# WMA11 Pure Mathematics 1 (P1) May/June 2025 Paper 01

Pearson Edexcel International A Level WMA11 Pure Mathematics 1 (P1) past paper 01, May/June 2025. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma11/2025-may-june-paper-01/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_may-june_2025_paper_01_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International A Level
- Subject: WMA11 Pure Mathematics 1 (P1) (https://mathvsarham.com/past-papers/wma11/)
- Session: May/June 2025
- Paper: 01
- Component code: WMA11/01
- 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
Given that
[Diagram or table: see page 2 of the paper]
express each of the following in the form kx^n where k and n are fully simplified constants.
(a) p^1/2 [1]
(b) ( pq)^–1 [2]
(c) pq^2 [2]

Question 2
The curve C has equation
[Diagram or table: see page 4 of the paper]
(a) Find dy/dx writing your answer in simplest form. [2]
The point P lies on C.
Given that
• the x coordinate of P is 2^k where k is a constant • the gradient of C at the point P is 16
(b) find the value of k. [3]

Question 3
Find
[Diagram or table: see page 6 of the paper]
writing your answer in simplest form. [5]

Question 4
[Diagram or table: see page 8 of the paper]
Figure 1 shows a sketch of part of the curve with equation
[Diagram or table: see page 8 of the paper]
where x is measured in degrees.
The points P and Q lie on the curve and are shown in Figure 1.
(a) State the coordinates of P. [1]
(b) State the coordinates of Q. [2]
(c) State the number of solutions of the equation
(i) 4 cos x = 3 in the interval 0 < x  18 000°
(ii) 5 + 4 cos x = 1 in the interval –720° < x  720°
(iii) 4 cos x – 3 = 1 in the interval –1080°  x  1080° [3]

Question 5
In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
The line l_1 has equation
[Diagram or table: see page 10 of the paper]
The line l_2 passes through the origin and is perpendicular to l_1
(a) Find an equation for l_2 [2]
The lines l_1 and l_2 intersect at the point P.
(b) Use algebra to find the coordinates of P. [3]
(c) Hence find the shortest distance from l_1 to the origin.
Write your answer as a fully simplified surd. [2]

Question 6
[Diagram or table: see page 14 of the paper]
The shaded area in Figure 2 shows the plan view of a helicopter landing pad.
The area consists of the major sector AOB of a circle centre O joined to a triangle AOC.
Given that
• AO = OB = 15 m • BC = 2 m • CBO is a straight line • angle ACO = 0.6 radians
(a) show that angle COA is 1.847 radians to 3 decimal places. [3]
(b) Find the total area of the helicopter landing pad. Give your answer in m^2 to 3 significant figures. [3]
(c) Find the perimeter of the helicopter landing pad. Give your answer in metres to 3 significant figures. [3]

Question 7
[Diagram or table: see page 18 of the paper]
Figure 3 shows a sketch of part of the curve C_1
Given that C_1
• has equation y = f (x) where f (x) is a cubic function • touches the x-axis at the origin and cuts the x-axis at x = 4 • passes through the point (10, 120)
(a) find f (x) [3]
The curve C_2 has equation y = 1.2x (8 – x)
On the following page there is a copy of Figure 3 called Diagram 1.
(b) On Diagram 1 sketch a graph of the curve C_2 [2]
(c) Use algebra to find the coordinates of the points where C_1 and C_2 intersect. Show each stage of your working. [5]
[Diagram or table: see page 19 of the paper]

Question 8
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
A curve has equation y = f (x), x > 0
The point P (4, 12) lies on the curve.
Given that
• f′ (x) = 3 x + kx^2 where k is a constant
• the equation of the tangent to the curve at P has equation y = 10x + c where c is a constant
(a)(i) show that k = 1/4
(ii) find the value of c [4]
(b) Hence find the value of f′′ (x) at P. [3]
(c) Find f (x). [4]

Question 9
y
[Diagram or table: see page 26 of the paper]
In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
Figure 4 shows a sketch of
• the graph C_1 with equation y = 2x
• the graph C_2 with equation y = 12 – x
(a) Describe fully the single transformation that would transform
(i) the graph with equation y = x onto C_1
(ii) the graph with equation y = – x onto C_2 [4]
The graphs C_1 and C_2 meet at the point P, as shown in Figure 4.
(b)(i) Show that the x coordinate of P is a solution of
[Diagram or table: see page 26 of the paper]
(ii) Hence find, in simplest form, the exact coordinates of P. [6]

Question 10
In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
[Diagram or table: see page 30 of the paper]
(a) Find the exact solutions to the given equation for k = 4.5 [3]
(b) Find the set of possible values of k for which the given equation has no real roots. [4]