# Edexcel Jan 2021 IAL Pure Maths WMA11/01

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Edexcel Jan 2021 IAL Pure Maths WMA11/01 question paper

Edexcel Jan 2021 IAL Pure Maths WMA11/01 mark scheme

1. A curve has equation
(a) Find, in simplest form, dy/dx
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
2. A tree was planted.
Exactly 3 years after it was planted, the height of the tree was 2m.
Exactly 5 years after it was planted, the height of the tree was 2.4m.
Given that the height, H metres, of the tree, t years after it was planted, can be modelled by the equation
H3 = pt2 + q
where p and q are constants,
(a) find, to 3 significant figures where necessary, the value of p and the value of q
Exactly T years after the tree was planted, its height was 5m.
(b) Find the value of T according to the model, giving your answer to one decimal place
3. Figure 1 shows a sketch of part of the curve C1 with equation y = 4cos x°
The point P and the point Q lie on C1 and are shown in Figure 1.
(a) State
(i) the coordinates of P,
(ii) the coordinates of Q.
The curve C2 has equation y = 4 cos x° + k, where k is a constant.
Curve CC2
has a minimum y value of –1
The point R is the maximum point on CC2 with the smallest positive x coordinate.
(b) State the coordinates of R.
4. 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.
The quadratic curve C passes through P and has a minimum point at Q.
(b) Find an equation for C.
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.
5. 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 = 6m
• angle AOD is an obtuse angle
• OCD is a straight line
find
(a) the size of angle AOD, in radians, to 3 decimal places,
(b) the length of arc ABC, in metres, to one decimal place,
(c) the total area of the viewing platform, in m2, to one decimal place

1. (a) Sketch the curve with equation
(b) On a separate diagram, sketch the curve with equation
stating the coordinates of the point of intersection with the x-axis and, in terms of k, the equation of the horizontal asymptote.
(c) Find the range of possible values of k for which the curve with equation
2. In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
f(x) = 2x - 3√x - 5, x > 0
(a) Solve the equation
f(x) = 9
(b) Solve the equation
f"(x) = 6
3. Figure 4 shows a sketch of part of the curve C with equation y = f(x), where f(x) = (3x – 2)2(x – 4)
(a) Deduce the values of x for which f(x) > 0
(b) Expand f(x) to the form
ax3 + bx2 + cx + d
where a, b, c and d are integers to be found.
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.
4. Find
(ii) A curve C has equation y = f(x).
Given
• fʹ(x) = x2 + 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).

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