# WMA11 Pure Mathematics 1 (P1) January 2021 Paper 01

Pearson Edexcel International A Level WMA11 Pure Mathematics 1 (P1) past paper 01, January 2021. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma11/2021-january-paper-01/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_january_2021_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 2021
- 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
A curve has equation
[Diagram or table: see page 2 of the paper]
(a) Find, in simplest form,
[3]
The point P lies on the curve and has x coordinate 1/2
(b) Find an equation of the normal to the curve at P, writing your answer in the form ax + by + c = 0, where a, b and c are integers to be found. [5]

Question 2
A tree was planted.
Exactly 3 years after it was planted, the height of the tree was 2 m.
Exactly 5 years after it was planted, the height of the tree was 2.4 m.
Given that the height, H metres, of the tree, t years after it was planted, can be modelled by the equation
[Diagram or table: see page 4 of the paper]
where p and q are constants,
(a) find, to 3 significant figures where necessary, the value of p and the value of q. [4]
Exactly T years after the tree was planted, its height was 5 m.
(b) Find the value of T according to the model, giving your answer to one decimal place. [2]

Question 3
[Diagram or table: see page 8 of the paper]
Figure 1 shows a sketch of part of the curve C_1 with equation y = 4 cos x°
The point P and the point Q lie on C_1 and are shown in Figure 1.
(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 k is a constant.
Curve C_2 has a minimum y value of –1
The point R is the maximum point on C_2 with the smallest positive x coordinate.
(b) State the coordinates of R. [2]

Question 4
[Diagram or table: see page 10 of the paper]
The points P and Q, as shown in Figure 2, have coordinates (–2,13) and (4, –5) respectively.
The straight line l passes through P and Q.
(a) Find an equation for l, writing your answer in the form y = mx + c, where m and c are integers to be found. [3]
The quadratic curve C passes through P and has a minimum point at Q.
(b) Find an equation for C. [3]
The region R, shown shaded in Figure 2, lies in the second quadrant and is bounded by C and l only.
(c) Use inequalities to define region R. [2]

Question 5
[Diagram or table: see page 14 of the paper]
Figure 3 shows the plan view of a viewing platform at a tourist site.
The shape of the viewing platform consists of a sector ABCOA of a circle, centre O, joined to a triangle AOD.
Given that
● OA = OC = 6 m ● AD = 14 m ● angle ADC = 0.43 radians ● angle AOD is an obtuse angle ● OCD is a straight line
find
(a) the size of angle AOD, in radians, to 3 decimal places, [3]
(b) the length of arc ABC, in metres, to one decimal place, [2]
(c) the total area of the viewing platform, in m^2, to one decimal place. [4]

Question 6
(a) Sketch the curve with equation
[Diagram or table: see page 18 of the paper]
[2]
(b) On a separate diagram, sketch the curve with equation
[Diagram or table: see page 18 of the paper]
stating the coordinates of the point of intersection with the x-axis and, in terms of k, the equation of the horizontal asymptote. [3]
(c) Find the range of possible values of k for which the curve with equation
[Diagram or table: see page 18 of the paper]
does not touch or intersect the line with equation y = 3x + 4 [5]

Question 7
[Diagram or table: see page 22 of the paper]
Solutions relying on calculator technology are not acceptable.
[Diagram or table: see page 22 of the paper]
(a) Solve the equation
[Diagram or table: see page 22 of the paper]
[4]
(b) Solve the equation
[Diagram or table: see page 22 of the paper]
[5]

Question 8
[Diagram or table: see page 26 of the paper]
Figure 4 shows a sketch of part of the curve C with equation y = f (x), where
[Diagram or table: see page 26 of the paper]
(a) Deduce the values of x for which f (x) > 0 [1]
(b) Expand f (x) to the form
[Diagram or table: see page 26 of the paper]
where a, b, c and d are integers to be found. [3]
The line l, also shown in Figure 4, passes through the y intercept of C and is parallel to the x-axis.
The line l cuts C again at points P and Q, also shown in Figure 4.
(c) Using algebra and showing your working, find the length of line PQ. Write your answer in the form k 3, where k is a constant to be found.
[Diagram or table: see page 26 of the paper]
[5]

Question 9
(i) Find
[Diagram or table: see page 30 of the paper]
giving your answer in simplest form. [5]
(ii) A curve C has equation y = f(x).
Given
● fʹ(x) = x^2+ ax + b where a and b are constants
● the y intercept of C is –8
● the point P(3, –2) lies on C
● the gradient of C at P is 2
find, in simplest form, f(x). [6]
[Diagram or table: see page 32 of the paper]