Free Printable Variations

1.

State what type of variation the equation represents.

a)

Direct

b)

Inverse

c)

Joint

d)

None

2.

If x varies inversely as v, and x = 35 when v = 3, find x when v = 15.

a)

7

b)

9

c)

5

d)

21

3.

What is the constant (k) in this inverse variation?
y = 400/x

a)

x

b)

y

c)

400

d)

Not enough information given

4.

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

5.

Write an equation

The cost C of fish varies directly as its weight w in kilogram.

a)

C =kw

b)

W=kc

c)

K= Cw

d)

K =w/c

6.

Write an equation

The distance D travelled by a car is directly proportional to its speed s.

a)

S=kd

b)

D=k/s

c)

D=ks

d)

K=Ds

7.

What is the constant in the equation y=5k?

a)

5

b)

4

c)

3

d)

2

8.

if y varies directly as x, and y=30 and x=5. What is the constant of the variation?

a)

3

b)

6

c)

9

d)

12

9.

What type of variation does this scenario represent?
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

10.

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

a)

direct variation

b)

inverse variation

c)

joint variation

d)

none of these

11.

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

a)

direct variation

b)

inverse variation

c)

joint variation

d)

none of these

12.

What is the standard equation of direct variation?

a)

y = kx

b)

y = k/x

c)

y = kxz

d)

y = kx/z

13.

y is directly proportional to x, and y = 24 when x = 4.

What is the value of y when x = 3?

a)

18

b)

20

c)

23

d)

43

14.

y is inversely proportional to x, and y = 8 when x = 3

What is the equation?

a)

y = 24x

b)

y = 24/x

c)

y = 24

d)

x = 24

15.

If y varies inversely as x and y = 3 when x = 4. What is its equation?

a)

y = 12x

b)

y = 12/x

c)

y = x/12

d)

y = 12

16.

which of the following statements illustrate a direct variation?

a)

z=knd

b)

a=kb

c)

c=k/d

d)

f=abc

17.

What does the Direct Variation Equation look like?

a)

y=b

b)

y=x

c)

y=mx+c

d)

Y=kx

18.

1. The equation xy = 25 represents:

a)

direct variation

b)

inverse variation

c)

joint variation

d)

none of these

19.

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

a)

Yes; ¼

b)

Yes; 2

c)

Yes; 4

d)

No

20.

3. What is the constant (k) in this inverse variation?

a)

12

b)

24

c)

48

d)

Not enough information given

21.

4. Which of the following is NOT a direct variation?

a)

y = -2x

b)

y = 1/2x

c)

2x + 3y = 2

d)

3y = 4x

22.

5.

a)

direct variation

b)

inverse variation

c)

neither direct nor inverse variation

23.

6.

a)

direct variation

b)

inverse variation

c)

neither direct nor inverse variation

24.

7. The value of y varies directly with x. Which function represents the relationship between x and y if y = 12 when x = 6.

a)

y=2X

b)

y=4x

c)

y=1/3x

d)

y=3/8x

25.

8. Which of the following represents direct variation?

a)

y = kx

b)

y = k/x

c)

y = x/k

d)

y = mx + b

26.

9. Which of the given graphs is a direct variation?

a)

A

b)

B

c)

C

d)

D

27.

10. A type of variation that involves 3 or more quantities that may vary directly.

a)

Direct Variation

b)

Inverse Variation

c)

Joint Variation

d)

Combined Variation

28.

11. A type of variation that involves 3 or more quantities that may vary directly.

a)

Direct Variation

b)

Inverse Variation

c)

Joint Variation

d)

Combined Variation

29.

12. The cost c varies directly as the number of n pencils is written as

a)

n = k/c

b)

k = cn

c)

c = kn

d)

c = k/n

30.

13. Which of the following phrases illustrate an inverse variation?

a)

The area of the wall to the amount of paint used to cover it

b)

The amount of money raised in a concert to the number of tickets sold

c)

The time a teacher spends in checking papers to the number of students

d)

The age of a used car to its resale value

31.

14. This is a variation where one quantity varies directly to other quantity and inversely to the other quantity.

a)

Direct Variation

b)

Inverse Variation

c)

Joint Variation

d)

Combined Variation

32.

15. Find the constant of variation;

c varies inversely as d and c = 7 when d = 4

a)

28

b)

11

c)

21x

d)

15

33.

If p varies directly as q , the equation can be written as

a)

p = k/q

b)

p = kq

c)

pq = k

d)

pk = q

34.

