plumiCalculus with hyperbolic functions: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on H.3 Calculus with 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 Calculus with hyperbolic functions, as a list
- June 2025, Paper 1, Q18 (15 marks): The diagram shows part of the graph of = 15cosech y x and part of the graph of = + 1 4sinh 2 y x O x y 18 (a) Solve the inequality < + 1 15 cosech 4sinh 2 x x G
- June 2024, Paper 1, Q14 (7 marks): Solve the differential equation dy dx + ytanh x = sinh3 x given that y = 3 when x = ln2 Give your answer in an exact form. [7 marks]
- June 2023, Paper 2, Q1 (1 mark): Given that y = sinx + sinhx , find d2y dx2 + y Circle your answer. [1 mark] 2 sin x −2 sin x 2 sinhx −2 sinhx
- June 2022, Paper 1, Q3 (1 mark): Given that y = sechx , find dy dx Tick (3) one box. [1 mark] sech x tanhx − sech x tanhx cosech x cothx − cosech x cothx
- 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 2021, Paper 2, Q12 (12 marks): The integral Sn is defined by Sn = (a 0 xn sinhx dx (n ≤ 0) 12 (a) Show that for n ≤ 2 Sn = n(n − 1)Sn−2 + an cosh a − nan−1 sinha [7 marks] 12 (b) Hence show t
- June 2019, Paper 2, Q5 (4 marks): A curve has equation y = coshx Show that the arc length of the curve from x = a to x = b , where 0 < a < b , is equal to sinh b − sinha [4 marks]
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