plumiHyperbolic functions: Edexcel A‑Level Further Maths questions
Every Edexcel A-Level Further Maths exam question on CP.8 Hyperbolic functions, 2018–2025, with its mark scheme and examiner’s report.
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All 10 questions on Hyperbolic functions, as a list
- June 2025, Core Pure 1, Q2 (5 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Determine the exact values of
- June 2025, Core Pure 1, Q9 (9 marks): (i) The curves with equations y x = 3 4 sinh and y x tanh 1 5 intersect at just one point P (a) Use algebra to show that the x coordinate of P satisfies the equ
- June 2024, Core Pure 2, Q1 (7 marks): (a) Using the definition of sinh x in terms of exponentials, prove that 4 3 3 3 sinh sinh sinh x x x (2) (b) Hence solve the equation sinh sinh 3 19 x x = givin
- June 2022, Core Pure 1, Q2 (4 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Determine the values of x for
- June 2022, Core Pure 1, Q9 (6 marks): (i) (a) Explain why cosh x x 0 ∞∫ d is an improper integral. (1) (b) Show that cosh x x 0 ∞∫ d is divergent. (3) (ii) 4 sinh x = p cosh x where p is a real cons
- 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)
- June 2019, Core Pure 2, Q1 (10 marks): (a) Prove that tanh–1 (x) = 1 2 ln 1 1 + − ⎛ ⎝⎜ ⎞ ⎠⎟ x x –k x k stating the value of the constant k. (5) (b) Hence, or otherwise, solve the equation 2x = tanh l
- June 2019, Core Pure 2, Q3 (6 marks): f ( ) x x = + 1 4 9 2 (a) Using a substitution, that should be stated clearly, show that f (x)dx = A sinh–1 (Bx) + c where c is an arbitrary constant and A an
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