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2012

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

Mathematics 9709/31 Oct/Nov 2012 past paper

Cambridge A Level Mathematics (9709) Paper 3 (Pure Mathematics 3), variant 1, Oct/Nov 2012: 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
47
Open the question paperMark scheme

File names: 9709_w12_qp_31 ยท 9709_w12_ms_31

Grade thresholds for 9709/31 Oct/Nov 2012

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
47390019

Topics in this paper

Which syllabus chapters 9709/31 Oct/Nov 2012 tested, by marks. Each chapter links to every past-paper question on it.

ChapterQuestionsMarks
Trigonometry321
Vectors111
Iteration110
Complex Numbers110
Differential Equations18
Binomial17
Inequalities and Modulus14
Indices, Surds and Logs14

Questions in 9709/31 Oct/Nov 2012

  1. Question 1Inequalities and Modulus ยท 4 marks

    Find the set of values of x satisfying the inequality โ€ฆ

  2. Question 2Indices, Surds and Logs ยท 4 marks
  3. Question 3Trigonometry ยท 5 marks
  4. Question 4Binomial ยท 7 marks

    When (1 + ax)โˆ’2, where a is a positive constant, is expanded in ascending powers of x, the coef๏ฌcients of x and x3 are equal. (i) Find the exact value of a. (ii) When a has this value, obtain the โ€ฆ

  5. Question 5Trigonometry ยท 8 marks

    (i) By differentiating 1 cos x, show that if y = sec x then dy dx = sec x tan x. (ii) Show that 1 secx โˆ’tan x โ‰กsec x + tan x. (iii) Deduce that 1 (sec x โˆ’tan โ€ฆ

  6. Question 6Differential Equations ยท 8 marks

    The variables x and y are related by the differential equation x dy dx โ€ฆ

  7. Question 7Trigonometry ยท 8 marks

    The equation of a curve is ln(xy) โ€ฆ

  8. Question 8Iteration ยท 10 marks

    O y M x The diagram shows the curve โ€ฆ

  9. Question 9Complex Numbers ยท 10 marks

    The complex number 1 + (โˆš2)i is denoted by u. The polynomial โ€ฆ

  10. Question 10Vectors ยท 11 marks

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

Other Mathematics papers from Oct/Nov 2012

Questions students ask

Where can I get the 9709/31 Oct/Nov 2012 mark scheme?
Open the mark scheme above - it is the official Cambridge scheme for this exact paper (9709_w12_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 2012?
47 marks out of 75.
Which topics came up in 9709/31 Oct/Nov 2012?
Mostly Trigonometry, Vectors, Iteration. The full list is in the table above.
Do I need an account to open 9709/31 Oct/Nov 2012?
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.