plumiCalculus with hyperbolic functions: OCR MEI A‑Level Further Maths questions
OCR MEI A-Level Further Maths past-paper questions on 8.3 Calculus with hyperbolic functions, 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 4 questions on Calculus with hyperbolic functions, as a list
- 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 2023, Core Pure, Q11 (7 marks): y d - 11 Solve the differential equation cosh x x 2 y sinh x cosh x , given that y = when x 1 0 . [7] = = d
- 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
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