9709 Pure Mathematics 1 May/June 2020 Paper 11

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

1. Question 1

   4 marks

   Using arithmetic-progression sum formulae to determine unknown first term and common difference.

   Question paper p.2 · Mark scheme p.6

2. Question 2

   5 marks

   Finding a specified coefficient by selecting appropriate terms from two binomial expansions.

   Question paper p.3 · Mark scheme p.6

3. Question 3 (a)

   3 marks

   Modelling repeated percentage growth as a geometric progression.

   Question paper p.4 · Mark scheme p.7

4. Question 3 (b)

   2 marks

   Using a geometric-series sum to calculate accumulated receipts over a fixed period.

   Question paper p.4 · Mark scheme p.7

5. Question 4 (a)

   2 marks

   Question paper p.5 · Mark scheme p.7

6. Question 4 (b)

   2 marks

   Interpreting a vertical translation from a tangency condition.

   Question paper p.5 · Mark scheme p.7

7. Question 4 (c)

   1 mark

   Question paper p.5 · Mark scheme p.7

8. Question 5 (a)

   3 marks

   Finding a tangency condition between a straight line and a rectangular hyperbola using a repeated-root discriminant.

   Question paper p.6 · Mark scheme p.8

9. Question 5 (b)

   3 marks

   Using the discriminant to determine when a line meets a curve at two distinct real points.

   Question paper p.6 · Mark scheme p.8

10. Question 6 (a)

    4 marks

    Solving for constants from a function composition and an inverse-function condition.

    Question paper p.7 · Mark scheme p.9

11. Question 6 (b)

    2 marks

    Composing two linear functions and simplifying the result.

    Question paper p.7 · Mark scheme p.9

12. Question 7 (a)

    3 marks

    Question paper p.8 · Mark scheme p.10

13. Question 7 (b)

    3 marks

    Solving a trigonometric equation on a complete interval after applying a proven identity.

    Question paper p.9 · Mark scheme p.10

14. Question 8

    6 marks

    Combining circular-arc geometry, right-triangle trigonometry, and perimeter calculation.

    Question paper p.10 · Mark scheme p.10

15. Question 9 (a)

    4 marks

    Differentiating a composite polynomial and then finding its second derivative.

    Question paper p.12 · Mark scheme p.11

16. Question 9 (b)

    3 marks

    Locating stationary points from the first derivative.

    Question paper p.13 · Mark scheme p.11

17. Question 9 (c)

    2 marks

    Classifying stationary points with the second-derivative test.

    Question paper p.13 · Mark scheme p.11

18. Question 10 (a)

    4 marks

    Constructing the equation of a circle when the endpoints of a diameter are known.

    Question paper p.14 · Mark scheme p.12

19. Question 10 (b)

    4 marks

    Finding a tangent to a circle using the perpendicular-radius property.

    Question paper p.15 · Mark scheme p.12

20. Question 10 (c)

    3 marks

    Reflecting a circle in its tangent line.

    Question paper p.15 · Mark scheme p.12

21. Question 11 (a)

    6 marks

    Finding curve intersections and a point whose tangent has a prescribed parallel direction.

    Question paper p.16 · Mark scheme p.13

22. Question 11 (b)

    6 marks

    Finding a volume of revolution for a region between two graphs.

    Question paper p.17 · Mark scheme p.13