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Multivariable calculus: OCR MEI A‑Level Further Maths questions

Every OCR MEI A-Level Further Maths exam question on FP.10 Multivariable calculus, 2018–2025, with its mark scheme and examiner’s report.

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847 questions

  1. Q4

    June 2025 · Extra Pure

    16 marksFP.10 Multivariable calculus
    The whole paper ↗
    June 2025 Extra Pure, question 4: 2 2 4 A surface, S, is defined in 3-D by z f ( , ) x y where ( , ) f x y x 12 xy 96 y 30 . = = - + + You are given that the point (0, 0, 30) on S is a stationar

  2. Q1

    June 2024 · Extra Pure

    17 marksFP.10 Multivariable calculus
    The whole paper ↗
    June 2024 Extra Pure, question 1: A surface, S, is defined in 3-D by z f ( , ) x y where ( , ) f x y 12 x 30 y 6 xy . = = - + (a) Determine the coordinates of any stationary points on the surfac

  3. Q1

    June 2023 · Extra Pure

    7 marksFP.10 Multivariable calculus
    The whole paper ↗
    June 2023 Extra Pure, question 1: 2 1 A surface is defined in 3-D by z 3 x 6 xy y . = + + Determine the coordinates of any stationary points on the surface. [7]

  4. Q3

    June 2023 · Extra Pure

    8 marksFP.10 Multivariable calculusCP.6 Further vectors
    The whole paper ↗
    June 2023 Extra Pure, question 3: 2 2 3 A surface, S, is defined by ( , , ) g x y z 0 where ( , , ) g x y z 2 x x y 2 xy 27 z . The normal to = = - + + a k and the tangent plane to S at the poin

  5. Q5

    June 2022 · Extra Pure

    16 marksFP.10 Multivariable calculus
    The whole paper ↗
    June 2022 Extra Pure, question 5: x 2 x y ( 2 2 ) 5 A surface S is defined by z f ( , ), x y where ( , ) f x y y e - + + . = = f 2 (a) (i) Find . [1] x 2 f 2 x 2 x y 2 ( 2 2 ) (ii) Show that ( x

  6. Q1

    November 2021 · Extra Pure

    11 marksFP.10 Multivariable calculus
    The whole paper ↗
    November 2021 Extra Pure, question 1: In this question you must show detailed reasoning. 3 2 2 A surface S is defined by z f ( , ) x y where ( , ) f x y x x y 2 y . = = + - (a) On the coordinate axe

  7. Q5

    November 2021 · Extra Pure

    6 marksFP.10 Multivariable calculusCP.6 Further vectors
    The whole paper ↗
    November 2021 Extra Pure, question 5: 2 2 5 A surface S is defined for z 0 by x y 2 z 126 . C is the set of points on S for which the H + + = 1 r radians. tangent plane to S at that point intersects

  8. Q6

    November 2020 · Extra Pure

    17 marksFP.10 Multivariable calculusCP.6 Further vectors
    The whole paper ↗
    November 2020 Extra Pure, question 6: 4 2 2 6 A surface S is defined by z f ( , ) x y 4 x 4 y 17 x y . = = + - (a) (i) Show that there is only one stationary point on S. [5] The value of z at the st

  9. Q2

    June 2019 · Extra Pure

    11 marksFP.10 Multivariable calculus
    The whole paper ↗
    June 2019 Extra Pure, question 2: 2 2 A surface S is defined by z 4 x 4 y 4 x 8 y 11 . = + - + + (a) Show that the point P (0.5, -1, 6) is the only stationary point on S. [2] (b) (i) On the axes
All 9 questions on Multivariable calculus, as a list
  1. June 2025, Extra Pure, Q4 (16 marks): 2 2 4 A surface, S, is defined in 3-D by z f ( , ) x y where ( , ) f x y x 12 xy 96 y 30 . = = - + + You are given that the point (0, 0, 30) on S is a stationar
  2. June 2024, Extra Pure, Q1 (17 marks): A surface, S, is defined in 3-D by z f ( , ) x y where ( , ) f x y 12 x 30 y 6 xy . = = - + (a) Determine the coordinates of any stationary points on the surfac
  3. June 2023, Extra Pure, Q1 (7 marks): 2 1 A surface is defined in 3-D by z 3 x 6 xy y . = + + Determine the coordinates of any stationary points on the surface. [7]
  4. June 2023, Extra Pure, Q3 (8 marks): 2 2 3 A surface, S, is defined by ( , , ) g x y z 0 where ( , , ) g x y z 2 x x y 2 xy 27 z . The normal to = = - + + a k and the tangent plane to S at the poin
  5. June 2022, Extra Pure, Q5 (16 marks): x 2 x y ( 2 2 ) 5 A surface S is defined by z f ( , ), x y where ( , ) f x y y e - + + . = = f 2 (a) (i) Find . [1] x 2 f 2 x 2 x y 2 ( 2 2 ) (ii) Show that ( x
  6. November 2021, Extra Pure, Q1 (11 marks): In this question you must show detailed reasoning. 3 2 2 A surface S is defined by z f ( , ) x y where ( , ) f x y x x y 2 y . = = + - (a) On the coordinate axe
  7. November 2021, Extra Pure, Q5 (6 marks): 2 2 5 A surface S is defined for z 0 by x y 2 z 126 . C is the set of points on S for which the H + + = 1 r radians. tangent plane to S at that point intersects
  8. November 2020, Extra Pure, Q6 (17 marks): 4 2 2 6 A surface S is defined by z f ( , ) x y 4 x 4 y 17 x y . = = + - (a) (i) Show that there is only one stationary point on S. [5] The value of z at the st
  9. June 2019, Extra Pure, Q2 (11 marks): 2 2 A surface S is defined by z 4 x 4 y 4 x 8 y 11 . = + - + + (a) Show that the point P (0.5, -1, 6) is the only stationary point on S. [2] (b) (i) On the axes

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