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2021

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

Mathematics 9709/33 May/June 2021 past paper

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

File names: 9709_s21_qp_33 ยท 9709_s21_ms_33

Grade thresholds for 9709/33 May/June 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
5649413224

Topics in this paper

Which syllabus chapters 9709/33 May/June 2021 tested, by marks. Each chapter links to every past-paper question on it.

ChapterQuestionsMarks
Trigonometry216
Indices, Surds and Logs215
Complex Numbers110
Vectors19
Differentiation17
Partial Fractions17
Iteration17
Binomial14

Questions in 9709/33 May/June 2021

  1. Question 1Binomial ยท 4 marks

    Expand 1 + 3x 2 3 in ascending powers of x, up to and including the term in x3, simplifying the coe๏ฌƒcients.

  2. Question 2Indices, Surds and Logs ยท 5 marks
  3. Question 3Differentiation ยท 7 marks

    The parametric equations of a curve are โ€ฆ

  4. Question 4Partial Fractions ยท 7 marks
  5. Question 5Trigonometry ยท 7 marks

    (a) By ๏ฌrst expanding tan21 + 21, show that the equation tan โ€ฆ

  6. Question 6Iteration ยท 7 marks

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

  7. Question 7Trigonometry ยท 9 marks

    x y O P M N For the curve shown in the diagram, the normal to the curve at the point P with coordinates x, y meets the x-axis at N. The point M is the foot of the perpendicular โ€ฆ

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

    x y O M The diagram shows the curve y = ln x x4 and its maximum point M. (a) Find the exact coordinates of M. (b) By using integration by parts, show that for all โ€ฆ

  9. Question 9Vectors ยท 9 marks

    The quadrilateral ABCD is a trapezium in which AB and DC are parallel. With respect to the origin O, the position vectors of A, B and C are given by โˆ’โˆ’ยฟ OA โ€ฆ

  10. Question 10Complex Numbers ยท 10 marks

    (a) Verify that โˆ’1 + 2i is a root of the equation โ€ฆ

Other Mathematics papers from May/June 2021

Questions students ask

Where can I get the 9709/33 May/June 2021 mark scheme?
Open the mark scheme above - it is the official Cambridge scheme for this exact paper (9709_s21_ms_33), and on a wide screen it sits beside the question you are reading.
What was the grade threshold for an A in 9709/33 May/June 2021?
56 marks out of 75, a C needed 41.
Which topics came up in 9709/33 May/June 2021?
Mostly Trigonometry, Indices, Surds and Logs, Complex Numbers. The full list is in the table above.
Do I need an account to open 9709/33 May/June 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.