# WMA12 Pure Mathematics 2 (P2) Oct/Nov 2024 Paper 01

Pearson Edexcel International A Level WMA12 Pure Mathematics 2 (P2) past paper 01, Oct/Nov 2024. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma12/2024-oct-nov-paper-01/
- PDF: https://mathvsarham.com/papers/wma12/WMA12_oct-nov_2024_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 2024
- 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 continuous curve 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]
Using the trapezium rule with all the values of y in the given table,
(a) find an estimate for
[Diagram or table: see page 2 of the paper]
giving your answer to one decimal place. [3]
(b) Using your answer to part (a) and making your method clear, estimate
[Diagram or table: see page 2 of the paper]
[2]

Question 2
A sequence of numbers u_1, u_2, u_3, ... is defined by
[Diagram or table: see page 4 of the paper]
where k is a constant.
(a) Show that u_5= 7
[Diagram or table: see page 4 of the paper]
[3]
Given that u_r  30 
(b) find the value of k.
[Diagram or table: see page 4 of the paper]
[2]
(c) Hence find the value of u_r
[Diagram or table: see page 4 of the paper]
[2]

Question 3
[Diagram or table: see page 6 of the paper]
where A and B are integers.
Given that when f (x) is divided by (x + 3) the remainder is 55
(a) show that
[Diagram or table: see page 6 of the paper]
[2]
Given also that (2x – 5) is a factor of f (x),
(b) find the value of A and the value of B. [3]
(c) Hence find the quotient when f (x) is divided by (x – 7) [2]

Question 4
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
The curve C has equation
[Diagram or table: see page 10 of the paper]
(a) Find dy/dx giving each term in simplest form. [2]
(b) Hence find the x coordinate of the stationary point of C. [2]
(c)(i) Find d y/dx_2 giving each term in simplest form.
(ii) Hence determine the nature of the stationary point of C, giving a reason for your answer. [2]
(d) State the range of values of x for which y is decreasing. [1]

Question 5
(a) Find, in terms of a, the first 3 terms, in ascending powers of x, of the binomial expansion of
[Diagram or table: see page 12 of the paper]
where a is a non‑zero constant. Give each term in simplest form. [3]
[Diagram or table: see page 12 of the paper]
Given that the constant term in the expansion of f (x) is 576
(b) find the value of a. [4]

Question 6
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
Using the laws of logarithms, solve
[Diagram or table: see page 14 of the paper]
[5]

Question 7
Jem pays money into a savings scheme, A, over a period of 300 months.
Jem pays £20 into scheme A in month 1, £20.50 in month 2, £21 in month 3 and so on, so that the amounts Jem pays each month form an arithmetic sequence.
(a) Show that Jem pays £69.50 into scheme A in month 100 [1]
(b) Find the total amount that Jem pays into scheme A over the period of 300 months. [2]
Kim pays money into a different savings scheme, B, over the same period of 300 months.
In a model, the amounts Kim pays into scheme B increase by the same percentage each month, so that the amounts Kim pays each month form a geometric sequence.
Given that Kim pays
• £20 into scheme B in month 1
• £250 into scheme B in month 300
(c) use the model to calculate, to the nearest £10, the difference between the total amount paid into scheme A and the total amount paid into scheme B over the period of 300 months. [3]

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 20 of the paper]
Figure 1 shows a sketch of part of the curve C_1 with equation
[Diagram or table: see page 20 of the paper]
and part of the curve C_2 with equation
[Diagram or table: see page 20 of the paper]
The curves C_1 and C_2 intersect at the points P and Q as shown in Figure 1.
(a) Use algebra to find the x coordinate of P and the x coordinate of Q. [4]
The finite region R, shown shaded in Figure 1, is bounded by C_1 and C_2
(b) Use algebraic integration to find the exact area of R. [4]

Question 9
[Diagram or table: see page 24 of the paper]
Solutions relying entirely on calculator technology are not acceptable.
(a) Show that the equation
[Diagram or table: see page 24 of the paper]
can be written as
[Diagram or table: see page 24 of the paper]
[3]
(b) Hence solve, for –π < x < π, the equation
[Diagram or table: see page 24 of the paper]
giving your answers to 3 significant figures. [4]

Question 10
The circle C has equation
[Diagram or table: see page 26 of the paper]
(a) Find
(i) the coordinates of the centre of C,
(ii) the exact value of the radius of C. [3]
The line L has equation y = mx + 1, where m is a constant.
Given that L is the tangent to C at the point P,
(b) show that
[Diagram or table: see page 26 of the paper]
[3]
(c) Hence find the possible pairs of coordinates of P. [4]

Question 11
(i) Prove by counter example that the statement
[Diagram or table: see page 30 of the paper]
is false. [2]
(ii) Use proof by exhaustion to prove that if m is an integer that is not divisible by 3, then
[Diagram or table: see page 30 of the paper]
is divisible by 3 [4]