# WMA12 Pure Mathematics 2 (P2) Oct/Nov 2021 Paper 01

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

- Page: https://mathvsarham.com/past-papers/wma12/2021-oct-nov-paper-01/
- PDF: https://mathvsarham.com/papers/wma12/WMA12_oct-nov_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: Oct/Nov 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
The first three terms, in ascending powers of x, of the binomial expansion of (1 + kx)^16 are
[Diagram or table: see page 2 of the paper]
where k and p are constants.
(a) Find, in simplest form,
(i) the value of k
(ii) the value of p [3]
[Diagram or table: see page 2 of the paper]
Using the value of k found in part (a),
(b) find the term in x^2 in the expansion of g (x). [3]

Question 2
A sequence is defined by
[Diagram or table: see page 4 of the paper]
where k is a positive constant.
(a) Find, in terms of k, an expression for u_3 [2]
Given that u = 117
[Diagram or table: see page 4 of the paper]
(b) find the value of k. [3]

Question 3
[Diagram or table: see page 6 of the paper]
Figure 1 shows a sketch of part of the curve with equation y = log_10 x
The region R, shown shaded in Figure 1, is bounded by the curve, the line with equation x = 2, the x-axis and the line with equation x = 14
Using the trapezium rule with four strips of equal width,
(a) show that the area of R is approximately 10.10 [3]
(b) Explain how the trapezium rule could be used to obtain a more accurate estimate for the area of R. [1]
(c) Using the answer to part (a) and making your method clear, estimate the value of
(i) log_10 x dx ∫_2
(ii) log_10 100x^3 dx ∫_2 [4]

Question 4
[Diagram or table: see page 10 of the paper]
(a) State the value of the remainder when f (x) is divided by (2x − 3) [1]
(b) Use the factor theorem to show that (x − 3) is a factor of f (x) [2]
(c) Hence,
(i) factorise f (x)
(ii) show that the equation f (x) = 0 has only one real root. [5]

Question 5
A company that owned a silver mine
• extracted 480 tonnes of silver from the mine in year 1 • extracted 465 tonnes of silver from the mine in year 2 • extracted 450 tonnes of silver from the mine in year 3
and so on, forming an arithmetic sequence.
(a) Find the mass of silver extracted in year 14 [2]
After a total of 7770 tonnes of silver was extracted, the company stopped mining.
Given that this occurred at the end of year N,
(b) show that
[Diagram or table: see page 14 of the paper]
[3]
(c) Hence, state the value of N. [1]

Question 6
(i) The circle C_1 has equation
[Diagram or table: see page 16 of the paper]
(a) Find the coordinates of the centre of C_1 [2]
(b) State the possible range in values for k. [2]
(ii) The point P( p, 0) , the point Q(−2, 10) and the point R(8, −14) lie on a different circle, C_2
Given that
• p is a positive constant • QR is a diameter of C_2
find the exact value of p. [4]

Question 7
(i) A geometric sequence has first term 4 and common ratio 6 Given that the n^th term is greater than 10^100, find the minimum possible value of n. [3]
(ii) A different geometric sequence has first term a and common ratio r.
Given that
• the second term of the sequence is −6 • the sum to infinity of the series is 25
(a) show that
[Diagram or table: see page 20 of the paper]
[3]
(b) Write down the solutions of
[Diagram or table: see page 20 of the paper]
[1]
Hence,
(c) state the value of r, giving a reason for your answer, [1]
(d) find the sum of the first 4 terms of the series. [2]

Question 8
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
[Diagram or table: see page 24 of the paper]
Figure 2 shows a sketch of part of the curve C with equation
[Diagram or table: see page 24 of the paper]
The point M is the maximum turning point of C and is shown in Figure 2.
Given that the x coordinate of M is 2
(a) show that k = 28 [3]
(b) Determine the range of values of x for which y is increasing. [2]
The line l passes through M and is parallel to the x-axis.
The region R, shown shaded in Figure 2, is bounded by the curve C, the line l and the y-axis.
(c) Find, by algebraic integration, the exact area of R. [5]

Question 9
(a) Prove that for all positive values of x and y,
[Diagram or table: see page 28 of the paper]
[3]
(b) Prove by counter-example that this inequality does not hold when x and y are both negative. [1]

Question 10
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
(i) Solve, for − π/2 < x < π/2
[Diagram or table: see page 30 of the paper]
[5]
(ii) Solve, for 0 < θ < 360°
[Diagram or table: see page 30 of the paper]
giving your answers, as appropriate, to one decimal place. [5]
[Diagram or table: see page 32 of the paper]