9709 Pure Mathematics 3 Oct/Nov 2024 Paper 32

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

1. Question 1

   4 marks · 4/75

   This assesses the use of the binomial expansion for a square root with a fractional power.

   Question paper p.2 · Mark scheme p.6

2. Question 2 (a)

   2 marks · 6/75

   This assesses the use of sketches and intersections to establish the number of roots of a trigonometric equation on a stated interval.

   Question paper p.3 · Mark scheme p.7

3. Question 2 (b)

   1 mark · 7/75

   This assesses the connection between a convergent fixed-point iteration and the equation whose root it approaches.

   Question paper p.3 · Mark scheme p.7

4. Question 3

   5 marks · 12/75

   This assesses finding complex square roots by comparing Cartesian components and solving the resulting algebraic equation.

   Question paper p.4 · Mark scheme p.8

5. Question 4

   3 marks · 15/75

   This assesses solving an exponential equation by applying index laws and logarithms.

   Question paper p.5 · Mark scheme p.9

6. Question 5 (a)

   2 marks · 17/75

   This assesses the argument rules for powers and quotients of complex numbers in polar form.

   Question paper p.6 · Mark scheme p.9

7. Question 5 (b)

   2 marks · 19/75

   This assesses the geometric effect of complex conjugation on an Argand diagram and on an argument.

   Question paper p.6 · Mark scheme p.10

8. Question 6

   4 marks · 23/75

   This assesses linearising an exponential model with logarithms and recovering its constants from two points.

   Question paper p.7 · Mark scheme p.10

9. Question 7 (a)

   3 marks · 26/75

   This assesses the use of the double-angle identity for tangent to transform a trigonometric equation into a polynomial in tan x.

   Question paper p.8 · Mark scheme p.12

10. Question 7 (b)

    3 marks · 29/75

    This assesses solving a transformed tangent equation and selecting all exact angles in a specified interval.

    Question paper p.9 · Mark scheme p.12

11. Question 8 (a)

    4 marks · 33/75

    This assesses differentiation of parametric equations and formation of dy/dx.

    Question paper p.10 · Mark scheme p.13

12. Question 8 (b)

    4 marks · 37/75

    This assesses finding a normal to a parametrically defined curve at a specified parameter value.

    Question paper p.11 · Mark scheme p.13

13. Question 9 (a)

    2 marks · 39/75

    This assesses vector manipulation in a three-dimensional trapezium.

    Question paper p.12 · Mark scheme p.14

14. Question 9 (b)

    5 marks · 44/75

    This assesses finding the intersection of two three-dimensional lines representing the diagonals of a trapezium.

    Question paper p.12 · Mark scheme p.14

15. Question 9 (c)

    4 marks · 48/75

    Question paper p.13 · Mark scheme p.15

16. Question 10 (a)

    3 marks · 51/75

    This assesses related rates involving the volume of a sphere and a net flow rate.

    Question paper p.14 · Mark scheme p.16

17. Question 10 (b)

    3 marks · 54/75

    This assesses polynomial division when the divisor is a linear expression in the radius.

    Question paper p.14 · Mark scheme p.16

18. Question 10 (c)

    6 marks · 60/75

    This assesses separation of variables, integration using an algebraic division result, and application of an initial condition.

    Question paper p.15 · Mark scheme p.17

19. Question 10 (d)

    1 mark · 61/75

    This assesses evaluation of the radius-time formula at a specified radius.

    Question paper p.15 · Mark scheme p.17

20. Question 11 (a)

    5 marks · 66/75

    This assesses quotient-rule differentiation and the determination of a stationary point exactly.

    Question paper p.16 · Mark scheme p.18

21. Question 11 (b)

    9 marks · 75/75

    This assesses integration of a rational exponential function by substitution and partial fractions.

    Question paper p.17 · Mark scheme p.20