# WMA11 Pure Mathematics 1 (P1) Oct/Nov 2023 Paper 01

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

- Page: https://mathvsarham.com/past-papers/wma11/2023-oct-nov-paper-01/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_oct-nov_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: Oct/Nov 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
Given that
[Diagram or table: see page 2 of the paper]
find, in simplest form,
dy
(a) 
[3]
d^2 y
(b) _2
[2]

Question 2
Given that
[Diagram or table: see page 4 of the paper]
express each of the following in the form kx^n where k and n are simplified constants.
(a) a^1/2 [1]
16
(b) _3 b [1]
 ab ^4/3
(c)     2  [2]

Question 3
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
(a) Write 8 /215/3  in the form a 3 + b 5 where a and b are integers to be found.
[3]
(b) Hence, or otherwise, solve
[Diagram or table: see page 6 of the paper]
giving your answer in simplest form. [3]

Question 4
[Diagram or table: see page 8 of the paper]
Figure 1 shows a sketch of part of the curve C with equation y = 1/x + 2
(a) State the equation of the asymptote of C that is parallel to the y-axis. [1]
(b) Factorise fully x^3 + 4x^2 + 4x [2]
A copy of Figure 1, labelled Diagram 1, is shown on the next page.
(c) On Diagram 1, add a sketch of the curve with equation
[Diagram or table: see page 8 of the paper]
On your sketch, state clearly the coordinates of each point where this curve cuts or meets the coordinate axes. [3]
(d) Hence state the number of real solutions of the equation
[Diagram or table: see page 8 of the paper]
giving a reason for your answer. [1]
[Diagram or table: see page 9 of the paper]
Diagram 1 copy of Diagram 1
Only use the copy of Diagram 1 if you need to redraw your answer to part (c).

Question 5
[Diagram or table: see page 10 of the paper]
Figure 2 shows the plan view of a frame for a flat roof.
The shape of the frame consists of triangle ABD joined to triangle BCD.
Given that
• BD = x m
• CD = (1 + x) m
• BC = 5 m
• angle BCD = θ°
(a) show that cos θ° = 13 + x/5 + 5x [2]
Given also that
• x = 2 3
• angle BAC = 30°
• ADC is a straight line
(b) find the area of triangle ABC, giving your answer, in m^2, to one decimal place. [5]

Question 6
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
The equation
[Diagram or table: see page 14 of the paper]
where p is a constant, has two distinct real roots.
(a) Show that
[Diagram or table: see page 14 of the paper]
[3]
(b) Hence, using algebra, find the range of possible values of p [3]

Question 7
The curve C has equation y = f(x) where x > 0
Given that
4x^2  10  7x^1/2 • fʹ(x) =
[Diagram or table: see page 16 of the paper]
• the point P(4, –1) lies on C
(a)(i) find the value of the gradient of C at P
(ii) Hence find the equation of the normal to C at P, giving your answer in the form ax + by + c = 0 where a, b and c are integers to be found. [4]
(b) Find f(x). [6]

Question 8
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
The curve C_1 has equation
[Diagram or table: see page 20 of the paper]
The curve C_2 has equation
[Diagram or table: see page 20 of the paper]
(a) Show that C_1 and C_2 meet when
[Diagram or table: see page 20 of the paper]
[2]
Given that C_1 and C_2 meet at points P and Q
(b) find, using algebra, the exact distance PQ [5]

Question 9
[Diagram or table: see page 24 of the paper]
Figure 3 shows the plan view of the area being used for a ball-throwing competition.
Competitors must stand within the circle C and throw a ball as far as possible into the target area, PQRS, shown shaded in Figure 3.
Given that
• circle C has centre O
• P and S are points on C
• OPQRSO is a sector of a circle with centre O
• the length of arc PS is 0.72 m
• the size of angle POS is 0.6 radians
(a) show that OP = 1.2 m [1]
Given also that
• the target area, PQRS, is 90 m^2
• length PQ = x metres
(b) show that
[Diagram or table: see page 24 of the paper]
[3]
(c) Hence calculate the total perimeter of the target area, PQRS, giving your answer to the nearest metre. [3]

Question 10
[Diagram or table: see page 28 of the paper]
Figure 4 shows a sketch of part of the curve C_1 with equation
[Diagram or table: see page 28 of the paper]
where n is a constant.
The curve C_1 cuts the positive x-axis for the first time at point P(270, 0), as shown in Figure 4.
(a)(i) State the value of n
(ii) State the period of C_1 [2]
The point Q, shown in Figure 4, is a minimum point of C_1
(b) State the coordinates of Q. [2]
The curve C_2 has equation y  2sin x  k, where k is a constant.
The point R / a, 12 /5  and the point S / a,  3 /5 , both lie on C
Given that a is a constant less than 90
(c) find the value of k. [2]

Question 11
[Diagram or table: see page 30 of the paper]
Figure 5 shows part of the curve C with equation y = f (x) where
[Diagram or table: see page 30 of the paper]
(a) Write 2x^2  12x  14 in the form
[Diagram or table: see page 30 of the paper]
where a, b and c are constants to be found. [3]
Given that C has a minimum at the point P
(b) state the coordinates of P [1]
The line l intersects C at (–1, 28) and at P as shown in Figure 5.
(c) Find the equation of l giving your answer in the form y = mx + c where m and c are constants to be found. [3]
The finite region R, shown shaded in Figure 5, is bounded by the x-axis, l, the y-axis, and C.
(d) Use inequalities to define the region R. [3]