# WMA11 Pure Mathematics 1 (P1) May/June 2022 Paper 01

Pearson Edexcel International A Level WMA11 Pure Mathematics 1 (P1) past paper 01, May/June 2022. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma11/2022-may-june-paper-01/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_may-june_2022_paper_01_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International A Level
- Subject: WMA11 Pure Mathematics 1 (P1) (https://mathvsarham.com/past-papers/wma11/)
- Session: May/June 2022
- Paper: 01
- Component code: WMA11/01
- 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
Find
[Diagram or table: see page 2 of the paper]
giving your answer in simplest form. [4]

Question 2
In the triangle ABC,
[Diagram or table: see page 4 of the paper]
(a) Use the sine rule to find the value of sin x° , giving your answer to 4 decimal places. [2]
Given also that AB is the longest side of the triangle,
(b) find the value of x, giving your answer to 2 decimal places. [3]

Question 3
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
[Diagram or table: see page 6 of the paper]
(i) Show that is an integer and find its value.
[2]
(ii) Simplify
[Diagram or table: see page 6 of the paper]
giving your answer in the form a + b 5 where a and b are rational numbers. [3]

Question 4
[Diagram or table: see page 8 of the paper]
Figure 1 shows a sketch of a curve with equation y = f(x)
The curve has a minimum at P(−1, 0) and a maximum at Q  3/ 2 , 2/
[Diagram or table: see page 8 of the paper]
The line with equation y = 1 is the only asymptote to the curve.
On separate diagrams sketch the curves with equation
(i) y = f(x) − 2 [3]
(ii) y = f(−x) [3]
On each sketch you must clearly state • the coordinates of the maximum and minimum points • the equation of the asymptote

Question 5
The curve C has equation y = f(x)
Given that • f(x) is a quadratic expression • the maximum turning point on C has coordinates (−2, 12) • C cuts the negative x-axis at −5
(a) find f(x) [4]
The line l_1 has equation y = 4/5 x
Given that the line l_2 is perpendicular to l_1 and passes through (−5, 0)
(b) find an equation for l_2 , writing your answer in the form y = mx + c where m and c are constants to be found. [3]
[Diagram or table: see page 10 of the paper]
Figure 2 shows a sketch of the curve C and the lines l_1 and l_2
(c) Define the region R, shown shaded in Figure 2, using inequalities. [2]

Question 6
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
(a) Given that
[Diagram or table: see page 14 of the paper]
[2]
(b) Hence solve the simultaneous equations
[Diagram or table: see page 14 of the paper]
Give your answers in fully simplified surd form. [5]

Question 7
The curve C has equation y = f(x), x > 0
Given that
• f′(x) = 2/x + A/x_2 + 3 , where A is a constant
• f′′(x) = 0 when x = 4
(a) find the value of A. [4]
Given also that
• f(x) = 8 3 , when x = 12
(b) find f(x) , giving each term in simplest form. [5]

Question 8
[Diagram or table: see page 22 of the paper]
Figure 3 shows a sketch of the outline of the face of a ceiling fan viewed from below.
The fan consists of three identical sections congruent to OABCDO, shown in Figure 3, where • OABO is a sector of a circle with centre O and radius 9 cm • OBCDO is a sector of a circle with centre O and radius 84 cm
• angle AOD = 2π/3 radians
Given that the length of the arc AB is 15 cm,
(a) show that the length of the arc CD is 35.9 cm to one decimal place. [3]
The face of the fan is modelled to be a flat surface.
Find, according to the model,
(b) the perimeter of the face of the fan, giving your answer to the nearest cm, [2]
(c) the surface area of the face of the fan.
Give your answer to 3 significant figures and make your units clear. [5]

Question 9
[Diagram or table: see page 26 of the paper]
Figure 4 shows part of the graph of the curve with equation y = sin x
Given that sin α = p , where 0 < α < 90°
(a) state, in terms of p , the value of
(i) 2 sin (180° − α)
(ii) sin (α − 180°)
(iii) 3 + sin (180° + α) [3]
A copy of Figure 4, labelled Diagram 1, is shown on page 27.
On Diagram 1,
(b) sketch the graph of y = sin 2x [2]
(c) Hence find, in terms of α, the x coordinates of any points in the interval 0 < x < 180° where
[Diagram or table: see page 26 of the paper]
[3]
[Diagram or table: see page 27 of the paper]

Question 10
[Diagram or table: see page 28 of the paper]
Figure 5 shows a sketch of the curve C with equation
[Diagram or table: see page 28 of the paper]
where k is a constant.
(a) Find dy/dx [2]
The line l, shown in Figure 5, is the normal to C at the point A with x coordinate − 7/2
Given that l is also a tangent to C at the point B,
(b) show that the x coordinate of the point B is a solution of the equation
[Diagram or table: see page 28 of the paper]
[4]
(c) Hence find the x coordinate of B, justifying your answer. [2]
Given that the y intercept of l is −1
(d) find the value of k. [4]
[Diagram or table: see page 32 of the paper]