plumiMaclaurin series: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 4.4 Maclaurin series, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 8 questions on Maclaurin series, as a list
- June 2025, Core Pure 2, Q8 (8 marks): Given that y x x = cos sinh x (a) show that d d 4 4 y x ky = where k is a constant to be determined. (5) (b) Hence determine the first three non-zero terms of t
- June 2025, Further Pure 1, Q4 (8 marks): y x 15 2e (a) Show that d d e e e 2 2 2 2 2 30 15 3 2 y x x x x (3) (b) Hence determine the Maclaurin series expansion for y, in ascending powers of x, up to an
- June 2024, Core Pure 2, Q2 (8 marks): f(x) = tanh 1 3 6 3 2 x x x < (a) Show that f′(x) = – 1 2 3 x + (4) (b) Hence determine f′′(x) (1) (c) Hence show that the Maclaurin series for f(x), up
- June 2023, Core Pure 2, Q2 (6 marks): (a) Write down the Maclaurin series of e x, in ascending power of x, up to and including the term in x 3 (1) (b) Hence, without differentiating, determine the M
- June 2023, Further Pure 1, Q6 (12 marks): y = ln(e 2x cos 3x) – 1 2 < x < 1 2 (a) Show that d d y x x 2 3 3 tan (2) (b) Determine d d 4 4 y x (3) (c) Hence determine the first 3 non-zero terms in ascend
- June 2022, Core Pure 2, Q9 (8 marks): y = cosh n x n 5 (a) (i) Show that d d 2 2 y x = n 2 cosh n x – n(n – 1)cosh n – 2 x (4) (ii) Determine an expression for d d 4 4 y x (2) (b) Hence determine
- November 2021, Core Pure 1, Q2 (7 marks): (a) Use the Maclaurin series expansion for cos x to determine the series expansion of cos2 3 x in ascending powers of x, up to and including the term i
- November 2021, Core Pure 2, Q3 (6 marks): f (x) = arcsin x −1 x 1 (a) Determine the first two non-zero terms, in ascending powers of x, of the Maclaurin series for f (x) , giving each coefficient in
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