# WMA11 Pure Mathematics 1 (P1) Oct/Nov 2024 Paper 01

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

- Page: https://mathvsarham.com/past-papers/wma11/2024-oct-nov-paper-01/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_oct-nov_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: Oct/Nov 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
The line l_1 passes through the point A(–5, 20) and the point B(3, –4).
(a) Find an equation for l_1 giving your answer in the form y = mx + c, where m and c are constants. [3]
The line l_2 is perpendicular to l_1 and passes through the midpoint of AB
(b) Find an equation for l_2 giving your answer in the form px  qy  r  0 , where p, q and r are integers. [3]

Question 2
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
(i) Simplify fully
[Diagram or table: see page 4 of the paper]
[3]
(ii) Find the exact value of a such that
[Diagram or table: see page 4 of the paper]
Write your answer in the form p 3 + q where p and q are fully simplified rational constants. [4]

Question 3
In this question you must show all stages of your working.
[Diagram or table: see page 6 of the paper]
(a) Find f(x) dx
[4]
(b)(i) Show that when f ′(x) = 0
[Diagram or table: see page 6 of the paper]
(ii) Hence state the value of x for which
[Diagram or table: see page 6 of the paper]
[5]

Question 4
[Diagram or table: see page 10 of the paper]
Figure 1 shows a sketch of part of the curves C_1 and C_2
Given that C_1
• has equation y = f(x) where f(x) is a quadratic function
• cuts the x‑axis at the origin and at x = 4
• has a minimum turning point at (2, –4.8)
(a) find f(x) [3]
Given that C_2
• has equation y = g(x) where g(x) is a cubic function
• cuts the x‑axis at the origin and meets the x‑axis at x = 4
• passes through the point (6, 7.2)
(b) find g(x) [3]
The curves C_1 and C_2 meet in the first quadrant at the point P, shown in Figure 1.
(c) Use algebra to find the coordinates of P. [4]

Question 5
A plot of land OAB is in the shape of a sector of a circle with centre O.
Given
• OA = OB = 5 km
• angle AOB = 1.2 radians
(a) find the perimeter of the plot of land. [2]
[Diagram or table: see page 14 of the paper]
A point P lies on OB such that the line AP divides the plot of land into two regions R_1 and R_2 as shown in Figure 2.
Given that
[Diagram or table: see page 14 of the paper]
(b) show that the area of R_2= 3.75 km^2 [3]
(c) Find the length of AP, giving your answer to the nearest 100 m. [4]

Question 6
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
(a) Sketch the curve C with equation
[Diagram or table: see page 18 of the paper]
State on your sketch
• the equation of the vertical asymptote
• the coordinates of the intersection of C with the y‑axis [3]
The straight line l has equation y = kx – 4, where k is a constant.
Given that l cuts C at least once,
(b)(i) show that
[Diagram or table: see page 18 of the paper]
(ii) find the range of possible values for k. [6]

Question 7
[Diagram or table: see page 22 of the paper]
Figure 3 shows a plot of part of the curve C_1 with equation
[Diagram or table: see page 22 of the paper]
where x is measured in radians.
Points P and Q lie on the curve and are shown in Figure 3.
(a) State
(i) the coordinates of P
(ii) the coordinates of Q [3]
The curve C_2 has equation y = –4 cos x + k where x is measured in radians and k is a constant.
Given that C_2 has a maximum y value of 11
(b)(i) state the value of k
(ii) state the coordinates of the minimum point on C_2 with the smallest positive x coordinate. [3]
On the opposite page there is a copy of Figure 3 labelled Diagram 1.
(c) Using Diagram 1, state the number of solutions of the equation
[Diagram or table: see page 22 of the paper]
giving a reason for your answer. [2]
[Diagram or table: see page 23 of the paper]

Question 8
A curve C has equation y = f(x).
The point P with x coordinate 3 lies on C
Given
• f ′(x) = 4x^2+ kx + 3 where k is a constant
• the normal to C at P has equation y   1/24 x  5
(a) show that k = –5 [3]
(b) Hence find f(x). [4]

Question 9
[Diagram or table: see page 26 of the paper]
Figure 4 shows a sketch of the curve C with equation y = f(x), where
[Diagram or table: see page 26 of the paper]
(a) Deduce the range of values of x for which f(x)  0 [1]
(b) Find f ′(x) giving your answer in simplest form. [3]
The point R(–4, 84) lies on C.
Given that the tangent to C at the point P is parallel to the tangent to C at the point R
(c) find the x coordinate of P. [4]
(d) Find the point to which R is transformed when the curve with equation y = f(x) is transformed to the curve with equation,
(i) y = f(x – 3)
(ii) y = 4f(x) [2]