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

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

- Page: https://mathvsarham.com/past-papers/wma13/2025-may-june-paper-01a/
- PDF: https://mathvsarham.com/papers/wma13/WMA13_may-june_2025_paper_01A_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: 01A
- Component code: WMA13/01A
- 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
The point P(6, –2) lies on the continuous curve with equation y = f (x), x ∈ .
Find the point to which P is mapped when the curve with equation y = f (x) is transformed to the curve with equation
(a) y = 2f (3x) [2]
(b) y = f (x – 2) + 8 [2]
(c) y = f^–1(x) [1]

Question 2
[Diagram or table: see page 4 of the paper]
The equation f (x) = 0 has a single root α.
(a) Show that α lies in the interval [1, 2] [2]
(b) Show that the equation f (x) = 0 can be written as
[Diagram or table: see page 4 of the paper]
where k is a constant to be found. [2]
(c) Using the iteration formula
[Diagram or table: see page 4 of the paper]
with x_1 = 1 and the value of k found in part (b), find, to 4 decimal places,
(i) the value of x_3
(ii) the value of α. [3]

Question 3
The curve C has equation
[Diagram or table: see page 6 of the paper]
(a) Find dy/dx in terms of y, giving the answer in simplest form. [4]
A point P lies on C.
Given that
• the gradient of the tangent to C at P is 1/3
• the point P lies above the x‑axis
(b) find the coordinates of P.
(Solutions relying entirely on calculator technology are not acceptable.) [4]

Question 4
[Diagram or table: see page 10 of the paper]
Figure 1 shows a sketch of part of the curve C with equation y = g (x) where
[Diagram or table: see page 10 of the paper]
(a)(i) find the values of the constants A, B and C
(ii) show that D = 0 [4]
The finite region R, shown shaded in Figure 1, is bounded by C, the x‑axis and the lines with equations x = 2 and x = 3
(b) Find the exact area of region R using algebraic integration. Give the answer in the form α + ln β where α and β are constants to be found. [4]

Question 5
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 14 of the paper]
The point A with x coordinate π/3 lies on C.
(a) Use algebraic differentiation to find the gradient of the tangent to C at A. Give the answer in simplest form. [3]
(b) Express 5 cos 2x – 12 sin 2x in the form
[Diagram or table: see page 14 of the paper]
where R > 0 and 0 < α < π/2
Find the exact value of R and find the value of α to 3 decimal places. [3]
A point P lies on C.
Given that the gradient of the tangent to C at P is 6
(c) find the greatest possible value for the x coordinate of P. Give the answer to 2 decimal places. [4]

Question 6
[Diagram or table: see page 18 of the paper]
Figure 2 shows a sketch of the curve with equation y = f (x) where
[Diagram or table: see page 18 of the paper]
(a) Show that
[Diagram or table: see page 18 of the paper]
where P, Q and n are constants to be found. [4]
(b) Hence find
(i) the x coordinates of the stationary points on the curve with equation y = f (x),
(ii) the range of the function g defined by
[Diagram or table: see page 18 of the paper]
(Solutions relying entirely on calculator technology are not acceptable.) [4]

Question 7
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
(a) Write sin 4θ in the form
[Diagram or table: see page 22 of the paper]
where P, Q and n are constants to be found. [3]
(b) Use the result from part (a) to show that, for x ≠ kπ/2 where k ∈ , the equation
[Diagram or table: see page 22 of the paper]
can be written in the form
[Diagram or table: see page 22 of the paper]
[3]
(c) Use the result from part (b) to solve, for 0 < x < π, x ≠ π/2 , the equation
[Diagram or table: see page 22 of the paper]
giving the answers in radians to 3 significant figures. [4]

Question 8
The functions f and g are defined by
[Diagram or table: see page 26 of the paper]
where a is a positive constant.
(a) Find the exact value of fg (2a) [2]
(b) Find f^–1 [3]
[Diagram or table: see page 26 of the paper]
Figure 3 shows a sketch of the curve with equation y = g (x)
Indicate clearly on your sketch the equation of the horizontal asymptote. [3]
Given that the larger solution is 8
(d)(i) find the value of a,
(ii) find the value of the smaller solution. [4]

Question 9
The amount of an antibiotic, x milligrams, in the bloodstream of a horse, t hours after the antibiotic had been administered, is given by the formula
[Diagram or table: see page 30 of the paper]
where D milligrams is the dose of the antibiotic given to the horse.
A dose of 30 mg of the antibiotic is given to the horse.
(a) Find the amount of the antibiotic in the bloodstream of the horse 8 hours after the dose is given. Give your answer in mg to 2 decimal places. [2]
A second dose of 20 mg is given to the horse 8 hours after the first dose.
(b) Show that the amount of the antibiotic in the bloodstream of the horse, 2 hours after the second dose is given, is 17.5 mg to one decimal place. [1]
No more doses of the antibiotic are given. At time T hours after the second dose is given, the amount of the antibiotic in the bloodstream is 10 mg.
(c) Find the value of T, giving your answer to 2 decimal places.
(Solutions relying entirely on calculator technology are not acceptable.) [4]