9709 Pure Mathematics 1 Oct/Nov 2024 Paper 12

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

1. Question 1 (a)

   3 marks · 3/75

   Reading amplitude, period, and vertical displacement from the graph of a sinusoidal function.

   Question paper p.2 · Mark scheme p.6

2. Question 1 (b)(i)

   1 mark · 4/75

   Question paper p.2 · Mark scheme p.6

3. Question 1 (b)(ii)

   1 mark · 5/75

   Question paper p.2 · Mark scheme p.6

4. Question 2 (a)

   2 marks · 7/75

   Finding the sum of a specified number of terms in an arithmetic progression.

   Question paper p.3 · Mark scheme p.7

5. Question 2 (b)

   3 marks · 10/75

   Using arithmetic-series sums to form and solve a condition involving two different numbers of terms.

   Question paper p.3 · Mark scheme p.7

6. Question 3 (a)

   3 marks · 13/75

   Finding a simplified finite-difference expression for the gradient of a chord on a quadratic curve.

   Question paper p.4 · Mark scheme p.8

7. Question 3 (b)

   2 marks · 15/75

   Connecting the limiting gradient of a chord with the derivative or tangent gradient at a point.

   Question paper p.4 · Mark scheme p.8

8. Question 4 (a)

   2 marks · 17/75

   Selecting the constant term in a binomial expansion containing negative powers of x.

   Question paper p.5 · Mark scheme p.8

9. Question 4 (b)

   4 marks · 21/75

   Finding a constant term after multiplying a binomial expansion by a polynomial.

   Question paper p.5 · Mark scheme p.9

10. Question 5 (a)(i)

    1 mark · 22/75

    Evaluating a rational function at a permitted input.

    Question paper p.6 · Mark scheme p.9

11. Question 5 (a)(ii)

    2 marks · 24/75

    Sketching the inverse of a restricted rational function by reflection.

    Question paper p.6 · Mark scheme p.9

12. Question 5 (a)(iii)

    4 marks · 28/75

    Finding the algebraic rule and domain of the inverse of a restricted rational function.

    Question paper p.6 · Mark scheme p.10

13. Question 5 (b)

    3 marks · 31/75

    Solving an equation involving a composition of two functions and a rational function.

    Question paper p.7 · Mark scheme p.11

14. Question 6

    6 marks · 37/75

    Modelling the perimeter and area of a composite plate made from circular sectors and solving the resulting simultaneous conditions.

    Question paper p.8 · Mark scheme p.12

15. Question 7 (a)

    3 marks · 40/75

    Completing the square for a quadratic and reading the vertex from vertex form.

    Question paper p.10 · Mark scheme p.13

16. Question 7 (b)

    5 marks · 45/75

    Finding the area between a parabola and a line using their intersections and integration.

    Question paper p.10 · Mark scheme p.14

17. Question 8 (a)

    2 marks · 47/75

    Rewriting a circle equation by completing the square in both variables.

    Question paper p.12 · Mark scheme p.17

18. Question 8 (b)(i)

    3 marks · 50/75

    Finding the equation of a circle’s normal from the equation of its tangent at a known point.

    Question paper p.12 · Mark scheme p.17

19. Question 8 (b)(ii)

    5 marks · 55/75

    Using tangency information to determine the constants in a circle equation.

    Question paper p.12 · Mark scheme p.18

20. Question 9 (a)

    7 marks · 62/75

    Determining parameters and a second intersection point when a line and quadratic curve share a specified point.

    Question paper p.14 · Mark scheme p.21

21. Question 9 (b)

    3 marks · 65/75

    Using the discriminant to determine when a line and quadratic curve have no real intersections.

    Question paper p.15 · Mark scheme p.23

22. Question 10 (a)

    3 marks · 68/75

    Finding a normal to a curve from its derivative at a specified point.

    Question paper p.16 · Mark scheme p.23

23. Question 10 (b)

    4 marks · 72/75

    Recovering a function from its derivative and an initial point.

    Question paper p.16 · Mark scheme p.24

24. Question 10 (c)

    3 marks · 75/75

    Question paper p.17 · Mark scheme p.24