plumiInverse hyperbolic functions: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on H.2 Inverse 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 14 questions on Inverse hyperbolic functions, as a list
- June 2025, Paper 1, Q14 (6 marks): (a) Using the exponential definitions of sinh x and cosh x, prove that ( ) 1 1 1 coth ln 2 1 x x x − + = − [3 marks] 14 (b) Hence, solve the equatio
- June 2025, AS Paper 1, Q7 (4 marks): (a) Geraldine wants to show that tanh–1 x = 1 2 In ( 1 + x 1 – x) She writes her steps as follows: Let ⇐ ⇐ ⇐ ⇐ ⇐ ⇐ ∴ y = tanh–1 x tanh y = x e y + e–y e y – e–y
- June 2024, Paper 1, Q9 (8 marks): (a) It is given that _ p = In(r + √ r2 + 1) Starting from the exponential definition of the sinh function, show that sinh p = r [4 marks] 9 (b) Solve the equati
- June 2024, Paper 1, Q17 (7 marks): By making a suitable substitution, show that ∫ 1 –2√ x2 + 6x + 8 dx = 2√ 15 – 1 2 cosh–1 (4) [7 marks]
- June 2024, AS Paper 1, Q6 (4 marks): (a) On the axes below, sketch the graph of y = cosh x Indicate the value of any intercept of the curve with the axes. [2 marks] x y O 6 (b) Solve the equation c
- June 2023, Paper 2, Q4 (1 mark): It is given that f (x) = cosh−1 (x − 3) Which of the sets listed below is the greatest possible domain of the function f ? Circle your answer. [1 mark] fx : x ×
- June 2022, Paper 1, Q6 (8 marks): (a) Given that jxj < 1 , prove that tanh−1 x = 1 2 ln 1 + x 1 − x [4 marks] 6 (b) Solve the equation 20 sech2 x − 11 tanhx = 16 Give your answer in logarithmic
- June 2022, AS Paper 1, Q15 (6 marks): The two values of y that satisfy the equation sinh2 y − sinhy − 2 = 0 are y1 and y2 15 (a) Hamzah is asked to find the value of y1 + y2 He writes his answer as
- November 2021, Paper 1, Q4 (5 marks): Show that the solutions to the equation 3 tanh2 x − 2 sech x = 2 can be expressed in the form x = × ln (a + b p ) where a and b are integers to be found. You ma
- November 2021, AS Paper 1, Q12 (5 marks): The equation x3 − 2x2 − x + 2 = 0 has three roots. One of the roots is 2 12 (a) Find the other two roots of the equation. [1 mark] 12 (b) Hence, or otherwise, s
- November 2020, Paper 1, Q12 (8 marks): (a) Use the definition of the cosh function to prove that cosh−1 x a = ln x + x2 − a2 p a ! for a > 0 [6 marks] 12 (b) The formulae booklet gives the integral o
- November 2020, AS Paper 1, Q8 (8 marks): (a) Prove that tanh−1 x = 1 2 ln 1 + x 1 − x [5 marks] 8 (b) Prove that the graphs of y = sinh x and y = cosh x do not intersect. [3 marks]
- June 2019, Paper 1, Q1 (1 mark): Which one of these functions has the set fx : jxj < 1g as its greatest possible domain? Circle your answer. [1 mark] cosh x cosh−1 x tanhx tanh−1 x
- June 2019, AS Paper 1, Q9 (7 marks): (a) Saul is solving the equation 2 cosh x + sinh2 x = 1 He writes his steps as follows: 2 coshx + sinh2 x = 1 2 cosh x + 1 − cosh2 x = 1 2 coshx − cosh2 x = 0 c
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