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

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

- Page: https://mathvsarham.com/past-papers/wma11/2025-may-june-paper-01a/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_may-june_2025_paper_01A_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: 01A
- Component code: WMA11/01A
- 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
[Diagram or table: see page 2 of the paper]
The curve C, shown in Figure 1,
• has equation y = f (x) , x ∈ 
• cuts the x-axis at –1
• has a maximum turning point at P (2, 5)
• has a horizontal asymptote with equation y = 3
The curve C has no other turning points or asymptotes.
(a) Find the coordinates of the point to which P is transformed when the curve with equation y = f (x) is transformed to the curve with equation
(i) y = f (x) + 7
(ii) y = 3 f (x) [2]
Given that the line with equation y = k , where k is a constant, cuts or meets C exactly once,
(b) state the range of possible values of k. [2]
(c) Write down the solution of the equation
[Diagram or table: see page 2 of the paper]
[1]

Question 2
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
A vessel that contained some water started to leak from a hole in its base.
The volume of water in the vessel 25 minutes after the leak started was 6 m^3
The volume of water in the vessel 64 minutes after the leak started was 3.3 m^3
The volume of water, V m^3 , in the vessel t minutes after the leak started, is modelled by the equation
[Diagram or table: see page 4 of the paper]
where a and b are constants.
(a) Find the value of a and the value of b. [4]
(b) Using the equation of the model,
(i) find the initial volume of water in the vessel,
(ii) find the time taken, after the leak started, for the vessel to empty. Give your answer to the nearest minute. [3]

Question 3
[Diagram or table: see page 6 of the paper]
Figure 2 shows part of the graph of the trigonometric function with equation y = f (x) , where x is measured in degrees.
(a) Write down an expression for f (x) . [2]
(b) State the number of solutions of the equation
(i) f (x) = 2 in the interval –720°  x  720°
(ii) f (x) = –3 in the interval –720°  x  720° [2]

Question 4
In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
(i) Using the laws of indices, solve
[Diagram or table: see page 8 of the paper]
[3]
(ii) Solve the equation
[Diagram or table: see page 8 of the paper]
giving the answer in the form a + b 3 , where a and b are rational numbers. [4]
[Diagram or table: see page 12 of the paper]

Question 5
[Diagram or table: see page 12 of the paper]
(a) Find y dx writing the answer in simplest form. ∫ [3]
(b)(i) Find dy/dx writing the answer in simplest form. [3]
(ii) Hence find the exact solutions of the equation dy/dx = 3
[Diagram or table: see page 12 of the paper]
[4]

Question 6
In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
The curve C_1 has equation y = (x + 5)(3x + 2)(2x – 5)
The curve C_2 has equation y = 3x^2– 33x – 50
Use algebra to find the x coordinates of the points of intersection of C_1 and C_2 [5]

Question 7
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
(a) Sketch the curve C with equation
[Diagram or table: see page 18 of the paper]
State on your sketch
• the equation of the vertical asymptote
• the coordinates of the point of intersection of C with the y-axis [3]
The straight line l has equation y = mx – 4 , where m is a constant.
Given that l cuts C at least once,
(b)(i) show that
[Diagram or table: see page 18 of the paper]
(ii) find the range of values of m. [6]

Question 8
[Diagram or table: see page 22 of the paper]
Figure 3 shows a sketch of a line l and a quadratic curve C.
Given that l passes through (–3, 0) and (2, 18)
(a) find an equation for l in the form y = mx + c where m and c are constants. [3]
Given that
• C and l intersect at the points (–3, 0) and (2, 18)
• C crosses the y-axis at (0, –6)
(b) find an equation for C. [4]
The region R, shown shaded in Figure 3, is bounded by C, l and the y-axis.
(c) Use inequalities to define R. [2]

Question 9
[Diagram or table: see page 26 of the paper]
Figure 4 shows the outline of a sign that is used to advertise a bird sanctuary.
The sign is composed of a triangle CPQ joined to a sector QCRTQ of a circle, centre C.
Given that
• angle QPR = 0.8 radians
• PQ = 0.5 m
• PC = 1.84 m
• PRC is a straight line
(a) find the radius, CQ, of the sector, in metres to 3 decimal places. [2]
(b) Hence show that angle PCQ is 0.236 radians to 3 decimal places. [2]
(c) Find the total area of the sign, giving your answer in m^2 to one decimal place. [3]
(d) Find the total perimeter of the sign, giving your answer in metres to one decimal place. [2]

Question 10
The curve C has equation y = f (x) .
Given that
k • f ′ (x) = x(x − 3)/5 where k is a constant
• the point P with x coordinate 4 lies on C
• the equation of the normal to C at P is y = – 5/4 x + 2
(a) find an equation of the tangent to C at P, giving your answer in the form y = mx + c , where m and c are constants, [3]
(b) find the value of k, [2]
(c) find f (x) , writing the answer in simplest form. [5]