plumiIntegrating with inverse trig and hyperbolic functions: OCR MEI A‑Level Further Maths questions
OCR MEI A-Level Further Maths past-paper questions on 5.4 Integrating with inverse trig and hyperbolic functions, 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 13 questions on Integrating with inverse trig and hyperbolic functions, as a list
- June 2025, Core Pure, Q7 (8 marks): In this question you must show detailed reasoning. 3y 1 1 1 By first expressing x 2 - in partial fractions, show that d x ln n , where m and n = m 2 4 x 4 - 3 a
- June 2025, Core Pure, Q10 (4 marks): In this question you must show detailed reasoning. 1 y 2 2 Evaluate d x . Give your answer in exact form. [4] 2 x x 1 - + 0
- June 2025, Core Pure, Q16 (12 marks): In this question you must show detailed reasoning. x 3 + The diagram shows the curve with equation y . = 2 x 9 + y R x O x = 4 The region R, shown shaded in the
- June 2024, Core Pure, Q4 (4 marks): 4 The equation of a curve is y , where k is a positive constant. The region between the = 2 2 k x + x-axis, the y-axis and the line x k is rotated through r 2 r
- June 2024, Core Pure, Q16 (6 marks): In this question you must show detailed reasoning. y 1 c m a b 3 1 + Show that d x ln , where a, b and c are integers to be determined. [6] = c 2 x x 1 + + 0
- June 2023, Core Pure, Q15 (5 marks): In this question you must show detailed reasoning. y 2 1 Evaluate dx , giving your answer in terms of r. [5] 2 1 2 x x + - 1
- June 2022, Core Pure, Q2 (5 marks): In this question you must show detailed reasoning. y 3 1 Find the exact value of d x . [5] 2 x 4 x 5 - + 3
- June 2022, Core Pure, Q7 (9 marks): In this question you must show detailed reasoning. y 3 x 1 + 1 Show that ) d x ln 2 . [9] = 2 2 x x ( 1 )( 1 - + 2
- November 2021, Core Pure, Q4 (4 marks): In this question you must show detailed reasoning. 1 Determine the mean value of between x =- and x 1 = . Give your answer to 3 significant 1 2 x 1 4 + figures.
- November 2021, Core Pure, Q16 (14 marks): 16 (a) Show using exponentials that cosh 2 u 1 2 sinh u . [4] = + y 2 2 x (b) Show that d x 2 2 2 ln ( 1 2 ) . [10] = - + 2 4 x + 0
- November 2020, Core Pure, Q3 (4 marks): In this question you must show detailed reasoning. 1 y 1 3 dx , expressing your answer in terms of r. [4] Find 2 4 9 x - 0
- June 2019, Core Pure, Q6 (4 marks): In this question you must show detailed reasoning. 3 y 1 Find d x . [4] 2 4 x + 2
- June 2019, Core Pure, Q15 (8 marks): In this question you must show detailed reasoning. 3 J N y 3 5 1 1 2 + KK OO Show that d x ln . [8] = 2 2 2 4 x 4 x 2 3 - + L P 4
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