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- 1. Multiple Choice
Which of the following is an appropriate unit for change in area/change in time?
feet/second
inches2/hour
square feet/day
gallons/year
centimeters3/month
- 2. Multiple Choice
Which of the following is an appropriate unit for change in volume/change in time?
feet3/second
inches2/hour
square feet/day
gallons/year
centimeters3/month
- 3. Multiple Choice
Which of the following is an appropriate unit for change in circumference/change in time?
feet/second
inches/hour
square feet/day
gallons/year
centimeters/month
- 4. Multiple ChoiceRachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the ladder sliding down the wall when the tip of the ladder is 5 ft high?3 ft/sec-7.2 ft/sec7.2 ft/sec12
- 5. Multiple ChoiceRachel is standing atop a 13ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3ft/sec. How fast is the angle changing between the base of the ladder and the ground when the ladder is 5 ft high?-0.6 rad/sec0.8 rad/sec0.6 rad/sec-0.8 rad/sec
- 6. Multiple ChoiceRachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the angle between the tip of the ladder and the house changing when the ladder is 5 ft high?0.8 rad/sec-0.8 rad/sec0.6 rad/sec-0.6 rad/sec
- 7. Multiple ChoiceBrandon is starting to clean up after a birthday party. He begins deflating each spherical balloon by puncturing a hole in each. The air leaves the balloon at a constant rate of 2 cm3/sec. How fast is the diameter changing when the diameter is 8 cm?-1/(16π) cm/sec-1/16 cm/sec-1/(4π) cm/sec1/(4π) cm/sec
- 8. Multiple Choice
Brandon is starting to clean up after a birthday party. He begins deflating each spherical balloon by puncturing a hole in each. The air leaves the balloon at a constant rate of 2 cm3/sec. How long is the diameter when the diameter is decreasing at a rate of 3 cm/sec?
0.424 cm
0.651 cm
1.333 cm
1.155 cm
- 9. Multiple ChoiceLouisa and Karis were each dropped off at the same bus stop. Louisa lives north of the bus stop and Karis lives to the east. Louisa’s bus drops her off at 3:30 whereas Karis is dropped off ten minutes later. Louisa runs home at a constant rate of 6 mph and Karis runs home at 3 mph. How fast is the distance between them changing at 4:00?6.512 mph7.115 mph6.708 mph6.641 mph
- 10. Multiple ChoiceLouisa and Karis were each dropped off at the same bus stop. Louisa lives north of the bus stop and Karis lives to the east. Louisa’s bus drops her off at 3:30 whereas Karis is dropped off ten minutes later. Louisa runs home at a constant rate of 6 mph and Karis runs home at 3 mph. How fast is the area formed by Louisa, Karis and the bus stop changing at 4:00?7.5 mi2/hr9 mi2/hr8 mi2/hr6.25 mi2/hr
- 11. Multiple ChoiceA water tank, shaped like an inverted circular cone, has a base radius of 6 ft and a height of 9 ft. The tank is completely full and needs to be drained. The valve is opened and the water begins to decrease at a rate of 2 ft3/sec. How fast is the height of the water changing when the water is 2 ft deep?-9/(8π) ft/sec9/(8π) ft/sec-8/(9π) ft/sec8/(9π) f/tsec
- 12. Multiple ChoiceA water tank, shaped like an inverted circular cone, has a base radius of 6 ft and a height of 9 ft. The tank is completely full and needs to be drained. The valve is opened and the water begins to decrease at a rate of 2 ft3/sec. How fast is the radius changing when the water is 2 ft deep?4/(3π) ft/sec3/(4π)ft/sec-3/(4π) ft/sec-4/(3π) ft/sec
- 13. Multiple Choice
Chris is sitting on the edge of a dock tossing rocks into the water. As each rock hits the water, small circles appear traveling outward from the point of impact. The radius of the circle is increasing at a rate of 5 in/sec. How fast is the area increasing when the circumference of the largest circle is 4 in?
40 in2/sec
20 in2/sec
20π in2/sec
40π in2/sec
- 14. Multiple Choice
Chris is sitting on the edge of a dock tossing rocks into the water. As each rock hits the water, small circles appear traveling outward from the point of impact. The radius of the circle is increasing at a rate of 5 in/sec. How fast is the area increasing when the diameter of the largest circle is 8 in?
80π in2/sec
20π in2/sec
60π in2/sec
40π in2/sec
- 15. Multiple Choice
A particle moves along the curve
y = sin2(πx).
As it reaches the point (5/4, 1/2), the y-coordinate is increasing at a rate of 2 in/s. How fast is the x-coordinate of the point changing at that instant?
2π in/s
√2 / π in/s
2 in/s
2/π in/s
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