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Worksheetsdirect and inverse variation
Total questions: 53
Worksheet time: 2hrs 54mins
Name
Class
Date
1.
Y varies directly with x, and y is 84 when x is 16. Which equation represents this situation?
a)
y=1344x
b)
y=100x
c)
y=5.25x
d)
y=4/21x
2.
Is the given table a direct variation? If so, what is the constant of variation?
a)
Yes; 1/3
b)
Yes; 3
c)
Yes; 5
d)
No
3.
Which of the given graphs is a direct variation?
a)
A
b)
B
c)
C
d)
D
4.
What kind of equation is this?
xy=8
xy=8
a)
Linear Equation
b)
Direct Variation
c)
Inverse Variation
d)
Joint Variation
5.
Is the given table a direct or inverse variation? What is the constant of variation?
a)
Direct, 12
b)
Inverse, 12
c)
Direct, 1/12
d)
Inverse, 1/12
6.
The number of hours to paint a house varies inversely with the number of painters working. A 2400-square foot house can be painted in 27 hours by 6 painters. How many painters would need to work in order to paint the house in 18 hours?
a)
8 painters
b)
10 painters
c)
9 painters
d)
11 painters
7.
Boyle’s Law states that, for a fixed amount of gas, the volume of the gas at a constant temperature is inversely proportional to the pressure. If a certain gas occupies 9.84 liters at a pressure of 50 centimeters of mercury (cm Hg), what is the approximate pressure when the volume is increased to 12 liters?
a)
39.8 cm Hg
b)
41.0 cm Hg
c)
43.2 cm Hg
d)
45.1 cm Hg
8.
The time it takes to fly from Los Angeles to New York varies inversely as the speed of the plane. If the trip takes 6 hours at 900 km/h, how long would it take at 800 km/h?
a)
5.33 hours
b)
6.75 hours
c)
12 hours
d)
10 hours
9.
Trina's paycheck earnings varies directly as the number of hours she works. If she works 19 hours and earns $187.15, what should she earn if she worked 40 hours?
a)
$394
b)
$443.25
c)
$472.80
d)
$512.20
10.
The gas pressure in a chamber varies directly with the temperature in the chamber. If the pressure in the chamber is 150 atmospheres (atm) when the chamber is at 50 degrees, what is the pressure in the chamber when the temperature of the chamber is 75 degrees?
a)
175 atm
b)
200 atm
c)
225 atm
d)
275 atm
11.
y varies directly as x, if y=12 when x=5, find y when x=3
a)
36/5
b)
15/12
c)
12/5
d)
12/15
12.
y varies directly as x, if y=4 when x=3, find x when y=-12
a)
-16
b)
16
c)
-9
d)
9
13.
Points (3,10) and (x, 15) represent a direct variation. Find x.
a)
50
b)
5
c)
3.5
d)
4.5
14.
y varies inversely as x, if y = -3 when x = -6, find y when x = 14.
a)
11
b)
-11
c)
9/7
d)
7/9
15.
Which equation represents an inverse variation?
a)
y = 40/x
b)
y = 40x
c)
y/x = 40
d)
x = y/40
16.
determine the constant of variation given
{(-15,3) (-5,1) (0,0) (10,-2)}
{(-15,3) (-5,1) (0,0) (10,-2)}
a)
-1/5
b)
10
c)
2
d)
-5
17.
Which equation below represents a direct variation?
a)
y = -2x
b)
y = -3x -5
c)
y = -1
d)
x + 3y = 15
18.
The image is an example of the graph of a(n)
a)
direct variation
b)
inverse variation
c)
neither
d)
both
19.
If y varies inversely as x and y=2 as x = 8, find x when y= -7
a)
1/4
b)
4
c)
16
d)
16/-7
20.
The sales at a baseball game vary directly with the number of people attending. If sales for a game are $12,000 when 800 people attend, determine attendance if sales are $30,000
a)
1200 people
b)
1500 people
c)
2000 people
d)
2400 people
21.
The width of a rectangle varies inversely with its length. if the width is 4 when the length is 18, find the width when the length is 8.
a)
9
b)
72
c)
36
d)
2
22.
The gallons of water used to take a shower varies directly with the number of minutes in the shower. If an 8 minute shower uses 48 gallons of water, find the constant of variation.
a)
1/6
b)
6
c)
8
d)
48
23.
The table represents
a)
direct variation
b)
inverse variation
c)
neither
d)
both
24.
In a direct variation, y = 39 when x = 3.
Find the value of y when x = 2.
Find the value of y when x = 2.
a)
26
b)
3
c)
58.5
d)
2
25.
A person’s weekly pay is directly proportional to the number of hours worked. Shawn’s pay is $123.00 for 20 hours of work. What is the constant of variation?
a)
k = 123
b)
k = 20
c)
k = 6.15
d)
k = 0.16
26.
The amount of money earned on a job is directly proportional to the number of hours worked. If $70.00 is earned in 5 hours, how much money is earned in 22 hours of work?
a)
$2
b)
$308
c)
$1.57
d)
$265
27.
a)
direct variation
b)
inverse variation
c)
neither direct nor inverse variation
28.
a)
direct variation
b)
inverse variation
c)
neither direct nor inverse variation
29.
What type of variation does this scenario represent?
The length of time you charge your cell phone
and the battery power
The length of time you charge your cell phone
and the battery power
a)
direct variation
b)
inverse variation
c)
joint variation
d)
none of these
30.
