plumiMaclaurin series: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on D.4 Maclaurin series, 2019–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
Questions from
Paper
All papers
Exam
All years
Loading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDF
All 10 questions on Maclaurin series, as a list
- June 2025, Paper 1, Q11 (7 marks): The function f is defined by ( ) ( ) f e 1 1 x x x = ∈ + 11 (a) Show that ( ) ( ) e e f e 2 3 1 x x x '' x − + = + [3 marks] 11 (b) Hence, find the Maclaurin
- June 2025, AS Paper 1, Q4 (1 mark): Find the first two non-zero terms of the Maclaurin series expansion of cos (2x) Tick () one box. [1 mark] 1 – x2 1 – 2x2 2 – x2 2 – 2x2
- June 2024, Paper 2, Q18 (4 marks): In this question you may use results from the formulae booklet without proof. Use the binomial series for (1 + x)n and the Maclaurin’s series for sin x to find
- June 2024, AS Paper 1, Q15 (7 marks): (a) Use Maclaurin’s series expansion for In(1 + x) to show that the first three terms of the Maclaurin’s series expansion of In(1 + 3x) are 3x – 9 2 x2 + 9x3 [1
- June 2023, AS Paper 1, Q6 (6 marks): (a) Find and simplify the first five terms in the Maclaurin series for e2x [2 marks] 6 (b) Hence, or otherwise, write down the first five terms in the Maclaurin
- June 2022, Paper 2, Q8 (10 marks): (a) The function f is defined as f (x) = sec x 8 (a) (i) Show that f (4)(0) = 5 [4 marks] 8 (a) (ii) Hence find the first three non-zero terms of the Maclaurin
- November 2021, AS Paper 1, Q7 (3 marks): Show that the Maclaurin series for ln (e + 2ex) is 1 + 2x − 2x2 + ax3 − ::: where a is to be determined. [3 marks]
- November 2020, Paper 2, Q11 (8 marks): (a) Starting from the series given in the formulae booklet, show that the general term of the Maclaurin series for sin x x × cos x is (×1)r+1 2r (2r + 1)!x2r [4
- June 2019, Paper 1, Q2 (1 mark): The first two non-zero terms of the Maclaurin series expansion of f (x) are x and − 1 2x3 Which one of the following could be f (x)? Circle your answer. [1 mark
- June 2019, AS Paper 1, Q10 (6 marks): (a) Using the definition of coshx and the Maclaurin series expansion of ex, find the first three non-zero terms in the Maclaurin series expansion of cosh x. [3
Questions, mark schemes and examiner’s reports are © AQA, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? AQA A-Level Further Maths past papers.
The Plumi iPad app also offers exam-style questions with AI feedback on your handwritten working.