Cambridge A Level · 9709 · Paper 3 · Pure Mathematics 3
Mathematics 9709/31 May/June 2010 past paper
Cambridge A Level Mathematics (9709) Paper 3 (Pure Mathematics 3), variant 1, May/June 2010: 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
- 63
File names: 9709_s10_qp_31 · 9709_s10_ms_31
Grade thresholds for 9709/31 May/June 2010
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.
| A | B | C | D | E |
|---|---|---|---|---|
| 63 | 57 | 0 | 0 | 29 |
Topics in this paper
Which syllabus chapters 9709/31 May/June 2010 tested, by marks. Each chapter links to every past-paper question on it.
| Chapter | Questions | Marks |
|---|---|---|
| Trigonometry | 4 | 30 |
| Vectors | 1 | 12 |
| Complex Numbers | 1 | 9 |
| Iteration | 1 | 8 |
| Linear Law | 1 | 6 |
| Differential Equations | 1 | 6 |
| Inequalities and Modulus | 1 | 4 |
Questions in 9709/31 May/June 2010
- Question 1
- Question 2
- Question 3
The variables x and y satisfy the equation xny = C, where n and C are constants. When …
- Question 4
(i) Using the expansions of cos(3x −x) and cos(3x + x), prove that 1 2(cos 2x −cos 4x) ≡sin 3x sin x. (ii) Hence show that …
- Question 5
- Question 6
A O B C r x rad The diagram shows a semicircle ACB with centre O and radius r. The angle BOC is x radians. The area of the shaded segment is a quarter of the area of the semicircle. …
- Question 7
The complex number 2 + 2i is denoted by u. (i) Find the modulus and argument of u. (ii) Sketch an Argand diagram showing the points representing the complex numbers 1, i and u. Shade the region whose points represent …
- Question 8
- Question 9
O P x y –1 1 The diagram shows the curve …
- Question 10
The lines l and m have vector equations …
Other Mathematics papers from May/June 2010
- 9709/11 Pure Mathematics 1
- 9709/12 Pure Mathematics 1
- 9709/13 Pure Mathematics 1
- 9709/32 Pure Mathematics 3
- 9709/33 Pure Mathematics 3
- 9709/41 Mechanics
- 9709/42 Mechanics
- 9709/43 Mechanics
- 9709/51 Mechanics 2 (old syllabus, not in topicals)
- 9709/52 Mechanics 2 (old syllabus, not in topicals)
- 9709/53 Mechanics 2 (old syllabus, not in topicals)
- 9709/61 Probability & Statistics 1 (Paper 6 until 2019)
- 9709/62 Probability & Statistics 1 (Paper 6 until 2019)
- 9709/63 Probability & Statistics 1 (Paper 6 until 2019)