# WMA11 Pure Mathematics 1 (P1) January 2025 Paper 01

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

- Page: https://mathvsarham.com/past-papers/wma11/2025-january-paper-01/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_january_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: January 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
Find
[Diagram or table: see page 2 of the paper]
giving your answer in simplest form. [4]

Question 2
In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
Given that
• the point A has coordinates 2 3, 5
• the point B has coordinates 7 3, 8
• the straight line l_1 passes through A and B
(a) show that the gradient of l_1 is p 3, where p is a rational constant to be found. You must show each step of your working. [2]
The straight line l_2 is perpendicular to l_1 and passes through A.
(b) Find the equation of l_2, giving your answer in the form y = mx + c, where m and c are constants. [3]

Question 3
The population of a town was monitored.
Exactly 5 years after monitoring began, the population was 58 000
Exactly 10 years after monitoring began, the population was 65 000
Given that the population of the town, P thousand, t years after monitoring began can be modelled by the equation
[Diagram or table: see page 6 of the paper]
where a and b are constants,
(a) find the value of a and the value of b. [3]
According to the model, exactly T years after monitoring began, the population was 85 000
Making your method clear,
(b) find the value of T, giving your answer to one decimal place.
[Diagram or table: see page 6 of the paper]
[2]

Question 4
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
(i) Given that
[Diagram or table: see page 10 of the paper]
express, in simplest form, in terms of y and a
(a) a^3^x^+^1 [1]
5
(b) 
[3]
(ii)(a) Use the substitution p = 9^t to show that the equation
[Diagram or table: see page 10 of the paper]
can be rewritten as
[Diagram or table: see page 10 of the paper]
[2]
(b) Hence solve
[Diagram or table: see page 10 of the paper]
[3]

Question 5
In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
The curve C has equation
[Diagram or table: see page 14 of the paper]
(a) Find dy/dx , giving your answer in simplest form. [2]
Given that
• the point P lies on C
• the line with equation y = k – 5x, where k is a constant, is the tangent to C at P
(b) show that the x coordinate of P satisfies the equation
[Diagram or table: see page 14 of the paper]
[2]
(c) Hence find the value of k. [4]

Question 6
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), x > 0
Given that
• the point P(4, –5) lies on C
2x^2 + ax + b • f ′(x) = , where a and b are constants 4 x
• the gradient of the tangent to C at P is 7
(a) show that
[Diagram or table: see page 18 of the paper]
[2]
Given also that a + b = –9
(b) find, in simplest form, f(x) [7]
Curve C is transformed to the curve with equation y = f(x – 3)
Given that point P is transformed to the point Q,
(c) state the coordinates of Q. [1]

Question 7
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
[Diagram or table: see page 22 of the paper]
where k is a positive constant.
(a) Sketch the graph of C.
Show on your sketch
• the coordinates of any points of intersection of C with the coordinate axes
• the equation of the horizontal asymptote to C
stating each in terms of k. [3]
The line l has equation y = –kx – 6
Given that l intersects C at 2 distinct points,
(b) find the range of possible values of k. [5]

Question 8
[Diagram or table: see page 26 of the paper]
Figure 1 shows a sketch of a design for a badge. The design consists of a triangle OAB joined to a sector OBC of a circle with centre O In the design
• OB = 3.4 cm
• AB = 1.9 cm
• angle AOB = π/6 radians
• angle OAB > π/2 radians
Making your method clear,
(a) find the size of angle OAB, giving your answer in radians to 4 significant figures, [3]
(b) find the area of triangle OAB, in cm^2, giving your answer to 3 significant figures. [2]
Given that the ratio of the area of sector OBC to the area of triangle OAB is 3 : 2
(c) show that angle BOC is 0.462 radians to 3 significant figures. [3]
(d) Hence find the perimeter of the badge, in cm, to the nearest integer. [5]

Question 9
[Diagram or table: see page 30 of the paper]
(a) Express 6x − 27/4 − x^2 in the form a + b(x + c)^2 where a, b and c are constants to
be found. [3]
Figure 2 shows part of a sketch of curve C_1 with equation
[Diagram or table: see page 30 of the paper]
Given that the point P is the maximum point on C_1
(b) state the coordinates of P [2]
Figure 2 also shows part of a sketch of curve C_2 with equation
[Diagram or table: see page 30 of the paper]
where k is a constant and x is measured in radians.
Given that C_1 and C_2 intersect on the x‑axis at point A and at point B, as shown in Figure 2,
(c)(i) state the x coordinate of B
(ii) state the value of k
(iii) state the period of C_2 [3]
The line segment L joins P and B. The region R, shown shaded in Figure 2, is bounded by L, C_1 and C_2
(d) Use inequalities to define R. [5]