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Worksheets

Direct, Inverse, Joint, Combined

Total questions: 25

Worksheet time: 58mins

Name
Class
Date
1.

Which table is an example of Inverse Variation?

a)
b)
c)
d)
2.

The data shown in the table is best described as

a)

Inverse Variation

b)

Direct Variation

c)

Neither

d)

Joint Variation

3.

Suppose that x and y vary inversely. Write a function that models each inverse variation if x = 6 when y = 2.

a)

y = 12 / x

b)

y = x / 12

c)

y = 3 / x

d)

y = x / 3

4.

Write a function that models for the following situation; z varies jointly with x and y and inversely with w.

a)

z = (kxy) / w

b)

z = (xy) / w

c)

z = (kx) / yw

d)

z = (k) / xyw

5.

Each pair of values if from a direct variation. Find the missing value.

(4, 10) , (8, y)

a)

20

b)

2.5

c)

5 / 2

d)

5

6.

Each ordered pair is from an inverse variation. Find the constant of variation.

(5, 10)

a)

50

b)

1 / 2

c)

2

d)

25

7.

Fundraising In a bake sale, you recorded the number of muffins sold and the amount of sales in a table as shown.

What is a function that relates the sales and the number of muffins?

a)

s = 2.5m

b)

s = 3m

c)

s = 192m

d)

Direct Variation

8.

Fundraising In a bake sale, you recorded the number of muffins sold and the amount of sales in a table as shown.

How many muffins would you have to sale to make at least $250.00?

a)

83

b)

84

c)

100

d)

192

9.

Painting The number of buckets of paint n needed to paint a fence varies directly with the total area a of the fence and inversely with the amount of paint p in a bucket. It takes three 1-gallon buckets of paint to paint 84 square feet of fence. How many 1-gallon buckets will be needed to paint 120 square feet of fence?

a)

4

b)

36

c)

5

d)

17

10.

Potential Energy On Earth with a gravitational acceleration g, the potential energy stored in an object varies directly with its mass m and its vertical height h.

What is an equation that models the potential energy of a 3-kg skateboard that is sliding down a ramp?

a)

PE = gmh

b)

PE = mh

c)

PE = 3gh

d)

PE = g2h

11.

Potential Energy On Earth with a gravitational acceleration g, the potential energy stored in an object varies directly with its mass m and its vertical height h.

The acceleration due to gravity is g = -9.8 m/s^2. What is the height of the ramp if the 3-kg skateboard has a potential energy of -39.2 kg m^2/s^2?

a)

2

b)

4/3

c)

8

d)

12

12.

Suppose that x and y vary inversely. Write a function that models each inverse variation if x = 10 when y = 5.

a)

y = 50 / x

b)

y = x / 50

c)

y = 2 / x

d)

y = x / 2

13.

Write a function that models for the following situation; z varies inversely with the product of w and y.

a)

z = kwy

b)

z = k / wy

c)

z = yw

d)

z = kw / y

14.

Each pair of values if from a direct variation. Find the missing value.

(2, 6) , (3, y)

a)

9

b)

18

c)

5 / 2

d)

5

15.

Each ordered pair is from an inverse variation. Find the constant of variation.

(3, 9)

a)

27

b)

3

c)

1/3

d)

25

16.

Each pair of values if from a direct variation. Find the missing value.

(2, 6) , (x, 6)

a)

9

b)

18

c)

5 / 2

d)

2

17.
a)
direct variation
b)
inverse variation
c)
neither direct nor inverse variation
18.
a)
direct variation
b)
inverse variation
c)
neither direct nor inverse variation
19.

The time required to process a shipment of goods at Wal-Mart varies directly with the number of items in the

shipment and inversely with the number of workers assigned. If 15,000 items can be processed by 8 workers in 10 hours, then how long would it take 12 workers to process 20,000 items?

a)

6.5 hours

b)

7.75 hours

c)

8.9 hours

d)

10.2 hours

20.
When dealing with direct and inverse variation, the K represents what?
a)
Kangaroo
b)
K-Mart's Blue Light Special
c)
Constant
d)
King Cobra Snake
21.
Which of the given graphs is a direct variation?
a)
A
b)
B
c)
C
d)
D
22.
What kind of equation is this?
xy=8
a)
Linear Equation
b)
Direct Variation
c)
Inverse Variation
d)
Joint Variation
23.
Determine the type of variation:
a)
Direct
b)
Inverse
c)
Neither
24.
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
25.

Which equation represents an inverse variation?

a)

y=−3x+5y=-3x+5

b)

y=−2xy=-2x

c)

y=x8y=\frac{x}{8}

d)

y=8xy=\frac{8}{x}