# WMA12 Pure Mathematics 2 (P2) May/June 2024 Paper 01R

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

- Page: https://mathvsarham.com/past-papers/wma12/2024-may-june-paper-01r/
- PDF: https://mathvsarham.com/papers/wma12/WMA12_may-june_2024_paper_01R_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 2024
- Paper: 01R
- Component code: WMA12/01R
- 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 sequence u_1 , u_2 , u_3 , … satisfies
[Diagram or table: see page 2 of the paper]
• u_1 = 7
• u_3 = 4
(a) find the value of u_2 [2]
(b) find u  2r 
[3]

Question 2
The table shows corresponding values of x and y for a continuous curve with equation y = f ( x) between x = –4 and x = 5, where a is a constant.
[Diagram or table: see page 4 of the paper]
The trapezium rule is used with all the y values in the table to find an approximation for
[Diagram or table: see page 4 of the paper]
Given that the value of this approximation is 19.3
(a) find the value of the constant a to 3 significant figures. [3]
(b) Use the given answer of 19.3 to find an approximate value for
[Diagram or table: see page 4 of the paper]
[2]

Question 3
A circle has equation
[Diagram or table: see page 6 of the paper]
(a) Find
(i) the coordinates of the centre of the circle,
(ii) the radius of the circle. [3]
Given that P is the point on the circle that is nearest the origin O,
(b) find the exact length of OP [2]

Question 4
(a) Find the first 4 terms, in ascending powers of x , of the binomial expansion of
giving each coefficient in simplest form. [4]
(b) Hence find the coefficient of x^2 in the expansion of
[Diagram or table: see page 8 of the paper]
[3]

Question 5
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
The depth of water, D metres, in a harbour on a particular day is given by the equation
[Diagram or table: see page 10 of the paper]
where t is the number of hours after midnight.
(a) Show that the depth of water in the harbour at 2 am is just over 4 metres. [1]
(b) Find, to the nearest minute, the first time after midday when the depth of water in the harbour is exactly 6 metres. [5]

Question 6
[Diagram or table: see page 12 of the paper]
where p and q are constants.
Given that
• (2x + 3) is a factor of f (x)
• f ( x) has a remainder of –5 when divided by (x + 2)
(a)(i) show that p = 10
(ii) find the value of q. [5]
(b) Hence find the range of values of x for which f ( x) is decreasing.
(Solutions based entirely on calculator technology are not acceptable.) [4]

Question 7
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
(i) Solve, for 0  x < 2π , the equation
[Diagram or table: see page 16 of the paper]
giving the answers in radians to 3 decimal places. [5]
(ii) Given that
• 0 < θ < 90°
• cos θ = 1/3
find, in simplest form, the exact value of tan θ [2]

Question 8
(i)(a) In an arithmetic series the first term is a and the common difference is d.
Show that
[Diagram or table: see page 18 of the paper]
[3]
(b) Hence find
[Diagram or table: see page 18 of the paper]
[3]
(ii) Given that the first three terms of a geometric series are
[Diagram or table: see page 18 of the paper]
where k is a constant,
(a) show that
[Diagram or table: see page 18 of the paper]
[3]
Given also that this series is convergent,
(b) find the value of S_∞ [4]

Question 9
Given that
[Diagram or table: see page 22 of the paper]
(a) verify that t = 4 is a solution of the above equation, [2]
(b) show that
[Diagram or table: see page 22 of the paper]
[3]
(c) Hence, using algebra and showing your working, solve
[Diagram or table: see page 22 of the paper]
giving each answer in simplest form.
(Solutions based entirely on calculator technology are not acceptable.) [4]

Question 10
[Diagram or table: see page 26 of the paper]
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
Figure 1 shows a sketch of part of the curve C with equation
[Diagram or table: see page 26 of the paper]
The point P is the stationary point on C.
(a) Find, using calculus, the x coordinate of P. [4]
The finite region R, shown shaded in Figure 1, is bounded by the curve C, the x-axis and the line with equation x = 1
(b) Using calculus, calculate the exact area of R. [5]