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2011

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

Mathematics 9709/31 Oct/Nov 2011 past paper

Cambridge A Level Mathematics (9709) Paper 3 (Pure Mathematics 3), variant 1, Oct/Nov 2011: 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
58
Open the question paperMark scheme

File names: 9709_w11_qp_31 ยท 9709_w11_ms_31

Grade thresholds for 9709/31 Oct/Nov 2011

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
58530024

Topics in this paper

Which syllabus chapters 9709/31 Oct/Nov 2011 tested, by marks. Each chapter links to every past-paper question on it.

ChapterQuestionsMarks
Trigonometry217
Indices, Surds and Logs214
Complex Numbers110
Iteration18
Vectors18
Differential Equations17
Polynomials16
Differentiation15

Questions in 9709/31 Oct/Nov 2011

  1. Question 1Indices, Surds and Logs ยท 4 marks

    Using the substitution u = ex, or otherwise, solve the equation ex โ€ฆ

  2. Question 2Differentiation ยท 5 marks

    The parametric equations of a curve are โ€ฆ

  3. Question 3Polynomials ยท 6 marks

    The polynomial x4 + 3x3 + ax + 3 is denoted by p(x). It is given that p(x) is divisible by โ€ฆ

  4. Question 4Differential Equations ยท 7 marks

    The variables x and ฮธ are related by the differential equation sin 2ฮธ dx โ€ฆ

  5. Question 5Iteration ยท 8 marks

    (i) By sketching a suitable pair of graphs, show that the equation secx โ€ฆ

  6. Question 6Trigonometry ยท 8 marks

    (i) Express cos x + 3 sin x in the form R cos(x โˆ’ฮฑ), where โ€ฆ

  7. Question 7Vectors ยท 8 marks

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

  8. Question 8Trigonometry ยท 9 marks
  9. Question 9Indices, Surds and Logs ยท 10 marks

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

  10. Question 10Complex Numbers ยท 10 marks

    (a) Showing your working, ๏ฌnd the two square roots of the complex number 1 โˆ’(2โˆš6)i. Give your answers in the form x + iy, where x and y are exact. (b) On a sketch of an Argand diagram, shade the โ€ฆ

Other Mathematics papers from Oct/Nov 2011

Questions students ask

Where can I get the 9709/31 Oct/Nov 2011 mark scheme?
Open the mark scheme above - it is the official Cambridge scheme for this exact paper (9709_w11_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 2011?
58 marks out of 75.
Which topics came up in 9709/31 Oct/Nov 2011?
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 2011?
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.