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2019

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

Mathematics 9709/31 May/June 2019 past paper

Cambridge A Level Mathematics (9709) Paper 3 (Pure Mathematics 3), variant 1, May/June 2019: 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
56
Open the question paperMark scheme

File names: 9709_s19_qp_31 ยท 9709_s19_ms_31

Grade thresholds for 9709/31 May/June 2019

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
5647393021

Topics in this paper

Which syllabus chapters 9709/31 May/June 2019 tested, by marks. Each chapter links to every past-paper question on it.

ChapterQuestionsMarks
Trigonometry214
Complex Numbers113
Polynomials110
Vectors110
Iteration19
Differential Equations18
Indices, Surds and Logs14
Differentiation14
Integration13

Questions in 9709/31 May/June 2019

  1. Question 1Integration ยท 3 marks

    Use the trapezium rule with 3 intervals to estimate the value of โ€ฆ

  2. Question 2Indices, Surds and Logs ยท 4 marks

    Showing all necessary working, solve the equation ln2x โ€ฆ

  3. Question 3Differentiation ยท 4 marks

    Find the gradient of the curve x3 + 3xy2 โ€ฆ

  4. Question 4Trigonometry ยท 6 marks

    By ๏ฌrst expressing the equation cot 1 โˆ’cot1 โ€ฆ

  5. Question 5Differential Equations ยท 8 marks

    (i) Di๏ฌ€erentiate 1 sin21 with respect to 1. (ii) The variables x and 1 satisfy the di๏ฌ€erential equation x tan 1 dx d1 + cosec21 = 0, for โ€ฆ

  6. Question 6Trigonometry ยท 8 marks

    (i) By ๏ฌrst expanding sin2x + x, show that sin โ€ฆ

  7. Question 7Iteration ยท 9 marks

    x y O 4 a The diagram shows the curves โ€ฆ

  8. Question 8Polynomials ยท 10 marks
  9. Question 9Vectors ยท 10 marks
  10. Question 10Complex Numbers ยท 13 marks

    Throughout this question the use of a calculator is not permitted. The complex number โ€ฆ

Other Mathematics papers from May/June 2019

Questions students ask

Where can I get the 9709/31 May/June 2019 mark scheme?
Open the mark scheme above - it is the official Cambridge scheme for this exact paper (9709_s19_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 2019?
56 marks out of 75, a C needed 39.
Which topics came up in 9709/31 May/June 2019?
Mostly Trigonometry, Complex Numbers, Polynomials. The full list is in the table above.
Do I need an account to open 9709/31 May/June 2019?
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.