# WMA13 Pure Mathematics 3 (P3) Oct/Nov 2024 Paper 01

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

- Page: https://mathvsarham.com/past-papers/wma13/2024-oct-nov-paper-01/
- PDF: https://mathvsarham.com/papers/wma13/WMA13_oct-nov_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: Oct/Nov 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
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
Solve, for 0 < θ  360° , the equation
[Diagram or table: see page 2 of the paper]
giving your answers to one decimal place. [5]

Question 2
[Diagram or table: see page 4 of the paper]
Figure 1 shows a sketch of the curve with equation
[Diagram or table: see page 4 of the paper]
(a) Find dy/dx in terms of y. [2]
The point P lies on the curve and is shown in Figure 1.
Given that the tangent to the curve at P is parallel to the y‑axis,
(b) find the coordinates of P. [3]

Question 3
[Diagram or table: see page 6 of the paper]
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
Figure 2 shows a sketch of the curve with equation y = f (x) , where
[Diagram or table: see page 6 of the paper]
(a) Solve the equation
[Diagram or table: see page 6 of the paper]
[3]
(b) Find the set of values of x for which
[Diagram or table: see page 6 of the paper]
[4]

Question 4
The number of bacteria on a surface is being monitored.
The number of bacteria, N, on the surface, t hours after monitoring began is modelled by the equation
[Diagram or table: see page 10 of the paper]
Use the equation of the model to answer parts (a) to (c).
(a) Find the initial number of bacteria on the surface. [1]
(b) Show that the equation of the model can be written in the form
[Diagram or table: see page 10 of the paper]
where a and b are constants to be found. Give the value of b to 2 decimal places. [3]
(c) Hence find the rate of growth of bacteria on the surface exactly 5 hours after monitoring began. [2]

Question 5
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
(a) Show that sin 3x can be written in the form
[Diagram or table: see page 12 of the paper]
where P and Q are constants to be found. [4]
(b) Hence or otherwise, solve, for 0 < θ  360° , the equation
[Diagram or table: see page 12 of the paper]
giving your answers, in degrees, to one decimal place as appropriate. [4]

Question 6
The functions f and g are defined by
[Diagram or table: see page 16 of the paper]
(a) Find gf(2) [2]
(b) Find f^–1 [3]
(c) Solve the equation
[Diagram or table: see page 16 of the paper]
[3]

Question 7
[Diagram or table: see page 20 of the paper]
The curve C has equation y = f (x) , where
[Diagram or table: see page 20 of the paper]
(a) Show that
[Diagram or table: see page 20 of the paper]
where k is a constant to be found. [4]
The point P, shown in Figure 3, is the minimum turning point on C.
(b) Find the coordinates of P. [2]
(c) Hence find the range of the function g defined by
[Diagram or table: see page 20 of the paper]
[2]
The point Q with coordinates  1/ 2 , 3 /8  lies on C.
(d) Find the coordinates of the point to which Q is mapped when C is transformed to the curve with equation
[Diagram or table: see page 20 of the paper]
[2]

Question 8
[Diagram or table: see page 24 of the paper]
The heart rate of a horse is being monitored. The heart rate H, measured in beats per minute (bpm), is modelled by the equation
[Diagram or table: see page 24 of the paper]
where t minutes is the time after monitoring began.
Figure 4 is a sketch of H against t.
Use the equation of the model to answer parts (a) to (e).
(a) State the initial heart rate of the horse. [1]
In the long term, the heart rate of the horse approaches L bpm.
(b) State the value of L. [1]
The heart rate of the horse reaches its maximum value after T minutes.
(c) Find the value of T, giving your answer to 3 decimal places.
[Diagram or table: see page 24 of the paper]
[5]
The heart rate of the horse is 37 bpm after M minutes.
(d) Show that M is a solution of the equation
[Diagram or table: see page 24 of the paper]
[2]
Using the iteration formula
[Diagram or table: see page 24 of the paper]
(e)(i) find, to 4 decimal places, the value of t_2
(ii) find, to 4 decimal places, the value of M [3]

Question 9
[Diagram or table: see page 28 of the paper]
Figure 5 shows a sketch of part of the curve C with equation y = f (x) where
[Diagram or table: see page 28 of the paper]
(a) Find f′ (x) , giving the answer in simplest form. [3]
The line l is the normal to C at the point P(2, 6)
(b) Show that an equation for l is
[Diagram or table: see page 28 of the paper]
[3]
(c) Write f (x) in the form Ax + B + D/2x + 1 where A, B and D are constants. [3]
The region R, shown shaded in Figure 5, is bounded by C, l and the x‑axis.
(d) Use algebraic integration to find the exact area of R, giving your answer in the form P + Q ln 3 , where P and Q are rational constants.
[Diagram or table: see page 28 of the paper]
[5]