SCORING GUIDE
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A+ |
3340 |
B |
2527 |
D+ |
1819 |
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A |
3032 |
C+ |
2324 |
D |
1517 |
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B+ |
2829 |
C |
2022 |
F |
014 |
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Multiple choice, graphing calculator
required. The usual scoring rules apply. Mark the letter of the best or
closest choice on your bubble sheet. |
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1. |
The volume of water
remaining in an irregularly shaped bucket at time t is given by the function V(t). Water is
leaking from the bucket in such a way that V(t) is a decreasing exponential function. If k is a positive constant, which of the following could be a
correct differential equation? |
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(A) V ข(t) = ekt |
(D) V ข(t) = kV(t) |
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2. |
Suppose in #1 that the
particular solution for V(t) is given by V(t) = 0.45e0.03t ft3, where time t is in seconds. If the bucket is lifted straight upward at a constant
velocity of ฝ ft/sec, starting from ground level at time t = 0, compute the amount of liquid (cubic feet) that leaks out
as the bucket travels from ground level to a height of 2 ft. |
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(A) 0.026 |
(D) 0.874 |
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3. |
In #2, how many cubic feet
of water per second are leaking out of the bucket at the instant when the
bucket is at the midpoint of its trip (i.e., 1 ft above ground)? |
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(A) 0.0120 |
(D) 0.424 |
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4. |
Water weighs 62.4 lbs. per
cubic foot. Again referring to the scenario described in problems 1 through
3, compute the work done in lifting the leaky bucket from ground level to a
height of 2 ft. |
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(A) 52.921 ft-lbs. |
(D) 56.160 ft-lbs. |
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5. |
A confetti bomb scatters
tiny bits of paper in a circular region 16 m in diameter. The density of
paper varies according to the rule d(r) = 0.05(1 0.0000015r2) g/cm2, where
r denotes the distance [in cm] from the
center of the explosion. In other words, density is 0.05 g/cm2 at
the very center and 0.002 g/cm2 at the outer edge of the circular
region. What is the density of paper particles at a point 4 m from the center
of the explosion? |
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(A) 0.0499988 g/cm2 |
(D) 0.038 g/cm2 |
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6. |
In #5, compute the total
mass of the confetti scattered within the given region. |
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(A) 22 kg |
(D) 52 kg |
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7. |
An Antarctic core sample of
ice is brought to the surface for analysis. The sample forms a cylinder of
radius 10 cm and height 1500 cm. The ice at the bottom has a density of 12
g/cm3 because of compaction, but the ice at the top is only 5 g/cm3.
In between, the density varies linearly. Compute the density at the midpoint
of the core sample. |
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(A) 5 g/cm3 |
(D) 9.5 g/cm3 |
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8. |
Continuing with #8, compute
the total mass of the core sample. |
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(A) 3885 kg |
(D) 4015 kg |
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For #9 and #10, a mans
desirability as a husband is a function of his age (a) in years. His desirability at age 18 is 1 unit. The
instantaneous rate of change of desirability, in units per year, is the
product of an earning-power growth factor, which is 1.05a 18, and a looks factor, which is |
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9. |
Compute the instantaneous
rate of change, in units per year, for a man on his 26th birthday. |
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(A) 0.5 |
(D) 0.8 |
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10. |
Compute the desirability of
a 50-year-old man. |
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(A) 12.432 |
(D) 15.432 |
