9709 Pure Mathematics 1 Oct/Nov 2024 Paper 11

20 questions and parts, 75 marks in total. Marks come from the published mark scheme.

1. Question 1

   4 marks · 4/75

   This tests selection of appropriate terms in a binomial expansion and extraction of their coefficients.

   Question paper p.2 · Mark scheme p.6

2. Question 2

   4 marks · 8/75

   This tests using differentiation and the stationary-point condition to determine unknown constants in a curve equation.

   Question paper p.3 · Mark scheme p.6

3. Question 3

   5 marks · 13/75

   This tests solving a sector-area problem and combining arc lengths with straight-line lengths to obtain a perimeter.

   Question paper p.4 · Mark scheme p.7

4. Question 4

   5 marks · 18/75

   This tests proving that a line and a quadratic curve have real intersections for every value of a parameter.

   Question paper p.5 · Mark scheme p.7

5. Question 5 (a)

   3 marks · 21/75

   This tests solving a gradient equation involving a square root.

   Question paper p.6 · Mark scheme p.8

6. Question 5 (b)

   4 marks · 25/75

   This tests finding a curve from its derivative by integration and using a point to determine the integration constant.

   Question paper p.6 · Mark scheme p.9

7. Question 6 (a)

   4 marks · 29/75

   Question paper p.7 · Mark scheme p.9

8. Question 6 (b)

   3 marks · 32/75

   Question paper p.7 · Mark scheme p.10

9. Question 7 (a)

   4 marks · 36/75

   This tests differentiating a fractional-power function and forming the tangent at a specified point.

   Question paper p.8 · Mark scheme p.10

10. Question 7 (b)

    4 marks · 40/75

    This tests finding an area under a curve by integrating a function written with a fractional power.

    Question paper p.9 · Mark scheme p.11

11. Question 8 (a)

    3 marks · 43/75

    This tests using trigonometric identities and the sign of cosine in the second quadrant to express an expression in terms of sine.

    Question paper p.10 · Mark scheme p.11

12. Question 8 (b)

    5 marks · 48/75

    Question paper p.11 · Mark scheme p.12

13. Question 9 (a)

    4 marks · 52/75

    This tests determining where a cubic function is decreasing from the sign of its derivative.

    Question paper p.12 · Mark scheme p.12

14. Question 9 (b)

    4 marks · 56/75

    This tests using equality of the curve's gradient and a line's gradient to find a tangent line.

    Question paper p.13 · Mark scheme p.13

15. Question 10 (a)

    3 marks · 59/75

    This tests linking selected terms of an arithmetic progression to the geometric-progression condition.

    Question paper p.14 · Mark scheme p.13

16. Question 10 (b)

    5 marks · 64/75

    This tests calculating and comparing the sums of a finite arithmetic progression and a finite geometric progression.

    Question paper p.15 · Mark scheme p.14

17. Question 11 (a)

    3 marks · 67/75

    Question paper p.16 · Mark scheme p.14

18. Question 11 (b)

    2 marks · 69/75

    Question paper p.16 · Mark scheme p.14

19. Question 11 (c)

    2 marks · 71/75

    This tests sketching a domain-restricted quadratic and justifying that the resulting function is one-to-one.

    Question paper p.17 · Mark scheme p.15

20. Question 11 (d)

    4 marks · 75/75

    This tests obtaining an inverse function and representing it as the reflection of the original restricted graph.

    Question paper p.17 · Mark scheme p.15