plumiMaclaurin series: OCR A‑Level Further Maths questions
OCR 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 7 questions on Maclaurin series, as a list
- June 2025, Pure Core 2, Q8 (12 marks): A function f (x) is defined by f (x) = xsinh 2x. 2 n 0 d f d f n (a) Prove by induction that 4 ( x sinh 2 x n cosh 2 x ) for n 0 where d is defined as H = + 2 n
- June 2024, Pure Core 1, Q9 (6 marks): ^ h up to and including the term in x4. 2 9 (a) Find the Maclaurin series of x [3] ln ( 1 ) + ^ h and 2 y x The diagram below shows parts of the graphs of the c
- June 2023, Pure Core 1, Q7 (11 marks): An engineer is modelling the motion of a particle P of mass 0.5 kg in a wind tunnel. P is modelled as travelling in a straight line. The point O is a fixed poin
- November 2021, Pure Core 1, Q2 (8 marks): 2 You are given that ( ) f x tan - ( 1 x ) . = + (a) (i) Find the value of ( ) f 0 . [1] (ii) Determine the value of f l ( ) 0 . [2] 1 (iii) Show that f ( ) 0 .
- November 2021, Pure Core 2, Q10 (6 marks): In this question you must show detailed reasoning. ex 2 (a) By using an appropriate Maclaurin series prove that if x 2 0 then 1 + . x [2] t 2 (b) Hence, by usin
- November 2020, Pure Core 2, Q10 (10 marks): 10 Let ( ) f x sin - ( ) x . = (a) (i) Determine f ll ( )x . [2] (ii) Determine the first two non-zero terms of the Maclaurin expansion for ( )x f . [3] (iii) B
- June 2019, Pure Core 2, Q10 (7 marks): (a) Use differentiation to find the first two non-zero terms of the Maclaurin expansion of c m. 1 + ln cos x [4] 2 c m c m. 1 3 (b) By considering the root of t
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