# WMA11 Pure Mathematics 1 (P1) May/June 2023 Paper 01

Pearson Edexcel International A Level WMA11 Pure Mathematics 1 (P1) past paper 01, May/June 2023. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma11/2023-may-june-paper-01/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_may-june_2023_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 2023
- 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
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
Solve the inequality
[Diagram or table: see page 2 of the paper]
[4]

Question 2
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
A rectangular sports pitch has length x metres and width y metres, where x > y
Given that the perimeter of the pitch is 350 m,
(a) write down an equation linking x and y [1]
Given also that the area of the pitch is 7350 m^2
(b) write down a second equation linking x and y [1]
(c) hence find the value of x and the value of y [4]

Question 3
(a) Express 3x^2+ 12x + 13 in the form
[Diagram or table: see page 6 of the paper]
where a, b and c are integers to be found. [3]
(b) Hence sketch the curve with equation y = 3x^2+ 12x + 13
On your sketch show clearly
• the coordinates of the y intercept
• the coordinates of the turning point of the curve [3]

Question 4
In this question you must show all stages of your working.
(a) Write
[Diagram or table: see page 8 of the paper]
where A, B, p and q are constants to be found. [4]
(b) Hence find dy/dx giving each coefficient in simplest form. [3]

Question 5
[Diagram or table: see page 10 of the paper]
Figure 1 shows the plan for a garden.
In the plan
• OA and CD are perpendicular to OD
• AB is an arc of the circle with centre O and radius 4 metres
• BC is parallel to OD
• OD is 6 metres, OA is 4 metres and CD is 1.5 metres
(a) Show that angle AOB is 1.186 radians to 4 significant figures. [2]
(b) Find the perimeter of the garden, giving your answer in metres to 3 significant figures. [4]
(c) Find the area of the garden, giving your answer in square metres to 3 significant figures. [4]

Question 6
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
(a) Expand and simplify
[Diagram or table: see page 14 of the paper]
[2]
(b) Express 1/3 + 2 in the form p + q 2 where p and q are integers.
[2]
(c) Use the results of parts (a) and (b), or otherwise, to show that
[Diagram or table: see page 14 of the paper]
[3]

Question 7
[Diagram or table: see page 18 of the paper]
The region R_1 , shown shaded in Figure 2, is defined by the inequalities
[Diagram or table: see page 18 of the paper]
where k is a constant.
The line x = a, where a is a constant, passes through the intersection of the lines y = 2 and y = kx
Given that the area of R_1 is 27/4 square units,
(a) find
(i) the value of a
(ii) the value of k [4]
(b) Define the region R_2 , also shown shaded in Figure 2, using inequalities. [2]

Question 8
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
(a) Find the equation of the tangent to the curve with equation
[Diagram or table: see page 20 of the paper]
at the point P(4, 12)
Give your answer in the form ax + by + c = 0 where a, b and c are integers. [5]
The curve with equation y = f (x) also passes through the point P(4, 12)
Given that
[Diagram or table: see page 20 of the paper]
(b) find f (x) giving the coefficients in simplest form. [5]

Question 9
(i) 
[Diagram or table: see page 24 of the paper]
Figure 3 shows part of the graph of the trigonometric function with equation y = f (x)
(a) Write down an expression for f (x) [2]
On a separate diagram,
(b) sketch, for –2π < x < 2π , the graph of the curve with equation y = f / x + π /4 
Show clearly the coordinates of all the points where the curve intersects the coordinate axes. [3]
(ii) 
[Diagram or table: see page 24 of the paper]
Figure 4 shows part of the graph of the trigonometric function with equation y = g(x)
(a) Write down an expression for g(x) [2]
On a separate diagram,
(b) sketch, for –2π < x < 2π , the graph of the curve with equation y = g(x) – 2
Show clearly the coordinates of the y intercept. [2]

Question 10
[Diagram or table: see page 28 of the paper]
Figure 5 shows a sketch of the quadratic curve C with equation
[Diagram or table: see page 28 of the paper]
The line l_1 also shown in Figure 5,
• has gradient 1/2
• intersects C on the negative x-axis and at the point P
(a)(i) Write down an equation for l_1 [1]
(ii) Find, in terms of b, the coordinates of P [3]
Given that the line l_2 is perpendicular to l_1 and intersects C on the positive x-axis,
(b) find, in terms of b, an equation for l_2 [2]
Given also that l_2 intersects C at the point P
(c) show that another equation for l_2 is
[Diagram or table: see page 28 of the paper]
[2]
(d) Hence, or otherwise, find the value of b [2]