Free Printable Alg 2 Ch. 7 Multiple Choice Part

1.

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

2.

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

a)

y = 26

b)

y = 3

c)

y = 58.5

d)

y = 2

3.

Is this a direct variation?
y=2x

a)

yes

b)

no

4.

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)

$440

c)

$472.80

d)

$512.20

5.

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. Find the amount of pay for 31 hours of work.

a)

$3813

b)

$620

c)

$190.65

d)

$4.96

6.

Write an equation for this relationship.

a)

y=4x

b)

y=1/8x

c)

y=1/4x

d)

y=8x

7.

Write the equation for the table given.

a)

y = 1/3x

b)

y = 3x

c)

y = 1/2x

8.

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

9.

Given that y varies inversely with x, if x =7 and y = 4, what is y when x = 2?

a)

y = 14

b)

y = 10

c)

y = 2

d)

y = -14

10.

x and y vary inversely. Given (5, 20), what is the constant k?

a)

k = 4

b)

k = 5

c)

k = 25

d)

k = 100

11.

Does the equation show an inverse variation?
y=10/x

a)

yes

b)

no

12.

What kind of variation does this equation show?
y = 6x

a)

Inverse Variation

b)

Direct Variation

c)

No Variation

d)

Joint Variation

13.

Given the following equation, identify the constant k.
y = 54/x

a)

There is one.

b)

k = x

c)

54

d)

y = k

14.

Given (32, 15) and (12, y). Find the constant k, and then find the missing y value.

a)

y = 40

b)

y = 48

c)

y = -40

d)

y = -48

15.

True or False:
Direct Variation passes through the origin of a graph and inverse variation does not.

a)

True

b)

False

16.

Does the table show an inverse variation?

a)

Yes

b)

No

17.

What kind of variation is shown in this graph?

a)

Inverse

b)

Direct

18.

What kind of variation is shown in the graph?

a)

Direct

b)

Inverse

19.

If y varies jointly with the product of x and z, and y = 105 when x = 5 and z = 7, find y when x = 9 and z = 10.

a)

y = 270

b)

y = 180

c)

y = 360

d)

y = 255

20.

If y varies jointly with the product of x and z, and y = 1000 when x = 10 and z = 20, find y when x = 8 and z = 10.

a)

y = 100

b)

y = 200

c)

y = 300

d)

y = 400

21.

The variable x is in joint variation with y and z. When the values of y and z are 4 and 6, x is 16. What is the value of x when y = 8 and z =12?

a)

x = 32

b)

x = 64

c)

x = 48

d)

x = 96

22.

A is in joint variation with B and square of C. When A = 144, B = 4 and C = 3. Then what is the value of A when B = 6 and C = 4?

a)

A= 12

b)

A= 24

c)

A= 36

d)

A= 48

23.

If a varies jointly as b and the square root of c, and a = 21 when b = 5 and c = 36, find a when b = 9 and c = 225.

a)

a = 126

b)

a = 196

c)

a = 256

d)

a = 289

24.

z varies jointly with x and y. If x = 2, y = 3 and z = 4, find z when x = -6 and y = 2.

a)

z = - 6

b)

z = - 8

c)

z = -10

d)

z = -12

25.

z varies jointly with x and y. If x = 5, y = -1, and z = 10. Find z when x = -1/2 and y = 7.

a)

z = 5

b)

z = 6

c)

z = 7

d)

z = 8

26.

If y varies directly as x and inversely as z, and y = 24 when x = 48 and z = 4, find x when y = 44 and z = 6.

a)

x = 126

b)

x = 132

c)

x = 148

d)

x = 154

27.

If f varies directly as g and inversely as the square of h, and f = 20 when g = 50 and h = 5, find f when g = 18 and h = 6.

a)

f = 4

b)

f = 5

c)

f = 8

d)

f = 10

28.

If y varies jointly as a and b and inversely as 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.

a)

y = 8

b)

y = 16

c)

y = 24

d)

y = 32

29.

The number of minutes needed to solve an exercise set of variation problems varies directly as the number of problems and inversely as the number of people working on the solutions. It takes 4 people 36 minutes to solve 18 problems. How many minutes will it take 6 people to solve 42 problems.

a)

56 minutes

b)

52 minutes

c)

48 minutes

d)

44 minutes

30.

If x varies directly as y and inversely as z, and x = 10 when y = 5 and z = 3, for what value of z will x = 3 and y = 4?

a)

z = 2

b)

z = 4

c)

z = 6

d)

z = 8

31.

