# WMA13 Pure Mathematics 3 (P3) May/June 2022 Paper 01

Pearson Edexcel International A Level WMA13 Pure Mathematics 3 (P3) past paper 01, May/June 2022. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma13/2022-may-june-paper-01/
- PDF: https://mathvsarham.com/papers/wma13/WMA13_may-june_2022_paper_01_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International A Level
- Subject: WMA13 Pure Mathematics 3 (P3) (https://mathvsarham.com/past-papers/wma13/)
- Session: May/June 2022
- Paper: 01
- Component code: WMA13/01
- 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 curve C has equation
[Diagram or table: see page 2 of the paper]
(a) Find dy/dx [2]
Given that the point P  1/ 3 , 1 lies on C,
[Diagram or table: see page 2 of the paper]
(b) find the equation of the normal to C at P. Write your answer in the form ax + by + c = 0 where a, b and c are integers to be found. [4]

Question 2
The functions f and g are defined by
[Diagram or table: see page 4 of the paper]
(a) Find the value of fg(5) [2]
(b) Find f ^–1 [3]
(c) Solve the equation
[Diagram or table: see page 4 of the paper]
[4]

Question 3
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
Given that k is a positive constant,
(a) find
[Diagram or table: see page 8 of the paper]
[2]
Given also that
[Diagram or table: see page 8 of the paper]
(b) find the value of k [4]

Question 4
[Diagram or table: see page 10 of the paper]
The number of subscribers to an online video streaming service, N, is modelled by the equation
[Diagram or table: see page 10 of the paper]
where a and b are constants and t is the number of years since monitoring began.
The line in Figure 1 shows the linear relationship between t and log_10 N
The line passes through the points (0, 3.08) and (5, 3.85)
Using this information,
(a) find an equation for this line. [2]
(b) Find the value of a and the value of b, giving your answers to 3 significant figures. [3]
When t = T the number of subscribers is 500 000
According to the model,
(c) find the value of T [2]

Question 5
[Diagram or table: see page 14 of the paper]
Figure 2 shows part of the graph with equation y = f(x), where
and k is a positive constant.
The graph intersects the y‑axis at the point A and has a minimum point at B as shown.
(a)(i) Find the y coordinate of A
(ii) Find, in terms of k, the x coordinate of B [2]
(b) Find, in terms of k, the range of values of x that satisfy the inequality [3]
Given that the line y = 3 – 2x intersects the graph y = f(x) at two distinct points,
(c) find the range of possible values of k [3]

Question 6
[Diagram or table: see page 18 of the paper]
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
The function f is defined by
[Diagram or table: see page 18 of the paper]
(a) Show that
[Diagram or table: see page 18 of the paper]
where k is an integer to be found. [4]
(b) Hence, find the values of x for which f′(x) = 0 [1]
Figure 3 shows a sketch of the curve C with equation y = f(x).
The curve has a local maximum at the point P
(c) Find the exact coordinates of P [2]
The function g is defined by
[Diagram or table: see page 18 of the paper]
(d) Find the range of g [3]

Question 7
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
(a) Show that the equation
[Diagram or table: see page 22 of the paper]
can be written as
[Diagram or table: see page 22 of the paper]
[4]
(b) Hence solve, for 0 < θ < π/2 , the equation
[Diagram or table: see page 22 of the paper]
giving your answers to 3 significant figures. [4]

Question 8
[Diagram or table: see page 26 of the paper]
Figure 4 is a graph showing the velocity of a sprinter during a 100 m race.
The sprinter’s velocity during the race, v m s^–1, is modelled by the equation
[Diagram or table: see page 26 of the paper]
where t seconds is the time after the sprinter begins to run.
According to the model,
(a) find, using calculus, the sprinter’s maximum velocity during the race. [5]
Given that the sprinter runs 100 m in T seconds, such that
[Diagram or table: see page 26 of the paper]
(b) show that T is a solution of the equation
[Diagram or table: see page 26 of the paper]
[4]
The iteration formula
[Diagram or table: see page 26 of the paper]
is used to find an approximate value for T
Using this iteration formula with T_1= 10
(c) find, to 4 decimal places,
(i) the value of T_2
(ii) the time taken by the sprinter to run the race, according to the model. [3]

Question 9
[Diagram or table: see page 30 of the paper]
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
Figure 5 shows the curve with equation
[Diagram or table: see page 30 of the paper]
The point M, shown in Figure 5, is the minimum point on the curve.
(a) Show that the x coordinate of M is a solution of the equation
[Diagram or table: see page 30 of the paper]
[4]
(b) Hence find, to 3 significant figures, the x coordinate of M. [5]
[Diagram or table: see page 32 of the paper]