plumiIntegrating with inverse trig and hyperbolic functions: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on E.4 Integrating with inverse trig and hyperbolic functions, 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.
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All 7 questions on Integrating with inverse trig and hyperbolic functions, as a list
- June 2025, Paper 2, Q12 (5 marks): Find the value of d + + ∫ 5 2 1 1 6 5 x x x Give your answer in the form ( ) + + + ln 8 3 5 15 a b c where a, b and c are integers. [5 marks]
- June 2025, Paper 2, Q16 (5 marks): The diagram shows a design for a table top. x y O The table top is modelled as being bounded by the lines . = 0 5 x and . = 1 5 x , and the curves defined by .
- June 2024, Paper 1, Q17 (7 marks): By making a suitable substitution, show that ∫ 1 –2√ x2 + 6x + 8 dx = 2√ 15 – 1 2 cosh–1 (4) [7 marks]
- June 2023, Paper 2, Q14 (10 marks): The function f is defined by f (x) = 1 4x2 + 16x + 19 (x 2 R) 14 (a) Show, without using calculus, that the graph of y = f (x) has a stationary point at −2, 1 3
- November 2021, Paper 1, Q14 (12 marks): The hyperbola H has equation y2 − x2 = 16 The circle C has equation x2 + y2 = 32 The diagram below shows part of the graph of H and part of the graph of C. x y
- November 2020, Paper 1, Q12 (8 marks): (a) Use the definition of the cosh function to prove that cosh−1 x a = ln x + x2 − a2 p a ! for a > 0 [6 marks] 12 (b) The formulae booklet gives the integral o
- June 2019, Paper 1, Q11 (7 marks): Find the general solution of the differential equation x dy dx − 2y = x3 4 − 2x − x2 p where 0 < x < 5 p − 1 [7 marks]
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