# WMA12 Pure Mathematics 2 (P2) Oct/Nov 2020 Paper 01

Pearson Edexcel International A Level WMA12 Pure Mathematics 2 (P2) past paper 01, Oct/Nov 2020. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma12/2020-oct-nov-paper-01/
- PDF: https://mathvsarham.com/papers/wma12/WMA12_oct-nov_2020_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: Oct/Nov 2020
- 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
(a) Find the first 4 terms, in ascending powers of x, of the binomial expansion of
[Diagram or table: see page 2 of the paper]
giving each term in its simplest form. [4]
(b) Hence find the constant term in the series expansion of
[Diagram or table: see page 2 of the paper]
[3]

Question 2
[Diagram or table: see page 6 of the paper]
(a) Complete the table below, giving the values of y to 3 decimal places.
[Diagram or table: see page 6 of the paper]
[1]
(b) Use the trapezium rule, with all the values of y from the completed table, to find an approximate value for
[Diagram or table: see page 6 of the paper]
[3]

Question 3
[Diagram or table: see page 8 of the paper]
where a and b are constants.
When f(x) is divided by (x + 4), the remainder is –108
(a) Use the remainder theorem to show that
[Diagram or table: see page 8 of the paper]
[2]
Given also that (2x – 1) is a factor of f(x),
(b) find the value of a and the value of b. [3]
(c) Find f′(x). [1]
(d) Hence find the exact coordinates of the stationary points of the curve with equation y = f(x). [4]

Question 4
The points P and Q have coordinates (–11, 6) and (–3, 12) respectively.
Given that PQ is a diameter of the circle C,
(a)(i) find the coordinates of the centre of C,
(ii) find the radius of C. [4]
(b) Hence find an equation of C. [2]
(c) Find an equation of the tangent to C at the point Q giving your answer in the form ax + by + c = 0 where a, b and c are integers to be found. [3]

Question 5
Ben is saving for the deposit for a house over a period of 60 months.
Ben saves £100 in the first month and in each subsequent month, he saves £5 more than the previous month, so that he saves £105 in the second month, £110 in the third month, and so on, forming an arithmetic sequence.
(a) Find the amount Ben saves in the 40th month. [2]
(b) Find the total amount Ben saves over the 60‑month period. [3]
Lina is also saving for a deposit for a house.
Lina saves £600 in the first month and in each subsequent month, she saves £10 less than the previous month, so that she saves £590 in the second month, £580 in the third month, and so on, forming an arithmetic sequence.
Given that, after n months, Lina will have saved exactly £18 200 for her deposit,
(c) form an equation in n and show that it can be written as
[Diagram or table: see page 16 of the paper]
[3]
(d) Solve the equation in part (c). [2]
(e) State, with a reason, which of the solutions to the equation in part (c) is not a sensible value for n. [1]

Question 6
[Diagram or table: see page 20 of the paper]
Figure 1 shows a sketch of part of the curves C_1 and C_2 with equations
[Diagram or table: see page 20 of the paper]
The curves C_1 and C_2 intersect at the points A and B as shown in Figure 1.
The point A has coordinates (1, 4).
Using algebra and showing all steps of your working,
(a) find the coordinates of the point B. [4]
The finite region R, shown shaded in Figure 1, is bounded by C_1 and C_2
(b) Use algebraic integration to find the exact area of R. [5]

Question 7
(i) Show that
[Diagram or table: see page 24 of the paper]
[3]
(ii) Solve, for 0  x < 90°, the equation
[Diagram or table: see page 24 of the paper]
giving your answers in degrees to one decimal place.
[Diagram or table: see page 24 of the paper]
[4]

Question 8
A geometric series has first term a and common ratio r.
(a) Prove that the sum of the first n terms of this series is given by
[Diagram or table: see page 26 of the paper]
[3]
The second term of a geometric series is –320 and the fifth term is 512/25
(b) Find the value of the common ratio. [2]
(c) Hence find the sum of the first 13 terms of the series, giving your answer to 2 decimal places. [3]

Question 9
(i) Find the exact value of x for which
[Diagram or table: see page 30 of the paper]
[4]
(ii) Given that
[Diagram or table: see page 30 of the paper]
(a) show that
[Diagram or table: see page 30 of the paper]
[4]
(b) Hence find the value of y, giving your answer to 3 decimal places. [2]
[Diagram or table: see page 32 of the paper]