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AS & A Level Further Mathematics 9231 · Further Pure Mathematics 1 (for Paper 1) · 1.5

Polar coordinates: past paper questions

176 real questionsasked in 10 of the last 10 exam series2020–2025usually: Find, Sketch, Show, Use, Give

Real questions on polar coordinates

The newest 20 of 176 written questions. Open one to see it on the real paper.

  1. 9231/11 · October/November 2025 · Q6a[3]

    3-mark question — its maths and diagrams are best seen on the paper.

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  2. 9231/11 · October/November 2025 · Q6b[4]

    4-mark “Find” question — its maths and diagrams are best seen on the paper.

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  3. 9231/11 · October/November 2025 · Q6c[5]

    5-mark “Find” question — its maths and diagrams are best seen on the paper.

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  4. 9231/11 · October/November 2025 · Q6d[3]

    3-mark “Find” question — its maths and diagrams are best seen on the paper.

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  5. 9231/11 · October/November 2025 · Q7a[2]

    2-mark “Find” question — its maths and diagrams are best seen on the paper.

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  6. 9231/11 · October/November 2025 · Q7b[3]

    3-mark “Show” question — its maths and diagrams are best seen on the paper.

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  7. 9231/11 · October/November 2025 · Q7c[3]

    3-mark “Sketch” question — its maths and diagrams are best seen on the paper.

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  8. 9231/12 · October/November 2025 · Q4a(i)[2]

    2-mark question — its maths and diagrams are best seen on the paper.

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  9. 9231/12 · October/November 2025 · Q4a(ii)[2]

    2-mark question — its maths and diagrams are best seen on the paper.

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  10. 9231/12 · October/November 2025 · Q5a[2]

    2-mark question — its maths and diagrams are best seen on the paper.

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  11. 9231/12 · October/November 2025 · Q5b[4]

    4-mark “Find” question — its maths and diagrams are best seen on the paper.

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  12. 9231/12 · October/November 2025 · Q5c[4]

    4-mark “Show” question — its maths and diagrams are best seen on the paper.

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  13. 9231/12 · October/November 2025 · Q5d[2]

    2-mark question — its maths and diagrams are best seen on the paper.

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  14. 9231/13 · October/November 2025 · Q6a[3]

    3-mark question — its maths and diagrams are best seen on the paper.

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  15. 9231/13 · October/November 2025 · Q6b[4]

    4-mark “Find” question — its maths and diagrams are best seen on the paper.

    See it on the paper →
  16. 9231/13 · October/November 2025 · Q6c[5]

    5-mark “Find” question — its maths and diagrams are best seen on the paper.

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  17. 9231/13 · October/November 2025 · Q6d[3]

    3-mark “Find” question — its maths and diagrams are best seen on the paper.

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  18. 9231/13 · October/November 2025 · Q7a[2]

    2-mark “Find” question — its maths and diagrams are best seen on the paper.

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  19. 9231/13 · October/November 2025 · Q7b[3]

    3-mark “Show” question — its maths and diagrams are best seen on the paper.

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  20. 9231/22 · October/November 2025 · Q1[4]

    4-mark “Find” question — its maths and diagrams are best seen on the paper.

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What examiners said

Most proofs were complete. The best solutions stated that r ≠ 0 before dividing.

— Examiner report, October/November 2023, 9231/11 Q6(a) (Cambridge)

The majority of candidates found the result θ = π6 . For a complete solution the possibility that cosθ = 0 should have been considered. Candidates are reminded to express polar coordinates in the form (r ,θ )

— Examiner report, October/November 2023, 9231/11 Q6(b) (Cambridge)

Most diagrams were of acceptable shape and labelled correctly. Good sketches clearly showed C1 as a semi-circle with P on the right-hand side of C1 .

— Examiner report, October/November 2023, 9231/11 Q6(c) (Cambridge)

Past papers, syllabus and examiner reports © UCLES (Cambridge University Press & Assessment). Questions are matched to topics from the official syllabus. AssessPro is independent and not endorsed by Cambridge.

Polar coordinates — AS & A Level Further Mathematics 9231 past paper questions | AssessPro