# WMA12 Pure Mathematics 2 (P2) January 2020 Paper 01

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

- Page: https://mathvsarham.com/past-papers/wma12/2020-january-paper-01/
- PDF: https://mathvsarham.com/papers/wma12/WMA12_january_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: January 2020
- Paper: 01
- Component code: WMA12/01
- Time allowed: 90 minutes
- Total marks: 75
- Pages: 28

## 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 y = log_2 (2x)
The values of y are given to 2 decimal places as appropriate.
[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 log (2x)dx, giving your answer to one decimal place.
[Diagram or table: see page 2 of the paper]
[3]
Using your answer to part (a) and making your method clear, estimate
[Diagram or table: see page 2 of the paper]
(b)(i) ^2 dx ∫_2 5
(ii) log  2/ x dx
[Diagram or table: see page 2 of the paper]
[4]

Question 2
One of the terms in the binomial expansion of (3 + ax)^6, where a is a constant, is 540x^4
(a) Find the possible values of a. [4]
(b) Hence find the term independent of x in the expansion of
[Diagram or table: see page 4 of the paper]
[3]

Question 3
[Diagram or table: see page 6 of the paper]
(a) Use the factor theorem to show that (2x + 3) is a factor of f(x). [2]
(b) Hence, using algebra, write f(x) as a product of three linear factors. [4]
(c) Solve, for π/2 < θ < π, the equation
[Diagram or table: see page 6 of the paper]
giving your answers to 3 significant figures. [2]

Question 4
[Diagram or table: see page 8 of the paper]
Figure 1 shows a sketch of the curve with equation
[Diagram or table: see page 8 of the paper]
The finite region R, shown shaded in Figure 1, is bounded by the curve, the y - axis and the line with equation y = 17
Find the exact area of R. [6]

Question 5
[Diagram or table: see page 10 of the paper]
Solutions relying on calculator technology are not acceptable.
A colony of bees is being studied.
The number of bees in the colony at the start of the study was 30 000
Three years after the start of the study, the number of bees in the colony is 34 000
A model predicts that the number of bees in the colony will increase by p % each year, so that the number of bees in the colony at the end of each year of study forms a geometric sequence.
Assuming the model,
(a) find the value of p, giving your answer to 2 decimal places. [3]
According to the model, at the end of N years of study the number of bees in the colony exceeds 75 000
(b) Find, showing all steps in your working, the smallest integer value of N. [5]

Question 6
The circle C has equation
[Diagram or table: see page 12 of the paper]
(a) Find
(i) the coordinates of the centre of C,
(ii) the exact radius of C. [3]
The line with equation y = k, where k is a constant, is a tangent to C.
(b) Find the possible values of k. [2]
The line with equation y = p, where p is a negative constant, is a chord of C.
Given that the length of this chord is 4 units,
(c) find the value of p. [3]

Question 7
(a) Show that the equation
[Diagram or table: see page 16 of the paper]
may be rewritten in the form
[Diagram or table: see page 16 of the paper]
[3]
(b) Hence solve, for 0  x  90°, the equation
[Diagram or table: see page 16 of the paper]
giving your answers to 2 decimal places. [4]

Question 8
(i) An arithmetic series has first term a and common difference d.
Prove that the sum to n terms of this series is
[Diagram or table: see page 18 of the paper]
[3]
(ii) A sequence u_1, u_2, u_3,… is given by
[Diagram or table: see page 18 of the paper]
Find the value of
(a) u_5 [1]
(b) u ∑_n ^n^=^1 [3]

Question 9
(a) Sketch the curve with equation
[Diagram or table: see page 22 of the paper]
showing the coordinates of any points of intersection with the coordinate axes. [2]
The curve with equation y = 6 meets the curve with equation y = 3 × 4 at the point P.
(b) Show that the x coordinate of P is
[Diagram or table: see page 22 of the paper]
[5]

Question 10
A curve C has equation
[Diagram or table: see page 26 of the paper]
where k is a constant.
The point P with x coordinate 1/2 lies on C.
Given that P is a stationary point of C,
(a) show that k = − 3/2 [4]
(b) Determine the nature of the stationary point at P, justifying your answer. [2]
The curve C has a second stationary point.
(c) Using algebra, find the x coordinate of this second stationary point. [4]
[Diagram or table: see page 28 of the paper]