# WMA12 Pure Mathematics 2 (P2) January 2022 Paper 01

Pearson Edexcel International A Level WMA12 Pure Mathematics 2 (P2) past paper 01, January 2022. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma12/2022-january-paper-01/
- PDF: https://mathvsarham.com/papers/wma12/WMA12_january_2022_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 2022
- Paper: 01
- Component code: WMA12/01
- Time allowed: 90 minutes
- Total marks: 75
- Pages: 36

## Question paper text

Extracted automatically from the PDF; diagrams are missing and notation may be imperfect.

Question 1
The table below shows corresponding values of x and y for
[Diagram or table: see page 2 of the paper]
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) Using your answer to part (a) and making your method clear, estimate
(i) ^6^−^x 2 dx ∫_5
(ii) 3 + 2^5^−^x dx ( ) ∫_5 [4]

Question 2
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
The curve C has equation
[Diagram or table: see page 6 of the paper]
(a) Find dy/dx , giving each term in simplest form. [2]
(b) Hence find the coordinates of the stationary point of C. [4]
^2 y
(c) Find d/dx_2 and hence determine the nature of the stationary point of C. [2]

Question 3
(a) Find the first 4 terms, in ascending powers of x, of the binomial expansion of
[Diagram or table: see page 8 of the paper]
where k is a non‑zero constant. Give each term in simplest form. [4]
[Diagram or table: see page 8 of the paper]
In the expansion of f(x), the constant term is 3 times the coefficient of x.
(b) Find the value of k. [3]

Question 4
Using the laws of logarithms, solve
[Diagram or table: see page 12 of the paper]
[5]

Question 5
[Diagram or table: see page 14 of the paper]
where A and B are integers.
Given that
• when f(x) is divided by (x – 1) the remainder is k
• when f(x) is divided by (x + 1) the remainder is –10k
• k is a constant
(a) show that
[Diagram or table: see page 14 of the paper]
[3]
Given also that (3x – 2) is a factor of f(x),
(b) find the value of A and the value of B. [3]
(c) Hence find the quadratic expression g(x) such that
[Diagram or table: see page 14 of the paper]
[2]

Question 6
[Diagram or table: see page 18 of the paper]
The points P(23, 14), Q(15, –30) and R(–7, –26) lie on the circle C, as shown in Figure 1.
(a) Show that angle PQR = 90° [2]
(b) Hence, or otherwise, find
(i) the centre of C,
(ii) the radius of C. [3]
Given that the point S lies on C such that the distance QS is greatest,
(c) find an equation of the tangent to C at S, giving your answer in the form ax + by + c = 0, where a, b and c are integers to be found. [3]

Question 7
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
(i) Solve, for –90° < x < 90°, the equation
[Diagram or table: see page 22 of the paper]
giving your answers to one decimal place. [4]
(ii) Solve, for 0 < θ < 2π, the equation
[Diagram or table: see page 22 of the paper]
giving your answers to 3 significant figures. [4]

Question 8
A metal post is repeatedly hit in order to drive it into the ground.
Given that
• on the 1st hit, the post is driven 100 mm into the ground
• on the 2nd hit, the post is driven an additional 98 mm into the ground
• on the 3rd hit, the post is driven an additional 96 mm into the ground
• the additional distances the post travels on each subsequent hit form an
[Diagram or table: see page 26 of the paper]
(a) show that the post is driven an additional 62 mm into the ground with the 20th hit. [1]
(b) Find the total distance that the post has been driven into the ground after 20 hits. [2]
Given that for each subsequent hit after the 20th hit
• the additional distances the post travels form a geometric sequence with
• on the 22nd hit, the post is driven an additional 60 mm into the ground
(c) find the value of r, giving your answer to 3 decimal places. [2]
After a total of N hits, the post will have been driven more than 3 m into the ground.
(d) Find, showing all steps in your working, the smallest possible value of N. [4]

Question 9
[Diagram or table: see page 30 of the paper]
• the curve C with equation y = x – x^2
• the line l with equation y = mx, where m is a constant and 0 < m < 1
The line and the curve intersect at the origin O and at the point P.
(a) Find, in terms of m, the coordinates of P. [2]
The region R_1, shown shaded in Figure 2, is bounded by C and l.
(b) Show that the area of R_1 is
[Diagram or table: see page 30 of the paper]
[5]
The region R_2, also shown shaded in Figure 2, is bounded by C, the x‑axis and l.
Given that the area of R_1 is equal to the area of R_2
(c) find the exact value of m. [3]

Question 10
(i) Prove by counter example that the statement
[Diagram or table: see page 34 of the paper]
is not true. [1]
(ii) Use proof by exhaustion to prove that if n is an integer then
[Diagram or table: see page 34 of the paper]
is always even. [4]
[Diagram or table: see page 36 of the paper]