# WMA13 Pure Mathematics 3 (P3) May/June 2025 Paper 01

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

- Page: https://mathvsarham.com/past-papers/wma13/2025-may-june-paper-01/
- PDF: https://mathvsarham.com/papers/wma13/WMA13_may-june_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: May/June 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) Find the value of gf (1) [2]
(b) Find the range of f [2]
(c) Find f^–1(x) [2]
(d) Solve f^–1(x) = f(x) [2]

Question 2
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
[Diagram or table: see page 6 of the paper]
(a) Express f (x) in the form R cos(x + α) where R and α are constants, R > 0
and 0 < α < π/2
Give the exact value of R and give the value of α, in radians, to 3 decimal places. [3]
[Diagram or table: see page 6 of the paper]
(b) Using the answer to part (a), find
(i) the minimum value of g (x), giving your answer as a fully simplified fraction,
(ii) the smallest positive value of x for which this minimum value occurs, giving your answer to 3 decimal places. [4]

Question 3
[Diagram or table: see page 8 of the paper]
Figure 1 shows a linear relationship between log_10 y and log_10 x
The line passes through the points (–3.5, 0) and (0, –2) as shown.
(a) Find an equation linking log_10 y with log_10 x [2]
(b) Hence, or otherwise, express y in the form px^q where p and q are rational constants. [3]

Question 4
The function f is defined by
[Diagram or table: see page 10 of the paper]
(a) Show that
[Diagram or table: see page 10 of the paper]
[3]
(b) Hence find fʹ(x) giving your answer in simplest form. [2]

Question 5
Find
(i)  ∫ [2]
(ii) ^2_3/2
[2]

Question 6
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
The temperature, θ°C, of a computer processor, t minutes after the computer is switched off, is modelled by the equation
[Diagram or table: see page 14 of the paper]
where A and k are positive constants.
Given that the temperature of the processor was 75°C when the computer was switched off,
(a) find the value of A. [2]
Given also that it takes 5 minutes for the temperature of the processor to decrease from 75°C to 25°C,
(b) find the value of k, giving your answer to 3 significant figures. [3]
At time T minutes, the temperature of the processor is decreasing at a rate of 9°C per minute.
(c) Find the value of T according to the model, giving your answer to 2 decimal places. [3]

Question 7
A continuous curve has equation
[Diagram or table: see page 18 of the paper]
The curve has a stationary point at the point P.
(a) Show, using calculus, that the x coordinate of P is a solution of the equation
[Diagram or table: see page 18 of the paper]
[4]
Using the iteration formula
[Diagram or table: see page 18 of the paper]
(b) find the value of
(i) x_2
(ii) x_4
giving your answers to 4 decimal places. [3]
(c) Using a suitable interval and a suitable function which should be stated, show that the x coordinate of P is 0.430 correct to 3 decimal places. [2]

Question 8
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
(a) Prove that
[Diagram or table: see page 22 of the paper]
[3]
(b) Hence solve, for 0 < θ < π/2
[Diagram or table: see page 22 of the paper]
giving your answers to 2 decimal places. [5]

Question 9
[Diagram or table: see page 26 of the paper]
Figure 2 shows a sketch of the curve C with equation
[Diagram or table: see page 26 of the paper]
The curve intersects the y-axis at the points A and B as shown.
(a) Find the exact value of the y coordinate of
• point A
• point B [3]
(b) Show that
[Diagram or table: see page 26 of the paper]
where p and q are integers to be found. [4]
The normal to C at A and the tangent to C at B intersect at the point D.
Using
• the answer to part (b)
• the sketch of curve C in Figure 2
(c) find, in simplest form, the exact x coordinate of D. [4]

Question 10
[Diagram or table: see page 30 of the paper]
Figure 3 shows a sketch of part of the graph with equation y = f (x), where
and k is a positive constant.
The graph
• cuts the y-axis at the point A
• has a vertex at the point P
(a) Find, in simplest form in terms of k,
(i) the y coordinate of A
(ii) the coordinates of P [3]
(b) Find, in terms of k, the range of values of x which satisfy [3]
Given that the line with equation y = 3x + 1 intersects the graph of y = f (x) at 2 distinct points,
(c) find the range of values of k. [4]