Page 40 - Ranger SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 2 Differentiation
22. The volume of a cube increases at a rate dy
of 3 cm /s. If the volume of the cube is (a) dx  0
3
125 cm , find the rate of change of dy
3
(a) its side, (b) dx = 0
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(b) its surface area. dy
23. Given that a circle has a radius of r cm, (c) dx  0
a circumference of C cm and an area of
A cm . 2
2
dC 1 Paper
(a) Show that = .
dA r x 2
(b) The area of the circle increases at 1. Given that y = px + r where p and r are
a rate of 3 cm /s, find the rate of non-zeros. 2 2
2
change of the circumference when (a) Show that d y 2 = 2r 3 .
the radius is 4 cm. 2 dx (px + r)
(b) If y = x has a stationary point
8 dy px + r
24. Given y = x 2 , find the value of dx when at (3, 3), find the values of p and
x = –2. Hence, find the approximate r. Hence, show that the point is a
value for 8 . minimum point.
(–2.01) 2
2
25. Given y = 5t + t and x = 2 – 2t. 2. The tangent to the curve y = x – 4 at
2
dy x = a intersects the x-axis and y-axis
(a) Find in terms of x. at P and Q respectively. Given a is a
dx
HOTS
(b) If t changes from 3.01 to 3, find the positive integer. HOTS
approximate change in y. (a) Show that the area of the triangle
26. A coil of wire of length 25 cm is shaped OPQ where O is the origin is
2
2
into a sector of a circle with radius r cm (a + 4) .
4a
and the angle at the centre is θ radians. (b) Hence, find the minimum area of the
If the radius of the sector increases by triangle.
4% when r = 6, find the corresponding
percentage change in the area, A cm , of 3. A rectangle ABCD is inscribed in a
2
the sector. semicircle with a radius of 5 cm and
27. The diagram below shows a graph centre O as shown in the diagram below.
y = f(x) and the line y = g(x).
B C
y
D
x cm Form 5
B C
A D
O
x
0 A Given that the width of the rectangle is
x cm.
Point A lies on the straight line while (a) Show that the area of the rectangle is
points B, C and D lie on the curve. State 2x cm .
x
2
2
25 –
the point/points which satisfy/satisfies (b) Hence, determine the maximum area
the following conditions. of the rectangle.
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02 Ranger Mate Tambahan Tg5.indd 193 25/02/2022 9:23 AM