What is the x-Intercept?

a)

(0, 0)

b)

(4, 0)

c)

(5, 0)

d)

(-5, 0)

32.

What are the zeros?

a)

x= 2/3

b)

x= 4, x = -2

c)

x= -8, x = 1

d)

x= -4, x = 2

33.

What are the asymptotes?

a)

x=1, x= 2, y =1, y= 2

b)

x= 2, x=-2, y = 1

c)

x=2 y =-1

d)

x=1 y =2, y =-2

34.

What is the horizontal asymptote to this function?

a)

y=4

b)

y=0

c)

y=-2

d)

y=1

35.

What (if any) holes exist?

a)

(2, -4)

b)

(2, 3)

c)

(-3, 2)

d)

(3, -4)

36.

What is/are the vertical asymptote(s)?

a)

x=-2

b)

x=2 and x=3

c)

x=-3

d)

x=3

37.

What is the horizontal asymptote?

a)

y = -4

b)

y = 1

c)

x = 1

d)

y = -6

38.

Factor and cancel out in order to simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

39.

Simplify the rational function

a)

1/(x + 5)

b)

1/(x - 5)

c)

(x - 5)(x + 5)

d)

(x - 5)/[(x - 5)(x + 5)]

40.

Simplify (look for common factors that you can factor out and cancel out)

a)

4x³/(x+2)

b)

4x³/(x+10)

c)

2x³/(5x+1)

d)

2x³/(x+5)

41.

Simplify

a)

(n-2)/(n+2)

b)

(n+2)/(n-2)

c)

1/(n+2)

d)

1/(n-2)

42.

Which asymptote(s) are determined by looking at the denominator?

a)

vertical

b)

horizontal

c)

end behavior

d)

none

43.

What are the asymptotes?

a)

x=-1 y = -3

b)

x=1 y = -3

c)

x=-1 y =3

d)

x=1, y=3

44.

Find the coordinates of the hole.

a)

(-3, -3)

b)

(-3, 3)

c)

(3, -3)

d)

(3, 3)

45.

What is the domain?

a)

All real numbers

b)

All real numbers except 4

c)

All real numbers except 2

d)

All real numbers except 2 and -2

46.

Is there a hole or a vertical asymptote?

a)

A hole when x = 2

b)

A vertical asymptote at x = 2

c)

there is no hole or vertical asymptote

47.

Match the graph to the correct rational equation below.

a)

f(x)=x²/(x²+x-12)

b)

f(x)=4x²/(x²-x-12)

c)

f(x)=(2x²-2)/2x²

d)

f(x)=x/(x²+x-12)

48.

What is the end behavior as x approaches negative infinity?

a)

y approaches negative infinity

b)

y approaches positive infinity

c)

y approaches 1

d)

y approaches 2

49.

What is the Horizontal Asymptote?

a)

y= 5

b)

y= -6

c)

y= 1

d)

y= 5/-6

50.

What is the Horizontal Asymptote?

a)

y= 0

b)

y= 4

c)

y= 5

d)

y= -5

51.

What is the Horizontal Asymptote?

a)

y= 6

b)

y= 2

c)

y= 1

d)

y= 0

52.

a)

A

b)

B

c)

C

d)

D

53.

a)

A

b)

B

c)

C

d)

D

54.

a)

A

b)

B

c)

C

d)

D

55.

a)

A

b)

B

c)

C

d)

D

56.

a)

A

b)

B

c)

C

d)

D

57.

a)

A

b)

B

c)

C

d)

D

58.

Simplify the expression

a)

(12n² + 28n + 4) / (2n-5)(n+2)

b)

(12n² - 28n + 4) / (2n-5)(n+2)

c)

(8n) / (3n + 3)

d)

(12n² + 2n -3) / (2n-5)(n+2)

59.

Add.

a)

A

b)

B

c)

C

d)

D

60.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

61.

Simplify

$\frac{m}{3m+6}-\frac{4m}{m+2}$

a)

$-\frac{11m}{3\left(m+2\right)}$

b)

$\frac{13m}{3\left(m+2\right)}$

c)

$\frac{m}{3\left(m+2\right)^2}$

d)

$-\frac{3m}{m+2}$

62.

