# WMA13 Pure Mathematics 3 (P3) May/June 2024 Paper 01

Pearson Edexcel International A Level WMA13 Pure Mathematics 3 (P3) past paper 01, May/June 2024. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma13/2024-may-june-paper-01/
- PDF: https://mathvsarham.com/papers/wma13/WMA13_may-june_2024_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 2024
- 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
[Diagram or table: see page 2 of the paper]
Figure 1 shows a sketch of the graph with equation y = f (x) where
[Diagram or table: see page 2 of the paper]
The point P, shown in Figure 1, is the vertex of the graph.
(a) State the coordinates of P [2]
(b) Use algebra to solve
[Diagram or table: see page 2 of the paper]
[2]
(c) Find the point to which P is mapped, when the graph with equation y = f (x) is transformed to the graph with equation y = 3f (x – 2) [2]
[Diagram or table: see page 4 of the paper]

Question 2
[Diagram or table: see page 4 of the paper]
(a) Write g (x) in the form
[Diagram or table: see page 4 of the paper]
where A, B and C are integers to be found. [3]
(b) Hence use algebraic integration to show that
[Diagram or table: see page 4 of the paper]
where α and β are integers to be found. [4]

Question 3
(i) The variables x and y are connected by the equation
[Diagram or table: see page 8 of the paper]
Sketch the graph of log_10 y against log_10 x
Show on your sketch the coordinates of the points of intersection of the graph with the axes. [3]
(ii) 
[Diagram or table: see page 8 of the paper]
Figure 2 shows the linear relationship between log_3 N and t.
Show that N = ab^t where a and b are constants to be found. [3]

Question 4
[Diagram or table: see page 10 of the paper]
(a) Write f (x) in the form
[Diagram or table: see page 10 of the paper]
where a, b and c are integers to be found. [3]
(b) Use the answer to part (a) to write f (x) in the form
[Diagram or table: see page 10 of the paper]
where R > 0 and 0 < α < π/2
Give the exact value of R and give the value of α in radians to 3 significant figures. [3]
(c) Hence, or otherwise,
(i) state the maximum value of f (x)
(ii) find the second smallest positive value of x at which a maximum value of f (x) occurs. Give your answer to 3 significant figures. [3]

Question 5
The functions f and g are defined by
[Diagram or table: see page 14 of the paper]
(a) Find f^–1(22) [2]
(b) Use differentiation to prove that g is an increasing function. [3]
(c) Find g^–1 [3]
(d) Find the range of fg [2]

Question 6
[Diagram or table: see page 18 of the paper]
Solutions relying entirely on calculator technology are not acceptable.
Figure 3 shows a sketch of part of the curve with equation
[Diagram or table: see page 18 of the paper]
The line l, shown in Figure 3, is the normal to the curve at the point P (8, 5)
(a) Use calculus to show that an equation of l is
[Diagram or table: see page 18 of the paper]
[5]
The region R, shown shaded in Figure 3, is bounded by the curve, the x-axis and l.
(b) Use algebraic integration to find the exact area of R. [4]

Question 7
[Diagram or table: see page 22 of the paper]
Solutions relying entirely on calculator technology are not acceptable.
(a) Given that
[Diagram or table: see page 22 of the paper]
[4]
(b) Hence or otherwise, solve, for 0  θ < 180°
[Diagram or table: see page 22 of the paper]
[4]

Question 8
[Diagram or table: see page 26 of the paper]
Figure 4 is a graph showing the path of a golf ball after the ball has been hit until it first hits the ground.
The vertical height, h metres, of the ball above the ground has been plotted against the horizontal distance travelled, x metres, measured from where the ball was hit.
The ball travels a horizontal distance of d metres before it first hits the ground.
The ball is modelled as a particle travelling in a vertical plane above horizontal ground.
The path of the ball is modelled by the equation
[Diagram or table: see page 26 of the paper]
(a) Find the value of d, giving your answer to 2 decimal places.
[Diagram or table: see page 26 of the paper]
[3]
(b) Show that the maximum value of h occurs when
[Diagram or table: see page 26 of the paper]
[4]
Using the iteration formula
[Diagram or table: see page 26 of the paper]
(c)(i) find the value of x_2 to 2 decimal places,
(ii) find, by repeated iteration, the horizontal distance travelled by the golf ball before it reaches its maximum height. Give your answer to 2 decimal places. [3]

Question 9
[Diagram or table: see page 30 of the paper]
The curve shown in Figure 5 has equation
[Diagram or table: see page 30 of the paper]
The point P / k, π /3  lies on the curve.
(a) Verify that k = 2 [1]
(b)(i) Find dx/dy in terms of y
(ii) Hence show that dy/dx  1/x  1
[6]
The normal to the curve at P cuts the x-axis at the point N.
(c) Find the exact area of triangle OPN, where O is the origin.
Give your answer in the form aπ + bπ^2 where a and b are constants. [3]