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Polar coordinates: OCR MEI A‑Level Further Maths questions

Every OCR MEI A-Level Further Maths exam question on CP.7 Polar coordinates, 2018–2025, with its mark scheme and examiner’s report.

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847 questions

  1. Q6

    June 2025 · Core Pure

    9 marksCP.7 Polar coordinates
    The whole paper ↗
    June 2025 Core Pure, question 6: 2 2 6 The figure below shows the curve with cartesian equation ( x y ) xy . + = y x O 2 (a) Show that the polar equation of the curve is r a sin b , where a and

  2. Q9

    June 2024 · Core Pure

    8 marksCP.7 Polar coordinates
    The whole paper ↗
    June 2024 Core Pure, question 9: A curve has polar equation r a sin 3i , for 0 G r, where a is a positive constant. = i G (a) Sketch the curve. Indicate the parts of the curve where r is negati

  3. Q7

    June 2023 · Core Pure

    6 marksCP.7 Polar coordinates
    The whole paper ↗
    June 2023 Core Pure, question 7: The diagram below shows the curve with polar equation r a 1 ( 2 sin ) for 0 2 r where , i = - i G G a is a positive constant. O A = 0 θ B C The curve crosses th

  4. Q5

    June 2022 · Core Pure

    7 marksCP.7 Polar coordinates
    The whole paper ↗
    June 2022 Core Pure, question 5: (a) Sketch the polar curve r a 1 ( cos ), 0 2 , where a is a positive constant. [2] 1 = - i i r G (b) Determine the exact area of the region enclosed by the cur

  5. Q1

    June 2022 · Further Pure with Technology

    20 marksFP.4 Coordinate systems and conicsCP.7 Polar coordinates
    The whole paper ↗
    June 2022 Further Pure with Technology, question 1: (a) A family of curves is given by the equation 2 2 x y 2 axy = (*) 1 + + where the parameter a is a real number. You may find it helpful to use a slider (for a

  6. Q14

    November 2021 · Core Pure

    14 marksCP.7 Polar coordinates
    The whole paper ↗
    November 2021 Core Pure, question 14: A curve has polar equation r a ( cos 2 sin ) , where a is a positive constant and 0 G r. = i + i i G (a) Determine the polar coordinates of the point on the cur

  7. Q5

    November 2020 · Core Pure

    8 marksCP.7 Polar coordinates
    The whole paper ↗
    November 2020 Core Pure, question 5: Fig. 5 shows the curve with polar equation r a 3 ( 2 cos ) for , where a is a = + i - r G i G r constant. B A O = 0 i Fig. 5 (a) Write down the polar coordinate

  8. Q7

    June 2019 · Core Pure

    8 marksCP.7 Polar coordinates
    The whole paper ↗
    June 2019 Core Pure, question 7: ^ h 2 2 2 2 7 A curve has cartesian equation x y 2 c xy , where c is a positive constant. + = 2 2 (a) Show that the polar equation of the curve is r c sin 2 . [
All 8 questions on Polar coordinates, as a list
  1. June 2025, Core Pure, Q6 (9 marks): 2 2 6 The figure below shows the curve with cartesian equation ( x y ) xy . + = y x O 2 (a) Show that the polar equation of the curve is r a sin b , where a and
  2. June 2024, Core Pure, Q9 (8 marks): A curve has polar equation r a sin 3i , for 0 G r, where a is a positive constant. = i G (a) Sketch the curve. Indicate the parts of the curve where r is negati
  3. June 2023, Core Pure, Q7 (6 marks): The diagram below shows the curve with polar equation r a 1 ( 2 sin ) for 0 2 r where , i = - i G G a is a positive constant. O A = 0 θ B C The curve crosses th
  4. June 2022, Core Pure, Q5 (7 marks): (a) Sketch the polar curve r a 1 ( cos ), 0 2 , where a is a positive constant. [2] 1 = - i i r G (b) Determine the exact area of the region enclosed by the cur
  5. June 2022, Further Pure with Technology, Q1 (20 marks): (a) A family of curves is given by the equation 2 2 x y 2 axy = (*) 1 + + where the parameter a is a real number. You may find it helpful to use a slider (for a
  6. November 2021, Core Pure, Q14 (14 marks): A curve has polar equation r a ( cos 2 sin ) , where a is a positive constant and 0 G r. = i + i i G (a) Determine the polar coordinates of the point on the cur
  7. November 2020, Core Pure, Q5 (8 marks): Fig. 5 shows the curve with polar equation r a 3 ( 2 cos ) for , where a is a = + i - r G i G r constant. B A O = 0 i Fig. 5 (a) Write down the polar coordinate
  8. June 2019, Core Pure, Q7 (8 marks): ^ h 2 2 2 2 7 A curve has cartesian equation x y 2 c xy , where c is a positive constant. + = 2 2 (a) Show that the polar equation of the curve is r c sin 2 . [

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