plumiMaclaurin series: OCR MEI A‑Level Further Maths questions
OCR MEI 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, Core Pure, Q8 (7 marks): The function ( )x f is defined as ( ) f x ln ( 1 x ) , for x 2- . 1 = + f ( ) n (a) Prove by mathematical induction that the nth derivative of ( ) f x , ( )x ,
- June 2024, Core Pure, Q10 (6 marks): 10 (a) Write down the first three terms of the Maclaurin series for ln ( 1 x ) . [1] + n (b) Use these three terms to show that ln ( . 1 125 ) , where n is an i
- June 2023, Core Pure, Q4 (6 marks): (a) (i) Given that ( )x f 1 2 x , find and . [2] f l ( )x f m ( )x = + (ii) Hence, find the first three terms of the Maclaurin series for 1 2 x . [2] + 143 (b)
- June 2022, Core Pure, Q9 (12 marks): The function ( )x f is defined by ( ) f x ln ( 1 sinh x ). = + (a) Given that k lies in the domain of this function, explain why k must be greater than ln ( 2 1
- November 2021, Core Pure, Q5 (6 marks): (a) Use a Maclaurin series to find a quadratic approximation for ln ( 1 2 x ) . [1] + (b) Find the percentage error in using the approximation in part (a) to ca
- November 2020, Core Pure, Q13 (9 marks): (a) Using exponentials, prove that sinh 2 x 2 cosh sinh x x . [2] = 2 (b) Hence show that if ( ) f x sinh x , then f ″( ) x 2 cosh 2 x . [2] = = 2 are all zero.
- June 2019, Core Pure, Q5 (5 marks): Using the Maclaurin series for cos x 2 , show that, for small values of x, 2 2 4 6 sin x ax bx cx , . + + where the values of a, b and c are to be given in exac
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