9709 Pure Mathematics 1 May/June 2020 Paper 13

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

1. Question 1

   4 marks

   Finding the parameter values for which a straight line and a quadratic curve meet at two different points.

   Question paper p.2 · Mark scheme p.6

2. Question 2

   4 marks

   Recovering a curve equation from its derivative and one point on the curve.

   Question paper p.3 · Mark scheme p.6

3. Question 3 (a)

   1 mark

   Question paper p.4 · Mark scheme p.7

4. Question 3 (b)

   1 mark

   Question paper p.4 · Mark scheme p.7

5. Question 3 (c)

   2 marks

   Question paper p.4 · Mark scheme p.7

6. Question 4 (a)

   1 mark

   Question paper p.5 · Mark scheme p.7

7. Question 4 (b)

   3 marks

   Applying a binomial expansion after substituting a polynomial expression and collecting powers.

   Question paper p.5 · Mark scheme p.7

8. Question 5

   6 marks

   Finding a cord length involving tangents to a circle and a major circular arc.

   Question paper p.6 · Mark scheme p.8

9. Question 6 (a)

   4 marks

   Using related rates and the chain rule for a point moving along a curve.

   Question paper p.8 · Mark scheme p.8

10. Question 6 (b)

    3 marks

    Finding a position from a specified related rate.

    Question paper p.9 · Mark scheme p.9

11. Question 7 (a)

    4 marks

    Question paper p.10 · Mark scheme p.9

12. Question 7 (b)

    4 marks

    Solving a trigonometric equation by using an identity established in the preceding part.

    Question paper p.11 · Mark scheme p.10

13. Question 8 (a)

    3 marks

    Question paper p.12 · Mark scheme p.10

14. Question 8 (b)(i)

    3 marks

    Finding the common difference of an arithmetic progression in terms of sin θ.

    Question paper p.13 · Mark scheme p.10

15. Question 8 (b)(ii)

    3 marks

    Calculating a finite arithmetic-series sum after assigning a particular angle.

    Question paper p.13 · Mark scheme p.11

16. Question 9 (a)

    2 marks

    Question paper p.14 · Mark scheme p.11

17. Question 9 (b)

    1 mark

    Question paper p.14 · Mark scheme p.11

18. Question 9 (c)

    3 marks

    Finding the inverse of a restricted quadratic function and its domain.

    Question paper p.15 · Mark scheme p.11

19. Question 9 (d)

    3 marks

    Finding the composition gf and determining its range from restricted domains.

    Question paper p.15 · Mark scheme p.12

20. Question 10 (a)

    4 marks

    Deriving the equation of a perpendicular bisector from two Cartesian points.

    Question paper p.16 · Mark scheme p.12

21. Question 10 (b)

    5 marks

    Finding a circle when its chord endpoints and the line containing its centre are known.

    Question paper p.17 · Mark scheme p.12

22. Question 11 (a)

    4 marks

    Using stationary-point information to relate the parameters in a cubic curve.

    Question paper p.18 · Mark scheme p.13

23. Question 11 (b)

    7 marks

    Finding the area between a cubic curve and the straight line joining the origin to its maximum point.

    Question paper p.19 · Mark scheme p.14