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2023

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

Mathematics 9709/31 May/June 2023 past paper

Cambridge A Level Mathematics (9709) Paper 3 (Pure Mathematics 3), variant 1, May/June 2023: the question paper and its official mark scheme, 10 questions worth 75 marks, with the grade thresholds. Free to open, no account needed.

Questions
10
Marks
75
Grade A from
52
Open the question paperMark scheme

File names: 9709_s23_qp_31 ยท 9709_s23_ms_31

Grade thresholds for 9709/31 May/June 2023

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
5245362617

Topics in this paper

Which syllabus chapters 9709/31 May/June 2023 tested, by marks. Each chapter links to every past-paper question on it.

ChapterQuestionsMarks
Trigonometry214
Complex Numbers112
Vectors110
Partial Fractions110
Iteration110
Linear Law18
Graphs14
Binomial14
Indices, Surds and Logs13

Questions in 9709/31 May/June 2023

  1. Question 1Indices, Surds and Logs ยท 3 marks
  2. Question 2Graphs ยท 4 marks
  3. Question 3Binomial ยท 4 marks

    Find the coe๏ฌƒcient of x3 in the binomial expansion of โ€ฆ

  4. Question 4Trigonometry ยท 6 marks

    (a) Show that the equation sin 21 + cos โ€ฆ

  5. Question 5Trigonometry ยท 8 marks

    The equation of a curve is x2y โˆ’ay2 = 4a3, where a is a non-zero constant. (a) Show that dy dx = 2xy 2ay โ€ฆ

  6. Question 6Vectors ยท 10 marks

    Relative to the origin O, the points A, B and C have position vectors given by โˆ’โˆ’ยฟ OA โ€ฆ

  7. Question 7Linear Law ยท 8 marks

    The variables x and y satisfy the di๏ฌ€erential equation cos 2x dy dx = 4 tan 2x sin2 3y , where โ€ฆ

  8. Question 8Partial Fractions ยท 10 marks
  9. Question 9Iteration ยท 10 marks
  10. Question 10Complex Numbers ยท 12 marks

Other Mathematics papers from May/June 2023

Questions students ask

Where can I get the 9709/31 May/June 2023 mark scheme?
Open the mark scheme above - it is the official Cambridge scheme for this exact paper (9709_s23_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 2023?
52 marks out of 75, a C needed 36.
Which topics came up in 9709/31 May/June 2023?
Mostly Trigonometry, Complex Numbers, Vectors. The full list is in the table above.
Do I need an account to open 9709/31 May/June 2023?
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.