# WMA11 Pure Mathematics 1 (P1) May/June 2021 Paper 01

Pearson Edexcel International A Level WMA11 Pure Mathematics 1 (P1) past paper 01, May/June 2021. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma11/2021-may-june-paper-01/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_may-june_2021_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 2021
- 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
The curve C has equation
[Diagram or table: see page 2 of the paper]
(a) Find dy/dx , giving your answer in simplest form. [4]
The point P (4, 3) lies on C.
(b) Find the equation of the normal to C at the point P. Write your answer in the form ax + by + c = 0, where a, b and c are integers to be found. [4]

Question 2
In this question you must show all stages of your working.
[Diagram or table: see page 4 of the paper]
where a is a positive constant.
Given f(–1) = 32
(a)(i) show that the only possible value for a is 3
(ii) Using a = 3 solve the equation
[Diagram or table: see page 4 of the paper]
[5]
(b) Hence find all real solutions of
(i) 3y + 26y^2/3 – 9y^1/3 = 0
(ii) 3(9^3 ) + 26(9^2 ) – 9(9 ) = 0 [5]

Question 3
In this question you must show all stages of your working.
[Diagram or table: see page 8 of the paper]
Figure 1 shows the plan view of a flower bed. The flowerbed is in the shape of a triangle ABC with
● AB = p metres
● AC = q metres
● BC = 2 2 metres
● angle BAC = 60°
(a) Show that
[2]
Given that side AC is 2 metres longer than side AB, use algebra to find
(b)(i) the exact value of p,
(ii) the exact value of q. [5]
Using the answers to part (b),
(c) calculate the exact area of the flower bed. [2]

Question 4
Find
[Diagram or table: see page 12 of the paper]
writing each term in simplest form. [6]

Question 5
[Diagram or table: see page 14 of the paper]
The share value of two companies, company A and company B, has been monitored over a 15-year period.
The share value P_A of company A, in millions of pounds, is modelled by the equation
[Diagram or table: see page 14 of the paper]
where t is the number of years after monitoring began.
The share value P_B of company B, in millions of pounds, is modelled by the equation
[Diagram or table: see page 14 of the paper]
where t is the number of years after monitoring began.
Figure 2 shows a graph of both models.
Use the equations of one or both models to answer parts (a) to (d).
(a) Find the difference between the share value of company A and the share value of company B at the point monitoring began. [2]
(b) State the maximum share value of company A during the 15-year period. [1]
(c) Find, using algebra and showing your working, the times during this 15-year period when the share value of company A was greater than the share value of company B. [4]
(d) Explain why the model for company A should not be used to predict its share value when t = 20 [1]

Question 6
The curve C has equation y = f(x), x > 0
Given that
● C passes through the point P (8, 2)
● fʹ (x) = + 3 − 2 x
(a) find the equation of the tangent to C at P. Write your answer in the form y = mx + c, where m and c are constants to be found. [3]
(b) Find, in simplest form, f(x). [5]

Question 7
[Diagram or table: see page 22 of the paper]
The line l_1 has equation 4y + 3x = 48
The line l_1 cuts the y-axis at the point C, as shown in Figure 3.
(a) State the y coordinate of C. [1]
The point D (8, 6) lies on l_1
The line l_2 passes through D and is perpendicular to l_1
The line l_2 cuts the y-axis at the point E as shown in Figure 3.
(b) Show that the y coordinate of E is − 14/3 [3]
A sector BCE of a circle with centre C is also shown in Figure 3.
Given that angle BCE is 1.8 radians,
(c) find the length of arc BE. [3]
The region CBED, shown shaded in Figure 3, consists of the sector BCE joined to the triangle CDE.
(d) Calculate the exact area of the region CBED. [3]

Question 8
The curve C_1 has equation
[Diagram or table: see page 26 of the paper]
(a) Write 3x^2+ 6x + 9 in the form
[Diagram or table: see page 26 of the paper]
where a, b and c are constants to be found. [3]
The point P is the minimum point of C_1
(b) Deduce the coordinates of P. [1]
A different curve C_2 has equation
[Diagram or table: see page 26 of the paper]
where A, B, C and D are constants.
Given that C_2
● passes through P
● intersects the x-axis at –4, –2 and 3
(c) find, making your method clear, the values of A, B, C and D. [5]

Question 9
[Diagram or table: see page 30 of the paper]
Figure 4 shows a sketch of the curve with equation
[Diagram or table: see page 30 of the paper]
The line l, shown in Figure 4, is an asymptote to y = tan x
(a) State an equation for l. [1]
A copy of Figure 4, labelled Diagram 1, is shown on the next page.
(b)(i) On Diagram 1, sketch the curve with equation
[Diagram or table: see page 30 of the paper]
stating the equation of the horizontal asymptote of this curve.
(ii) Hence, giving a reason, state the number of solutions of the equation
[Diagram or table: see page 30 of the paper]
in the region –2π  x  2π [4]
(c) State the number of solutions of the equation tan x = 1/x + 1 in the region
(i) 0  x  40π
(ii) –10π  x  5/2π [2]
[Diagram or table: see page 31 of the paper]
[Diagram or table: see page 32 of the paper]