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2025

Cambridge A Level · 9709 · Paper 3 · Pure Mathematics 3

Mathematics 9709/31 Oct/Nov 2025 past paper

Cambridge A Level Mathematics (9709) Paper 3 (Pure Mathematics 3), variant 1, Oct/Nov 2025: the question paper and its official mark scheme, 11 questions worth 75 marks, with the grade thresholds. Free to open, no account needed.

Questions
11
Marks
75
Grade A from
58
Open the question paperMark scheme

File names: 9709_w25_qp_31 · 9709_w25_ms_31

Grade thresholds for 9709/31 Oct/Nov 2025

The minimum raw marks Cambridge set for each grade on this component (out of 75). Thresholds change every session and variant, so always compare your score with the paper you actually sat.

ABCDE
5849403121

Topics in this paper

Which syllabus chapters 9709/31 Oct/Nov 2025 tested, by marks. Each chapter links to every past-paper question on it.

ChapterQuestionsMarks
Trigonometry213
Complex Numbers211
Polynomials111
Vectors110
Indices, Surds and Logs29
Differential Equations18
Iteration18
Differentiation15

Questions in 9709/31 Oct/Nov 2025

  1. Question 1Indices, Surds and Logs · 4 marks
  2. Question 2Trigonometry · 5 marks
  3. Question 3Trigonometry · 8 marks
  4. Question 4Differentiation · 5 marks
  5. Question 5Complex Numbers · 6 marks
  6. Question 6Complex Numbers · 5 marks
  7. Question 7Indices, Surds and Logs · 5 marks

    The parametric equations of a curve are ( ), ln …

  8. Question 8Differential Equations · 8 marks

    The variables x and y satisfy the differential equation …

  9. Question 9Iteration · 8 marks

    (a) By sketching a suitable pair of graphs, show that the equation sec x 2 ex =- has only one root in the interval …

  10. Question 10Polynomials · 11 marks
  11. Question 11Vectors · 10 marks

    With respect to the origin O, the points …

Other Mathematics papers from Oct/Nov 2025

Questions students ask

Where can I get the 9709/31 Oct/Nov 2025 mark scheme?
Open the mark scheme above - it is the official Cambridge scheme for this exact paper (9709_w25_ms_31), and on a wide screen it sits beside the question you are reading.
What was the grade threshold for an A in 9709/31 Oct/Nov 2025?
58 marks out of 75, a C needed 40.
Which topics came up in 9709/31 Oct/Nov 2025?
Mostly Trigonometry, Complex Numbers, Polynomials. The full list is in the table above.
Do I need an account to open 9709/31 Oct/Nov 2025?
No. Every paper opens for free without signing in. A free account also saves your pen marks and records your score against the grade thresholds.