# WMA12 Pure Mathematics 2 (P2) May/June 2021 Paper 01

Pearson Edexcel International A Level WMA12 Pure Mathematics 2 (P2) past paper 01, May/June 2021. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma12/2021-may-june-paper-01/
- PDF: https://mathvsarham.com/papers/wma12/WMA12_may-june_2021_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 2021
- 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
Adina is saving money to buy a new computer. She saves £5 in week 1, £5.25 in week 2, £5.50 in week 3 and so on until she has enough money, in total, to buy the computer.
She decides to model her savings using either an arithmetic series or a geometric series.
Using the information given,
(a)(i) state with a reason whether an arithmetic series or a geometric series should be used,
(ii) write down an expression, in terms of n, for the amount, in pounds (£), saved in week n. [3]
Given that the computer Adina wants to buy costs £350
(b) find the number of weeks it will take for Adina to save enough money to buy the computer. [4]

Question 2
[Diagram or table: see page 4 of the paper]
Figure 1 shows a sketch of the curve with equation y = 4^x
A copy of Figure 1, labelled Diagram 1, is shown on the next page.
(a) On Diagram 1, sketch the curve with equation
(i) y = 2^x
(ii) y = 4^x – 6
Label clearly the coordinates of any points of intersection with the coordinate axes. [4]
The curve with equation y = 2^x meets the curve with equation y = 4^x – 6 at the point P.
(b) Using algebra, find the exact coordinates of P. [4]
[Diagram or table: see page 5 of the paper]

Question 3
(i) Prove that for all single digit prime numbers, p,
[Diagram or table: see page 6 of the paper]
[2]
(ii) Show, using algebra, that for n  ¥
[Diagram or table: see page 6 of the paper]
[3]

Question 4
(a) Find, in ascending powers of x, up to and including the term in x^3, the binomial expansion of
[Diagram or table: see page 10 of the paper]
fully simplifying each coefficient. [4]
(b) Use the answer to part (a) to find an approximation for 2.0125^13
Give your answer to 3 decimal places. [3]
Without calculating 2.0125^13
(c) state, with a reason, whether the answer to part (b) is an overestimate or an underestimate. [1]

Question 5
[Diagram or table: see page 14 of the paper]
Figure 2 shows a sketch of part of the graph of the curves C_1 and C_2
The curves intersect when x = 2.5 and when x = 4
A table of values for some points on the curve C_1 is shown below, with y values given to 3 decimal places as appropriate.
[Diagram or table: see page 14 of the paper]
Using the trapezium rule with all the values of y in the table,
(a) find, to 2 decimal places, an estimate for the area bounded by the curve C_1, the line with equation x = 2.5, the x-axis and the line with equation x = 4 [4]
The curve C_2 has equation
[Diagram or table: see page 14 of the paper]
(b) Find / x − 3x + 9/ dx
[3]
The region R, shown shaded in Figure 2, is bounded by the curves C_1 and C_2
(c) Use the answers to part (a) and part (b) to find, to one decimal place, an estimate for the area of the region R. [3]

Question 6
A circle has equation
[Diagram or table: see page 18 of the paper]
where k is a positive constant.
Given that the x-axis is a tangent to this circle,
(a) find the value of k. [3]
The circle meets the coordinate axes at the points R, S and T.
(b) Find the exact area of the triangle RST. [4]

Question 7
(a) Given that
[Diagram or table: see page 22 of the paper]
[4]
(b) Show that –4 is a root of this cubic equation. [2]
(c) Hence, using algebra and showing each step of your working, solve
[Diagram or table: see page 22 of the paper]
[4]

Question 8
[Diagram or table: see page 26 of the paper]
(i) Solve, for 0 < θ < 360°, the equation
[Diagram or table: see page 26 of the paper]
giving your answers to one decimal place. [4]
(ii)(a) Show that the equation
[Diagram or table: see page 26 of the paper]
can be written in the form
[Diagram or table: see page 26 of the paper]
where a, b and c are constants to be found.
(b) Hence solve for − π/2  x  π/2 the equation
[Diagram or table: see page 26 of the paper]
[6]

Question 9
[Diagram or table: see page 30 of the paper]
Figure 3 shows a sketch of a square based, open top box.
The height of the box is h cm, and the base edges each have length l cm.
Given that the volume of the box is 250 000 cm^3
(a) show that the external surface area, S cm^2, of the box is given by
[Diagram or table: see page 30 of the paper]
[3]
(b) Use algebraic differentiation to show that S has a stationary point when h = 250 where k is a rational constant to be found. [5]
(c) Justify by further differentiation that this value of h gives the minimum external surface area of the box. [2]
[Diagram or table: see page 32 of the paper]