plumiHyperbolic functions: WJEC A‑Level Further Maths questions
Every WJEC A-Level Further Maths exam question on 4.7 Hyperbolic functions, 2018–2025, with its mark scheme and examiner’s report.
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All 17 questions on Hyperbolic functions, as a list
- Summer 2025, Unit 4, Q3 (7 marks): 2 e x e x d cosh cosh x as 2 2 2 sinh 2 x x x 3. (a) By writing , show that . [3] d x 2 2 x 3 sinh x 2 d x (b) Hence, find . [4]
- Summer 2025, Unit 4, Q5 (6 marks): 5. The region R is bounded by the curve x = sinh 2y, the y-axis and the line y = 1. Find the volume of the solid generated when R is rotated through four right
- Summer 2025, Unit 4, Q7 (12 marks): 7. (a) Differentiate each of the following with respect to x, simplifying your answer where possible. cos 1 2 1 (i) y x [3] 3 sinh 4 (ii) y x x [3]
- Summer 2025, Unit 4, Q10 (18 marks): 3 2 12 5 2 6 x x x x 2 10. (a) (i) Show that can be written as . [2] 3 2 2 3 6 3 2 2 3 6 x x x x x x 3 2 2 x x 12 d x (ii) Hence, find
- Summer 2024, Unit 4, Q2 (13 marks): x ( ) cosh 2 The function f is defined by f x 2. . x up to and including the term in x4. cosh 2 (a) State the Maclaurin series expansion for [2] g x ( )
- Summer 2024, Unit 4, Q5 (14 marks): 5. Find each of the following integrals. 3 x (a) [8] d x 2 1 x x (b) sinh2 x [6] d x 4 2 cosh x 9cosh x
- Summer 2024, Unit 4, Q8 (11 marks): d y 4 sinh 1 4 3 as sinh 4 3 y x y x , show that 8. (a) By writing . [5] d x 2 16 x 24 x 10 x y e 3 sinh 2 x (b) Show that the graph of
- Summer 2023, Unit 4, Q1 (5 marks): The functions f and g have domains (–1, ∞) and (0, ∞) respectively and are defined by 1. f (x) = cosh x, g(x) = x2 – 1. (a) State the domain and range of fg. [2
- Summer 2023, Unit 4, Q8 (11 marks): 8. The function f is defined by 1 ( ) = f x . x2 + 4x + 3 (a) Find the mean value of the function f for 0 X x X 2, giving your answer correct to three decimal p
- Summer 2023, Unit 4, Q11 (14 marks): 11. Evaluate the integrals 0∫ (a) e2x [5] sinh xdx, −2 3 5 (b) d x [9] . 2 1 9 3 x x 2
- Summer 2022, Unit 4, Q1 (8 marks): ( ) ( ) = cosh3x − 3coshx. −∞,∞ f x 1. A function f has domain and is defined by Show that the graph of y = f(x) has only one stationary point. (a) [5] (b) Find
- Summer 2022, Unit 4, Q7 (8 marks): Express 4x2 +10x − 24 in the form a x + b )2 + c , where a, b, c are constants whose ( 7. (a) values are to be found. [3] (b) Hence evaluate the integral 5∫ 6 d
- Summer 2022, Unit 4, Q8 (6 marks): ( ). x2 +1 By writing x = sinh y, show that sinh−1 x = ln x + 8. [6]
- Summer 2022, Unit 4, Q11 (15 marks): (a) Differentiate each of the following with respect to x. 11. y = e3x sin−1 x (i) ( ) y = ln cosh2 2x2 + 7x ( ) (ii) [7] Find the equations of the tangents to
- Summer 2019, Unit 4, Q9 (14 marks): dy Given that y = sin–1(cosθ ), where 0 X θX π, show that , where the value of k is dθ = k 9. (a) to be determined. [4] x = π y = x3 tan−1 4x (b) Find the value
- Summer 2019, Unit 4, Q11 (9 marks): Find the area of the region enclosed by the curve y = x sinhx, the x-axis and the lines 11. (a) x = 0 and x = 1. [4] The region R is bounded by the curve y = co
- Summer 2019, Unit 4, Q12 (14 marks): 4∫ 1 dx 12. (a) Evaluate , giving your answer correct to three decimal places. [3] x2 − 4 3 2∫ 9 − x2 dx = ln 25 k (b) Given that , find the value of k. [5] 4 1
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