# WMA12 Pure Mathematics 2 (P2) May/June 2019 Paper 01

Pearson Edexcel International A Level WMA12 Pure Mathematics 2 (P2) past paper 01, May/June 2019. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma12/2019-may-june-paper-01/
- PDF: https://mathvsarham.com/papers/wma12/WMA12_may-june_2019_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 2019
- 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 sequence a_1, a_2, a_3, ... is defined by
[Diagram or table: see page 2 of the paper]
Find the value of
(a)(i) a_2
(ii) a_107 [2]
(b) (2a – 1) ∑_n [2]

Question 2
A circle C has equation
[Diagram or table: see page 4 of the paper]
(a)(i) the coordinates of the centre of C,
(ii) the exact value of the radius of C. [3]
The point P(5, 4) lies on C.
(b) Find the equation of the tangent to C at P, writing your answer in the form y = mx + c, where m and c are constants to be found. [4]

Question 3
(i) Use algebra to prove that for all real values of x
[Diagram or table: see page 6 of the paper]
[3]
(ii) Show that the following statement is untrue.
[Diagram or table: see page 6 of the paper]
[1]

Question 4
(a) Find the first four terms, in ascending powers of x, of the binomial expansion of
[Diagram or table: see page 8 of the paper]
[4]
(b) Given that x is small, so terms in x^4 and higher powers of x may be ignored, show
[Diagram or table: see page 8 of the paper]
where a and b are constants to be found. [3]

Question 5
A company makes a particular type of watch.
The annual profit made by the company from sales of these watches is modelled by the equation
[Diagram or table: see page 10 of the paper]
where P is the annual profit measured in thousands of pounds and £x is the selling price of the watch.
According to this model,
(a) find, using calculus, the maximum possible annual profit. [6]
(b) Justify, also using calculus, that the profit you have found is a maximum. [2]

Question 6
[Diagram or table: see page 12 of the paper]
Given (x – 3) is a factor of f(x),
(a) show that k = 9 [2]
(b) Using algebra and showing each step of your working, fully factorise f(x). [4]
(c) Solve, for 0 - ș  360q, the equation
[Diagram or table: see page 12 of the paper]
giving your answers to one decimal place. [2]

Question 7
Kim starts working for a company.
Ɣ In year 1 her annual salary will be £16 200
Ɣ In year 10 her annual salary is predicted to be £31 500
Model A assumes that her annual salary will increase by the same amount each year.
(a) According to model A, determine Kim’s annual salary in year 2. [3]
Model B assumes that her annual salary will increase by the same percentage each year.
(b) According to model B, determine Kim’s annual salary in year 2. Give your answer to the nearest £10 [3]
(c) Calculate, according to the two models, the difference between the total amounts that Kim is predicted to earn from year 1 to year 10 inclusive. Give your answer to the nearest £10 [3]

Question 8
(i) Find the exact solution of the equation
[Diagram or table: see page 20 of the paper]
giving your answer in the form a + b log_23, where a and b are constants to be found. [4]
(ii) Using the laws of logarithms, solve
[Diagram or table: see page 20 of the paper]
[5]

Question 9
(a) Show that the equation
[Diagram or table: see page 24 of the paper]
can be written in the form
[Diagram or table: see page 24 of the paper]
[4]
(b) Hence solve, for 0 - x  π/2
[Diagram or table: see page 24 of the paper]
giving your answers, where appropriate, to 2 decimal places. [4]

Question 10
[Diagram or table: see page 28 of the paper]
Figure 1 shows a sketch of part of the curve C with equation y = f(x) where
[Diagram or table: see page 28 of the paper]
(a) find the range of values of x for which f(x) is increasing, [4]
(b) show that ⎛ 36/⎝ + 2x − 13⎞/⎠ dx = 0
[4]
The point P(2, 0) and the point Q(6, 0) lie on C.
Given ⎛ 36/⎝ + 2x − 13⎞/⎠ dx = −8 ⎜ ⎟
[Diagram or table: see page 28 of the paper]
(c)(i) state the value of ⎛ 36/⎝ + 2x − 13⎞/⎠ dx
[Diagram or table: see page 28 of the paper]
(ii) find the value of the constant k such that ⎛ 36/⎝ + 2x + k⎞/⎠ dx = 0
[3]
[Diagram or table: see page 32 of the paper]