Free Printable VARIATIONS

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VARIATIONS

Total questions: 25

Worksheet time: 34mins

Name

Class

Date

1. Which of the following statements represents a direct variation?

The distance travelled by a taxi and the fare

The air pollution to the health hazard and life expectancy

The volume of a cylindrical container and its height and radius

The number of persons sharing a pizza and the size of the slices of pizza

2. What is the equation that represents the statement “L varies directly as the square of M”?

$L=kM^2$

$L=\frac{k}{M^2}$

$M=kL^2$

$M=\frac{k}{L^2}$

3. The area of the wall (W) is directly proportional to the amount of paint (P) needed to paint the wall. If 2 gallons of paint are needed to paint a 40 m² wall, how many gallons of paint are needed to paint a wall with an area of 200 m²?

What is the equation that best describes the given statement?

P = kW

P = k / W

W = kP

W = k / P

4. The area of the wall (W) is directly proportional to the amount of paint (P) needed to paint the wall. If 2 gallons of paint are needed to paint a 40 m² wall, how many gallons of paint are needed to paint a wall with an area of 200 m²?

Which of the following is the constant of variation or proportionality (k)?

k = 10

k = 20

k = 30

k = 40

5. The area of the wall (W) is directly proportional to the amount of paint (P) needed to paint the wall. If 2 gallons of paint are needed to paint a 40 m² wall, how many gallons of paint are needed to paint a wall with an area of 200 m²?

What is the equation of variation that defines the relation?

$P=\frac{10}{W}$

$P=40W$

$W=\frac{30}{P}$

$W=20P$

6. The area of the wall (W) is directly proportional to the amount of paint (P) needed to paint the wall. If 2 gallons of paint are needed to paint a 40 m² wall, how many gallons of paint are needed to paint a wall with an area of 200 m²?

What is the final answer in the given problem?

5 gallons

10 gallons

15 gallons

20 gallons

7. Which of the following statements describes an inverse variation?

The amount of electricity consumed and bill of the electricity

The air pollution to the health hazard and life expectancy

The volume of a cylindrical container and its height and radius

The number of persons sharing a pizza and the size of the slices of pizza

8. What is the equation that represents the statement “P varies inversely as the cube of Q”?

$P=kQ^2$

$P=\frac{k}{Q^3}$

$Q=kP^3$

$Q=\frac{k}{P^3}$

9. The distance (d) from the center of a seesaw varies inversely as the weight (w) of a person, Guen who weighs 100 lbs. sits 4 feet from the fulcrum. How far from the fulcrum must Patricia to balance Guen if he weighs 80 lbs?

Which of the following equations best describes the problem?

$w=kd$

$w=\frac{k}{d}$

$d=kw$

$d=\frac{k}{w}$

10.

10. The distance (d) from the center of a seesaw varies inversely as the weight (w) of a person, Guen who weighs 100 lbs. sits 4 feet from the fulcrum. How far from the fulcrum must Patricia to balance Guen if he weighs 80 lbs?

What is the value of k (constant of variation/ proportionality)?

k = 400

k = 200

k = 100

k = 25

11.

11. The distance (d) from the center of a seesaw varies inversely as the weight (w) of a person, Guen who weighs 100 lbs. sits 4 feet from the fulcrum. How far from the fulcrum must Patricia to balance Guen if he weighs 80 lbs?

What is the equation of variation?

$w=\frac{200}{d}$

$w=100d$

$d=\frac{400}{w}$

$d=25w$

12.

12. The distance (d) from the center of a seesaw varies inversely as the weight (w) of a person, Guen who weighs 100 lbs. sits 4 feet from the fulcrum. How far from the fulcrum must Patricia to balance Guen if he weighs 80 lbs?

What is the final answer in the given problem?

5 feet

8 feet

10 feet

16 feet

13.

13. What statement represents joint variation?

The distance travelled by a taxi and the fare

The air pollution to the health hazard and life expectancy

The volume of a cylindrical container and its height and radius

Savings and Expenditure

14.

