# WMA13 Pure Mathematics 3 (P3) Oct/Nov 2025 Paper 01

Pearson Edexcel International A Level WMA13 Pure Mathematics 3 (P3) past paper 01, Oct/Nov 2025. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma13/2025-oct-nov-paper-01/
- PDF: https://mathvsarham.com/papers/wma13/WMA13_oct-nov_2025_paper_01_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International A Level
- Subject: WMA13 Pure Mathematics 3 (P3) (https://mathvsarham.com/past-papers/wma13/)
- Session: Oct/Nov 2025
- Paper: 01
- Component code: WMA13/01
- Time allowed: 90 minutes
- Total marks: 75
- Pages: 32

## Question paper text

Extracted automatically from the PDF; diagrams are missing and notation may be imperfect.

Question 1
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
The functions f and g are defined by
[Diagram or table: see page 2 of the paper]
(a) State the range of f [1]
(b) Find g^–1 [3]
(c) Find fg(0) [2]
(d) Find the exact value of a for which
[Diagram or table: see page 2 of the paper]
[3]

Question 2
[Diagram or table: see page 6 of the paper]
y  ( (x)
[Diagram or table: see page 6 of the paper]
Figure 1 shows a sketch of part of the curve with equation y = f (x) where
[Diagram or table: see page 6 of the paper]
(a) Show that f (x) = 0 has a root α in the interval [1, 2] [2]
(b) Show that the equation f (x) = 0 can be written in the form
[Diagram or table: see page 6 of the paper]
[2]
Using the iteration formula
[Diagram or table: see page 6 of the paper]
find, to 4 decimal places,
(c)(i) the value of x_3
(ii) the value of α [3]

Question 3
The share price, £V, of a company is being monitored.
A graph is drawn of log_10 V against t, where t is the number of years after monitoring began.
The graph is a straight line passing through the points (0, 2) and (5, 2.25)
Using this information,
(a) find an equation for the line in the form
[Diagram or table: see page 10 of the paper]
where m and c are constants. [2]
(b) Write the answer to part (a) in the form
[Diagram or table: see page 10 of the paper]
where a and b are constants to be found.
Give the exact value of a and the value of b to 3 significant figures. [3]
When t = T, the rate of increase in the share price of the company was £50 per year.
(c) Find the value of T, giving your answer to the nearest integer.
[Diagram or table: see page 10 of the paper]
[4]

Question 4
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
(a) f (x) = 3 sin 2x – 3 cos 2x
Express f (x) in the form R sin (2x – α) , where R and α are constants,
[Diagram or table: see page 14 of the paper]
Give the exact value of R and the exact value of α. [3]
[Diagram or table: see page 14 of the paper]
(b) g(x)  x > 0
[Diagram or table: see page 14 of the paper]
Using the answer to part (a),
(i) write down the exact minimum value of g(x) ,
(ii) find the smallest value of x for which this minimum value occurs.
You must make your method clear. [3]

Question 5
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
The number of squirrels in a forest is being studied.
The number of squirrels, N, in the forest, t years after the start of the study, is modelled by the equation
[Diagram or table: see page 16 of the paper]
(a) Find the number of squirrels in the forest at the start of the study. [1]
(b) Find dN/dt [2]
The number of squirrels in the forest is at a maximum when t = T
Using the answer to part (b),
(c) show that e^0.2^T = A , where A is a constant to be found. [2]
(d) Hence find the maximum number of squirrels in the forest.
Show your working and give your answer to the nearest whole number. [3]

Question 6
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
(i) Given y = ln (2x^2 + 5) find dy/dx [2]
(ii) A curve C has equation y = f (x) where
[Diagram or table: see page 20 of the paper]
where k is a positive integer, k > 1
Given that
[Diagram or table: see page 20 of the paper]
find the greatest possible value of k [5]

Question 7
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
A curve C has equation
[Diagram or table: see page 22 of the paper]
where k is a constant.
Given that C has two distinct turning points, find the range of possible values of k. [7]

Question 8
[Diagram or table: see page 26 of the paper]
Figure 2 shows a sketch of the graph C_1 with equation
[Diagram or table: see page 26 of the paper]
and a sketch of the graph C_2 with equation
[Diagram or table: see page 26 of the paper]
where a and b are constants.
Graphs C_1 and C_2 intersect at point P, point Q and point R, as shown in Figure 2.
Given that P has coordinates (–2, 25)
(a) show that
[Diagram or table: see page 26 of the paper]
[2]
Given also that R has coordinates (2, 9)
(b) find the value of a and the value of b [3]
Using the answer to part (b),
(c) state the coordinates of the vertex of C_2 [2]
(d) Find, using algebra, the coordinates of Q. Show each stage of your working.
[Diagram or table: see page 26 of the paper]
[6]

Question 9
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
(a) Express
[Diagram or table: see page 30 of the paper]
in terms of sin 2θ and cos 2θ only. [3]
(b) Hence show that the equation
[Diagram or table: see page 30 of the paper]
can be written in the form
[Diagram or table: see page 30 of the paper]
[3]
(c) Hence solve, for 0 < x < 90° , the equation
[Diagram or table: see page 30 of the paper]
giving your answers to one decimal place. [3]