# WMA11 Pure Mathematics 1 (P1) May/June 2020 Paper 01

Pearson Edexcel International A Level WMA11 Pure Mathematics 1 (P1) past paper 01, May/June 2020. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma11/2020-may-june-paper-01/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_may-june_2020_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 2020
- 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
Given that
[Diagram or table: see page 2 of the paper]
find the values of the constants a, b and c. [3]

Question 2
[Diagram or table: see page 4 of the paper]
(a) Express f(x) in the form
[Diagram or table: see page 4 of the paper]
where a, b and c are integers to be found. [3]
The curve with equation y = f(x) – 7 crosses the x‑axis at the points P and Q and crosses the y‑axis at the point R.
(b) Find the area of the triangle PQR, giving your answer in the form m n where m and n are integers to be found. [4]

Question 3
[Diagram or table: see page 8 of the paper]
Figure 1 shows the design for a badge.
The design consists of two congruent triangles, AOC and BOC, joined to a sector AOB of a circle centre O.
 Angle AOB = α  AO = OB = 3 cm  OC = 5 cm
Given that the area of sector AOB is 7.2 cm^2
(a) show that α = 1.6 radians. [2]
(b) Hence find
(i) the area of the badge, giving your answer in cm^2 to 2 significant figures,
(ii) the perimeter of the badge, giving your answer in cm to one decimal place. [8]

Question 4
Use algebra to solve the simultaneous equations
[Diagram or table: see page 12 of the paper]
You must show all stages of your working. [7]
[Diagram or table: see page 14 of the paper]

Question 5
(i) 
[Diagram or table: see page 14 of the paper]
Figure 2 shows a sketch of the curve with equation y = f(x).
The curve passes through the points (–5, 0) and (0, –3) and touches the x‑axis at the point (2, 0).
On separate diagrams sketch the curve with equation
(a) y = f(x + 2)
(b) y = f(–x)
On each diagram, show clearly the coordinates of all the points where the curve cuts or touches the coordinate axes. [6]
(ii) 
[Diagram or table: see page 14 of the paper]
Figure 3 shows a sketch of the curve with equation
[Diagram or table: see page 14 of the paper]
where k is a constant.
The curve meets the y‑axis at the point (0, 3 ) and passes through the points ( p, 0) and (q, 0).
Find
(a) the value of k,
(b) the exact value of p and the exact value of q. [3]

Question 6
The point A has coordinates (–4, 11) and the point B has coordinates (8, 2).
(a) Find the gradient of the line AB, giving your answer as a fully simplified fraction. [2]
The point M is the midpoint of AB. The line l passes through M and is perpendicular to AB.
(b) Find an equation for l, giving your answer in the form px + qy + r = 0 where p, q and r are integers to be found. [4]
The point C lies on l such that the area of triangle ABC is 37.5 square units.
(c) Find the two possible pairs of coordinates of point C. [5]

Question 7
The curve C has equation
[Diagram or table: see page 22 of the paper]
(a) Sketch the graph of C. On your sketch you should show the coordinates of any points of intersection with the coordinate axes and state clearly the equations of any asymptotes. [3]
The line l has equation y = 4x + k, where k is a constant.
Given that l meets C at two distinct points,
(b) show that
[Diagram or table: see page 22 of the paper]
[4]
(c) Hence find the range of possible values for k. [4]

Question 8
The curve C has equation
[Diagram or table: see page 26 of the paper]
(a) Show that
[Diagram or table: see page 26 of the paper]
[4]
The line l_1 is the tangent to C at the point where x = 6
(b) Find the equation of l_1, giving your answer in the form y = mx + c, where m and c are constants to be found. [4]
The line l_2 is the tangent to C at the point where x = α
Given that l_1 and l_2 are parallel and distinct,
(c) find the value of α [3]

Question 9
A curve with equation y = f(x) passes through the point (9, 10).
Given that
[Diagram or table: see page 30 of the paper]
find f(x), fully simplifying each term. [6]
[Diagram or table: see page 32 of the paper]