plumiHyperbolic functions and identities: OCR A‑Level Further Maths questions
OCR A-Level Further Maths past-paper questions on 8.1 Hyperbolic functions and identities, 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.
All papers
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 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 13 questions on Hyperbolic functions and identities, as a list
- June 2025, Pure Core 2, Q10 (8 marks): u 10 (a) Find e - as a percentage of sinh u for the following values of u. 2 • u = 2 • u = 5 [1] (b) Find, as a percentage of sinh u, the difference between sin
- June 2024, Pure Core 1, Q7 (9 marks): - , show that (a) By using the definitions of cosh u and sinh u in terms of eu and e u 7 sinh 2 u 2 sinh cosh u u . [2] / The equation of a curve, C, is y 16 co
- June 2024, Pure Core 2, Q6 (11 marks): J N 1 1 KKK OOO for 0 6 In polar coordinates, the equation of a curve, C, is r 6 sin ( 2 ) sinh r. = G G i i i 3 2 L P The pole of the polar coordinate system c
- June 2024, Pure Core 2, Q7 (10 marks): bx + x 7 (a) Express 17 coshx - 15 sinhx in the form e - ( a e c ) where a, b and c are integers to be determined. [3] 1 A function is defined by ( ) f x . The
- June 2023, Pure Core 2, Q5 (7 marks): In this question you must show detailed reasoning. (a) Using the definitions of sinh x and cosh x in terms of exponentials, show that x x x [2] sinh 2 2 sinh co
- June 2022, Pure Core 1, Q1 (6 marks): In this question you must show detailed reasoning. 41 (a) Show that cosh ( 2 ln 3 ) . [2] = 9 The region R is bounded by the curve with equation y sinh x , the
- June 2022, Pure Core 2, Q5 (7 marks): (a) By using the exponential definitions of sinh x and cosh x, prove the identity 2 2 cosh 2 x cosh x sinh x . [2] / + (b) Hence find an expression for cosh 2x
- November 2021, Pure Core 1, Q8 (8 marks): You are given that ( ) f x 4 sinh x 3 cosh x . = + (a) Show that the curve y f ( ) x has no turning points. [3] = (b) Determine the exact solution of the equati
- November 2021, Pure Core 2, Q5 (8 marks): In this question you must show detailed reasoning. 2 (a) Using the definition of cosh x in terms of exponentials, show that cosh 2 x 2 cosh x - . [2] 1 / (b) So
- November 2020, Pure Core 1, Q8 (10 marks): 8 (a) Using exponentials, show that cosh 2 u 2 sinh u 1 . [2] / + (b) By differentiating both sides of the identity in part (a) with respect to u, show that sin
- November 2020, Pure Core 2, Q9 (11 marks): Two thin poles, OA and BC, are fixed vertically on horizontal ground. A chain is fixed at A and C such that it touches the ground at point D as shown in the dia
- June 2019, Pure Core 1, Q5 (7 marks): The diagram shows part of the curve y 5 cosh x 3 sinh x . = + y x O (a) Solve the equation cosh 5 x 3 sinh x 4 giving your solution in exact form. [4] + = (b) I
- June 2019, Pure Core 1, Q7 (6 marks): 7 The function sech x is defined by sec h x . = cosh x x 2 e (a) Show that sec h x . [2] = 2 x e 1 + y (b) Using a suitable substitution, find sech x x d . [4]
Questions, mark schemes and examiner’s reports are © OCR, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? OCR A-Level Further Maths past papers.
The Plumi iPad app also offers exam-style questions with AI feedback on your handwritten working.