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”?


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 onequarter 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 onequarter 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.

Short Answer


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

Directions: Type in your answer. Round your answer to the nearest integer.
The volume of a container varies jointly with the square of its radius, r, and its
height, h. The container has a height of 10 centimeters, and radius of 6 centimeters,
and a volume of 377 cubic centimeters. What is the volume of a container with a radius of 4
centimeters and a height of 4 centimeters?
