# WMA12 Pure Mathematics 2 (P2) May/June 2023 Paper 01

Pearson Edexcel International A Level WMA12 Pure Mathematics 2 (P2) past paper 01, May/June 2023. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma12/2023-may-june-paper-01/
- PDF: https://mathvsarham.com/papers/wma12/WMA12_may-june_2023_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 2023
- 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 continuous curve C has equation y = f(x).
A table of values of x and y for y = f(x) is shown below.
[Diagram or table: see page 2 of the paper]
Use the trapezium rule with all the values of y in the table to find an approximation for
[Diagram or table: see page 2 of the paper]
giving your answer to 3 decimal places. [3]

Question 2
In this question you must show all stages of your working.
[Diagram or table: see page 4 of the paper]
where a is a constant.
Given that (2x – 3) is a factor of f(x),
(a) use the factor theorem to show that a = –3 [2]
(b) Hence show that the equation f(x) = 0 has only one real root. [4]

Question 3
A circle C has centre (2, 5)
Given that the point P(8, –3) lies on C
(a)(i) find the radius of C
(ii) find an equation for C [3]
(b) Find the equation of the tangent to C at P giving your answer in the form ax + by + c = 0 where a, b and c are integers to be found. [4]

Question 4
The binomial expansion, in ascending powers of x, of
[Diagram or table: see page 8 of the paper]
where p is a constant, can be written in the form
[Diagram or table: see page 8 of the paper]
where A, B, C and D are constants.
(a) Find the value of A [1]
Given that
• B = 18D
• p < 0
(b) find
(i) the value of p
(ii) the value of C [6]

Question 5
Use the laws of logarithms to solve
[Diagram or table: see page 12 of the paper]
[5]

Question 6
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
A software developer released an app to download.
The numbers of downloads of the app each month, in thousands, for the first three months after the app was released were
[Diagram or table: see page 14 of the paper]
where k is a constant.
Given that the numbers of downloads each month are modelled as a geometric series,
(a) show that k^2– 7k – 60 = 0 [2]
(b) predict the number of downloads in the 4th month. [4]
The total number of all downloads of the app is predicted to exceed 3 million for the first time in the Nth month.
(c) Calculate the value of N according to the model. [3]

Question 7
The height of a river above a fixed point on the riverbed was monitored over a 7‑day period.
The height of the river, H metres, t days after monitoring began, was given by
[Diagram or table: see page 18 of the paper]
Given that H has a stationary value at t = α
(a) use calculus to show that α satisfies the equation
[Diagram or table: see page 18 of the paper]
[5]
(b) Hence find the value of α, giving your answer to 3 decimal places. [1]
(c) Use further calculus to prove that H is a maximum at this value of α. [2]

Question 8
(i) A student writes the following statement:
“When a and b are consecutive prime numbers, a^2+ b^2 is never a multiple of 10”
Prove by counter example that this statement is not true. [2]
(ii) Given that x and y are even integers greater than 0 and less than 6, prove by exhaustion, that
[Diagram or table: see page 20 of the paper]
[3]

Question 9
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
(a) Show that
[Diagram or table: see page 22 of the paper]
may be written as
[Diagram or table: see page 22 of the paper]
[3]
(b) Hence solve, for 0 < x < 360°
[Diagram or table: see page 22 of the paper]
giving your answers to one decimal place. [4]

Question 10
The curve C has equation
[Diagram or table: see page 26 of the paper]
where k is a positive constant.
(a) Show that
[Diagram or table: see page 26 of the paper]
where a and b are integers to be found. [5]
[Diagram or table: see page 26 of the paper]
Figure 1 shows a sketch of the curve C and the line l.
Given that l intersects C at the point A(1, 9) and at the point B(16, q) where q is a constant,
(b) show that k = 4 [2]
The region R, shown shaded in Figure 1, is bounded by C and l
Using the answers to parts (a) and (b),
(c) find the area of region R [3]

Question 11
A sequence u_1, u_2, u_3, ... is defined by
[Diagram or table: see page 30 of the paper]
where a and b are constants.
(a) Find, in terms of a and b,
(i) u_2
(ii) u_3 [2]
Given
• u  153 _n
• b = a + 9
(b) show that
[Diagram or table: see page 30 of the paper]
[3]
(c) Hence find the larger possible value of u_2 [3]