# WMA12 Pure Mathematics 2 (P2) May/June 2022 Paper 01

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

- Page: https://mathvsarham.com/past-papers/wma12/2022-may-june-paper-01/
- PDF: https://mathvsarham.com/papers/wma12/WMA12_may-june_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: May/June 2022
- 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
Find the first four terms, in ascending powers of x, of the binomial expansion of
[Diagram or table: see page 2 of the paper]
Give each coefficient as an integer. [4]

Question 2
[Diagram or table: see page 4 of the paper]
Figure 1 shows the graph of
[Diagram or table: see page 4 of the paper]
where x is in radians.
The table below shows some values of x and y for this graph, with values of y given to 3 decimal places.
[Diagram or table: see page 4 of the paper]
(a) Complete the table above, giving values of y to 3 decimal places. [2]
(b) Use the trapezium rule with all the y values in the completed table to find, to 2 decimal places, an estimate for
[Diagram or table: see page 4 of the paper]
[3]
(c) Use your answer to part (b) to find an estimate for
[Diagram or table: see page 4 of the paper]
[3]

Question 3
(i) Show that the following statement is false:
[Diagram or table: see page 8 of the paper]
[2]
(ii) Given that the points A(1, 0) , B(3, −10) and C(7, −6) lie on a circle, prove that AB is a diameter of this circle. [5]

Question 4
In this question you must show all stages of your working.
[Diagram or table: see page 12 of the paper]
Given that a and b are positive constants, solve the simultaneous equations
[Diagram or table: see page 12 of the paper]
[6]

Question 5
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
Solve, for −180° < θ  180° , the equation
[Diagram or table: see page 14 of the paper]
[6]

Question 6
In a geometric sequence u_1 , u_2 , u_3 , …
• the common ratio is r • u_2+ u_3 = 6 • u_4= 8
(a) Show that r satisfies
[Diagram or table: see page 16 of the paper]
[3]
Given that the geometric sequence has a sum to infinity,
(b) find u_1 [3]
(c) find S_∞ [2]

Question 7
[Diagram or table: see page 20 of the paper]
where A and B are constants.
Given that
• (x + 2) is a factor of f(x)
• f (x) dx = 176 ∫_3
find the value of A and the value of B. [7]

Question 8
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
A curve has equation
[Diagram or table: see page 22 of the paper]
(a) Find dy/dx [3]
(b) Hence find the coordinates of the stationary points of the curve. [5]

Question 9
A scientist is using carbon‑14 dating to determine the age of some wooden items.
The equation for carbon‑14 dating an item is given by
[Diagram or table: see page 24 of the paper]
• N grams is the amount of carbon‑14 currently present in the item • k grams was the initial amount of carbon‑14 present in the item • t is the number of years since the item was made • λ is a constant, with 0 < λ < 1
(a) Sketch the graph of N against t for k = 1 [2]
Given that it takes 5700 years for the amount of carbon‑14 to reduce to half its initial value,
(b) show that the value of the constant λ is 0.999878 to 6 decimal places. [2]
Given that Item A
• is known to have had 15 grams of carbon‑14 present initially • is thought to be 3250 years old
(c) calculate, to 3 significant figures, how much carbon‑14 the equation predicts is currently in Item A. [2]
Item B is known to have initially had 25 grams of carbon‑14 present, but only 18 grams now remain.
(d) Use algebra to calculate the age of Item B to the nearest 100 years. [3]

Question 10
The circle C has centre X (3, 5) and radius r
The line l has equation y = 2x + k , where k is a constant.
(a) Show that l and C intersect when
[Diagram or table: see page 28 of the paper]
[3]
Given that l is a tangent to C,
(b) show that 5r^2= (k + p)^2 , where p is a constant to be found. [3]
[Diagram or table: see page 28 of the paper]
• cuts the y‑axis at the point A • touches the circle C at the point B
as shown in Figure 2.
Given that AB = 2r
(c) find the value of k [6]
[Diagram or table: see page 32 of the paper]