plumiSeries: Edexcel International A Level Further Maths questions
Every Edexcel International A Level Further Maths exam question on FP2.2 Series, 2019–2025, with its mark scheme and examiner’s report.
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All 13 questions on Series, as a list
- June 2025, Further Pure 2 (FP2), Q5 (10 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Express 2 1 2 r r r ( )(
- June 2025 (A), Further Pure 2 (FP2), Q5 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Express 1 + 2 2 5 r + as
- January 2025, Further Pure 2 (FP2), Q4 (9 marks): (a) Express 4 1 2 r r r r in partial fractions. (b) Hence, using the method of differences, show that 1 4 1 2 2 n r n Pn Q r r r r n R n S where P, Q, R and S
- June 2024, Further Pure 2 (FP2), Q3 (8 marks): (a) Express 1 3 5 n n in partial fractions. (b) Hence, using the method of differences, show that for all positive integer values of n, 1 3 5 40 4 5 1 r r n pn
- January 2024, Further Pure 2 (FP2), Q3 (7 marks): (a) Show that for r 1 r r r r r A r r r r ( ) ( ) ( ) ( ) 1 1 1 1 where A is a constant to be determined. (b) Hence use the method of differences to determin
- June 2023, Further Pure 2 (FP2), Q1 (7 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (a) Show that, for r 2 2 2 2 r r r r
- January 2023, Further Pure 2 (FP2), Q2 (6 marks): (a) Express 1 2 1 2 1 2 3 n n n − ( ) + ( ) + ( ) in partial fractions. (b) Hence, using the method of differences, show that for all integer values of n, 1 2 1
- June 2022, Further Pure 2 (FP2), Q1 (5 marks): Given that 2 1 1 1 2 2 2 2 n n n A n B n + + ( ) ≡ + + ( ) (a) determine the value of A and the value of B (b) Hence show that, for n 5 2 1 1 1 2 2 2 2 5 r r
- January 2022, Further Pure 2 (FP2), Q6 (11 marks): Given that A > B > 0, by letting x = arctan A and y = arctan B (a) prove that arctan A – arctan B = arctan A B AB − + 1 (b) Show that when A = r + 2 a
- October 2021, Further Pure 2 (FP2), Q9 (9 marks): (a) Show that n5 − (n − 1)5 ≡ 5n4 − 10n3 + 10n2 − 5n + 1 (b) Hence, using the method of differences, show that for all integer values of n, r r n 4 1 =∑ = 1 30
- June 2021, Further Pure 2 (FP2), Q1 (8 marks): (a) Express 2 1 2 r r( ) − in partial fractions. (b) Hence find, in terms of n, 1 1 2 2 r r r n ( ) − =∑ Give your answer in the form n An B Cn n 2 1 + + + ( )
- January 2021, Further Pure 2 (FP2), Q2 (6 marks): (a) Show that, for r > 0 r r r r r r r r r r + + − + + + = + + + 2 1 3 1 2 4 1 2 ( ) ( )( ) ( )( ) (b) Hence show that r r r r n an b c n n r n + + + = + + + =∑
- October 2020, Further Pure 2 (FP2), Q2 (9 marks): (a) Write 3 1 1 1 r r r r + − + ( )( ) in partial fractions. (b) Hence find 3 1 1 1 2 r r r r r n ( )( ) n 2 giving your answer in the form an bn c n n 2 2 1
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