# WMA13 Pure Mathematics 3 (P3) May/June 2026 Paper 01

Pearson Edexcel International A Level WMA13 Pure Mathematics 3 (P3) past paper 01, May/June 2026. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma13/2026-may-june-paper-01/
- PDF: https://mathvsarham.com/papers/wma13/WMA13_may-june_2026_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 2026
- Paper: 01
- Component code: WMA13/01
- Time allowed: 90 minutes
- Total marks: 75
- Pages: 28

## Question paper text

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

Question 1
A curve has equation y = f (x) where
[Diagram or table: see page 2 of the paper]
(a) Find f ′(x) giving the answer in simplest form. [3]
The equation f ′(x) = 0 has a single root, α
(b) Show that α lies in the interval [0, 1] [2]
Given that the equation f ′(x) = 0 can be written as
[Diagram or table: see page 2 of the paper]
(c) use the iteration formula
[Diagram or table: see page 2 of the paper]
to find, to 4 decimal places,
(i) the value of x_3
(ii) the value of α [3]

Question 2
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 6 of the paper]
(a) State the range of f [1]
(b) Find g^–1 [3]
(c) Find gf (ln 7 ) [2]
(d) Find the value of a, a > 0, for which
[Diagram or table: see page 6 of the paper]
giving the answer in the form ln p where p is an irrational constant. [3]

Question 3
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
The curve C has equation y = f (x) where
[Diagram or table: see page 10 of the paper]
(a) Find f ′(x), giving the answer in the form
[Diagram or table: see page 10 of the paper]
where a, b and c are constants. [4]
(b) Hence find the coordinates of the turning point of C. [2]
The point P  5/ 2 , 10/ lies on C.
(c) Find the coordinates of the point to which P is mapped, when the curve with equation y = f (x) is transformed to the curve with equation y = f (2x) + 3 [2]

Question 4
In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
Using algebraic integration, find the exact value of
[Diagram or table: see page 12 of the paper]
[5]

Question 5
[Diagram or table: see page 14 of the paper]
The recycling of household waste in a particular town is being monitored.
The number of households in the town, H, recycling their household waste, t years after monitoring began, is modelled by the equation
[Diagram or table: see page 14 of the paper]
where a and b are constants.
The line in Figure 1 shows the linear relationship between t and log_10 H
The line passes through the points (0, 2.5) and (10, 3.25)
Using this information,
(a) find, to 3 significant figures, the value of a and the value of b [4]
(b) With reference to the model, interpret the value of the constant b [1]
(c) Find the value of dH/dt when t = 5 , giving the answer to 2 significant figures.
(Solutions relying entirely on calculator technology are not acceptable.) [2]

Question 6
The curve C has equation
[Diagram or table: see page 16 of the paper]
• the point P with y coordinate π/4 lies on C
• the tangent to C at P cuts the x-axis at the point Q
use calculus to find the x coordinate of Q [6]

Question 7
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
The selling price of a car is monitored over a 15-year period.
The selling price P_C of the car, in thousands of pounds, t years after monitoring began, is modelled by the equation
[Diagram or table: see page 18 of the paper]
Given that when t = T the selling price of the car is £15 000
(a) find, according to the model, the value of T. Give the answer to 2 decimal places. [3]
(b) Find the value of dP/dt^C when t = 5. Give the answer to 2 decimal places. [2]
The selling price of a van is monitored over the same 15-year period.
The selling price P_V of the van, in thousands of pounds, t years after monitoring began, is modelled by the equation
[Diagram or table: see page 18 of the paper]
where m is a constant.
[Diagram or table: see page 18 of the paper]
Given that P_V = 36 when t = 0
(c)(i) state the value of m
(ii) find the difference between the initial selling price of the car and the initial selling price of the van. [3]
When t = α, the selling price of the car is equal to the selling price of the van.
(d) Find, using algebra and showing your working, the value of α, giving the answer to 3 significant figures. [4]

Question 8
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
(a) Show that
[Diagram or table: see page 22 of the paper]
[2]
(b) Hence show that the equation
[Diagram or table: see page 22 of the paper]
can be written as
[Diagram or table: see page 22 of the paper]
where a, b and c are integers to be found. [3]
(c) Hence, solve for 0 < x < 180°, x ≠ (45n)°, n ∈ , the equation
[Diagram or table: see page 22 of the paper]
giving the answers to one decimal place. [4]

Question 9
[Diagram or table: see page 26 of the paper]
Solutions relying entirely on calculator technology are not acceptable.
(a) Find  /  2x  5  4e / dx
[2]
Figure 2 shows a sketch of part of the curve C_1 and part of the graph C_2 The curve C_1 has equation
[Diagram or table: see page 26 of the paper]
The graph C_2 has equation
where a and b are positive integers.
(b) State, in terms of a and/or b, the coordinates of the maximum point of C_2 [2]
Given that
• C_1 intersects C_2 at x = 3
• C_2 crosses the y-axis at (0, 9)
(c) find the value of a and the value of b [3]
The region R, shown shaded in Figure 2, is bounded by C_1, C_2 , the x-axis and the y-axis.
(d) Find the area of R, giving the answer to 3 significant figures. [4]