# WMA12 Pure Mathematics 2 (P2) January 2023 Paper 01

Pearson Edexcel International A Level WMA12 Pure Mathematics 2 (P2) past paper 01, January 2023. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma12/2023-january-paper-01/
- PDF: https://mathvsarham.com/papers/wma12/WMA12_january_2023_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 2023
- 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
[Diagram or table: see page 2 of the paper]
Figure 1 shows a sketch of part of the curve with equation y = f (x)
The table below shows some corresponding values of x and y for this curve.
The values of y are given to 3 decimal places.
[Diagram or table: see page 2 of the paper]
Using the trapezium rule with all the values of y in the given table,
(a) obtain an estimate for
[Diagram or table: see page 2 of the paper]
giving your answer to 2 decimal places. [3]
(b) Use your answer to part (a) to estimate
(i) f (x) − 2 dx ( ) ∫_−_1
(ii) f (x − 2) dx ∫_1 [3]

Question 2
In this question you must show all stages of your working.
Solutions based entirely on calculator technology are not acceptable.
[Diagram or table: see page 4 of the paper]
A brick is in the shape of a cuboid with width x cm, length 3x cm and height h cm, as shown in Figure 2.
The volume of the brick is 972 cm^3
(a) Show that the surface area of the brick, S cm^2, is given by
[Diagram or table: see page 4 of the paper]
[3]
(b) Find dS/dx [1]
(c) Hence find the value of x for which S is stationary. [2]
(d) Find d S/dx_2 and hence show that the value of x found in part (c) gives the minimum
value of S. [2]
(e) Hence find the minimum surface area of the brick. [1]
[Diagram or table: see page 8 of the paper]

Question 3
[Diagram or table: see page 8 of the paper]
(a) Find the first 4 terms, in ascending powers of x, of the binomial expansion of f (x). Give each term in simplest form. [4]
Given that, in the binomial expansion of f (x), the coefficients of x, x^2 and x^3 are the first 3 terms of an arithmetic progression,
(b) find, using algebra, the possible values of k.
(Solutions relying entirely on calculator technology are not acceptable.) [3]

Question 4
(i) Using the laws of logarithms, solve
[Diagram or table: see page 10 of the paper]
[3]
(ii) Given that
[Diagram or table: see page 10 of the paper]
find y in terms of a, giving your answer in simplest form. [3]

Question 5
[Diagram or table: see page 12 of the paper]
where p and q are constants and p > 0
Given that (x – 3) is a factor of f (x)
(a) show that
[Diagram or table: see page 12 of the paper]
[2]
Given also that when f (x) is divided by (x + p) the remainder is 9
(b) show that
[Diagram or table: see page 12 of the paper]
[2]
(c) Hence find the value of p and the value of q. [3]
(d) Hence find a quadratic expression g(x) such that
[Diagram or table: see page 12 of the paper]
[2]

Question 6
The circle C has equation
[Diagram or table: see page 16 of the paper]
(a) Find
(i) the coordinates of the centre of C,
(ii) the exact radius of C. [3]
The point P lies on C.
Given that the tangent to C at P has equation x + 2y + 10 = 0
(b) find the coordinates of P [4]
(c) Find the equation of the normal to C at P, giving your answer in the form y = mx + c where m and c are integers to be found. [3]

Question 7
A geometric sequence has first term a and common ratio r, where r > 0
Given that
• the 3rd term is 20
• the 5th term is 12.8
(a) show that r = 0.8 [1]
(b) Hence find the value of a. [2]
Given that the sum of the first n terms of this sequence is greater than 156
(c) find the smallest possible value of n.
[Diagram or table: see page 20 of the paper]
[4]

Question 8
In this question you must show all stages of your working.
Solutions based entirely on calculator technology are not acceptable.
(i) Solve, for – π/2 < x < π, the equation
[Diagram or table: see page 22 of the paper]
giving your answers, in radians, to 2 decimal places. [4]
(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
In this question you must show all stages of your working.
Solutions based entirely on calculator technology are not acceptable.
[Diagram or table: see page 26 of the paper]
• the curve C with equation y = x^2– 4x + 5
• the line l with equation y = 2
The curve C intersects the y‑axis at the point D.
(a) Write down the coordinates of D. [1]
The curve C intersects the line l at the points E and F, as shown in Figure 3.
(b) Find the x coordinate of E and the x coordinate of F. [2]
Shown shaded in Figure 3 is
• the region R_1 which is bounded by C, l and the y‑axis
• the region R_2 which is bounded by C and the line segments EF and DF
area of R_1 Given that = k, where k is a constant, area of R_2
(c) use algebraic integration to find the exact value of k, giving your answer as a simplified fraction. [5]

Question 10
A student was asked to prove by exhaustion that
[Diagram or table: see page 30 of the paper]
The start of the student’s proof is shown in the box below.
[Diagram or table: see page 30 of the paper]
Complete this proof. [4]