# WMA11 Pure Mathematics 1 (P1) Oct/Nov 2022 Paper 01

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

- Page: https://mathvsarham.com/past-papers/wma11/2022-oct-nov-paper-01/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_oct-nov_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: Oct/Nov 2022
- Paper: 01
- Component code: WMA11/01
- Time allowed: 90 minutes
- Total marks: 75
- Pages: 28

## 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. [3]
The point R / 2 , 13/2  lies on C.  
(b) Find the equation of the tangent to C at the point R. Write your answer in the form ax + by + c = 0, where a, b and c are integers to be found. [3]

Question 2
Given that
[Diagram or table: see page 4 of the paper]
where a and b are constants,
(a) find the value of a and the value of b. [2]
(b) Hence find
[Diagram or table: see page 4 of the paper]
writing each term in simplest form. [5]

Question 3
The share price of a company is monitored.
Exactly 3 years after monitoring began, the share price was £1.05
Exactly 5 years after monitoring began, the share price was £1.65
The share price, £V, of the company is modelled by the equation
[Diagram or table: see page 6 of the paper]
where t is the number of years after monitoring began and p and q are constants.
(a) Find the value of p and the value of q. [3]
Exactly T years after monitoring began, the share price was £2.50
(b) Find the value of T, according to the model, giving your answer to one decimal place. [2]

Question 4
[Diagram or table: see page 8 of the paper]
(a) Solve
[Diagram or table: see page 8 of the paper]
[4]
(b) Hence solve
[Diagram or table: see page 8 of the paper]
giving your answer in simplified surd form. [2]

Question 5
[Diagram or table: see page 10 of the paper]
Solutions relying entirely on calculator technology are not acceptable.
The curve C has equation y = f(x), x > 0
Given that
12 x • f ′(x) = + – 4
• the point P(9, 8) lies on C
(a) find, in simplest form, f(x) [5]
The line l is the normal to C at P
(b) Find the coordinates of the point at which l crosses the y‑axis. [4]

Question 6
(a) Given that k is a positive constant such that 0 < k < 4 sketch, on separate axes, the graphs of
(i) y = (2x – k)(x + 4)^2
(ii) y = k/x_2
showing the coordinates of any points where the graphs cross or meet the coordinate axes, leaving coordinates in terms of k, where appropriate. [5]
(b) State, with a reason, the number of roots of the equation
[Diagram or table: see page 14 of the paper]
[1]

Question 7
[Diagram or table: see page 16 of the paper]
Figure 1 shows the curve with equation y = f(x).
The points P(–4, 6), Q(–1, 6), R(2, 6) and S(3, 6) lie on the curve.
(a) Using Figure 1, find the range of values of x for which
[Diagram or table: see page 16 of the paper]
[3]
(b) State the largest solution of the equation
[Diagram or table: see page 16 of the paper]
[1]
(c)(i) Sketch the curve with equation y = f(–x).
On your sketch, state the coordinates of the points to which P, Q, R and S are transformed.
(ii) Hence find the set of values of x for which
[Diagram or table: see page 16 of the paper]
[4]

Question 8
[Diagram or table: see page 20 of the paper]
Figure 2 shows the plan view of a design for a pond.
The design consists of a sector AOBX of a circle centre O joined to a quadrilateral AOBC.
• BC = 8 m
• OA = OB = 3 m
• angle AOB is 2π/3 radians
• angle BCA is π/6 radians
(a) Calculate (i) the exact area of the sector AOBX,
(ii) the exact perimeter of the sector AOBX. [5]
(b) Calculate the exact area of the triangle AOB. [2]
(c) Show that the length AB is 3 3 m. [2]
(d) Find the total surface area of the pond. Give your answer in m^2 correct to 2 significant figures. [5]

Question 9
[Diagram or table: see page 24 of the paper]
Figure 3 shows a sketch of the curve C with equation
[Diagram or table: see page 24 of the paper]
(a) Write 1/2 x^2– 10x + 22 in the form
[Diagram or table: see page 24 of the paper]
where a, b and c are constants to be found. [3]
The point M is the minimum turning point of C, as shown in Figure 3.
(b) Deduce the coordinates of M [2]
The line l is the normal to C at the point P, as shown in Figure 3.
Given that l has equation y = k – 1/8 x, where k is a constant,
(c)(i) find the coordinates of P
(ii) find the value of k [6]
[Diagram or table: see page 24 of the paper]
[Diagram or table: see page 25 of the paper]
Figure 4 is a copy of Figure 3. The finite region R, shown shaded in Figure 4, is bounded by l, C and the line through M parallel to the y‑axis.
(d) Identify the inequalities that define R. [3]