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AS & A Level Mathematics 9709 · Pure Mathematics 3 (for Paper 3) · 3.7

Vectors: past paper questions

86 real questionsasked in 9 of the last 10 exam series2020–2026usually: Find, Show, Calculate, State, Determine

Real questions on vectors

The newest 20 of 86 written questions. Open one to see it on the real paper.

  1. 9709/32 · May/June 2026 · Q9a[2]

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

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  2. 9709/32 · May/June 2026 · Q9b[4]

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

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  3. 9709/32 · May/June 2026 · Q9c[6]

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

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  4. 9709/31 · October/November 2025 · Q11a[2]

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

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  5. 9709/31 · October/November 2025 · Q11b[4]

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

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  6. 9709/31 · October/November 2025 · Q11c[4]

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

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  7. 9709/32 · October/November 2025 · Q11a[2]

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

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  8. 9709/32 · October/November 2025 · Q11b[3]

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

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  9. 9709/32 · October/November 2025 · Q11c[4]

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

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  10. 9709/33 · October/November 2025 · Q9a[3]

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

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  11. 9709/33 · October/November 2025 · Q9b[3]

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

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  12. 9709/33 · October/November 2025 · Q9c[3]

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

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  13. 9709/31 · May/June 2025 · Q8a[2]

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

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  14. 9709/31 · May/June 2025 · Q8b[4]

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

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  15. 9709/31 · May/June 2025 · Q8c[3]

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

    See it on the paper →
  16. 9709/32 · May/June 2025 · Q9a[2]

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

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  17. 9709/32 · May/June 2025 · Q9b[4]

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

    See it on the paper →
  18. 9709/32 · May/June 2025 · Q9c[3]

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

    See it on the paper →
  19. 9709/33 · May/June 2025 · Q9a[2]

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

    See it on the paper →
  20. 9709/33 · May/June 2025 · Q9b[4]

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

    See it on the paper →

What examiners said

Most candidates understood that to show that the lines are skew they need to show both that the two lines do not intersect and that the two lines are not parallel. Although the correct method was often seen, there were many arithmetic errors in attempts to show that the two lines do not intersect. Far less common was a correct method to show that the two lines were not parallel. Many solutions did...

— Examiner report, February/March 2025, 9709/32 Q8(a) (Cambridge)

This question was very well attempted, with correct answers usually seen in degrees rather than radians. Candidates who were not so successful in this part tended not to be using the direction vectors of the lines but instead using the position vectors of the two points found in part (a).

— Examiner report, February/March 2025, 9709/32 Q8(b) (Cambridge)

This question was answered well by many candidates. The most common approach being to resolve forces in two directions and using the resulting equations to solve for and X.

— Examiner report, February/March 2025, 9709/42 Q1 (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.

Vectors — AS & A Level Mathematics 9709 past paper questions | AssessPro