# WMA12 Pure Mathematics 2 (P2) January 2025 Paper 01

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

- Page: https://mathvsarham.com/past-papers/wma12/2025-january-paper-01/
- PDF: https://mathvsarham.com/papers/wma12/WMA12_january_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: January 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
The arithmetic series S is given by
Answer: S  2  5  8  11  ____  254
Find
(a) the number of terms in the series, [2]
(b) the sum of the series. [2]

Question 2
(a) Find the first 4 terms, in ascending powers of x, of the binomial expansion of
[Diagram or table: see page 4 of the paper]
giving each term in simplest form. [4]
This expansion is to be used to find an approximation for 2.05^8
(b) State the value of x that should be used.
[Diagram or table: see page 4 of the paper]
[1]

Question 3
[Diagram or table: see page 6 of the paper]
Figure 1 shows an open‑topped container used for holding water.
The container is in the shape of a cuboid and is made of sheet metal.
The base of the container is a rectangle 3x metres by x metres.
The height of the container is y metres as shown in Figure 1.
Given that the capacity of the container is 120 m^3
(a) show that the area A m^2 of the sheet metal used to make the container is given by
[Diagram or table: see page 6 of the paper]
where P and Q are positive constants to be found. [4]
(b) Use calculus to find the value of x for which A has a stationary value, giving your answer to 3 significant figures. [4]
(c) Find d A/dx_2 and hence show that the value of x found in part (b) gives the minimum
value of A. [2]

Question 4
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
Given that, in a particular geometric series,
• the sum of the first three terms is 70.2
• the sum to infinity is 75
find, for this series,
(a) the common ratio, [4]
(b) the first term. [2]

Question 5
[Diagram or table: see page 12 of the paper]
where a and b are constants.
Given that (3x – 4) is a factor of f(x),
(a) show that 16a + 9b = 56 [2]
Given further that when f(x) is divided by (x – 2) the remainder is b,
(b) find the value of a and the value of b. [4]
(c) Hence, using algebra, fully factorise f(x). [3]

Question 6
[Diagram or table: see page 16 of the paper]
The point A (–1, 2) and the point B (11, 6) both lie on a circle with centre P.
The point M is the midpoint of AB.
Given that the line l passes through M and P, as shown in Figure 2,
(a) find an equation for l, giving your answer in the form y = mx + c, where m and c are constants. [4]
Given that P has coordinates (7, k), where k is a constant,
(b) find the value of k, [1]
(c) find an equation for the circle. [3]

Question 7
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
(i) The table below shows values of x and y, where y = log_10 (x + 5), for x values between –1 and 4
[Diagram or table: see page 20 of the paper]
Using the trapezium rule with all the y values in the given table, show that
[Diagram or table: see page 20 of the paper]
where k is an integer to be found. [3]
(ii) Find the value of a such that
[Diagram or table: see page 20 of the paper]
[5]

Question 8
(i) A student states
[Diagram or table: see page 24 of the paper]
Show, by counter example, that this statement is not always true. [1]
(ii) Prove, using algebra, that for all odd integers n, the value of the expression
[Diagram or table: see page 24 of the paper]
is always even but never a multiple of 4 [4]

Question 9
[Diagram or table: see page 26 of the paper]
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
Figure 3 shows a sketch of part of the curve with equation
[Diagram or table: see page 26 of the paper]
The curve has a turning point at the point M, as shown in Figure 3.
(a) Using calculus, find the coordinates of M. [5]
The curve crosses the x‑axis at the point P, as shown in Figure 3.
(b) Use algebra to find the x coordinate of P. [2]
The finite region R, shown shaded in Figure 3, is bounded by the curve, the line through M parallel to the x‑axis and the line through P parallel to the y‑axis.
(c) Use algebraic integration to find the area of R, giving your answer to one decimal place. [5]

Question 10
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
(a) Show that
[Diagram or table: see page 30 of the paper]
[4]
(b) Hence solve, for 0 < x < 2π, the equation
[Diagram or table: see page 30 of the paper]
giving your answers to 3 significant figures. [4]