# WMA11 Pure Mathematics 1 (P1) January 2024 Paper 01

Pearson Edexcel International A Level WMA11 Pure Mathematics 1 (P1) past paper 01, January 2024. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma11/2024-january-paper-01/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_january_2024_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 2024
- 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
Find
[Diagram or table: see page 2 of the paper]
writing your answer in simplest form. [5]

Question 2
The triangle ABC is such that
• AB = 15 cm
• AC = 25 cm
• angle BAC = θ°
• area triangle ABC = 100 cm^2
(a) Find the value of sin θ° [2]
Given that θ > 90
(b) find the length of BC, in cm, to 3 significant figures. [3]

Question 3
The curve C has equation
[Diagram or table: see page 6 of the paper]
(a) Find dy/dx writing your answer in simplest form. [4]
The point P (2, 4) lies on C.
(b) Find an equation for the tangent to C at P writing your answer in the form ax + by + c = 0, where a, b and c are integers. [3]

Question 4
In this question you must show all stages of your working.
[Diagram or table: see page 8 of the paper]
(a) By substituting p = 2^x, show that the equation
[Diagram or table: see page 8 of the paper]
can be written in the form
[Diagram or table: see page 8 of the paper]
[3]
(b) Hence solve
[Diagram or table: see page 8 of the paper]
[3]

Question 5
[Diagram or table: see page 10 of the paper]
In this question you must show all stages of your working.
[Diagram or table: see page 10 of the paper]
The straight line l_1 , shown in Figure 1, passes through the points P(–2, 9) and Q(10, 6).
(a) Find the equation of l_1 , giving your answer in the form y = mx + c , where m and c are constants to be found. [3]
The straight line l_2 passes through the origin O and is perpendicular to l_1
The lines l_1 and l_2 meet at the point R as shown in Figure 1.
(b) Find the coordinates of R [4]
(c) Find the exact area of triangle OPQ. [3]

Question 6
[Diagram or table: see page 14 of the paper]
Figure 2 shows a plot of part of the curve C_1 with equation
[Diagram or table: see page 14 of the paper]
with x being measured in degrees.
The point P, shown in Figure 2, is a minimum point on C_1
(a) State the coordinates of P [2]
The point Q lies on a different curve C_2
Given that point Q
• is a maximum point on the curve
• is the maximum point with the smallest x coordinate, x > 0
(b) find the coordinates of Q when
(i) C_2 has equation y = 5 cos x – 2
(ii) C_2 has equation y = –5 cos x [4]

Question 7
(a) Sketch the graph of the curve C with equation
[Diagram or table: see page 16 of the paper]
where k is a positive constant.
Show on your sketch
• the coordinates of any points where C cuts the coordinate axes
• the equation of the vertical asymptote to C [4]
Given that the straight line with equation y = 9 – x does not cross or touch C
(b) find the range of values of k. [5]

Question 8
[Diagram or table: see page 18 of the paper]
Figure 3 shows a sketch of the plan view of a platform.
The plan view of the platform consists of a sector DOC of a circle centre O joined to a sector AOBEA of a different circle, also with centre O.
Given that
• angle AOB = 0.8 radians
• arc length CD = 9 m
• DA : AO = 3 : 5
(a) show that AO = 7.03 m to 3 significant figures. [3]
(b) Find the perimeter of the platform, in m, to 3 significant figures. [3]
(c) Find the total area of the platform, giving your answer in m^2 to the nearest whole number. [3]

Question 9
The curve C_1 has equation y = f (x).
Given that
• f (x) is a quadratic expression
• C_1 has a maximum turning point at (2, 20)
• C_1 passes through the origin
(a) sketch a graph of C_1 showing the coordinates of any points where C_1 cuts the coordinate axes, [2]
(b) find an expression for f (x). [3]
The curve C_2 has equation y = x(x^2– 4)
Curve C_1 and C_2 meet at the origin, and at the points P and Q
Given that the x coordinate of the point P is negative,
(c) using algebra and showing all stages of your working, find the coordinates of P [5]

Question 10
In this question you must show all stages of your working.
The curve C has equation y = f (x), x > 0
Given that
• the point P 2, 8 2 lies on C
• f'(x)  4 x^3  k/x_2 where k is a constant
• f''(x) = 0 at P
(a) find the exact value of k, [4]
(b) find f (x), giving your answer in simplest form. [4]