# WMA11 Pure Mathematics 1 (P1) January 2023 Paper 01

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

- Page: https://mathvsarham.com/past-papers/wma11/2023-january-paper-01/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_january_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: January 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
A curve C has equation
[Diagram or table: see page 2 of the paper]
(a) Find dy/dx giving your answer in simplest form. [3]
(b) Hence find the exact value of the gradient of the tangent to C at the point where x = 2 giving your answer in simplest form.
[Diagram or table: see page 2 of the paper]
[2]

Question 2
The points P, Q and R have coordinates (–3, 7), (9, 11) and (12, 2) respectively.
(a) Prove that angle PQR = 90° [3]
Given that the point S is such that PQRS forms a rectangle,
(b) find the coordinates of S. [2]

Question 3
Find
[Diagram or table: see page 6 of the paper]
giving your answer in simplest form. [5]

Question 4
Given that the equation
[Diagram or table: see page 8 of the paper]
has no real roots, find the range of possible values for k. [4]

Question 5
[Diagram or table: see page 10 of the paper]
(a) By substituting p = 3^x, show that the equation
[Diagram or table: see page 10 of the paper]
can be rewritten in the form
[Diagram or table: see page 10 of the paper]
[3]
(b) Hence solve
[Diagram or table: see page 10 of the paper]
[3]

Question 6
[Diagram or table: see page 12 of the paper]
Figure 1 shows the plan view for the design of a stage.
The design consists of a sector OBC of a circle, with centre O, joined to two congruent triangles OAB and ODC.
Given that
• angle BOC = 2.4 radians
• area of sector BOC = 40 m^2
• AOD is a straight line of length 12.5 m
(a) find the radius of the sector, giving your answer, in m, to 2 decimal places, [2]
(b) find the size of angle AOB, in radians, to 2 decimal places. [1]
Hence find
(c) the total area of the stage, giving your answer, in m^2, to one decimal place, [3]
(d) the total perimeter of the stage, giving your answer, in m, to one decimal place. [4]

Question 7
(a) On Diagram 1, sketch a graph of the curve C with equation
[Diagram or table: see page 16 of the paper]
[2]
The curve C is transformed onto the curve with equation y = 6/x − 2 x ≠ 2
(b) Fully describe this transformation. [2]
The curve with equation
[Diagram or table: see page 16 of the paper]
and the line with equation
[Diagram or table: see page 16 of the paper]
intersect at exactly two points, P and Q.
Given that the x coordinate of point P is –4
(c) find the value of k, [2]
(d) find, using algebra, the coordinates of point Q.
[Diagram or table: see page 16 of the paper]
[4]
[Diagram or table: see page 17 of the paper]
[Diagram or table: see page 19 of the paper]

Question 8
[Diagram or table: see page 20 of the paper]
Figure 2 shows a sketch of the straight line l and the curve C.
Given that l cuts the y‑axis at –12 and cuts the x‑axis at 4, as shown in Figure 2,
(a) find an equation for l, writing your answer in the form y = mx + c, where m and c are constants to be found. [2]
Given that C
• has equation y = f(x) where f(x) is a quadratic expression
• has a minimum point at (7, –18)
• cuts the x‑axis at 4 and at k, where k is a constant
(b) deduce the value of k, [1]
(c) find f(x). [3]
The region R is shown shaded in Figure 2.
(d) Use inequalities to define R. [2]

Question 9
[Diagram or table: see page 24 of the paper]
Figure 3 shows a sketch of
• the curve with equation y = tan x
• the straight line l with equation y = πx
in the interval –π < x < π
(a) State the period of tan x [1]
(b) Write down the number of roots of the equation
(i) tan x = (π + 2)x in the interval –π < x < π [1]
(ii) tan x = πx in the interval –2π < x < 2π [1]
(iii) tan x = πx in the interval –100π < x < 100π [1]

Question 10
[Diagram or table: see page 26 of the paper]
Figure 4 shows a sketch of part of the curve C with equation y = f(x), where
[Diagram or table: see page 26 of the paper]
(a) Use the given information to state the values of x for which
[Diagram or table: see page 26 of the paper]
[2]
(b) Expand (3x + 20)(x + 6)(2x – 3), writing your answer as a polynomial in simplest form. [3]
The straight line l is the tangent to C at the point where C cuts the y‑axis.
Given that l cuts C at the point P, as shown in Figure 4,
(c) find, using algebra, the x coordinate of P
[Diagram or table: see page 26 of the paper]
[5]

Question 11
A curve C has equation y = f(x), x > 0
Given that
• f ′′(x) = 4x +
• the point P has x coordinate 4 and lies on C
• the tangent to C at P has equation y = 3x + 4
(a) find an equation of the normal to C at P [2]
(b) find f(x), writing your answer in simplest form. [6]