$\frac{\left(x-3\right)}{x^2+3x-4}+\frac{2x}{x+4}$

a)

$\frac{\left(2x^2-x-3\right)}{\left(x+4\right)\left(x-1\right)}$

b)

$\frac{\left(2x^2-3x-3\right)}{\left(x+4\right)\left(x-1\right)}$

c)

$\frac{\left(3x-3\right)}{\left(x+4\right)\left(x-1\right)}$

d)

$\frac{\left(3x^2-x-3\right)}{\left(x+4\right)^2\left(x-1\right)}$

63.

Simplify

$-\frac{3x}{x^2-9}-\frac{4}{6-2x}$

a)

$-\frac{\left(x+6\right)}{\left(x+3\right)\left(x-3\right)}$

b)

$\frac{2\left(x+6\right)}{\left(x+3\right)\left(x-3\right)}$

c)

$-\frac{5x-6}{\left(x+3\right)\left(x-3\right)}$

d)

$\frac{\left(5x-6\right)}{\left(x+3\right)\left(x-3\right)}$

64.

Simplify

$\frac{2}{x-1}-\frac{4}{x^2-1}+\frac{x}{2}$

a)

$\frac{\left(x^3+3x-4\right)}{2\left(x^2-1\right)}$

b)

$\frac{\left(x^3+4x+12\right)}{2\left(x+1\right)^2}$

c)

$\frac{\left(3x-4\right)}{2\left(x-1\right)^2}$

d)

$\frac{\left(x^2+3x-4\right)}{2\left(x-1\right)^{ }}$

65.

a)

b)

c)

d)

66.

Add

$\frac{3x-2}{x+2}+\frac{2x}{4x-1}$

a)

$\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)}$

b)

$\frac{14x^2-9x-2}{\left(x+2\right)\left(4x-1\right)}\$

c)

$\frac{12x^2-7x+2}{\left(x+2\right)\left(4x-1\right)}\$

d)

$\frac{12x^2-9x+2}{\left(x+2\right)\left(4x-1\right)}\$

67.

Subtract

$\frac{x}{2x+3}-\frac{2x+1}{2x-3}$

a)

$\frac{-2x^2+11x-3}{\left(2x-3\right)\left(2x+3\right)}\$

b)

$\frac{-2x^2-11x-3}{\left(2x-3\right)\left(2x+3\right)}\$

c)

$\frac{-2x^2+5x+3}{\left(2x-3\right)\left(2x+3\right)}\$

d)

$\frac{-2x^2-5x+3}{\left(2x-3\right)\left(2x+3\right)}\$

68.

Add

$\frac{2}{x^2-x-20}+\frac{3}{x^2+7x+12}$

a)

$\frac{11}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\$

b)

$\frac{5}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\$

c)

$\frac{5x-11}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\$

d)

$\frac{5x-9}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\$

69.

Simplify (Add & Divide)

$\frac{\frac{1}{2x}+\frac{2}{3x}}{\frac{x-1}{x-3}}$

a)

$\frac{7x-21}{6x^2-6x}\$

b)

$\frac{7x+21}{6x^2-6x}\$

c)

$\frac{7x^2+21x}{6x^3-6x^2}\$

d)

$\frac{7x^2-21x}{6x^3-6x^2}\$

70.

Divide:

a)

(x+3)/(x+4)

b)

(x-3)/(x+4)

c)

(x+4)/(x-3)

d)

1

71.

Divide the rational expression below.

a)

(x+10)/(2x+5)

b)

(12x+30) / (15x-3)(2x+5)

c)

12/(x+10)

d)

(x+10)/(2x+5)

72.

Divide

a)

A

b)

B

c)

C

d)

D

73.

Multiply and Simplify

a)

4(x+3)/(x+2),

b)

(x+2)/4(x+1)

c)

(x+2)/4(x+3),

d)

4(x+1)/(x+2),

74.

Divide.

a)

(x-6)(x-5)

b)

(x-6)/(x-5)

c)

(x+6)/(x+5)

d)

x+6

75.

Multiply and Simplify

a)

4(x+3)/(x+2)

b)

(x+2)/4(x+1)

c)

(x+2)/4(x+3)

d)

4(x+1)/(x+2)

76.

Simplify.

a)

A

b)

B

c)

C

d)

D

77.

Simplify
(x²+6x+8)/(x²-x-6)

a)

(x+2)/(x-3)

b)

(x+4)/(x+2)

c)

(x+4)/(x-3)

d)

(x+2)/(x+2)

78.

a)

A

b)

B

c)

C

d)

D

79.

a)

A

b)

B

c)

C

d)

D

80.

