# WMA11 Pure Mathematics 1 (P1) Oct/Nov 2025 Paper 01

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

- Page: https://mathvsarham.com/past-papers/wma11/2025-oct-nov-paper-01/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_oct-nov_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: Oct/Nov 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
The curve C has equation
[Diagram or table: see page 2 of the paper]
(a) Find dy/dx writing the answer in simplest form. [3]
The point P  1/ 4 , 5 /2  lies on C.  
(b) Find the equation of the tangent to C at P, writing your answer in the form y = mx + c where m and c are integers. [3]

Question 2
Find
[Diagram or table: see page 4 of the paper]
writing the answer in simplest form. [5]

Question 3
The sides of a triangle are in the ratio 2 : 4 : 5
(a) Find the size of the largest angle of the triangle, in degrees, to one decimal place. [2]
Given that the area of the triangle is 140 cm^2
(b) find the length of the shortest side, in cm, to one decimal place. [3]

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) Find the real roots of the equation
[Diagram or table: see page 8 of the paper]
[4]

Question 5
[Diagram or table: see page 12 of the paper]
In this question you must show all stages of your working.
[Diagram or table: see page 12 of the paper]
(a) Express 2x^2– 16x + 50 in the form
[Diagram or table: see page 12 of the paper]
where a, b and c are constants to be found. [3]
Figure 1 shows a sketch of the curve C with equation y = 2x^2– 16x + 50
Given that in Figure 1
• M is the minimum point on C • line l passes through the origin and intersects C at the points M and P
(b) find, using algebra and showing your working, the x coordinate of P. [5]
The region R is shown shaded in Figure 1.
(c) Use inequalities to fully define R. [2]

Question 6
(a) Sketch the graph of the curve C with equation
[Diagram or table: see page 16 of the paper]
where k is a positive constant.
On your sketch show
• the coordinates of any points where C cuts the coordinate axes • the equation of the vertical asymptote to C [4]
The straight line l has equation
[Diagram or table: see page 16 of the paper]
Given that there is at least one point of intersection between l and C,
(b) find the range of possible values of k. [5]

Question 7
[Diagram or table: see page 20 of the paper]
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
Figure 2 shows the plan view of a design for a swimming pool.
The design consists of a sector POS of a circle centre O joined to a major sector QORTQ of a different circle, also with centre O.
Given that
• angle POS is 1.65 radians • the area of sector POS is 30 m^2 • PQ = 2.8 m
(a) show that, to 3 significant figures, OQ = 8.83 m [3]
(b) Find the total surface area of the swimming pool in m^2 to the nearest integer. [3]
(c) Find the total perimeter of the swimming pool in metres to 2 significant figures. [3]

Question 8
In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
A curve has equation y = f(x), x > 0
Given that
• f(x)  2x   k, where k is a constant
• the equation of the tangent to the curve at x = 2 is y  5x  3 2
(a) find the exact value of k. [2]
(b) Find an equation of the normal to the curve at x = 2 [2]
(c) Find f(x), writing your answer in simplest form. [4]

Question 9
[Diagram or table: see page 28 of the paper]
Figure 3 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]
The point P lies on y = f(x) and is shown in Figure 3.
(b) State the coordinates of the point to which P is transformed when the graph of y = f(x) is transformed to the graph with equation
  
(i) y  f x     6  [2]
(ii) y   1/2 f (x) [2]

Question 10
[Diagram or table: see page 30 of the paper]
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
Figure 4 shows a sketch of the curve C with equation
[Diagram or table: see page 30 of the paper]
The line l is the normal to C at the point P where x = 0
The line l also intersects C at points Q and R as shown in Figure 4.
(a) Find, using algebra, the x coordinate of point Q. [6]
The point T lies on C.
Given that
• the tangent to C at T is parallel to l • the x coordinate of T is positive
(b) find, using algebra, the exact x coordinate of T. [4]