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2021

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

Mathematics 9709/31 Oct/Nov 2021 past paper

Cambridge A Level Mathematics (9709) Paper 3 (Pure Mathematics 3), variant 1, Oct/Nov 2021: 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_w21_qp_31 ยท 9709_w21_ms_31

Grade thresholds for 9709/31 Oct/Nov 2021

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
5243352617

Topics in this paper

Which syllabus chapters 9709/31 Oct/Nov 2021 tested, by marks. Each chapter links to every past-paper question on it.

ChapterQuestionsMarks
Trigonometry322
Indices, Surds and Logs213
Complex Numbers112
Iteration110
Differentiation16
Integration16
Binomial16

Questions in 9709/31 Oct/Nov 2021

  1. Question 1Indices, Surds and Logs ยท 4 marks
  2. Question 2Trigonometry ยท 5 marks

    (a) Express 5 sin x โˆ’3 cos x in the form R sinx โˆ’!, where โ€ฆ

  3. Question 3Differentiation ยท 6 marks

    The curve with equation y = xe1โˆ’2x has one stationary point. (a) Find the coordinates of this point. (b) Determine whether the stationary point is a maximum or a minimum.

  4. Question 4Integration ยท 6 marks

    Using the substitution u = x, ๏ฌnd the exact value of โ€ฆ

  5. Question 5Trigonometry ยท 6 marks

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

  6. Question 6Binomial ยท 6 marks
  7. Question 7Indices, Surds and Logs ยท 9 marks

    (a) Given that y = lnln x, show that dy dx โ€ฆ

  8. Question 8Iteration ยท 10 marks

    The constant a is such that ร” 1 ln x x dx โ€ฆ

  9. Question 9Trigonometry ยท 11 marks

    Two lines l and m have equations โ€ฆ

  10. Question 10Complex Numbers ยท 12 marks

    The complex number 1 + 2i is denoted by u. The polynomial 2x3 + ax2 โ€ฆ

Other Mathematics papers from Oct/Nov 2021

Questions students ask

Where can I get the 9709/31 Oct/Nov 2021 mark scheme?
Open the mark scheme above - it is the official Cambridge scheme for this exact paper (9709_w21_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 2021?
52 marks out of 75, a C needed 35.
Which topics came up in 9709/31 Oct/Nov 2021?
Mostly Trigonometry, Indices, Surds and Logs, Complex Numbers. The full list is in the table above.
Do I need an account to open 9709/31 Oct/Nov 2021?
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.