Skip to content
AS & A Level Further Mathematics 9231 · Further Mechanics (for Paper 3) · 3.5

Linear motion under a variable force: past paper questions

28 real questionsasked in 9 of the last 10 exam series2020–2025usually: Find, Show, Write

Real questions on linear motion under a variable force

The newest 20 of 28 written questions. Open one to see it on the real paper.

  1. 9231/32 · May/June 2025 · Q5[6]

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

    See it on the paper →
  2. 9231/33 · May/June 2025 · Q2a[5]

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

    See it on the paper →
  3. 9231/32 · October/November 2024 · Q6b[4]

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

    See it on the paper →
  4. 9231/32 · October/November 2024 · Q7a[6]

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

    See it on the paper →
  5. 9231/32 · October/November 2024 · Q7b[5]

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

    See it on the paper →
  6. 9231/31 · May/June 2024 · Q4b[3]

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

    See it on the paper →
  7. 9231/32 · October/November 2023 · Q3a[4]

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

    See it on the paper →
  8. 9231/32 · May/June 2023 · Q1a[3]

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

    See it on the paper →
  9. 9231/31 · October/November 2022 · Q2a[4]

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

    See it on the paper →
  10. 9231/33 · October/November 2022 · Q2a[4]

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

    See it on the paper →
  11. 9231/31 · May/June 2022 · Q3[5]

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

    See it on the paper →
  12. 9231/31 · May/June 2022 · Q7a[4]

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

    See it on the paper →
  13. 9231/31 · May/June 2022 · Q7b[4]

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

    See it on the paper →
  14. 9231/31 · May/June 2022 · Q7c[3]

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

    See it on the paper →
  15. 9231/33 · May/June 2022 · Q2[5]

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

    See it on the paper →
  16. 9231/31 · October/November 2021 · Q6a[6]

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

    See it on the paper →
  17. 9231/31 · October/November 2021 · Q6b[2]

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

    See it on the paper →
  18. 9231/31 · October/November 2021 · Q7a[3]

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

    See it on the paper →
  19. 9231/31 · October/November 2021 · Q7b[4]

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

    See it on the paper →
  20. 9231/31 · October/November 2021 · Q7c[4]

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

    See it on the paper →

What examiners said

Many candidates correctly identified expressions for the kinetic and elastic potential energy in the two situations, equated them and obtained the correct answers, often in a very elegant way. Some candidates attempted a variety of incorrect approaches (SUVAT, equilibrium of forces), which invariably led to an incorrect answer and rarely gained any credit. A common mistake was to omit the coeffici...

— Examiner report, October/November 2022, 9231/31 Q2(a) (Cambridge)

Many candidates correctly identified expressions for the kinetic and elastic potential energy in the two situations, equated them and obtained the correct answers, often in a very elegant way. Some candidates attempted a variety of incorrect approaches (SUVAT, equilibrium of forces), which invariably led to an incorrect answer and rarely gained any credit. A common mistake was to omit the coeffici...

— Examiner report, October/November 2022, 9231/33 Q2(a) (Cambridge)

Many candidates were able to set up a differential equation and to solve it, including applying the boundary conditions. However, only some candidates realised that acceleration and velocity had opposite directions dv 4000 and therefore the correct differential equation was =− . Candidates who drew a diagram dt ( 5t + 4 )3 representing the situation and included the directions of acceleration and...

— Examiner report, May/June 2022, 9231/31 Q3 (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.

Linear motion under a variable force — AS & A Level Further Mathematics 9231 past paper questions | AssessPro