# WMA12 Pure Mathematics 2 (P2) May/June 2026 Paper 01

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

- Page: https://mathvsarham.com/past-papers/wma12/2026-may-june-paper-01/
- PDF: https://mathvsarham.com/papers/wma12/WMA12_may-june_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: May/June 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
[Diagram or table: see page 2 of the paper]
(a) Use the remainder theorem to find the remainder when f(x) is divided by (x – 2) [2]
(b) Hence, or otherwise, find the quotient when f(x) is divided by (x – 2) [2]

Question 2
[Diagram or table: see page 4 of the paper]
(i) Solve, for 0 < x  2π, the equation
[Diagram or table: see page 4 of the paper]
[3]
(ii) Solve, for 0 < θ < 180°, the equation
[Diagram or table: see page 4 of the paper]
giving the answer to one decimal place. [3]

Question 3
The first four terms of a sequence are
[Diagram or table: see page 6 of the paper]
(a) Decide, showing detailed reasoning, whether the sequence could be
(i) an arithmetic sequence,
(ii) a geometric sequence.
State, for each part, the value of u_3 if such a sequence is possible. [6]
(b) Given instead that
• the sequence is periodic of period 4
• u  141 ^i
find the value of u_3 [3]

Question 4
[Diagram or table: see page 10 of the paper]
(i) Show by counterexample that the statement
“ f n  5/2 n^3  5/2 n^2 19n  20 is a perfect cube for all positive integers n”
is not true. [3]
(ii) Prove that the following statement is true
[Diagram or table: see page 10 of the paper]
[3]

Question 5
The table below shows values of x and y for the curve C with equation y = f(x).
[Diagram or table: see page 12 of the paper]
(a) Using the trapezium rule with all the y values in the table, find an estimate for the area of the region bounded by C and the x‑axis between the lines with equations x = 0.9 and x = 5.1 [3]
0.9 m 0.9 m y
[Diagram or table: see page 12 of the paper]
Figure 1 shows a sketch of a solid concrete skateboard ramp. Figure 2 shows a graph of the cross‑section of the same ramp.
The ramp
• has a total length of 6 m
• has a platform at each end at a height of 1.5 m and with a length of 0.9 m
• has a curved section C with equation y = f(x), where x and y are in metres
• has a uniform cross‑section and is 2.5 m wide
as shown in Figure 1 and/or Figure 2.
(b) Using the answer to part (a), find an estimate for the volume of concrete in the whole of the ramp. [3]
(c) State, giving a reason for your answer, whether the answer for part (b) is an overestimate or an underestimate of the true volume of concrete in the whole of the skateboard ramp. [1]

Question 6
(i)(a) Sketch a graph of the curve with equation
[Diagram or table: see page 16 of the paper]
Show on your sketch
• the coordinates of any points at which the curve crosses the axes
• the equation of any asymptotes [3]
(b) Using logarithms and making your method clear, solve the equation
[Diagram or table: see page 16 of the paper]
giving the answer to 3 significant figures. [2]
(ii) Given that log_4 x = a, find in simplest form in terms of a
(a) log_4 (64x)  2  [2]
(b) log _4 _2   x  [3]

Question 7
(a) Find, in ascending powers of x, up to and including the term in x^2, the binomial expansion of
[Diagram or table: see page 18 of the paper]
fully simplifying each coefficient. [4]
(b) Use x = 1/10 and the answer to part (a) to show that an estimate for / 33/ is
[Diagram or table: see page 18 of the paper]
where k is an integer to be found. [3]
(c) Hence find a rational estimate for^101389 [2]

Question 8
[Diagram or table: see page 20 of the paper]
Figure 3 shows a sketch of a circle C and a parabola S.
The circle C has equation x^2+ y^2– 8x + 12y + 27 = 0
(a) Find
(i) the coordinates of the centre of C
(ii) the radius of C [3]
The parabola S
• has equation y  ax^2  3/2 x  3
• intersects C on the y‑axis at the point A (0, –3)
• intersects C again at the point B where AB is a diameter of C
Given that B is the minimum point of S,
(b) show that a = 3/32 [3]
The finite region R is bounded by S and C and is shown shaded in Figure 3.
(c) Use algebraic integration to find the exact area of R. [7]

Question 9
[Diagram or table: see page 24 of the paper]
Figure 4 shows a sketch of a design for a logo.
The design consists of a rectangle of base x cm and height y cm with two quarter circles of equal radius r cm joined to the top edge with a gap of 10 cm between the nearest point of each quarter circle, as shown in Figure 4.
(a) Show that the area, A cm^2, of the design is given by
[Diagram or table: see page 24 of the paper]
[2]
Given that
• the total area of the design is one square metre
• the perimeter, P cm, of the design is given by P  2 y  / 2  π /2  x  5π
(b) show that
[Diagram or table: see page 24 of the paper]
[4]
(c) Use algebraic differentiation to find the value of x that gives the minimum value for P, giving the answer to 3 significant figures. [3]
By considering d P/dx_2
(d) justify that the value for x found in part (c) gives the minimum value for P. [2]