Name:    AII.10 - Variation

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1

The time it takes to do a job is inversely proportional to the number of
workers. If 8 workers can do a job in 6 days, then 16 workers can do the
same job in —
 a. 1.5 days b. 3 days c. 6 days d. 12 days

2

Which equation represents the statement “r is inversely proportional to s and directly proportional to the cube of t”?
 a. b. c. d.

3

The electrical resistance of a wire varies directly as its length and       inversely as the square of its diameter. A wire with a length of 200 inches and a diameter of one-quarter of an inch has a resistance of 20 ohms. Find the electrical resistance in a 500 inch wire with the same diameter.
 a. 50 ohms b. 200 ohms c. 1250 ohms d. 5000 ohms

4

If a temperature is constant, the volume of a gas varies inversely as its pressure.  A gas with a pressure of 150 pounds per square inch occupies a volume of 25 cubic feet.  What is the constant of proportionality for this variation?
 a. 3750 b. 673 c. 6 d.

5

Kinetic energy varies jointly as the mass and the square of the velocity. A mass of 8 grams and a velocity of 5 centimeters per second has a kinetic energy of 100 ergs. Find the kinetic energy for a mass of 6 grams and a velocity of 9 centimeters per second.
 a. 1215 ergs b. 243 ergs c. 135 ergs d. 27 ergs

6

The electrical resistance of a wire varies directly as its length and inversely as the square of its diameter. A wire with a length of 200 inches and a diameter of one-quarter of an inch has a resistance of 20 ohms. Find the electrical resistance in a 500 inch wire with the same diameter.
 a. 2.5 ohms b. 12.5 ohms c. 50 ohms d. 62.5 ohms

Multiple Response
Identify one or more choices that best complete the statement or answer the question.

7

Which equations represent this situation?

A car’s stopping distance, d, varies directly with the speed it travels, s, and inversely with the friction value of the road surface, f.
 a. c. e. b. d. f.

8

Given x varies jointly with w and y, if when and , what is the value of x when and ?

9

The amount of time required to stack boxes varies directly with the number of boxes and inversely with the number of people who are stacking them.  If 2 people can stack 60 boxes in 10 minutes, how many minutes will be required for 6 people to stack 120 boxes?

10

Body mass index (BMI) is directly proportional to a person’s weight in pounds and inversely proportional to the square of a person’s height in inches.  A person with a BMI of 23.91 has a weight of 135 pounds and a height of 63 inches.  Rounded to the nearest hundredth, what is the BMI of a person with a weight of 145 pounds and a height of 65 inches?

11

If y varies inversely with the square of x, what is the constant of proportionality when and ?

12