# WMA12 Pure Mathematics 2 (P2) January 2026 Paper 01

Pearson Edexcel International A Level WMA12 Pure Mathematics 2 (P2) past paper 01, January 2026. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma12/2026-january-paper-01/
- PDF: https://mathvsarham.com/papers/wma12/WMA12_january_2026_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 2026
- Paper: 01
- Component code: WMA12/01
- 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
(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]
where k is a non‑zero constant. Give each term in simplest form. [4]
Given that, in this expansion, the coefficient of x^2 is 3 times the coefficient of x^3
(b) find, in simplest form, the value of k. [2]

Question 2
[Diagram or table: see page 4 of the paper]
Figure 1 shows a sketch of part of the curve C with equation y = 2^–0.1^x
The table below shows corresponding values of x and y for y = 2^–0.1^x
The y values are given to 4 decimal places.
[Diagram or table: see page 4 of the paper]
The region R, shown shaded in Figure 1, is bounded by C, the x‑axis and the lines with equations x = –4 and x = 11
(a) Use the trapezium rule with all the values of y in the table to find an estimate for the area of R. Give the answer to 2 decimal places. [3]
(b) State how you would use the trapezium rule to get a more accurate estimate for the true area of R. [1]
Using the answer to part (a) and showing your working,
(c) estimate the value of
[Diagram or table: see page 4 of the paper]
[2]

Question 3
(i) Given that
• f (x) = 4x^3+ 6x + k, where k is a constant
• (x + 2) is a factor of f (x)
find the remainder when f (x) is divided by (x – 5) [4]
(ii) Find the remainder, R, and the quotient, Q(x), when
[Diagram or table: see page 6 of the paper]
is divided by (2x + 3) [3]

Question 4
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
Given that k is a positive constant and
[Diagram or table: see page 8 of the paper]
find the possible values of k. [5]

Question 5
The circle C_1 has equation
[Diagram or table: see page 10 of the paper]
(a) Find
(i) the coordinates of the centre of C_1
(ii) the radius of C_1 [3]
The circle C_2 has
• centre (–k, 0) where k is a positive constant
• radius 5
Given that circles C_1 and C_2 touch
(b) find the exact value of k. [3]

Question 6
(i) Given that p and q are consecutive odd numbers, where p > q > 0, prove that
[Diagram or table: see page 12 of the paper]
is a multiple of 8 [4]
(ii) The curve C has equation
[Diagram or table: see page 12 of the paper]
Prove that C has no stationary points. [4]

Question 7
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
(i) Find the exact solution of the equation
[Diagram or table: see page 16 of the paper]
giving the answer in the form a + b log_25 where a and b are rational constants. [4]
(ii) Using the laws of logarithms, solve the equation
[Diagram or table: see page 16 of the paper]
[5]

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  θ < 180
[Diagram or table: see page 18 of the paper]
giving the answers to one decimal place. [5]
(ii) Solve, for 0  x < 2π
[Diagram or table: see page 18 of the paper]
giving the answers, in radians, in the form kπ where k is a rational constant. [5]

Question 9
A company mines lithium.
• in year 1, the company mined 12 400 tonnes of lithium
• in year 15, the company is predicted to mine 7 500 tonnes of lithium
Model A assumes that the mass of lithium the company mines will decrease by the same amount each year.
According to model A,
(a) find the mass of lithium the company will mine in year 5 [3]
(b) calculate the total mass of lithium the company will mine from year 1 to year 15 inclusive. [2]
Model B assumes that the mass of lithium the company mines will decrease by the same percentage each year.
(c) Find, according to model B, the mass of lithium the company will mine in year 10. Give the answer to the nearest 10 tonnes. [3]
According to model B, there is a limit to the total mass of lithium that can be mined.
(d) Calculate the value of this limit. Give the answer to the nearest 100 tonnes. [2]

Question 10
[Diagram or table: see page 26 of the paper]
Solutions relying entirely on calculator technology are not acceptable.
Figure 2 shows a sketch of the curve C with equation
[Diagram or table: see page 26 of the paper]
The point P is a stationary point on C.
(a) Use algebraic differentiation to find the exact x coordinate of P. [4]
The region R_1, shown shaded in Figure 2, is bounded by C and the x‑axis.
The region R_2, also shown shaded in Figure 2, is bounded by C, the x‑axis and the line with equation x = k, where k is a constant.
Given that the area of R_1 is equal to the area of R_2
(b) use algebraic integration to find the exact value of k. [4]