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Further calculus (option): OCR A‑Level Further Maths questions

Every OCR A-Level Further Maths exam question on FP.2 Further calculus (option), 2018–2025, with its mark scheme and examiner’s report.

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648 questions

  1. Q7

    June 2024 · Additional Pure Mathematics

    10 marksFP.2 Further calculus (option)
    The whole paper ↗
    June 2024 Additional Pure Mathematics, question 7: n x y 7 I dx for integers n Let 0 . = 2 n 3 x 1 + 0 3 + with respect to x, determine the exact value of I2 . [2] (a) By considering the derivative of x 1 n 1 (b

  2. Q4

    June 2023 · Additional Pure Mathematics

    7 marksFP.2 Further calculus (option)
    The whole paper ↗
    June 2023 Additional Pure Mathematics, question 4: I 2 " , is given for all integers n + , where = y n 2 n 4 The sequence An 0 by A I cos x x d . H = I n n n 0 " , increases monotonically. • Show that An " , con

  3. Q7

    June 2022 · Additional Pure Mathematics

    10 marksFP.2 Further calculus (option)
    The whole paper ↗
    June 2022 Additional Pure Mathematics, question 7: ^ h with respect to t. 3 2 2 7 (a) Differentiate 16 t [1] + 3 y n 2 Let I t 16 t d t for integers n H . 1 = + n 0 n 1 (b) Show that, for n H , ( 3 n 2 ) I 125 3

  4. Q7

    November 2021 · Additional Pure Mathematics

    8 marksFP.2 Further calculus (option)
    The whole paper ↗
    November 2021 Additional Pure Mathematics, question 7: y r n 7 Let I cos x x d for integers n 0 . 2 = H n 0 (a) Show that, for n 2 , n I ( n 1 ) I - . [4] H = - n n 2 (b) Use this reduction formula to deduce the exa

  5. Q3

    November 2020 · Additional Pure Mathematics

    9 marksFP.2 Further calculus (option)
    The whole paper ↗
    November 2020 Additional Pure Mathematics, question 3: n x 1 y 3 For integers n 0 , I d x . H = n 2 1 x 0 + 1 (a) For integers n 2 , show that I I . [3] H + = n 1 n n 2 - - (b) (i) Determine the exact value of I10.
All 5 questions on Further calculus (option), as a list
  1. June 2024, Additional Pure Mathematics, Q7 (10 marks): n x y 7 I dx for integers n Let 0 . = 2 n 3 x 1 + 0 3 + with respect to x, determine the exact value of I2 . [2] (a) By considering the derivative of x 1 n 1 (b
  2. June 2023, Additional Pure Mathematics, Q4 (7 marks): I 2 " , is given for all integers n + , where = y n 2 n 4 The sequence An 0 by A I cos x x d . H = I n n n 0 " , increases monotonically. • Show that An " , con
  3. June 2022, Additional Pure Mathematics, Q7 (10 marks): ^ h with respect to t. 3 2 2 7 (a) Differentiate 16 t [1] + 3 y n 2 Let I t 16 t d t for integers n H . 1 = + n 0 n 1 (b) Show that, for n H , ( 3 n 2 ) I 125 3
  4. November 2021, Additional Pure Mathematics, Q7 (8 marks): y r n 7 Let I cos x x d for integers n 0 . 2 = H n 0 (a) Show that, for n 2 , n I ( n 1 ) I - . [4] H = - n n 2 (b) Use this reduction formula to deduce the exa
  5. November 2020, Additional Pure Mathematics, Q3 (9 marks): n x 1 y 3 For integers n 0 , I d x . H = n 2 1 x 0 + 1 (a) For integers n 2 , show that I I . [3] H + = n 1 n n 2 - - (b) (i) Determine the exact value of I10.

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