# WMA11 Pure Mathematics 1 (P1) January 2020 Paper 01

Pearson Edexcel International A Level WMA11 Pure Mathematics 1 (P1) past paper 01, January 2020. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma11/2020-january-paper-01/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_january_2020_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 2020
- 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
Find, in simplest form,
[Diagram or table: see page 2 of the paper]
[4]

Question 2
Given y = 3^x, express each of the following in terms of y. Write each expression in its simplest form.
(a) 3^3^x [1]
(b) _x_−_2 3 [2]
(c) _2_−_3_x
[2]

Question 3
[Diagram or table: see page 6 of the paper]
Figure 1 shows part of the curve with equation y = x^2+ 3x – 2
The point P(3,16) lies on the curve.
(a) Find the gradient of the tangent to the curve at P. [2]
The point Q with x coordinate 3 + h also lies on the curve.
(b) Find, in terms of h, the gradient of the line PQ. Write your answer in simplest form. [3]
(c) Explain briefly the relationship between the answer to (b) and the answer to (a). [1]

Question 4
[Diagram or table: see page 8 of the paper]
Figure 2 shows the plan view of a house ABCD and a lawn APCDA.
ABCD is a rectangle with AB = 16 m.
APCOA is a sector of a circle centre O with radius 12 m.
The point O lies on the line DC, as shown in Figure 2.
(a) Show that the size of angle AOD is 1.231 radians to 3 decimal places. [2]
The lawn APCDA is shown shaded in Figure 2.
(b) Find the area of the lawn, in m^2, to one decimal place. [4]
(c) Find the perimeter of the lawn, in metres, to one decimal place. [3]

Question 5
(a) Find, using algebra, all solutions of
[Diagram or table: see page 12 of the paper]
[3]
(b) Hence find all real solutions of
[Diagram or table: see page 12 of the paper]
[4]

Question 6
The line l_1 has equation 3x – 4y + 20 = 0
The line l_2 cuts the x-axis at R(8,0) and is parallel to l_1
(a) Find the equation of l_2, writing your answer in the form ax + by + c = 0, where a, b and c are integers to be found. [3]
The line l_1 cuts the x-axis at P and the y-axis at Q.
Given that PQRS is a parallelogram, find
(b) the area of PQRS, [3]
(c) the coordinates of S. [2]

Question 7
[Diagram or table: see page 18 of the paper]
Figure 3 shows part of the curve C_1 with equation y = 3sin x, where x is measured in degrees.
The point P and the point Q lie on C_1 and are shown in Figure 3.
(a) State
(i) the coordinates of P,
(ii) the coordinates of Q. [3]
A different curve C_2 has equation y = 3sin x + k, where k is a constant.
The curve C_2 has a maximum y value of 10
The point R is the minimum point on C_2 with the smallest positive x coordinate.
(b) State the coordinates of R. [2]

Question 8
The straight line l has equation y = k(2x – 1), where k is a constant.
The curve C has equation y = x^2+ 2x + 11
Find the set of values of k for which l does not cross or touch C. [6]

Question 9
[Diagram or table: see page 22 of the paper]
A curve has equation
[Diagram or table: see page 22 of the paper]
Find the x coordinate of the point on the curve at which = 0
[6]

Question 10
The curve C_1 has equation y = f(x), where
[Diagram or table: see page 24 of the paper]
(a) Sketch C_1 showing the coordinates of any point where the curve touches or crosses the coordinate axes. [3]
(b) Hence or otherwise
(i) find the values of x for which f  1/ 4 x/ 0
(ii) find the value of the constant p such that the curve with equation y = f(x) + p passes through the origin. [2]
A second curve C_2 has equation y = g(x), where g(x) = f(x + 1)
(c)(i) Find, in simplest form, g(x). You may leave your answer in a factorised form.
(ii) Hence, or otherwise, find the y intercept of curve C_2 [3]

Question 11
A curve has equation y = f(x), where
[Diagram or table: see page 26 of the paper]
The point P(4, –50) lies on the curve.
Given that fʹ(x) = –4 at P,
(a) find the equation of the normal at P, writing your answer in the form y = mx + c, where m and c are constants, [3]
(b) find f(x). [8]
[Diagram or table: see page 28 of the paper]