plumiMaclaurin and Taylor series: Edexcel International A Level Further Maths questions
Every Edexcel International A Level Further Maths exam question on FP2.6 Maclaurin and Taylor series, 2019–2025, with its mark scheme and examiner’s report.
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All 15 questions on Maclaurin and Taylor series, as a list
- June 2025, Further Pure 2 (FP2), Q2 (5 marks): d d d d e 2 2 2 2 9 4 5 y x y x y x Given that y = 2 and d d y x = –1 at x = 3 , determine a Taylor series for y in ascending powers of (x – 3) , up to and incl
- June 2025 (A), Further Pure 2 (FP2), Q3 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Given that when y = arcsin 2x
- January 2025, Further Pure 2 (FP2), Q3 (8 marks): 2 2 d d 6 0 2 d d y y y xy x x x Given that d 3 d y x and y = 1 2 at x = 2 (a) determine the value of d d 3 3 y x at x = 2 (b) Hence determine the series expans
- June 2024, Further Pure 2 (FP2), Q2 (7 marks): x y x y d d 3 4 (a) Show that x y x ay y x by c y x d d d d d d 3 3 2 2 2 2 where a, b and c are integers to be determined. Given that y = 1 at x =
- June 2024, Further Pure 2 (FP2), Q7 (7 marks): Given that y = e x sin x (a) show that d d d d 6 6 2 2 y x k y x = where k is a constant to be determined. (b) Hence determine the first 5 non‑zero terms in the
- January 2024, Further Pure 2 (FP2), Q4 (9 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Determine, in ascending p
- June 2023, Further Pure 2 (FP2), Q6 (9 marks): Given that y = sec x (a) show that d d 3 3 2 y x x x p x q sec tan sec where p and q are integers to be determined. (b) Hence determine the Taylor series expans
- January 2023, Further Pure 2 (FP2), Q1 (8 marks): Given that y = ln(5 + 3x) (a) determine, in simplest form, d d 3 3 y x (b) Hence determine the Maclaurin series expansion of ln(5 + 3x), in ascending powers of
- January 2023, Further Pure 2 (FP2), Q4 (7 marks): d d y x y x = − 2 (a) Show that d d d d d d d d 4 4 3 3 2 2 y x Ay y x B y x y x = + where A and B are integers to be determined. Given that y = 1 at x = –1 (b)
- June 2022, Further Pure 2 (FP2), Q5 (8 marks): Given that y y x y x y d d d d 2 2 2 2 2 0 + − = y > 0 (a) determine d d 3 3 y x in terms of d d 2 2 y x , d d y x and y Given that y = 2 and d d y x
- January 2022, Further Pure 2 (FP2), Q5 (8 marks): y = 4 + ln x x > 1 2 (a) Show that d d 2 2 2 3 2 9 2 4 4 y x x x x = − + + ln ( ln ) (b) Hence, or otherwise, determine the Taylor series expansion about x = 1
- October 2021, Further Pure 2 (FP2), Q5 (8 marks): Given that y = tan2 x (a) show that d d 3y x3 = 8 tan x sec2 x (p sec2 x + q) where p and q are integers to be determined. (b) Hence determine the Taylor series
- June 2021, Further Pure 2 (FP2), Q4 (9 marks): Given that y y x y x y d d d d 2 2 2 4 3 0 − + = (a) show that d d d d d d 3 3 2 3 28 24 y x y y x y y x = − Given also that y = 8
- January 2021, Further Pure 2 (FP2), Q5 (9 marks): Given that 2 5 3 2 2 2 2 − ( ) + = x y x x y x y d d d d (a) show that d d d d d d d d d d 3 3 2 2 2 2 1 2 2 1 5 5 3 y x x x y x y x y x y x = − ( ) −
- October 2020, Further Pure 2 (FP2), Q1 (7 marks): d d 2 2 y x + 3x d d y x = 2 cos x (a) Express d d 3y x3 in terms of x, d d y x and d d 2 2 y x At x = 0 , y = 2 and d d y x = 5 (b) Determine the value of d d
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