# WMA11 Pure Mathematics 1 (P1) Oct/Nov 2021 Paper 01

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

- Page: https://mathvsarham.com/past-papers/wma11/2021-oct-nov-paper-01/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_oct-nov_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: Oct/Nov 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
Find
[Diagram or table: see page 2 of the paper]
giving each term in simplest form. [5]

Question 2
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
A curve has equation
[Diagram or table: see page 4 of the paper]
The points P and Q lie on the curve.
The gradient of the curve at both point P and point Q is 2
Find the x coordinates of P and Q. [5]

Question 3
(i) Solve
[Diagram or table: see page 6 of the paper]
[3]
(ii) 
[Diagram or table: see page 6 of the paper]
Figure 1 shows a sketch of the curve C and the straight line l.
The infinite region R, shown shaded in Figure 1, lies in quadrants 2 and 3 and is bounded by C and l only.
Given that
• l has a gradient of 3
• C has equation y = 2x^2 – 50
• C and l intersect on the negative x‑axis
use inequalities to define the region R. [3]

Question 4
[Diagram or table: see page 8 of the paper]
Figure 2 shows a sketch of the curve with equation y = f(x), where
[Diagram or table: see page 8 of the paper]
The point Q and the point R(k, 0) lie on the curve and are shown in Figure 2.
(a) State
(i) the coordinates of Q,
(ii) the value of k. [3]
(b) Given that there are exactly two solutions to the equation
[Diagram or table: see page 8 of the paper]
find the range of possible values for p. [2]

Question 5
The line l_1 has equation 3y – 2x = 30
The line l_2 passes through the point A(24, 0) and is perpendicular to l_1
Lines l_1 and l_2 meet at the point P
(a) Find, using algebra and showing your working, the coordinates of P. [5]
Given that l_1 meets the x‑axis at the point B,
(b) find the area of triangle BPA. [3]

Question 6
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
A curve C has equation y = f(x) where
[Diagram or table: see page 14 of the paper]
(a) Sketch a graph of C.
Show on your graph the coordinates of the points where C cuts or meets the coordinate axes. [3]
(b) Write f(x) in the form ax^3 + bx^2 + cx + d, where a, b, c and d are constants to be found. [3]
(c) Hence, find the equation of the tangent to C at the point where x = 1/3 [4]

Question 7
[Diagram or table: see page 18 of the paper]
Figure 3 shows the design for a sign at a bird sanctuary.
The design consists of a kite OABC joined to a sector OCXA of a circle centre O.
In the design
• OA = OC = 0.6 m
• AB = CB = 1.4 m
• Angle OAB = Angle OCB = 2 radians
• Angle AOC = θ radians, as shown in Figure 3
Making your method clear,
(a) show that θ = 1.64 radians to 3 significant figures, [4]
(b) find the perimeter of the sign, in metres to 2 significant figures, [2]
(c) find the area of the sign, in m^2 to 2 significant figures. [4]

Question 8
[Diagram or table: see page 22 of the paper]
Figure 4 shows a sketch of the curve C with equation
[Diagram or table: see page 22 of the paper]
The point M is the maximum turning point on C.
(a)(i) Write 4 + 12x – 3x^2 in the form
[Diagram or table: see page 22 of the paper]
where a, b and c are constants to be found.
(ii) Hence, or otherwise, state the coordinates of M. [5]
The line l_1 passes through O and M, as shown in Figure 4.
A line l_2 touches C and is parallel to l_1
(b) Find an equation for l_2 [5]

Question 9
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
[Diagram or table: see page 26 of the paper]
Figure 5 shows a sketch of the curve with equation y = f(x) where
[Diagram or table: see page 26 of the paper]
The point P(9, 3) lies on the curve and is shown in Figure 5.
On the next page there is a copy of Figure 5 called Diagram 1.
(a) On Diagram 1, sketch and clearly label the graphs of
[Diagram or table: see page 26 of the paper]
Show on each graph the coordinates of the point to which P is transformed. [3]
The graph of y = f(2x) meets the graph of y = f(x) + 3 at the point Q.
(b) Show that the x coordinate of Q is the solution of
[Diagram or table: see page 26 of the paper]
[3]
(c) Hence find, in simplest form, the coordinates of Q. [3]
[Diagram or table: see page 27 of the paper]
[Diagram or table: see page 29 of the paper]

Question 10
A curve has equation y = f(x), x > 0
Given that
• fʹ(x) = ax – 12x^1/3 , where a is a constant
• fʹʹ(x) = 0 when x = 27
• the curve passes through the point (1, –8)
(a) find the value of a. [3]
(b) Hence find f(x). [4]
[Diagram or table: see page 32 of the paper]