27 find the area inside one loop of the r 2 cos2θ and

27. Find the area inside one loop of the r 2 = cos2θ and identify the
curve
A. 1/2 ; lemniscate C. 9/2 ; cardioid
B. 16 : limacon D. π/8 ; four-leaved rose
28. Find the length of the arc of y=lnsecx from x=0 to x=π/3.
29. Find the arclength of the spiral r=e θ from θ =0 to θ =In2.
30. A solid has its base the circle x^2+y^2=9, and all cross sections
parallel to the y-axis are squares. Find the volume of the solid.
B. 344 D. 112
31. Find the average value of 1/x on [3, 5].
32. A particle moves on a straight line with a velocity v = (4 – 2t)^3 at
time t. Find the distance traveled from t = 0 to t = 3.
33. Find the volume of the solid of revolution formed by revolving the
region bounded by y = x 3 + 3, x = 0, x = 1 and y = 0 about x = 1.
34. A conical tank, 10meters deep and 8 meters across at the top, is
filled with water to a depth of 5 meters. The tank is emptied by
pumping the water over the top edge. How much work is done in
the process?
A. 5283 kJ C. 4580 kJ
B. 1625 kJ D. 1283 kJ
35. Find the differential equations of the family of lines passing
through the origin.
A. xdx – ydy = 0 C. xdx + ydy = 0
B. xdy – ydx = 0 D. ydx + xdy = 0
36. A bucket of water of mass 20 kg is pulled at constant velocity up
to a platform 40 meters above the ground. This takes 10 minutes,
during which time 5 kg of water drips out at a steady rate through
a hole in the bottom. Find the work needed to raise the bucket to
the platform.
B. 8660 J D. 6680 J
x + 4y
f ( x ) =
x 2 − 4
x − 2

Mathematics CERTC REVIEW CENTER
Refresher / Coaching 1
37. A certain population of bacteria grows such that its rate of change
is always proportional to the amount present. It doubles in 2
years. If in 3 years there are 20,000 of bacteria present, how
much is present initially?
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