plumiCalculus with hyperbolic functions: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 8.3 Calculus with 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.
Questions from
Paper
All papers
Exam
All years
Loading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDF
All 7 questions on Calculus with hyperbolic functions, as a list
- June 2025, Core Pure 2, Q8 (8 marks): Given that y x x = cos sinh x (a) show that d d 4 4 y x ky = where k is a constant to be determined. (5) (b) Hence determine the first three non-zero terms of t
- June 2023, Core Pure 2, Q1 (4 marks): initial line R O Figure 1 Figure 1 shows a sketch of the curve with polar equation 2 sinh cosh r θ θ 0 θ π The region R, shown shaded in Figure 1, is bounde
- June 2023, Core Pure 2, Q6 (6 marks): Given that y = e 2x sinh x prove by induction that for n ∈ d d e n n x n n y x x x 2 3 1 2 3 1 2 sinh cosh (6)
- June 2022, Core Pure 2, Q9 (8 marks): y = cosh n x n 5 (a) (i) Show that d d 2 2 y x = n 2 cosh n x – n(n – 1)cosh n – 2 x (4) (ii) Determine an expression for d d 4 4 y x (2) (b) Hence determine
- November 2021, Core Pure 1, Q9 (11 marks): (a) Use a hyperbolic substitution and calculus to show that x x x x x x k 2 2 2 1 1 2 1 − = − + + ∫ d arcosh where k is an arbitrary constant. (6) y O
- November 2021, Core Pure 2, Q7 (9 marks): Solutions based entirely on graphical or numerical methods are not acceptable. O y x R y = arsinh x y = β Figure 1 Figure 1 shows a sketch of part of the curve
- November 2020, Core Pure 2, Q1 (7 marks): The curve C has equation y = 31 sinh x − 2 sinh 2x x ∈ Determine, in terms of natural logarithms, the exact x coordinates of the stationary points of C. (7)
Questions, mark schemes and examiner’s reports are © Pearson Edexcel, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? Edexcel A-Level Further Maths past papers.
The Plumi iPad app also offers exam-style questions with AI feedback on your handwritten working.