# WMA11 Pure Mathematics 1 (P1) January 2026 Paper 01

Pearson Edexcel International A Level WMA11 Pure Mathematics 1 (P1) past paper 01, January 2026. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma11/2026-january-paper-01/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_january_2026_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: January 2026
- Paper: 01
- Component code: WMA11/01
- 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
[Diagram or table: see page 2 of the paper]
Find, in simplest form,
dy
(a)  dx [3]
(b) y dx ∫ [3]

Question 2
In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
(a) Given
[Diagram or table: see page 4 of the paper]
[2]
(b) Hence solve the simultaneous equations
[Diagram or table: see page 4 of the paper]
writing the answers in the form p + q 3 , where p and q are integers to be found. [4]

Question 3
(i) Find the range of values of z for which
[Diagram or table: see page 6 of the paper]
giving the answer in simplest form. [2]
(ii) 
[Diagram or table: see page 6 of the paper]
Figure 1 shows a plot of
• the line with equation y = x + 5
• the curve with equation y = x (x – 3)
On the opposite page there is a copy of Figure 1 labelled Diagram 1. On Diagram 1 represent the following inequality graphically.
[Diagram or table: see page 6 of the paper]
[3]
[Diagram or table: see page 7 of the paper]

Question 4
In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
The point A (–1, 8) and the point B (7, 2) lie on the line L_1
(a) Find an equation for L_1 in the form ax + by + c = 0 , where a, b and c are integers. [3]
The line L_2
• passes through A and is perpendicular to L_1
• cuts the x-axis at the point C
(b) Find the coordinates of C. [3]
(c) Hence find the area of triangle ABC. [3]

Question 5
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
[Diagram or table: see page 12 of the paper]
Figure 2 shows the logo for the tourist board of an island.
The logo consists of a sector BODCB of a circle centre O joined to a triangle AOD.
Given that
• ABO is a straight line
• OD = 3 cm
• AD = 8 cm
• angle AOD = 2.5 radians
(a) show that angle ODA is 0.415 radians to 3 significant figures. [3]
(b) Find the total area of the logo, in cm^2, to one decimal place. [3]
(c) Find the perimeter of the logo, ABCDA, in cm, to one decimal place. [3]

Question 6
[Diagram or table: see page 16 of the paper]
Figure 3 shows a sketch of the curve C with equation y = f (x) where f (x) is a cubic function in x.
The curve C
• cuts the x-axis at (–2, 0) and cuts the y-axis at (0, 10)
• touches the x-axis at (5, 0)
as shown in Figure 3.
(a) Deduce the roots of the equation
(i) f x = 0
(ii) f (x – 3) = 0 [2]
(b) Find an expression for f (x). You should leave your answer in factorised form. [3]
The curve C intersects the straight line y = 10 (x + 2) at exactly three points.
(c) Use algebra to find the exact x coordinates of the three points of intersection.
[Diagram or table: see page 16 of the paper]
[4]

Question 7
The curve C has equation
[Diagram or table: see page 20 of the paper]
(a) Show that dy/dx can be written in the form
[Diagram or table: see page 20 of the paper]
where p, q and r are constants to be found. [5]
(b) Hence state
(i) the minimum value of dy/dx
(ii) the value of x at which this minimum value occurs. [2]
Given that S is the point on C at which the gradient is a minimum,
(c) find the equation of the tangent to C at S, giving your answer in the form y = mx + c , where m and c are constants. [3]

Question 8
In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
A curve C has equation y = f (x) , x > 0
A point P lies on C.
Given that
• f ′ (x) = 4x +_2 – 4 x
• the equation of the tangent to C at P is y = 10x – 6 3
(a)(i) verify that 3 is a possible x coordinate of P,
(ii) find, using algebra, the other possible x coordinate of P. [6]
Given that the x coordinate of P is 3
(b) find an equation of the normal to C at P. [2]
(c) Find f (x) , writing your answer in simplest form. You must show each stage of your working. [4]

Question 9
[Diagram or table: see page 26 of the paper]
Figure 4 shows a sketch of part of the graph of the trigonometric function with equation y = f (x).
(a) Write down an expression for f (x). [2]
Copies of Figure 4 (labelled Diagram 1 and Diagram 2) can be found on the following pages.
(b)(i) On Diagram 1 sketch a graph of the curve with equation
[Diagram or table: see page 26 of the paper]
(ii) Hence find the number of solutions of the equation
[Diagram or table: see page 26 of the paper]
[3]
(c)(i) On Diagram 2 sketch a graph of the curve with equation
[Diagram or table: see page 26 of the paper]
(ii) Hence find the number of solutions of the equation
[Diagram or table: see page 26 of the paper]
giving a reason for your answer. [4]
(a) 
[Diagram or table: see page 27 of the paper]
Only use this copy if you need to redraw your graph.
[Diagram or table: see page 27 of the paper]
[Diagram or table: see page 28 of the paper]
Only use this copy if you need to redraw your graph.
[Diagram or table: see page 28 of the paper]