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2025

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

Mathematics 9709/31 May/June 2025 past paper

Cambridge A Level Mathematics (9709) Paper 3 (Pure Mathematics 3), variant 1, May/June 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
55
Open the question paperMark scheme

File names: 9709_s25_qp_31 · 9709_s25_ms_31

Grade thresholds for 9709/31 May/June 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
5549382716

Topics in this paper

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

ChapterQuestionsMarks
Differentiation217
Trigonometry217
Complex Numbers212
Iteration110
Differential Equations18
Polynomials15
Graphs13
Indices, Surds and Logs13

Questions in 9709/31 May/June 2025

  1. Question 1Graphs · 3 marks
  2. Question 2Indices, Surds and Logs · 3 marks
  3. Question 3Complex Numbers · 6 marks

    Find the complex numbers z for which …

  4. Question 4Differentiation · 6 marks

    The parametric equations of a curve are x etant = , tan …

  5. Question 5Polynomials · 5 marks
  6. Question 6Complex Numbers · 6 marks
  7. Question 7Trigonometry · 8 marks
  8. Question 8Trigonometry · 9 marks

    With respect to the origin O, the points A and B have position vectors …

  9. Question 9Iteration · 10 marks

    The constant a is such that a 1 ln …

  10. Question 10Differential Equations · 8 marks

    (a) Find the quotient and remainder when …

  11. Question 11Differentiation · 11 marks

Other Mathematics papers from May/June 2025

Questions students ask

Where can I get the 9709/31 May/June 2025 mark scheme?
Open the mark scheme above - it is the official Cambridge scheme for this exact paper (9709_s25_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 May/June 2025?
55 marks out of 75, a C needed 38.
Which topics came up in 9709/31 May/June 2025?
Mostly Differentiation, Trigonometry, Complex Numbers. The full list is in the table above.
Do I need an account to open 9709/31 May/June 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.