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All Edexcel A-level Further Maths topic questions

Edexcel A-level Further Maths · Topic CP-7

Polar coordinates questions

Practice questions covering polar coordinates from this specification. Attempt the questions below, then use the past-paper references to find more on Pearson's site.

Questions to attempt

6 questions on Polar coordinates, each with its mark scheme and worked method. Reveal the answer when you have had a go.

  1. CP-7.1 · Understand and use polar coordinates and be able to convert between polar and Cartesian coordinates.

    Q1
    ORIGINAL
    Year 2
    Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.

    1.

    Express the Cartesian point (−3,33)(-3,3\sqrt3) in polar form, taking r>0r>0 and 0≤θ<2π0\leq\theta<2\pi.

    (3)

    (Total for Question 1 is 3 marks)

  2. CP-7.1 · Understand and use polar coordinates and be able to convert between polar and Cartesian coordinates.

    Q2
    ORIGINAL
    Year 2
    Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.

    2.

    Convert the polar coordinates (4,π/6)(4,\pi/6) to Cartesian coordinates.

    (2)

    (Total for Question 2 is 2 marks)

  3. CP-7.2 · Sketch curves with r given as a function of theta, including use of trigonometric functions.

    Q3
    ORIGINAL
    Year 2
    Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.

    3.

    Sketch the polar curve r=2cos⁡θr=2\cos\theta. State its Cartesian equation, centre and radius.

    (4)

    (Total for Question 3 is 4 marks)

  4. CP-7.2 · Sketch curves with r given as a function of theta, including use of trigonometric functions.

    Q4
    ORIGINAL
    Year 2
    Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.

    4.

    Sketch the polar curve r=3r=3, labelling its key geometric features.

    (2)

    (Total for Question 4 is 2 marks)

  5. CP-7.3 · Find the area enclosed by a polar curve.

    Q5
    ORIGINAL
    Year 2
    Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.

    5.

    Determine the exact area enclosed by the loop r=3sin⁡θr=3\sin\theta.

    (5)

    (Total for Question 5 is 5 marks)

  6. CP-7.3 · Find the area enclosed by a polar curve.

    Q6
    ORIGINAL
    Year 2
    Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.

    6.

    Find the exact area of the sector enclosed by r=2r=2 and the rays θ=0\theta=0 and θ=π/3\theta=\pi/3.

    (3)

    (Total for Question 6 is 3 marks)

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Printable question pack — CP-7 Polar coordinatesAll 29 questions across 3 specification points — 23 more than the 6 above — with the full mark scheme. Guest accessible · browser print.

CP-7 Polar coordinates revision notes

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Find these in the real papers

9 past-paper references · 5 open at the question's page · newest series first

References open the specific Pearson question paper when it is available. Missing, login-only or unverified question-paper sources are labelled on the affected row. Question content remains on the exam board's website.

June 20241 question
June 20232 questions
June 20221 question
June 20211 question
June 20201 question
June 20191 question
sample2 questions

Reference rows contain series, paper, question number, marks and classification metadata only. Pearson's question papers open on Pearson's own website.

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