, for n ∈ + 2 9 1 4 1 3 9 3 1 n n n n n (ii) A sequence of numbers is defined by u u 1 2 1 4 = = u u u n n n n 2 1 6
- June 2024, Further Pure 1 (FP1), Q6 (9 marks): (a) Prove by induction that for n ∈ + 1 0 2 1 2 1 0 2 r r n n n where r is a constant. M N 4 0 0 5 1 2 0 2 4 The transformation r
- June 2024, Further Pure 1 (FP1), Q8 (6 marks): Prove by induction that for n ∈ + f(n) = 7 n – 1 + 8 2n + 1 is divisible by 57
- January 2024, Further Pure 1 (FP1), Q10 (10 marks): (i) Prove by induction that for n ∈ + 5 1 4 1 3 2 3 4 3 2 1 n n n n n n (ii) Prove by induction that for n ∈ + f(n) = 8 2n + 1 + 6 2n – 1 is d
- June 2023, Further Pure 1 (FP1), Q9 (5 marks): Prove, by induction, that for n ∈ , n 2 4 n + 6n – 10 is divisible by 18
- January 2023, Further Pure 1 (FP1), Q9 (6 marks): Prove by induction that for all positive integers n log log ( )! ! 2 1 2 2 1 r n n r n n
- June 2022, Further Pure 1 (FP1), Q9 (10 marks): (i) A sequence of numbers is defined by u1 = 3 un + 1 = 2un – 2n + 1 n 1 Prove by induction that, for n ∈ un = 5 × 2n – 1 – n × 2n (ii) Prove by induction t
- January 2022, Further Pure 1 (FP1), Q9 (14 marks): (a) Prove by induction that, for n ∈ r r n 3 1 1 4 =∑ = n 2(n + 1) 2 (b) Using the standard summation formulae, show that r r n =∑ 1 (r + 1)(r – 1) = 1 4 n(n
- October 2021, Further Pure 1 (FP1), Q9 (10 marks): (i) A sequence of numbers is defined by u1 = 0 u2 = –6 un + 2 = 5un + 1 – 6un n 1 Prove by induction that, for n ∈ + un = 3 × 2 n – 2 × 3 n (ii) Prove by in
- June 2021, Further Pure 1 (FP1), Q7 (11 marks): (a) Prove by induction that for n ∈ r n n n r n 2 1 6 1 2 1 = + + =∑ ( )( ) (b) Hence show that ( ) ( ) r n an bn c r n 2 2 1 2 6 + = + + =∑ where a, b and c
- June 2021, Further Pure 1 (FP1), Q8 (6 marks): Prove by induction that 4 n + 2 + 5 2n + 1 is divisible by 21 for all positive integers n.
- January 2021, Further Pure 1 (FP1), Q9 (12 marks): (i) A sequence of numbers u1, u2, u3,... is defined by u u u n n + = − = 1 1 1 3 2 1 1 ( ) Prove by induction that, for n ∈ + un n = − 3 2 3 1 (ii)
- October 2020, Further Pure 1 (FP1), Q8 (12 marks): (i) Prove by induction that, for n ∈ + 2 1 1 1 2 2 2 1 2 2 r r r n n r n − + = + =∑ ( ) ( ) (ii) Prove by induction that, for n ∈ + f(n) = 12 n + 2 × 5 n – 1
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