If m and n are dependent and independent variables respectively, which equation shows direct variation?

a)

mn = k

b)

m = kn

c)

m = k/n

d)

n = mk

35.

The number of hours h required to finish a job varies inversely as the number of workers w on the job. This relationship is written as

a)

h = kw

b)

h = k/w

c)

w = kh

d)

h/k = w

36.

An encoder can type n words in t hours. The formula that relates n to t is n = k/t . What kind

of variation is it?

a)

inverse

b)

direct

c)

joint

d)

combined

37.

Which of the following describes an inverse variation?

a)

b)

c)

d)

38.

y varies inversely as x and y = 50 when x = 4, find y when x = 40.

a)

5

b)

10

c)

40

d)

50

39.

If 2 men can do a portion of a job in 8 days, how many men can do the same job in 4 days?

a)

7

b)

6

c)

5

d)

4

40.

If p varies directly as q and inversely as r, then which of the following equations describes the relation among the three variables p, q and r?

a)

p = qr/r

b)

p = kr/q

c)

1/p = kr/q

d)

p = kq/r

41.

Translate into variation statement, “w varies jointly as c and the square of a and inversely as b”.

a)

w=\frac{ka^2c}{b}

b)

$w=\frac{kac}{b}$

c)

$w=\frac{ka^2b}{c}$

d)

$w=\frac{kac}{b^2}$

42.

If x varies as the square of y and inversely as z and x = 12 when y = 3 and z = 6, find x when

y = 9 and z = 6.

a)

105

b)

106

c)

107

d)

108

43.

This graph represents what kind of variation?

a)

Direct variation

b)

Inverse variation

c)

Joint variation

d)

Combined variation

44.

A single frog can finish 20 flies in 4 days. If 2 frog will feed on 20 flies they can finish it in 2 days. Therefore this represents what type of variation?

a)

Inverse variation

b)

Direct variation

c)

Combined variation

d)

Joint variation

45.

A pair of shoes cost PHP500. If Lily buys 2 pairs of shoes, she will spend PHP1,000. If she buys 3 pairs of shoes, she will spend PHP1,500. Therefore this represents what type of variation?

a)

Combined variation

b)

Joint variation

c)

Inverse variation

d)

Direct variation

46.

This graph represents what kind of variation?

a)

Joint variation

b)

Direct variation

c)

Combined variation

d)

Inverse variation

47.

If c is inversely proportional to d, and c=20 when d=5, find the value of c when d=25.

a)

100 & 4

b)

200 & 25

c)

250 & 15

d)

500 & 5

48.

This represents what type of variation?

a)

Combined variation

b)

Indirect variation

c)

Joint variation

d)

Direct variation

49.

j varies jointly with l and m. If m=15 when j=150 and l=5, find m when j=45and l=20.

a)

4 & 2/3

b)

5 & 3/4

c)

7 & 8/9

d)

2 & 9/8

50.

c= kad/b : This represents what kind of variation?

a)

Direct variation

b)

Inverse variation

c)

Combined variation

d)

Joint variation

51.

If e varies directly as f and inversely as g, and e=22 when f=11 and g=5, find the value of g when e=3 and f=6.

a)

5 & 10

b)

10 & 20

c)

15 & 30

d)

20 & 45

52.

If g is directly proportional to h, and g=12 when h=6, find the value of g when h=17.

a)

4 & 36

b)

1 & 37

c)

2 & 34

d)

6 & 38

53.

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

54.

In a direct variation, y = 39 when x = 3.
Find the value of y when x = 2.

a)

26

b)

3

c)

58.5

d)

2

55.

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

56.

a)

direct variation

b)

inverse variation

c)

neither direct nor inverse variation

57.

a)

direct variation

b)

inverse variation

c)

neither direct nor inverse variation

58.

What type of variation does this scenario represent?
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

59.

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

a)

direct variation

b)

inverse variation

c)

joint variation

d)

none of these

60.

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

a)

direct variation

b)

inverse variation

c)

joint variation

d)

none of these

61.

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.

a)

direct variation

b)

inverse variation

c)

joint variation

d)

none of these

62.

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.

a)

direct variation

b)

inverse variation

c)

joint variation

d)

none of these

63.

Which of the following represents direct variation?

a)

y = kx

b)

y = k/x

c)

y = x/k

d)

y = mx + b

64.

Which of the following represents indirect variation?

a)

y = kx

b)

y = k/x

c)

y = x/k

d)

y = mx + b

Variations

Total questions: 64

Worksheet time: 54mins

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