# WMA11 Pure Mathematics 1 (P1) May/June 2024 Paper 01

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

- Page: https://mathvsarham.com/past-papers/wma11/2024-may-june-paper-01/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_may-june_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: May/June 2024
- 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. [3]

Question 2
(i) Given that m = 2^n, express each of the following in simplest form in terms of m.
(a) 2^n^+^3 [1]
(b) 16^3^n [2]
(ii) In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
Solve the equation
[Diagram or table: see page 4 of the paper]
giving your answer in the form p + q 3 where p and q are integers. [3]

Question 3
[Diagram or table: see page 6 of the paper]
Figure 1 shows a sketch of the curve with equation y = f(x).
The curve passes through the points (–1, 0) and (0, 2) and touches the x‑axis at the point (3, 0).
On separate diagrams, sketch the curve with equation
(a) y = f(x + 3) [3]
(b) y = f(–3x) [3]
On each diagram, show clearly the coordinates of all the points where the curve cuts or touches the coordinate axes.

Question 4
The curve C_1 has equation
[Diagram or table: see page 8 of the paper]
and the curve C_2 has equation
[Diagram or table: see page 8 of the paper]
where k is a constant.
Given that C_1 and C_2 meet at a single point P
(a) show that
[Diagram or table: see page 8 of the paper]
[3]
(b) Hence find the coordinates of P [3]

Question 5
[Diagram or table: see page 10 of the paper]
Figure 2 shows the plan view of a garden.
The shape of the garden ABCDEA consists of a triangle ABE and a right‑angled triangle BCD joined to a sector BDE of a circle with radius 6 m and centre B.
The points A, B and C lie on a straight line with AB = 10.8 m
Angle BCD = π/2 radians, angle EBD = 1.3 radians and AE = 12.2 m
(a) Find the area of the sector BDE, giving your answer in m^2 [2]
(b) Find the size of angle ABE, giving your answer in radians to 2 decimal places. [2]
(c) Find the area of the garden, giving your answer in m^2 to 3 significant figures. [3]

Question 6
[Diagram or table: see page 14 of the paper]
Solutions relying on calculator technology are not acceptable.
Figure 3 shows
• the line l with equation y – 5x = 75
• the curve C with equation y = 2x^2 + x – 21
The line l intersects the curve C at the points P and Q, as shown in Figure 3.
(a) Find, using algebra, the coordinates of P and the coordinates of Q. [4]
The region R, shown shaded in Figure 3, is bounded by C, l and the x‑axis.
(b) Use inequalities to define the region R. [3]

Question 7
The curve C has equation y = f(x) where
[Diagram or table: see page 18 of the paper]
and k is a constant.
(a) Find, in simplest form,
(i) f ′(x)
(ii) f ′′(x) [3]
The curve with equation y = f ′(x) intersects the curve with equation y = f ′′(x) at the points A and B.
Given that the x coordinate of A is 5
(b) find the value of k. [2]
(c) Hence find the coordinates of B. [3]

Question 8
The curve C_1 has equation
[Diagram or table: see page 20 of the paper]
(a) Sketch the graph of C_1 showing the coordinates of any points of intersection with the coordinate axes. [3]
The curve C_2 has equation y = A/x where A is a constant.
(b) Show that the x coordinates of the points of intersection of C_1 and C_2 satisfy the equation
[Diagram or table: see page 20 of the paper]
[1]
(c) Hence find the range of possible values of A for which C_1 meets C_2 at 4 distinct points. [3]

Question 9
Given that
• the point A has coordinates (4, 2)
• the point B has coordinates (15, 7)
• the line l_1 passes through A and B
(a) find an equation for l_1, giving your answer in the form px + qy + r = 0 where p, q and r are integers to be found. [3]
The line l_2 passes through A and is parallel to the x‑axis.
The point C lies on l_2 so that the length of BC is 5 5
(b) Find both possible pairs of coordinates of the point C. [4]
(c) Hence find the minimum possible area of triangle ABC. [2]

Question 10
The curve C has equation y = f(x) where x > 0
Given that
• f ′(x) = 6x –
• the point P(4, 12) lies on C
(a) find the equation of the normal to C at P, giving your answer in the form y = mx + c where m and c are integers to be found, [4]
(b) find f(x), giving each term in simplest form. [6]
[Diagram or table: see page 30 of the paper]

Question 11
[Diagram or table: see page 30 of the paper]
Figure 4 shows a sketch of part of the curve C_1 with equation
[Diagram or table: see page 30 of the paper]
where x is measured in radians.
The point P shown in Figure 4 is a maximum point on C_1
(a) Find the coordinates of P. [2]
The curve C_2 has equation
[Diagram or table: see page 30 of the paper]
where k is a constant.
Given that the maximum value of y on C_2 is 3
(b) find the coordinates of the minimum point on C_2 which has the smallest positive x coordinate. [2]
The curve C_3 has equation
[Diagram or table: see page 30 of the paper]
where B is a positive constant.
Given that  π/ 4 , A/, where A is a constant, is the minimum point on C which has the
smallest positive x coordinate,
(c) find
(i) the value of A,
(ii) the smallest possible value of B. [2]