# WMA11 Pure Mathematics 1 (P1) Oct/Nov 2019 Paper 01

Pearson Edexcel International A Level WMA11 Pure Mathematics 1 (P1) past paper 01, Oct/Nov 2019. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wma11/2019-oct-nov-paper-01/
- PDF: https://mathvsarham.com/papers/wma11/WMA11_oct-nov_2019_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 2019
- 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
[Diagram or table: see page 2 of the paper]
Figure 1 shows a sector AOB of a circle with centre O and radius r cm.
The angle AOB is 1.25 radians.
Given that the area of the sector AOB is 15 cm^2
(a) find the exact value of r, [2]
(b) find the exact length of the perimeter of the sector. Write your answer in simplest form. [3]

Question 2
A tree was planted in the ground.
Exactly 2 years after it was planted, the height of the tree was 1.85 m.
Exactly 7 years after it was planted, the height of the tree was 3.45 m.
Given that the height, H metres, of the tree, t years after it was planted in the ground, can be modelled by the equation
[Diagram or table: see page 4 of the paper]
where a and b are constants,
(a) find the value of a and the value of b. [4]
(b) State, according to the model, the height of the tree when it was planted. [1]

Question 3
[Diagram or table: see page 6 of the paper]
Solutions relying on calculator technology are not acceptable.
[Diagram or table: see page 6 of the paper]
Figure 2 shows a sketch of the curve C with equation y = x^2– 5x + 13
The point M is the minimum point of C.
The straight line l passes through the origin O and intersects C at the points M and N as shown.
Find, showing your working,
(a) the coordinates of M, [3]
(b) the coordinates of N. [5]
[Diagram or table: see page 6 of the paper]
Figure 3 shows the curve C and the line l. The finite region R, shown shaded in Figure 3, is bounded by C, l and the y-axis.
(c) Use inequalities to define the region R. [2]

Question 4
A parallelogram ABCD has area 40 cm^2
Given that AB has length 10 cm, BC has length 6 cm and angle DAB is obtuse, find
(a) the size of angle DAB, in degrees, to 2 decimal places, [3]
(b) the length of diagonal BD, in cm, to one decimal place. [2]

Question 5
A curve has equation
[Diagram or table: see page 12 of the paper]
(a) Find dy/dx , giving the answer in simplest form. [3]
The point P ⎛/⎝ 4 ,11⎞/3 ⎠ lies on the curve.
(b) Find the equation of the normal to the curve at P. Write your answer in the form ax + by + c = 0, where a, b and c are integers to be found. [4]
[Diagram or table: see page 14 of the paper]

Question 6
The curve C has equation y = + k, where k is a positive constant.
(a) Sketch a graph of C, stating the equation of the horizontal asymptote and the coordinates of the point of intersection with the x-axis. [3]
The line with equation y = 10 – 2x is a tangent to C.
(b) Find the possible values for k. [5]

Question 7
[Diagram or table: see page 16 of the paper]
Figure 4 shows part of the curve with equation y = 2x^2+ 5
The point P(2,13) lies on the curve.
(a) Find the gradient of the tangent to the curve at P. [2]
The point Q with x coordinate 2 + h also lies on the curve.
(b) Find, in terms of h, the gradient of the line PQ. Give your answer in simplest form. [3]
(c) Explain briefly the relationship between the answer to (b) and the answer to (a). [1]

Question 8
Solve, using algebra, the equation
[Diagram or table: see page 18 of the paper]
Fully simplify your answers, writing them in the form a + b c, where a, b and c are integers to be found. [5]

Question 9
[Diagram or table: see page 20 of the paper]
Figure 5 shows a sketch of part of the curve C with equation y = sin ⎛ x ⎞/⎝ 12⎠ , where x is
measured in radians. The point M shown in Figure 5 is a minimum point on C.
(a) State the period of C. [1]
(b) State the coordinates of M. [1]
The smallest positive solution of the equation sin ⎛ x ⎞/⎝ 12⎠ k, where k is a constant, is Į
Find, in terms of Į,
(c)(i) the negative solution of the equation sin ⎛ x ⎞/⎝ 12⎠ k that is closest to zero,
(ii) the smallest positive solution of the equation cos ⎛ x ⎞/⎝ 12⎠ k.
[2]

Question 10
[Diagram or table: see page 22 of the paper]
Figure 6 shows a sketch of part of the curve with equation y = f(x), where
[Diagram or table: see page 22 of the paper]
(a) Deduce the values of x for which f(x) - 0 [2]
The curve crosses the y-axis at the point P, as shown.
(b) Expand f(x) to the form
[Diagram or table: see page 22 of the paper]
where a, b, c and d are integers to be found. [3]
(c) Hence, or otherwise, find
(i) the coordinates of P,
(ii) the gradient of the curve at P. [2]
The curve with equation y = f(x) is translated two units in the positive x direction to a curve with equation y = g(x).
(d)(i) Find g(x), giving your answer in a simplified factorised form.
(ii) Hence state the y intercept of the curve with equation y = g(x). [3]

Question 11
A curve has equation y = f(x).
The point P ⎛/⎝ 4 , 32⎞/3 ⎠ lies on the curve.
[Diagram or table: see page 26 of the paper]
Ɣ މމI x) = − 3
Ɣ މI x) = 5 at P
find
(a) the equation of the tangent to the curve at P, writing your answer in the form y = mx + c, where m and c are constants to be found, [2]
(b) f(x). [8]
[Diagram or table: see page 28 of the paper]