Free Printable direct and inverse variation

Worksheets

direct and inverse variation

Total questions: 20

Worksheet time: 38mins

Name

Class

Date

Y varies directly with x, and y is 84 when x is 16. Which equation represents this situation?

y=1344x

y=100x

y=5.25x

y=4/21x

Is the given table a direct variation? If so, what is the constant of variation?

Yes; 1/3

Yes; 3

Yes; 5

Is the given table a direct or inverse variation? What is the constant of variation?

Direct, 12

Inverse, 12

Direct, 1/12

Inverse, 1/12

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?

8 painters

10 painters

9 painters

11 painters

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?

5.33 hours

6.75 hours

12 hours

10 hours

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?

175 atm

200 atm

225 atm

275 atm

Which of the following represents direct variation?

y = kx

y = k/x

y = x/k

y = mx + b

Which of the following represents indirect variation?

y = kx

y = k/x

y = x/k

y = mx + b

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?

50 kg water

72 kg water

94 kg water

150 kg water

10.

y varies directly as the square of x and indirectly with z. If y is 8 when x is 4 and z is 6, find y when x is 8 and z is 4.

11.

Is the given table a direct variation? If so, what is the constant?

Yes; 1/4

Yes; 4

Yes; 2

12.

The cost per person to rent a mountain cabin varies inversely to the number of people who share the rent. If the cost is $36 per person when 5 people share, what is the cost per person when 8 people share?

$22.50

$57.60

$4.50

$12.50

13.

True or False: In a direct relationship the constant of variation is the product of x and y, and in an inverse relationship the constant of variation is the quotient of x and y.

True

False

14.

In a random sampling of 200 cars of a model, 3 have manufacturing defects. If there is a direct variation between the number of cars and the number of defects, how many of 10,000 cars of the same model will have a manufacturing defect?

150

200

250

300

15.

What type of variation does this scenario represent?
The length of time you charge your cell phone
and the battery power

direct variation

inverse variation

joint variation

none of these

16.

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

direct variation

inverse variation

joint variation

none of these

17.

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.

direct variation

inverse variation

joint variation

none of these

18.

Portions of cake and number of people in the party

Inverse variation

Direct variation

None

19.

Cost of a rent car share and the number of passengers that travel

Direct variation

Inverse variation

None

20.

Liters of gas and kilometers run

Direct variation

Inverse variation

None

100 %

direct and inverse variation

Total questions: 20

Worksheet time: 38mins

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