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Polar coordinates: OCR A‑Level Further Maths questions

Every OCR 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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648 questions

  1. Q6

    June 2025 · Pure Core 2

    6 marksCP.7 Polar coordinates
    The whole paper ↗
    June 2025 Pure Core 2, question 6: One of the regions bounded by two polar curves, C1 and C2, is used to model the face of a flat earring. The polar equations of C1 and C2 are C r : 2 = i 1 2 C r

  2. Q12

    June 2024 · Pure Core 1

    7 marksCP.7 Polar coordinates
    The whole paper ↗
    June 2024 Pure Core 1, question 12: For any positive parameter k, the curve Ck is defined by the polar equation 10 0 r k ( cos 1 ) , 2 . = i + + G i G r k For each value of k the curve is a single

  3. Q6

    June 2024 · Pure Core 2

    11 marksCP.7 Polar coordinates
    The whole paper ↗
    June 2024 Pure Core 2, question 6: J N 1 1 KKK OOO for 0 6 In polar coordinates, the equation of a curve, C, is r 6 sin ( 2 ) sinh r. = G G i i i 3 2 L P The pole of the polar coordinate system c

  4. Q10

    June 2023 · Pure Core 2

    7 marksCP.7 Polar coordinatesCP.8 Hyperbolic functions
    The whole paper ↗
    June 2023 Pure Core 2, question 10: In this question you must show detailed reasoning. A region, R, of the floor of an art gallery is to be painted for the purposes of an art installation. A suita

  5. Q5

    June 2022 · Pure Core 1

    11 marksCP.7 Polar coordinates
    The whole paper ↗
    June 2022 Pure Core 1, question 5: ^ h for 0 5 The diagram below shows the curve C with polar equation r 3 1 sin 2i 2 r. = - G i G C 0 i = O ^ h 2 3 2 4 (a) Show that a cartesian equation of C is

  6. Q2

    June 2022 · Pure Core 2

    5 marksCP.7 Polar coordinates
    The whole paper ↗
    June 2022 Pure Core 2, question 2: Two polar curves, C1 and C2, are defined by C r : 2 and C r : + where 0 1 2 r. = i = i G i G 1 2 C1 intersects the initial line at two points, the pole and the

  7. Q7

    November 2021 · Pure Core 1

    9 marksCP.7 Polar coordinates
    The whole paper ↗
    November 2021 Pure Core 1, question 7: 7 The diagram below shows the curve with polar equation r sin 3i for 0 r. = G G i 3 0 i = O (a) Find the values of i at the pole. [1] (b) Find the polar coordin

  8. Q11

    November 2020 · Pure Core 1

    8 marksCP.7 Polar coordinates
    The whole paper ↗
    November 2020 Pure Core 1, question 11: 3 11 A curve has cartesian equation x y 2 xy . + = C is the portion of the curve for which x 0 and y 0 . The equation of C in polar form is given H H 1 by r f i

  9. Q6

    November 2020 · Pure Core 2

    6 marksCP.7 Polar coordinates
    The whole paper ↗
    November 2020 Pure Core 2, question 6: The equation of a curve in polar coordinates is r ln ( 1 sin ) for b where a and b are = + i a G i G non-negative angles. The curve consists of a single closed

  10. Q9

    June 2019 · Pure Core 2

    11 marksCP.7 Polar coordinates
    The whole paper ↗
    June 2019 Pure Core 2, question 9: In this question you must show detailed reasoning. 1 e cos The diagram below shows the curve r sin i for 0 G r. = G i i 3 i = 0 O (a) Find the exact area enclos
All 10 questions on Polar coordinates, as a list
  1. June 2025, Pure Core 2, Q6 (6 marks): One of the regions bounded by two polar curves, C1 and C2, is used to model the face of a flat earring. The polar equations of C1 and C2 are C r : 2 = i 1 2 C r
  2. June 2024, Pure Core 1, Q12 (7 marks): For any positive parameter k, the curve Ck is defined by the polar equation 10 0 r k ( cos 1 ) , 2 . = i + + G i G r k For each value of k the curve is a single
  3. June 2024, Pure Core 2, Q6 (11 marks): J N 1 1 KKK OOO for 0 6 In polar coordinates, the equation of a curve, C, is r 6 sin ( 2 ) sinh r. = G G i i i 3 2 L P The pole of the polar coordinate system c
  4. June 2023, Pure Core 2, Q10 (7 marks): In this question you must show detailed reasoning. A region, R, of the floor of an art gallery is to be painted for the purposes of an art installation. A suita
  5. June 2022, Pure Core 1, Q5 (11 marks): ^ h for 0 5 The diagram below shows the curve C with polar equation r 3 1 sin 2i 2 r. = - G i G C 0 i = O ^ h 2 3 2 4 (a) Show that a cartesian equation of C is
  6. June 2022, Pure Core 2, Q2 (5 marks): Two polar curves, C1 and C2, are defined by C r : 2 and C r : + where 0 1 2 r. = i = i G i G 1 2 C1 intersects the initial line at two points, the pole and the
  7. November 2021, Pure Core 1, Q7 (9 marks): 7 The diagram below shows the curve with polar equation r sin 3i for 0 r. = G G i 3 0 i = O (a) Find the values of i at the pole. [1] (b) Find the polar coordin
  8. November 2020, Pure Core 1, Q11 (8 marks): 3 11 A curve has cartesian equation x y 2 xy . + = C is the portion of the curve for which x 0 and y 0 . The equation of C in polar form is given H H 1 by r f i
  9. November 2020, Pure Core 2, Q6 (6 marks): The equation of a curve in polar coordinates is r ln ( 1 sin ) for b where a and b are = + i a G i G non-negative angles. The curve consists of a single closed
  10. June 2019, Pure Core 2, Q9 (11 marks): In this question you must show detailed reasoning. 1 e cos The diagram below shows the curve r sin i for 0 G r. = G i i 3 i = 0 O (a) Find the exact area enclos

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