What type of variation does this scenario represent?
The outside temperature
and the number of layers of clothes you need to wear outside to feel comfortable
The outside temperature
and the number of layers of clothes you need to wear outside to feel comfortable
a)
direct variation
b)
inverse variation
c)
joint variation
d)
none of these
31.
What type of variation does this scenario represent?
You and some friends decide to buy 2 pizzas and split the cost evenly.
The number of friends who are sharing the cost of the pizzas
and the amount of money you pay for your share.
You and some friends decide to buy 2 pizzas and split the cost evenly.
The number of friends who are sharing the cost of the pizzas
and the amount of money you pay for your share.
a)
direct variation
b)
inverse variation
c)
joint variation
d)
none of these
32.
Suppose y varies inversely with x.
If y = 150 when x = 2, find y when x = 25.
If y = 150 when x = 2, find y when x = 25.
a)
300
b)
75
c)
1,875
d)
12
33.
The Height of a wave in California varies directly with the seconds that pass by. At 4 seconds, the wave is 6 feet high. How many seconds will give you a wave that is 10 feet high?
a)
y = 2/3x
b)
6
c)
6.6
d)
7
34.
The sales at a baseball game vary directly with the number of people attending. If sales for a game are $12,000 when 800 people attend, determine attendance if sales are $30,000
a)
1200 people
b)
1500 people
c)
2000 people
d)
2400 people
35.
The gallons of water used to take a shower varies directly with the number of minutes in the shower. If an 8 minute shower uses 48 gallons of water, find the constant of variation.
a)
1/6
b)
6
c)
8
d)
48
36.
Is the given table a direct variation? If so, what is the constant of variation?
a)
Yes; 1/3
b)
Yes; 3
c)
Yes; 5
d)
No
37.
Is the given table a direct or inverse variation? What is the constant of variation?
a)
Direct, 12
b)
Inverse, 12
c)
Direct, 1/12
d)
Inverse, 1/12
38.
The number of hours to paint a house varies inversely with the number of painters working. A 2400-square foot house can be painted in 27 hours by 6 painters. How many painters would need to work in order to paint the house in 18 hours?
a)
8 painters
b)
10 painters
c)
9 painters
d)
11 painters
39.
The time it takes to fly from Los Angeles to New York varies inversely as the speed of the plane. If the trip takes 6 hours at 900 km/h, how long would it take at 800 km/h?
a)
5.33 hours
b)
6.75 hours
c)
12 hours
d)
10 hours
40.
The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 65 miles per hour?
a)
308.05 ft
b)
295.75 ft
c)
296.09 ft
d)
253.5 ft
41.
The volume of wood in a tree varies jointly as the height of the tree and the square of the distance around the tree trunk. If the volume of wood is 15.84 cubic feet when the height is 22 feet and the distance around the trunk is 3 feet, what is the volume of wood obtained from a tree that is 32 feet tall having a measurement of 4 feet around the trunk?
a)
44.96 ft3
b)
49.96 ft3
c)
40.96 ft3
d)
32.96 ft3
42.
Suppose y varies directly as x.
If y = 22.5 when x = 15, find y when x = 20.
If y = 22.5 when x = 15, find y when x = 20.
a)
1.5
b)
337.5
c)
30
d)
16.875
43.
Suppose y varies inversely with x.
If y = 150 when x = 2, find y when x = 25.
If y = 150 when x = 2, find y when x = 25.
a)
300
b)
75
c)
1,875
d)
12
44.
Y varies directly with x, and y is 84 when x is 16. Which equation represents this situation?
a)
y=1344x
b)
y=100x
c)
y=5.25x
d)
y=4/21x
45.
The width of a rectangle varies inversely with its length. If the width is 6 when the length is 24, give an equation that shows the relationship.
a)
y = 4x
b)
y = 144x
c)
y = 4/x
d)
y = 144/x
46.
The Height of a wave in California varies directly with the seconds that pass by. At 4 seconds, the wave is 6 feet high. How many seconds will give you a wave that is 10 feet high?
a)
y = 2/3x
b)
6
c)
6.6
d)
7
47.
The number of kilograms of water in a person’s body varies directly as the person’s mass. A person with a mass of 90 kg contains 60 kg of water. How many kilograms of water are in a person whose mass is 75 kg?
a)
50 kg water
b)
72 kg water
c)
94 kg water
d)
150 kg water
48.
The interest received on a savings account varies directly with the amount deposited. Daniel received $55.35 in interest on $1230 he deposited. How much interest would Daniel have received if he had deposited $2000 into his account?
a)
34.04
b)
90.00
c)
1,285.35
d)
44,444.44
49.
Is the given table a direct variation? If so, what is the constant?
a)
Yes; 1/4
b)
Yes; 4
c)
Yes; 2
d)
No
50.
What is the constant (k) in this inverse variation?
a)
12
b)
24
c)
48
d)
Not enough information given
51.
What is the constant (k) in this inverse variation?
y = 400/x
y = 400/x
a)
x
b)
y
c)
400
d)
Not enough information given
52.
The equation
xy = 25 represents:
xy = 25 represents:
a)
direct variation
b)
inverse variation
c)
joint variation
d)
none of these
53.
The value of y varies directly with x. Which function represents the relationship between x and y if y = 14 when x = 6.
a)
y=20x
b)
y=84x
c)
y=7/3x
d)
y=3/7x
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