9709 Pure Mathematics 1 May/June 2020 Paper 12

26 questions and parts. Marks come from the published mark scheme.

1. Question 1 (a)

   2 marks

   Question paper p.2 · Mark scheme p.6

2. Question 1 (b)

   3 marks

   Question paper p.2 · Mark scheme p.6

3. Question 2 (a)

   3 marks

   This assesses converting a trigonometric equation into a quadratic involving sine.

   Question paper p.3 · Mark scheme p.6

4. Question 2 (b)

   2 marks

   This assesses solving a trigonometric quadratic and selecting an angle in a specified interval.

   Question paper p.3 · Mark scheme p.6

5. Question 3 (a)

   2 marks

   This assesses applying the sphere volume formula when volume changes at a constant rate.

   Question paper p.4 · Mark scheme p.7

6. Question 3 (b)

   3 marks

   This assesses using related rates for the volume and radius of a sphere.

   Question paper p.4 · Mark scheme p.7

7. Question 4

   5 marks

   This assesses determining an arithmetic progression from its general term and using its sum formula.

   Question paper p.5 · Mark scheme p.7

8. Question 5 (a)

   4 marks

   This assesses composing a linear function and finding its inverse.

   Question paper p.6 · Mark scheme p.8

9. Question 5 (b)

   2 marks

   Question paper p.6 · Mark scheme p.8

10. Question 6 (a)

    3 marks

    This assesses using the repeated-root condition for a line tangent to a quadratic curve.

    Question paper p.7 · Mark scheme p.9

11. Question 6 (b)

    3 marks

    This assesses rewriting a quadratic by completing the square and identifying its vertex.

    Question paper p.7 · Mark scheme p.9

12. Question 7 (a)

    2 marks

    This assesses applying the cosine rule in a triangle formed from radii and a midpoint.

    Question paper p.8 · Mark scheme p.10

13. Question 7 (b)

    2 marks

    Question paper p.9 · Mark scheme p.10

14. Question 7 (c)

    3 marks

    This assesses finding the area of a region formed by removing a triangle from a sector.

    Question paper p.9 · Mark scheme p.10

15. Question 8 (a)

    5 marks

    This assesses finding a volume of revolution about the y-axis using washers.

    Question paper p.10 · Mark scheme p.11

16. Question 8 (b)

    3 marks

    This assesses using differentiation and a parallel-gradient condition to locate a point on a curve.

    Question paper p.11 · Mark scheme p.11

17. Question 9 (a)

    3 marks

    This assesses finding the ranges of a restricted sinusoidal function and its scalar multiple.

    Question paper p.12 · Mark scheme p.12

18. Question 9 (b)

    2 marks

    Question paper p.12 · Mark scheme p.12

19. Question 9 (c)

    3 marks

    This assesses describing combined vertical and horizontal transformations of a function graph.

    Question paper p.12 · Mark scheme p.12

20. Question 10 (a)

    4 marks

    This assesses first and second differentiation of a function containing a cubic composite term.

    Question paper p.13 · Mark scheme p.13

21. Question 10 (b)

    3 marks

    This assesses finding stationary points by solving the derivative equation.

    Question paper p.13 · Mark scheme p.13

22. Question 10 (c)

    2 marks

    This assesses classifying stationary points using the second derivative.

    Question paper p.13 · Mark scheme p.13

23. Question 11 (a)

    3 marks

    This assesses extracting the centre and radius of a circle from its expanded equation.

    Question paper p.14 · Mark scheme p.14

24. Question 11 (b)

    3 marks

    This assesses finding a circle tangent by using the perpendicular relationship between a radius and tangent.

    Question paper p.14 · Mark scheme p.14

25. Question 11 (c)

    2 marks

    This assesses locating the second endpoint of a horizontal chord using circle symmetry.

    Question paper p.15 · Mark scheme p.14

26. Question 11 (d)

    3 marks

    This assesses finding the intersection of two tangents to a circle.

    Question paper p.15 · Mark scheme p.15