14. Carl instructed by her teacher to write on the board the equation that illustrates the sentence “The volume (V) of a cone varies jointly as its height (h) and the square of the radius (r) of its base. Which of the following equations should she present?

$V=khr^2$

$k=Vhr^2$

$V=\frac{kh}{r^2}$

$k=\frac{Vh}{r^2}$

15.

15. The area of a rectangle (A) varies jointly as its length (l) and width (w). If the length is 20 cm and the width is 10 cm, the area is 200 cm². Find the area if the length is 50 cm and the width is 30 cm.

What is the equation that best describes the given statement?

$k=Alw$

$k=\frac{Al}{w}$

$A=klw$

$A=\frac{kl}{w}$

16.

16. The area of a rectangle (A) varies jointly as its length (l) and width (w). If the length is 20 cm and the width is 10 cm, the area is 200 cm². Find the area if the length is 50 cm and the width is 30 cm.

Which of the following is the constant of variation or proportionality (k)?

k = 1

k = 2

k = 3

k = 4

17.

17. The area of a rectangle (A) varies jointly as its length (l) and width (w). If the length is 20 cm and the width is 10 cm, the area is 200 cm². Find the area if the length is 50 cm and the width is 30 cm.

What is the equation of variation that defines the relation?

$A=1lw$

$A=\frac{2l}{w}$

$k=3lw$

$k=\frac{2l}{w}$

18.

18. The area of a rectangle (A) varies jointly as its length (l) and width (w). If the length is 20 cm and the width is 10 cm, the area is 200 cm². Find the area if the length is 50 cm and the width is 30 cm.

What is the final answer?

1000 cm²

1250 cm²

1500 cm²

1750 cm²

19.

19. What statement represents combined variation?

The distance travelled by a taxi and the fare

The air pollution to the health hazard and life expectancy

The area of rectangular field and its length and width

The number of persons sharing a pizza and the size of the slices of pizza

20.

20. If r varies directly as s and inversely as t, which equation represents the relation?

$k=rst$

$k=\frac{rs}{t}$

$r=kst$

$r=\frac{ks}{t}$

21.

21. The acceleration (a) of an object varies directly as the force (f) exerted and inversely as its mass (m). If an acceleration of an object is 15 m/s² when the force exerted is 450 Newtons and the mass is 30 kg. Find the acceleration of a 50 kg object exerting a force of 350 Newtons.

Which of the following equations best describes the problem?

$a=kfm$

$a=\frac{kf}{m}$

$k=afm$

$k=\frac{af}{m}$

22.

22. The acceleration (a) of an object varies directly as the force (f) exerted and inversely as its mass (m). If an acceleration of an object is 15 m/s² when the force exerted is 450 Newtons and the mass is 30 kg. Find the acceleration of a 50 kg object exerting a force of 350 Newtons.

What is the value of k (constant of variation/ proportionality)?

k = 1

k = 3

k = 5

k = 7

23.

23. The acceleration (a) of an object varies directly as the force (f) exerted and inversely as its mass (m). If an acceleration of an object is 15 m/s² when the force exerted is 450 Newtons and the mass is 30 kg. Find the acceleration of a 50 kg object exerting a force of 350 Newtons.

Which of the following is the equation of variation that defines the relation?

$a=3fm$

$k=5fm$

$a=\frac{1f}{m}$

$k=\frac{7f}{m}$

24.

24. The acceleration (a) of an object varies directly as the force (f) exerted and inversely as its mass (m). If an acceleration of an object is 15 m/s² when the force exerted is 450 Newtons and the mass is 30 kg. Find the acceleration of a 50 kg object exerting a force of 350 Newtons.

What is the final answer?

5 m/s²

7 m/s²

9 m/s²

11 m/s²

25.

25. If y varies jointly with a and b and inversely with the square root of c, and y = 12 when a = 3, b = 2, and c = 64. Find y when a = 5, b = 2, and c = 25.

y = 8

y = 16

y = 24

y = 32

100 %

VARIATIONS

Total questions: 25

Worksheet time: 34mins

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