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

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

- Page: https://mathvsarham.com/past-papers/wma11/2024-may-june-paper-01r/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_may-june_2024_paper_01R_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: 01R
- Component code: WMA11/01R
- 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. [4]

Question 2
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
(a) Solve
[Diagram or table: see page 4 of the paper]
[2]
(b)(i) Write
[Diagram or table: see page 4 of the paper]
in the form (x + a)^2 + b where a and b are constants.
(ii) Hence solve
[Diagram or table: see page 4 of the paper]
[4]
(c) Hence find the values of x that satisfy both
[Diagram or table: see page 4 of the paper]
[1]

Question 3
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
[Diagram or table: see page 6 of the paper]
(a) Find dy/dx , giving each term in simplest form. [3]
(b) Find the solution of the equation
[Diagram or table: see page 6 of the paper]
writing the answer in the form 2^k where k is a constant. [3]

Question 4
The curve C has equation
[Diagram or table: see page 8 of the paper]
The straight line l has equation
[Diagram or table: see page 8 of the paper]
where k is a constant.
(a) Show that l meets C when
[Diagram or table: see page 8 of the paper]
[2]
(b) Hence find the value of k for which l is a tangent to C [3]

Question 5
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
(a) Fully factorise
[Diagram or table: see page 10 of the paper]
[2]
(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 a sketch of the entrance to a tunnel.
The shape of the entrance consists of a sector BCDF, of a circle centre F, joined to two congruent (identical) triangles ABF and EDF.
Given that
[Diagram or table: see page 12 of the paper]
(a) Show that angle AFB = 0.433 radians to 3 decimal places. [1]
(b) Find the perimeter of the entrance to the tunnel, ABCDEFA, in metres, to one decimal place. [4]
(c) Find the cross-sectional area of the entrance to the tunnel, ABCDEFA, in m^2, to one decimal place. [4]

Question 7
[Diagram or table: see page 16 of the paper]
The straight line l_1 shown in Figure 2 has equation 5y = 2x + 10
The points A and B lie on l_1 such that
• point A lies on the y-axis
• point B has x coordinate 10
(a) Find the distance AB writing your answer as a fully simplified surd. [3]
The straight line l_2 also shown in Figure 2
• passes through B
• is perpendicular to l_1
(b) Find an equation for l_2 writing your answer in the form ax + by + c = 0 , where a, b and c are integers. [4]
Line l_2 crosses the x-axis at the point C.
Point D is such that the points A, B, C and D form the vertices of a rectangle, shown shaded in Figure 2.
(c) Find the area of rectangle ABCD. [3]

Question 8
A curve C with equation y = f (x) passes through the point R(4, 13).
Given that
[Diagram or table: see page 20 of the paper]
(a) use integration to find f (x), giving your answer in simplest form. [5]
(b) Given that f (x) can be written in the form
[Diagram or table: see page 20 of the paper]
find the value of the constant p and the value of the constant q. [2]
(c) Sketch the graph of y = f (2x), showing the coordinates of any points where the curve touches or crosses the coordinate axes. [4]

Question 9
[Diagram or table: see page 24 of the paper]
Figure 3 shows a sketch of
• the curve with equation y = tan / x  π /6  for 0  x  2π
• part of the straight line l with equation y = π – x
(a) State the number of solutions of the equation
(i) tan / x  π /6  = π – x in the interval 0  x  2π
[Diagram or table: see page 24 of the paper]
(ii) tan / x  π /6  = π – x in the interval 0  x  100π
[Diagram or table: see page 24 of the paper]
(iii) tan / x  π /6  = π + x in the interval 0  x  2π
[3]
The line with equation x = a , shown in Figure 3, is the asymptote to the curve with the smallest positive x coordinate.
(b) State the value of a [1]
The line with equation x = b , also shown in Figure 3, is the asymptote to the curve with the second smallest positive x coordinate.
The line l meets x = a at point P and meets x = b at point Q as shown in Figure 3.
(c) Find the midpoint of the line segment PQ. [4]

Question 10
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
The curve C has equation
[Diagram or table: see page 26 of the paper]
The point P, which lies on C, has coordinates (2, –8)
(a) Show that an equation of the tangent to C at P is
[Diagram or table: see page 26 of the paper]
[5]
The point Q also lies on C.
Given that the tangent to C at Q is parallel to the tangent to C at P,
(b) find, using algebra and showing your working, the exact x coordinate of Q. [5]