# WMA13 Pure Mathematics 3 (P3) Oct/Nov 2020 Paper 01

Pearson Edexcel International A Level WMA13 Pure Mathematics 3 (P3) past paper 01, Oct/Nov 2020. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma13/2020-oct-nov-paper-01/
- PDF: https://mathvsarham.com/papers/wma13/WMA13_oct-nov_2020_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 2020
- 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
Solve, for 0  x < 360°, the equation
[Diagram or table: see page 2 of the paper]
giving your solutions to one decimal place.
[Diagram or table: see page 2 of the paper]
[5]

Question 2
A scientist monitored the growth of bacteria on a dish over a 30‑day period.
The area, N mm^2, of the dish covered by bacteria, t days after monitoring began, is modelled by the equation
[Diagram or table: see page 4 of the paper]
(a) Show that this equation may be written in the form
[Diagram or table: see page 4 of the paper]
where a and b are constants to be found. Give the value of a to the nearest integer and give the value of b to 3 significant figures. [4]
(b) Use the model to find the area of the dish covered by bacteria 30 days after monitoring began. Give your answer, in mm^2, to 2 significant figures. [2]

Question 3
[Diagram or table: see page 6 of the paper]
Figure 1 shows a sketch of a curve with equation y = f(x) where
[Diagram or table: see page 6 of the paper]
(a) Find, in simplest form, f ʹ(x). [4]
(b) Hence find the range of f. [3]

Question 4
[Diagram or table: see page 10 of the paper]
Figure 2 shows a sketch of part of the graph with equation y = f(x) where
[Diagram or table: see page 10 of the paper]
(a) Find f f (6) [2]
(b) Solve the equation f(x) = 5x [2]
Given that the equation f(x) = k , where k is a constant, has exactly two roots,
(c) state the set of possible values of k. [2]
The graph with equation y = f(x) is transformed onto the graph with equation y = af(x − b)
The vertex of the graph with equation y = af(x − b) is (6, 3).
Given that a and b are constants,
(d) find the value of a and the value of b. [2]

Question 5
(a) Show that
[Diagram or table: see page 14 of the paper]
[4]
(b) Hence find, using algebraic integration,
[Diagram or table: see page 14 of the paper]
[4]

Question 6
[Diagram or table: see page 16 of the paper]
Figure 3 shows a sketch of curve C_1 with equation y = 5e^x^−1 + 3
[Diagram or table: see page 16 of the paper]
The point P lies on C_1 and has y coordinate 18
(a) Find the x coordinate of P, writing your answer in the form ln k, where k is a constant to be found. [3]
The curve C_1 meets the curve C_2 at x = α and at x = β , as shown in Figure 3.
(b) Using a suitable interval and a suitable function that should be stated, show that to 3 decimal places α = 1.134 [3]
The iterative equation
[Diagram or table: see page 16 of the paper]
is used to find an approximation to β .
Using this iterative formula with x_1 = −3
(c) find the value of x_2 and the value of β , giving each answer to 6 decimal places. [3]

Question 7
(a) Express cos x + 4 sin x in the form R cos (x − α) where R > 0 and 0 < α < π/2
Give the exact value of R and give the value of α, in radians, to 3 decimal places. [3]
A scientist is studying the behaviour of seabirds in a colony.
She models the height above sea level, H metres, of one of the birds in the colony by the equation
[Diagram or table: see page 20 of the paper]
where t seconds is the time after it leaves the nest.
Find, according to the model,
(b) the minimum height of the seabird above sea level, giving your answer to the nearest cm, [2]
(c) the value of t, to 2 decimal places, when H = 10 [4]

Question 8
(i) The curve C has equation y = g(x) where
[Diagram or table: see page 24 of the paper]
(a) Find gʹ(x) [2]
(b) Hence find the x coordinate of the stationary point of C. [3]
(ii) A different curve has equation
[Diagram or table: see page 24 of the paper]
where f (x) is a function of e^x that should be found. [4]

Question 9
(a) Given that
[Diagram or table: see page 28 of the paper]
find the value of the constant P and show that Q = 5 [4]
The curve C has equation y = g(x), where
[Diagram or table: see page 28 of the paper]
g(x) = − 3 < x < 3.5 x ∈ 
[Diagram or table: see page 28 of the paper]
(b) Find the equation of the tangent to C at the point where x = 2 Give your answer in the form y = mx + c , where m and c are constants to be found. [5]
[Diagram or table: see page 28 of the paper]
Figure 4 shows a sketch of the curve C. The region R, shown shaded in Figure 4, is bounded by C, the y‑axis, the x‑axis and the line with equation x = 2
(c) Find the exact area of R, writing your answer in the form a + b ln2 , where a and b are constants to be found. [5]
[Diagram or table: see page 32 of the paper]