plumiSeries: Edexcel International A Level Further Maths questions
Every Edexcel International A Level Further Maths exam question on FP1.7 Series, 2019–2025, with its mark scheme and examiner’s report.
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All 12 questions on Series, 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), Q5 (7 marks): (a) Use the standard results for summations to show that for all positive integers n r r r n n a n b n c r n 1 5 1 4 1 where a, b and c are integers to be det
- June 2024, Further Pure 1 (FP1), Q7 (8 marks): In this question use the standard results for summations. (a) Show that for all positive integers n ( ) 12 2 3 2 3 2 1 r r An Bn r n where A and B are integers
- January 2024, Further Pure 1 (FP1), Q8 (8 marks): (a) Use the standard results for summations to show that, for all positive integers n, r r r n n n r n 2 3 1 1 2 1 2 2 1 2 (b) Hence show that, for all posi
- June 2023, Further Pure 1 (FP1), Q1 (4 marks): Use the standard results for r r n 2 1 and r r n 3 1 to show that, for all positive integers n r r n n an bn c r n 2 1 2 2 1 12 1 ( ) ( )( ) where a, b and c ar
- January 2023, Further Pure 1 (FP1), Q2 (6 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Use the standard results for
- June 2022, Further Pure 1 (FP1), Q8 (8 marks): (a) Use the standard results for r r n 2 1 =∑ and r r n =∑ 1 to show that for all positive integers n r n =∑ 0 (r + 1)(r + 2) = 1 3 (n + 1)(n + 2)(n + 3) (b) He
- 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), Q5 (8 marks): (a) Use the standard results for r r n 3 1 =∑ , r r n 2 1 =∑ and r r n =∑ 1 to show that for all positive integers n, r r n =∑ 1 (r –1)(r – 3) = 1 12 n(n + 1)(n
- 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
- January 2021, Further Pure 1 (FP1), Q5 (7 marks): (a) Using the formulae for r r n =∑ 1 and r r n 2 1 =∑ , show that ( )( ) ( )( ) r r n n n r n + + = + + =∑ 1 5 6 7 2 7 1 for all positive integers n. (b) Hence
- October 2020, Further Pure 1 (FP1), Q4 (9 marks): (a) Use the standard results for r r n 2 1 =∑ and r r n =∑ 1 to show that r n =∑ 1 (2r – 1)2 = 1 3 n(4n2 – 1) for all positive integers n. (b) Hence find the ex
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