# WMA11 Pure Mathematics 1 (P1) January 2022 Paper 01

Pearson Edexcel International A Level WMA11 Pure Mathematics 1 (P1) past paper 01, January 2022. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma11/2022-january-paper-01/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_january_2022_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 2022
- 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. [4]

Question 2
[Diagram or table: see page 4 of the paper]
(a) Express f(x) in the form
[Diagram or table: see page 4 of the paper]
where a, b and c are integers to be found. [3]
(b) Sketch the graph of the curve C with equation y = f(x), showing clearly the coordinates of the point where the curve crosses the y‑axis. [2]
(c) Write down the equation of the line of symmetry of C. [1]

Question 3
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
(i) 
[Diagram or table: see page 6 of the paper]
Express f(x) in the form ax^2+ bx 2 + c where a, b and c are integers to be found. [3]
(ii) Solve the equation
[Diagram or table: see page 6 of the paper]
giving your answer in the form p + q 3 where p and q are simplified fractions to be found. [4]

Question 4
[Diagram or table: see page 10 of the paper]
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
Figure 1 shows a line l with equation x + y = 6 and a curve C with equation y = 6x – 2x^2+ 1
The line l intersects the curve C at the points P and Q as shown in Figure 1.
(a) Find, using algebra, the coordinates of P and the coordinates of Q. [4]
The region R, shown shaded in Figure 1, is bounded by C, l and the x‑axis.
(b) Use inequalities to define the region R. [3]

Question 5
[Diagram or table: see page 12 of the paper]
Figure 2 shows a plan view of a semicircular garden ABCDEOA
The semicircle has
• centre O
• diameter AOE
• radius 3 m
The straight line BD is parallel to AE and angle BOA is 0.7 radians.
(a) Show that, to 4 significant figures, angle BOD is 1.742 radians. [1]
The flowerbed R, shown shaded in Figure 2, is bounded by BD and the arc BCD.
(b) Find the area of the flowerbed, giving your answer in square metres to one decimal place. [3]
(c) Find the perimeter of the flowerbed, giving your answer in metres to one decimal place. [3]

Question 6
The curve C has equation y = f(x) where x > 0
Given that
[Diagram or table: see page 16 of the paper]
• the point P(4, 20) lies on C
(a)(i) find the value of the gradient at P
(ii) Hence find the equation of the tangent 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), simplifying your answer. [7]

Question 7
[Diagram or table: see page 20 of the paper]
Figure 3 shows a sketch of part of the curve with equation y = f(x), where
[Diagram or table: see page 20 of the paper]
Given that the curve with equation y = f(x) – p passes through the point with coordinates (0, 50)
(a) find the value of the constant p. [2]
Given that the curve with equation y = f(x + q) passes through the origin,
(b) write down the possible values of the constant q. [2]
(c) Find f′(x). [4]
(d) Hence find the range of values of x for which the gradient of the curve with equation y = f(x) is less than –18 [3]

Question 8
The line l_1 has equation
[Diagram or table: see page 24 of the paper]
(a) Find the gradient of l_1 [1]
Given that
• the point A has coordinates (6, –2)
• the line l_2 passes through A and is perpendicular to l_1
(b) find the equation of l_2 giving your answer in the form y = mx + c, where m and c are constants to be found. [3]
The lines l_1 and l_2 intersect at the point M.
(c) Using algebra and showing all your working, find the coordinates of M.
[Diagram or table: see page 24 of the paper]
[3]
Given that the diagonals of a square ABCD meet at M,
(d) find the coordinates of the point C. [2]

Question 9
[Diagram or table: see page 28 of the paper]
Figure 4 shows part of the curve with equation
[Diagram or table: see page 28 of the paper]
where A is a constant.
The point P is a minimum point on the curve and has coordinates (30, –3) as shown in Figure 4.
(a) Write down the value of A. [1]
The point Q is shown in Figure 4 and is a maximum point.
(b) Find the coordinates of Q. [3]

Question 10
The curve C has equation
[Diagram or table: see page 30 of the paper]
(a) Sketch the graph of C.
On your sketch
• show the coordinates of any points of intersection with the coordinate axes
• state clearly the equations of any asymptotes [4]
The curve D has equation y = kx^2 where k is a constant.
Given that C meets D at 4 distinct points,
(b) find the range of possible values for k. [5]
[Diagram or table: see page 32 of the paper]