9709 Pure Mathematics 3 Oct/Nov 2024 Paper 33

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

1. Question 1 (a)

   2 marks · 2/75

   This assesses how to represent a fixed-modulus complex number with a restricted argument on an Argand diagram.

   Question paper p.2 · Mark scheme p.6

2. Question 1 (b)

   2 marks · 4/75

   This assesses how squaring a complex number changes its modulus and argument and how to display the resulting locus.

   Question paper p.2 · Mark scheme p.6

3. Question 2 (a)

   2 marks · 6/75

   This assesses the fixed-point justification for an iterative method.

   Question paper p.3 · Mark scheme p.7

4. Question 2 (b)

   3 marks · 9/75

   This assesses numerical root-finding by repeated fixed-point iteration.

   Question paper p.3 · Mark scheme p.8

5. Question 3 (a)

   3 marks · 12/75

   This assesses the linearisation of an exponential model using logarithms and the interpretation of a graph's gradient and intercept.

   Question paper p.4 · Mark scheme p.8

6. Question 3 (b)

   2 marks · 14/75

   This assesses the use of an exponential model to calculate a doubling time.

   Question paper p.4 · Mark scheme p.8

7. Question 4

   5 marks · 19/75

   Question paper p.5 · Mark scheme p.9

8. Question 5 (a)

   3 marks · 22/75

   Question paper p.6 · Mark scheme p.11

9. Question 5 (b)

   3 marks · 25/75

   Question paper p.7 · Mark scheme p.13

10. Question 6 (a)

    1 mark · 26/75

    This assesses reading the common point of two vector line equations.

    Question paper p.8 · Mark scheme p.13

11. Question 6 (b)

    3 marks · 29/75

    This assesses finding the acute angle between two lines from their direction vectors.

    Question paper p.8 · Mark scheme p.14

12. Question 6 (c)

    3 marks · 32/75

    This assesses finding the exact area of a triangle defined by points on two intersecting vector lines.

    Question paper p.9 · Mark scheme p.15

13. Question 7 (a)

    5 marks · 37/75

    This assesses differentiation of parametrically defined functions using the chain rule and a quotient of derivatives.

    Question paper p.10 · Mark scheme p.16

14. Question 7 (b)

    3 marks · 40/75

    This assesses finding a normal line to a parametric curve at a specified parameter value.

    Question paper p.11 · Mark scheme p.17

15. Question 8 (a)

    3 marks · 43/75

    This assesses decomposition of a rational function with two linear factors into partial fractions.

    Question paper p.12 · Mark scheme p.18

16. Question 8 (b)

    4 marks · 47/75

    This assesses obtaining a Maclaurin-style expansion by combining partial fractions with geometric-series expansions.

    Question paper p.13 · Mark scheme p.18

17. Question 8 (c)

    1 mark · 48/75

    This assesses identifying the common convergence interval for the power series used in a function expansion.

    Question paper p.13 · Mark scheme p.19

18. Question 9 (a)

    3 marks · 51/75

    This assesses polynomial division and identification of a quotient and remainder.

    Question paper p.14 · Mark scheme p.20

19. Question 9 (b)

    5 marks · 56/75

    Question paper p.15 · Mark scheme p.21

20. Question 10 (a)

    3 marks · 59/75

    This assesses forming a differential equation from volume flow rates and the chain rule.

    Question paper p.16 · Mark scheme p.22

21. Question 10 (b)

    5 marks · 64/75

    This assesses solving a first-order separable differential equation with an initial condition.

    Question paper p.17 · Mark scheme p.24

22. Question 11 (a)

    5 marks · 69/75

    This assesses locating a stationary minimum of a composite trigonometric function by differentiation.

    Question paper p.18 · Mark scheme p.25

23. Question 11 (b)

    6 marks · 75/75

    Question paper p.19 · Mark scheme p.26