# WMA12 Pure Mathematics 2 (P2) Oct/Nov 2022 Paper 01

Pearson Edexcel International A Level WMA12 Pure Mathematics 2 (P2) past paper 01, Oct/Nov 2022. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma12/2022-oct-nov-paper-01/
- PDF: https://mathvsarham.com/papers/wma12/WMA12_oct-nov_2022_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 2022
- 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
Given that a, b and c are integers greater than 0 such that
• c = b + 2
• a + b + c = 10
Prove, by exhaustion, that the product of a, b and c is always even.
You may use the table below to illustrate your answer. [3]
[Diagram or table: see page 2 of the paper]

Question 2
A curve C has equation y = f(x) where
[Diagram or table: see page 4 of the paper]
and k is a constant.
Given that when f(x) is divided by (4x – 5) the remainder is 243/32
(a) show that k = 2/5 [2]
(b) Find the first three terms, in ascending powers of x, of the binomial expansion of
[Diagram or table: see page 4 of the paper]
giving each term in simplest form. [3]
Using the solution to part (b) and making your method clear,
(c) find the gradient of C at the point where x = 0 [2]

Question 3
A sequence a_1, a_2, a_3, … is defined by
[Diagram or table: see page 8 of the paper]
Find the exact values of
(a)(i) a_1
(ii) a_2
(iii) a_3 [3]
(b) Hence find the exact value of
[Diagram or table: see page 8 of the paper]
You must make your method clear. [4]

Question 4
The weight of a baby mammal is monitored over a 16‑month period.
The weight of the mammal, w kg, is given by
[Diagram or table: see page 10 of the paper]
where t is the age of the mammal in months and a is a constant.
Given that the weight of the mammal was 10 kg when t = 3
(a) show that a = 1.072 correct to 3 decimal places. [3]
Using a = 1.072
(b) find an equation for t in terms of w [3]
(c) find the value of t when w = 15, giving your answer to 3 significant figures. [2]

Question 5
In this question you must show detailed reasoning.
Solutions relying entirely on calculator technology are not acceptable.
(a) Show that the equation
[Diagram or table: see page 12 of the paper]
can be written as
[Diagram or table: see page 12 of the paper]
[3]
(b) Hence solve for – π/2  x  π/2
[Diagram or table: see page 12 of the paper]
[5]

Question 6
The curve C_1 has equation y = f(x).
A table of values of x and y for y = f(x) is shown below, with the y values rounded to 4 decimal places where appropriate.
[Diagram or table: see page 16 of the paper]
(a) Use the trapezium rule with all the values of y in the table to find an approximation for
[Diagram or table: see page 16 of the paper]
giving your answer to 3 decimal places. [3]
[Diagram or table: see page 16 of the paper]
Figure 1 Figure 2
The region R, shown shaded in Figure 1, is bounded by
• the curve C_1
• the curve C_2 with equation y = 2 – 1/4 x^2
• the line with equation x = 2
• the y‑axis
The region R forms part of the design for a logo shown in Figure 2.
The design consists of the shaded region R inside a rectangle of width 2 and height 3
Using calculus and the answer to part (a),
(b) calculate an estimate for the percentage of the logo which is shaded. [4]

Question 7
The curve C has equation
[Diagram or table: see page 20 of the paper]
(a) Write the equation of C in the form
[Diagram or table: see page 20 of the paper]
where a, b, c and d are fully simplified constants. [3]
The curve C has three turning points.
Using calculus,
(b) show that the x coordinates of the three turning points satisfy the equation
[Diagram or table: see page 20 of the paper]
[3]
Given that the x coordinate of one of the turning points is 1
(c) find, using algebra, the exact x coordinates of the other two turning points.
[Diagram or table: see page 20 of the paper]
[3]

Question 8
A geometric sequence has first term a and common ratio r
Given that S_∞ = 3a
(a) show that r = 2/3 [2]
Given also that
[Diagram or table: see page 24 of the paper]
where u_k is the k^th term of this sequence,
(b) find the value of S_10 giving your answer to one decimal place. [5]

Question 9
In this question you must show detailed reasoning.
Solutions relying entirely on calculator technology are not acceptable.
[Diagram or table: see page 26 of the paper]
• the curve C_1 with equation y = x^3– 5x^2+ 3x + 14
• the circle C_2 with centre T
The point T is the minimum turning point of C_1
Using Figure 3 and calculus,
(a) find the coordinates of T [3]
The curve C_1 intersects the circle C_2 at the point A with x coordinate 2
(b) Find an equation of the circle C_2 [3]
The line l shown in Figure 3, is the tangent to circle C_2 at A
(c) Show that an equation of l is
[Diagram or table: see page 26 of the paper]
[3]
The region R, shown shaded in Figure 3, is bounded by C_1, l and the y‑axis.
(d) Find the exact area of R. [3]

Question 10
Given a = log2 3
(i) write, in simplest form, in terms of a,
(a) log2 9
(b) log2 /3/ 16 / [3]
(ii) Solve
[Diagram or table: see page 30 of the paper]
giving your answer, in simplest form, in terms of a. [4]