plumiMaclaurin series and partial fractions: WJEC A‑Level Further Maths questions
Every WJEC A-Level Further Maths exam question on 4.4 Maclaurin series and partial fractions, 2018–2025, with its mark scheme and examiner’s report.
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All 9 questions on Maclaurin series and partial fractions, as a list
- Summer 2025, Unit 4, Q1 (5 marks): Write down the Maclaurin series expansion for ex2 as far as the term in x6. Simplify your 1. (a) answer. [2] 1 2 0 e d x x (b) Hence, find an approximate valu
- Summer 2025, Unit 4, Q10 (18 marks): 3 2 12 5 2 6 x x x x 2 10. (a) (i) Show that can be written as . [2] 3 2 2 3 6 3 2 2 3 6 x x x x x x 3 2 2 x x 12 d x (ii) Hence, find
- Summer 2024, Unit 4, Q2 (13 marks): x ( ) cosh 2 The function f is defined by f x 2. . x up to and including the term in x4. cosh 2 (a) State the Maclaurin series expansion for [2] g x ( )
- Summer 2024, Unit 4, Q5 (14 marks): 5. Find each of the following integrals. 3 x (a) [8] d x 2 1 x x (b) sinh2 x [6] d x 4 2 cosh x 9cosh x
- Summer 2023, Unit 4, Q5 (7 marks): Write down and simplify the Maclaurin series for sin2x as far as the term in x5. 5. (a) [2] Using your answer to part (a), determine the Maclaurin series for co
- Summer 2023, Unit 4, Q8 (11 marks): 8. The function f is defined by 1 ( ) = f x . x2 + 4x + 3 (a) Find the mean value of the function f for 0 X x X 2, giving your answer correct to three decimal p
- Summer 2022, Unit 4, Q14 (10 marks): 14. Evaluate the integral 6x2 + 2x +16 4∫ dx , x3 − x2 + 3x − 3 2 giving your answer correct to three decimal places. [10]
- Summer 2019, Unit 4, Q4 (16 marks): dy −1 4. (a) Given that y = cot–1x, show that . dx = [5] x2 +1 6x2 −10x − 9 (b) Express in terms of partial fractions. [5] (2x + 3)(x2 +1) 6x2 − 8x − 6 ∫ (c) He
- Summer 2019, Unit 4, Q7 (6 marks): 7. (a) Write down the Maclaurin series expansion for 1n(1 – x) as far as the term in x3. [2] ⎛ ⎞ 1− x (b) Show that can be expressed in the form ax + bx2 + cx3
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