plumiHyperbolic functions and identities: OCR MEI A‑Level Further Maths questions
OCR MEI 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.
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All 6 questions on Hyperbolic functions and identities, as a list
- June 2025, Core Pure, Q14 (10 marks): - , show that 14 (a) By using the definition of cosh x and sinh x in terms of ex and e x 2 2 x x x [2] cosh sinh cosh 2 . + / J cosh x sinh x N KKK OOO and (b)
- June 2024, Core Pure, Q12 (12 marks): The diagram shows the curve with parametric equations x 2 cosh t sinh t , y cosh t 2 sinh t . = + = - y B A x O (a) The curve crosses the positive x-axis at A.
- June 2022, Core Pure, Q3 (6 marks): In this question you must show detailed reasoning. 2 Solve the equation 3 cosh x 2 sinh x , giving your solutions in exact logarithmic form. [6] = J N m 2 1
- June 2022, Core Pure, Q9 (12 marks): The function ( )x f is defined by ( ) f x ln ( 1 sinh x ). = + (a) Given that k lies in the domain of this function, explain why k must be greater than ln ( 2 1
- November 2021, Core Pure, Q16 (14 marks): 16 (a) Show using exponentials that cosh 2 u 1 2 sinh u . [4] = + y 2 2 x (b) Show that d x 2 2 2 ln ( 1 2 ) . [10] = - + 2 4 x + 0
- November 2020, Core Pure, Q13 (9 marks): (a) Using exponentials, prove that sinh 2 x 2 cosh sinh x x . [2] = 2 (b) Hence show that if ( ) f x sinh x , then f ″( ) x 2 cosh 2 x . [2] = = 2 are all zero.
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