# WMA12 Pure Mathematics 2 (P2) May/June 2025 Paper 01

Pearson Edexcel International A Level WMA12 Pure Mathematics 2 (P2) past paper 01, May/June 2025. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma12/2025-may-june-paper-01/
- PDF: https://mathvsarham.com/papers/wma12/WMA12_may-june_2025_paper_01_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International A Level
- Subject: WMA12 Pure Mathematics 2 (P2) (https://mathvsarham.com/past-papers/wma12/)
- Session: May/June 2025
- Paper: 01
- Component code: WMA12/01
- 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
(a) Find the first 4 terms, in ascending powers of x, of the binomial expansion of
[Diagram or table: see page 2 of the paper]
giving each term in simplest form. [4]
In the series expansion of
[Diagram or table: see page 2 of the paper]
the coefficient of the term in x^2 is 1316
(b) Use the answer to part (a) to find the value of k. [2]

Question 2
The line joining the points (–2, 5) and (4, 15) is the diameter of a circle C.
(a) Find an equation for C. [5]
(b) Hence find the exact coordinates of the point on C that is nearest the x-axis. [2]

Question 3
y
[Diagram or table: see page 6 of the paper]
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
Figure 1 shows a sketch of the curve C with equation
[Diagram or table: see page 6 of the paper]
The points P (1, 11) and Q (4, 5) lie on C and are shown in Figure 1.
The region R, shown shaded in Figure 1, is bounded by C and line segment PQ.
Use algebraic integration to find the area of R. [5]

Question 4
The function f(x) is defined by
[Diagram or table: see page 8 of the paper]
where a and b are constants.
Given that (x + 3) is a factor of f(x),
(a) show that
[Diagram or table: see page 8 of the paper]
[2]
Given further that when f(x) is divided by (2x – 1) the remainder is 7/4
(b) find the value of a and the value of b. [4]
(c) Using algebra, find the quotient and the remainder when f(x) is divided by (x – 2) [3]

Question 5
[Diagram or table: see page 12 of the paper]
The table above shows corresponding values of x and y for
[Diagram or table: see page 12 of the paper]
The values of y are given to 3 decimal places as appropriate.
(a) Using the trapezium rule with all the values of y in the given table, obtain an estimate for
[Diagram or table: see page 12 of the paper]
giving the answer to one decimal place. [3]
Using the answer to part (a) and making your method clear, estimate
 1
(b)(i) 3 dx    2
[Diagram or table: see page 12 of the paper]
(ii) 2^^x  2x dx
[Diagram or table: see page 12 of the paper]
[3]

Question 6
In this question you must show all stages of your working.
[Diagram or table: see page 14 of the paper]
(i) Solve
[Diagram or table: see page 14 of the paper]
[5]
(ii) The curves C_1 and C_2 with equations
[Diagram or table: see page 14 of the paper]
meet at the point P.
Find the exact coordinates of P, writing your answer in the form (log_3 a, b) where a and b are integers. [5]

Question 7
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
(i) A geometric series begins
[Diagram or table: see page 18 of the paper]
(a) Find the sum to infinity of this series. [2]
Given that the k th term of this series is less than 0.0005
(b) use algebra to find the smallest possible value of k. [3]
(ii) An arithmetic series begins
[Diagram or table: see page 18 of the paper]
Given that the sum of the first n terms of this series is S_n find the greatest possible value of S_n [4]

Question 8
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
(i) Solve, for 0  x < π, the equation
[Diagram or table: see page 22 of the paper]
giving the answers in radians in the form kπ, where k is a rational constant to be found. [3]
(ii) Solve, for 0  θ < 360°, the equation
[Diagram or table: see page 22 of the paper]
giving your answers, in degrees, to one decimal place. [5]

Question 9
[Diagram or table: see page 26 of the paper]
Figure 2 shows a sketch of an open container.
The sides CDEF and ABFE are rectangles.
The ends ADE and BCF are congruent (identical) right-angled triangles.
The container is made from metal of negligible thickness.
Given that
• AE = BF = 3x metres
• DE = CF = 2x metres
• AB = DC = EF = L metres
and the capacity of the container is 12 m^3
(a) show that the area of metal used to make the container, S m^2, is given by
[Diagram or table: see page 26 of the paper]
where P and Q are positive integers to be found. [4]
Given that x can vary,
(b) use algebraic calculus to find the minimum value of S, giving your answer to one decimal place. [5]
(c) Justify that the value of S found in part (b) is a minimum. [2]

Question 10
[Diagram or table: see page 30 of the paper]
Use algebra to prove by exhaustion that,
[Diagram or table: see page 30 of the paper]
is always a multiple of 3 [4]