plumiFurther calculus: OCR MEI A‑Level Further Maths questions
Every OCR MEI A-Level Further Maths exam question on CP.5 Further calculus, 2018–2025, with its mark scheme and examiner’s report.
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![June 2025 Core Pure, question 10: In this question you must show detailed reasoning. 1 y 2 2 Evaluate d x . Give your answer in exact form. [4] 2 x x 1 - + 0](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42001-jun25-10-qp.webp?v=3)
![June 2024 Core Pure, question 7: 2y 1 7 (a) Explain why d x is an improper integral. [1] 3 x 2 - 1 (b) In this question you must show detailed reasoning. Use an appropriate limit argument to ev](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42001-jun24-07-qp.webp?v=3)
![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](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42001-jun24-16-qp.webp?v=3)
![June 2023 Core Pure, question 15: In this question you must show detailed reasoning. y 2 1 Evaluate dx , giving your answer in terms of r. [5] 2 1 2 x x + - 1](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42001-jun23-15-qp.webp?v=3)
![June 2022 Core Pure, question 2: In this question you must show detailed reasoning. y 3 1 Find the exact value of d x . [5] 2 x 4 x 5 - + 3](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42001-jun22-02-qp.webp?v=3)
![June 2022 Core Pure, question 7: In this question you must show detailed reasoning. y 3 x 1 + 1 Show that ) d x ln 2 . [9] = 2 2 x x ( 1 )( 1 - + 2](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42001-jun22-07-qp.webp?v=3)
![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](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42001-nov21-16-qp.webp?v=3)
![November 2020 Core Pure, question 3: In this question you must show detailed reasoning. 1 y 1 3 dx , expressing your answer in terms of r. [4] Find 2 4 9 x - 0](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42001-nov20-03-qp.webp?v=3)
![June 2019 Core Pure, question 6: In this question you must show detailed reasoning. 3 y 1 Find d x . [4] 2 4 x + 2](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42001-jun19-06-qp.webp?v=3)
![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](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42001-jun19-15-qp.webp?v=3)
All 18 questions on Further calculus, as a list
- June 2025, Core Pure, Q7 (8 marks): In this question you must show detailed reasoning. 3y 1 1 1 By first expressing x 2 - in partial fractions, show that d x ln n , where m and n = m 2 4 x 4 - 3 a
- June 2025, Core Pure, Q10 (4 marks): In this question you must show detailed reasoning. 1 y 2 2 Evaluate d x . Give your answer in exact form. [4] 2 x x 1 - + 0
- June 2025, Core Pure, Q16 (12 marks): In this question you must show detailed reasoning. x 3 + The diagram shows the curve with equation y . = 2 x 9 + y R x O x = 4 The region R, shown shaded in the
- June 2024, Core Pure, Q4 (4 marks): 4 The equation of a curve is y , where k is a positive constant. The region between the = 2 2 k x + x-axis, the y-axis and the line x k is rotated through r 2 r
- June 2024, Core Pure, Q7 (5 marks): 2y 1 7 (a) Explain why d x is an improper integral. [1] 3 x 2 - 1 (b) In this question you must show detailed reasoning. Use an appropriate limit argument to ev
- 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
- June 2023, Core Pure, Q9 (6 marks): In an electrical circuit, the alternating current I amps is given by I a sin nt , where t is the time in = seconds and a and n are positive constants. The RMS v
- June 2023, Core Pure, Q15 (5 marks): In this question you must show detailed reasoning. y 2 1 Evaluate dx , giving your answer in terms of r. [5] 2 1 2 x x + - 1
- June 2022, Core Pure, Q2 (5 marks): In this question you must show detailed reasoning. y 3 1 Find the exact value of d x . [5] 2 x 4 x 5 - + 3
- June 2022, Core Pure, Q7 (9 marks): In this question you must show detailed reasoning. y 3 x 1 + 1 Show that ) d x ln 2 . [9] = 2 2 x x ( 1 )( 1 - + 2
- November 2021, Core Pure, Q2 (4 marks): In this question you must show detailed reasoning. 1 . Express the result Find the gradient of the curve y 6 arcsin ( 2 x ) at the point with x-coordinate 4 = i
- November 2021, Core Pure, Q4 (4 marks): In this question you must show detailed reasoning. 1 Determine the mean value of between x =- and x 1 = . Give your answer to 3 significant 1 2 x 1 4 + figures.
- 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, Q3 (4 marks): In this question you must show detailed reasoning. 1 y 1 3 dx , expressing your answer in terms of r. [4] Find 2 4 9 x - 0
- 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
- June 2019, Core Pure, Q4 (3 marks): In this question you must show detailed reasoning. 1 1 r Fig. 4 shows the region bounded by the curve y sec x , the x-axis, the y-axis and the line x . = = 2 2
- June 2019, Core Pure, Q6 (4 marks): In this question you must show detailed reasoning. 3 y 1 Find d x . [4] 2 4 x + 2
- 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
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