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2023

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

Mathematics 9709/31 Oct/Nov 2023 past paper

Cambridge A Level Mathematics (9709) Paper 3 (Pure Mathematics 3), variant 1, Oct/Nov 2023: 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
54
Open the question paperMark scheme

File names: 9709_w23_qp_31 ยท 9709_w23_ms_31

Grade thresholds for 9709/31 Oct/Nov 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
5445393224

Topics in this paper

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

ChapterQuestionsMarks
Differentiation320
Polynomials111
Vectors110
Complex Numbers29
Iteration18
Differential Equations17
Trigonometry16
Linear Law14

Questions in 9709/31 Oct/Nov 2023

  1. Question 1Differentiation ยท 5 marks

    Find the exact coordinates of the points on the curve โ€ฆ

  2. Question 2Complex Numbers ยท 4 marks

    On an Argand diagram, shade the region whose points represent complex numbers z satisfying the inequalities โ€ฆ

  3. Question 3Linear Law ยท 4 marks
  4. Question 4Complex Numbers ยท 5 marks

    The complex number u is de๏ฌned by โ€ฆ

  5. Question 5Trigonometry ยท 6 marks
  6. Question 6Differentiation ยท 6 marks

    The parametric equations of a curve are โ€ฆ

  7. Question 7Differential Equations ยท 7 marks

    The variables x and 1 satisfy the di๏ฌ€erential equation x tan 1 dx โ€ฆ

  8. Question 8Iteration ยท 8 marks

    (a) By sketching a suitable pair of graphs, show that the equation x = ex โˆ’3 has only one root. (b) Show by calculation that this root lies between 1 and 2. (c) Show that, if a sequence of values โ€ฆ

  9. Question 9Differentiation ยท 9 marks

    x y O M 3 The diagram shows the curve y = xeโˆ’1 4x2 , for x โ‰ฅ0, and its maximum point M. (a) Find the exact coordinates of M. (b) Using the substitution โ€ฆ

  10. Question 10Polynomials ยท 11 marks
  11. Question 11Vectors ยท 10 marks

Other Mathematics papers from Oct/Nov 2023

Questions students ask

Where can I get the 9709/31 Oct/Nov 2023 mark scheme?
Open the mark scheme above - it is the official Cambridge scheme for this exact paper (9709_w23_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 2023?
54 marks out of 75, a C needed 39.
Which topics came up in 9709/31 Oct/Nov 2023?
Mostly Differentiation, Polynomials, Vectors. The full list is in the table above.
Do I need an account to open 9709/31 Oct/Nov 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.