WMA13 Pure Mathematics 3 (P3): May/June 2026 Paper 01
WMA13/01
Pearson Edexcel International A Level Pure Mathematics 3 (P3), May/June 2026.
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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.
Sit this paper like the real exam
1 h 30 min · 75 marks
Questions
Rebuilt from the WMA13/01 May/June 2026 paper so it reads well on any screen. Diagrams and tables are shown from the original.
- 1
A curve has equation y = f (x) where
Loading diagram…From 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
Loading diagram…From page 2 of the paper. (c)use the iteration formula
Loading diagram…From page 2 of the paper. to find, to 4 decimal places,
(i)the value of x3
(ii)the value of α[3]
- 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
Loading diagram…From 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
Loading diagram…From page 6 of the paper. giving the answer in the form ln p where p is an irrational constant.[3]
- 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
Loading diagram…From page 10 of the paper. (a)Find f ′(x), giving the answer in the form
Loading diagram…From 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]
- 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
Loading diagram…From page 12 of the paper. [5]
- 5Loading diagram…
From 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
Loading diagram…From page 14 of the paper. where a and b are constants.
The line in Figure 1 shows the linear relationship between t and log10 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 dHdt when t = 5 , giving the answer to 2 significant figures.
(Solutions relying entirely on calculator technology are not acceptable.)[2]
- 6
The curve C has equation
Loading diagram…From page 16 of the paper. • the point P with y coordinate π4 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]
- 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 PC of the car, in thousands of pounds, t years after monitoring began, is modelled by the equation
Loading diagram…From 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 dPdtC 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 PV of the van, in thousands of pounds, t years after monitoring began, is modelled by the equation
Loading diagram…From page 18 of the paper. where m is a constant.
Loading diagram…From page 18 of the paper. Given that PV = 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]
- 8
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
(a)Show that
Loading diagram…From page 22 of the paper. [2]
(b)Hence show that the equation
Loading diagram…From page 22 of the paper. can be written as
Loading diagram…From 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
Loading diagram…From page 22 of the paper. giving the answers to one decimal place.[4]
- 9Loading diagram…
From 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 C1 and part of the graph C2 The curve C1 has equation
Loading diagram…From page 26 of the paper. The graph C2 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 C2[2]
Given that
• C1 intersects C2 at x = 3
• C2 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 C1, C2 , the x-axis and the y-axis.
(d)Find the area of R, giving the answer to 3 significant figures.[4]