Marks
2. (i) Find the ranges of values of x, between 0° and 180°, for
which cos 3x is positive. (4)
(ii) Find the length of the perimeter of a sector of a circle
of radius 3 units, if the area of the sector is 18 square
units. (4)
3. (i) Integrate with respect to v
(a) 8*3 + 1 — — ; (b) (3x - l)1. (3, 2)
a:3
(ii) If the sum of the length and the circumference of a
cylinder is 6 ft, find the circumference when the volume
is a maximum. (6)
4. (i) For what range of values of x is the function
x* — 8x — 9
both negative and decreasing ? (5)
(ii) Find a fourth proportional to
ak~2, ah+2, ak~3. (3)
(iii) Simplify
x-t (2x + l)s - 4x* (2x + 1)“4. (4)
5. (i) A quantity I is given by the formula
_ £
I = e io sin £
where t is in radian measure. Calculate, correct to three
significant figures, the value of I when f = 2, given that
e = 2-718 and 7r = 3-142. (6)
(ii) Solve the equation
4.4* + 2 = 9.2*. (4)
6. A sphere is expanding so that its volume is increasing at the
uniform rate of 3 c.c. per second. Find the rate of increase
of its surface at the instant when the radius is 5 cm.
Volume of sphere = - irr3 ;
3
Surface of sphere = 47rr2.
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