plumiHyperbolic functions: Edexcel International A Level Further Maths questions
Every Edexcel International A Level Further Maths exam question on FP3.1 Hyperbolic functions, 2019–2025, with its mark scheme and examiner’s report.
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All 10 questions on Hyperbolic functions, as a list
- June 2025, Further Pure 3 (FP3), Q1 (6 marks): (a) Use the definition of cosh x in terms of exponentials to show that 2 5 6 4 cosh cosh cosh cosh x x x x (b) Hence determine the exact values of x for which c
- January 2025, Further Pure 3 (FP3), Q1 (6 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Solve the equation 2 sinh 2 x
- June 2024, Further Pure 3 (FP3), Q4 (9 marks): (a) Use the definitions of hyperbolic functions in terms of exponentials to show that sinh (A + B) ≡ sinh A cosh B + cosh A sinh B (b) Hence express 10 sinh x +
- June 2023, Further Pure 3 (FP3), Q1 (5 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Solve the equation 7 cosh x +
- January 2023, Further Pure 3 (FP3), Q3 (6 marks): Solve the equation 4 1 tanh sech x x giving your answer in the form x k = ln where k is a fully simplified rational number.
- June 2022, Further Pure 3 (FP3), Q1 (7 marks): (a) Use the definitions of sinh x and cosh x in terms of exponentials to show that cosh A cosh B + sinh A sinh B ≡ cosh(A + B) (b) Hence find the value of x for
- January 2022, Further Pure 3 (FP3), Q1 (8 marks): 1 (a) Use the definitions of hyperbolic functions in terms of exponentials to prove that 8 cosh 4 x = cosh 4x + p cosh 2x + q where p and q are constants to be
- October 2021, Further Pure 3 (FP3), Q2 (6 marks): Given that cosh y = x and y < 0 use the definition of cosh y in terms of exponential functions to prove that y = ln x x − − ( ) 2 1
- June 2021, Further Pure 3 (FP3), Q1 (6 marks): (a) Using the definitions of hyperbolic functions in terms of exponentials, show that 1 – tanh 2 x ≡ sech 2 x (b) Solve the equation 2 sech 2 x + 3 tanh x = 3 g
- October 2020, Further Pure 3 (FP3), Q1 (7 marks): (a) Use the definition of sinh x in terms of exponentials to show that sinh 3x º 4 sinh3 x + 3 sinh x (b) Hence determine the exact coordinates of the points of
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