Skip to content
Try on iPad

Hyperbolic functions: OCR MEI A‑Level Further Maths questions

Every OCR MEI A-Level Further Maths exam question on CP.8 Hyperbolic functions, 2018–2025, with its mark scheme and examiner’s report.

Find questions847

847 questions

  1. Q14

    June 2025 · Core Pure

    10 marksCP.8 Hyperbolic functionsCP.3 Matrices
    The whole paper ↗
    June 2025 Core Pure, question 14: - , 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)

  2. Q12

    June 2024 · Core Pure

    12 marksCP.8 Hyperbolic functions
    The whole paper ↗
    June 2024 Core Pure, question 12: 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.

  3. Q16

    June 2024 · Core Pure

    6 marksCP.5 Further calculusCP.8 Hyperbolic functions
    The whole paper ↗
    June 2024 Core Pure, question 16: In this question you must show detailed reasoning. y 1 c m a b 3 1 + Show that d x ln , where a, b and c are integers to be determined. [6] = c 2 x x 1 + + 0

  4. Q11

    June 2023 · Core Pure

    7 marksCP.9 Differential equationsCP.8 Hyperbolic functions
    The whole paper ↗
    June 2023 Core Pure, question 11: 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

  5. Q3

    June 2022 · Core Pure

    6 marksCP.8 Hyperbolic functions
    The whole paper ↗
    June 2022 Core Pure, question 3: 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

  6. Q9

    June 2022 · Core Pure

    12 marksCP.4 Further algebra and functionsCP.8 Hyperbolic functions
    The whole paper ↗
    June 2022 Core Pure, question 9: 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

  7. Q16

    November 2021 · Core Pure

    14 marksCP.8 Hyperbolic functionsCP.5 Further calculus
    The whole paper ↗
    November 2021 Core Pure, question 16: 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

  8. Q10

    November 2020 · Core Pure

    7 marksCP.5 Further calculusCP.8 Hyperbolic functions
    The whole paper ↗
    November 2020 Core Pure, question 10: In this question you must show detailed reasoning. 1 2 The region in the first quadrant bounded by curve y cosh x , the y-axis, and the line y = 2 is = 2 rotate

  9. Q13

    November 2020 · Core Pure

    9 marksCP.8 Hyperbolic functionsCP.4 Further algebra and functions
    The whole paper ↗
    November 2020 Core Pure, question 13: (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.

  10. Q13

    June 2019 · Core Pure

    11 marksCP.8 Hyperbolic functions
    The whole paper ↗
    June 2019 Core Pure, question 13: 13 (a) Using the logarithmic form of arcosh x, prove that the derivative of arcosh x is . [5] 2 - x 1 2y (b) Hence find arcosh d x x , giving your answer in exa

  11. Q15

    June 2019 · Core Pure

    8 marksCP.5 Further calculusCP.8 Hyperbolic functions
    The whole paper ↗
    June 2019 Core Pure, question 15: In this question you must show detailed reasoning. 3 J N y 3 5 1 1 2 + KK OO Show that d x ln . [8] = 2 2 2 4 x 4 x 2 3 - + L P 4
All 11 questions on Hyperbolic functions, as a list
  1. 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)
  2. 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.
  3. June 2024, Core Pure, Q16 (6 marks): In this question you must show detailed reasoning. y 1 c m a b 3 1 + Show that d x ln , where a, b and c are integers to be determined. [6] = c 2 x x 1 + + 0
  4. 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
  5. 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
  6. 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
  7. 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
  8. November 2020, Core Pure, Q10 (7 marks): In this question you must show detailed reasoning. 1 2 The region in the first quadrant bounded by curve y cosh x , the y-axis, and the line y = 2 is = 2 rotate
  9. 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.
  10. June 2019, Core Pure, Q13 (11 marks): 13 (a) Using the logarithmic form of arcosh x, prove that the derivative of arcosh x is . [5] 2 - x 1 2y (b) Hence find arcosh d x x , giving your answer in exa
  11. June 2019, Core Pure, Q15 (8 marks): In this question you must show detailed reasoning. 3 J N y 3 5 1 1 2 + KK OO Show that d x ln . [8] = 2 2 2 4 x 4 x 2 3 - + L P 4

Questions, mark schemes and examiner’s reports are © OCR, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? Every OCR MEI A-Level Further Maths paper.

Rather write your answers by hand on iPad? Plumi marks them against the same mark schemes.