Simplify.

a)

A

b)

B

c)

C

d)

D

81.

Simplify.

a)

A

b)

B

c)

C

d)

D

82.

a)

20

b)

36/5

c)

1/20

d)

60/3

83.

a)

-5/14

b)

7/40

c)

5/14

d)

10/28

84.

Simplify.
$\frac{\frac{1}{3a-4}}{\frac{3a-4}{a-2}}$

a)

$\frac{3a^3-4a^2}{a^2-4a+4}$

b)

$\frac{a}{a-2}$

c)

$\frac{3a-4}{a-2}$

d)

$\frac{a-2}{9a^2-24a+16}$

85.

Simplify.
$\frac{\frac{1}{x}}{\frac{x-1}{16}}$

a)

$\frac{1}{x}$

b)

$\frac{16x-16}{x^3}$

c)

$\frac{16}{x^2-x}$

d)

$\frac{16}{x^2}$

86.

Simplify.
$\frac{\frac{x+4}{x-1}}{\frac{x+4}{x-1}+\frac{x-1}{x+2}}$

a)

$\frac{-8-x}{x^3+10x^2+32x+32}$

b)

$\frac{x^2+6x+8}{2x^2+4x+9}$

c)

$\frac{2x+3}{x^2+4x+4}$

d)

$\frac{2x^2+7x}{x^2+x-2}$

87.

Simplify.
$\frac{\frac{x+3}{x-5}}{\frac{5}{x+3}+\frac{5}{x-5}}$

a)

$\frac{x-2}{x^2-2x-15}$

b)

$\frac{5x^2-50x+125}{130-x}$

c)

$\frac{x^2+6x+9}{10x-10}$

d)

$\frac{x^2-2x+110}{125}$

88.

Simplify.
$\frac{\frac{u}{16}-\frac{9}{4}}{\frac{u^2}{16}+\frac{16}{u^2}}$

a)

$\frac{u^3-36u^2}{u^4+256}$

b)

$\frac{36-u^4}{225-3u^3}$

c)

$\frac{25u+100}{3u^2-125}$

d)

$-\frac{832u^2}{30000-75u^3}$

89.

Simplify.
$\frac{\frac{3x+2}{x^2}-\frac{3}{x^2}}{\frac{3x+2}{x^2}-\frac{3}{2}}$

a)

$\frac{6x-2}{6x+4-3x^2}$

b)

$\frac{29x^2+36x+12+3x^3}{27x^2+9x^5+12x^4+4x^3}$

c)

$\frac{18x^2+8x}{24+9x}$

d)

$\frac{-45x-30}{-12x-36x^2-16}$

90.

Solve!

a)

x = 2

b)

x = 6

c)

x = 4

d)

x = 8

91.

What is the least common multiple of x²-16 and x²+4x-32?

a)

(x + 4)(x – 4)(x + 8)

b)

(x-4)² (x+8)

c)

(x + 4)(x – 4)

d)

(x - 4)(x-4)²(x + 8)

92.

a)

x = -1

b)

x = 1

c)

x = -9

d)

x = 9

93.

Solve for x.

a)

x = 2

b)

x = 18/5

c)

x = 26/5

d)

x = 6

94.

Solve the equation for x.

a)

x = 6

b)

x = 12

c)

x = 0

d)

x = 3

95.

Solve

a)

x = 0 , 4

b)

x = 1 , 3

c)

x = -4 , 0

d)

x = 5 , 2

96.

Solve!

a)

x = 5

b)

x = 4

c)

x = 5.5

d)

x = -4

97.

Solve!

a)

x = 5

b)

x = 4

c)

x = 5.5

d)

x = -4

98.

Solve the equation for x.

a)

x = 7

b)

x = 6

c)

x = 14

d)

x = 0

99.

Solve :

a)

x = 6

b)

x = -6

c)

x = 6/7

d)

x = -6/7

100.

Solve for x

a)

x = 1/3

b)

x = -5.5

c)

x = 5.5

d)

x = 2.5

101.

Solve for x: $\frac{5}{3}-\frac{2}{x}=\frac{8}{x}$

a)

$x=2$

b)

$x=\frac{18}{5}$

c)

$x=\frac{26}{5}$

d)

$x=6$

102.

Solve: $\frac{3}{x-5}-\frac{20}{x^2-25}=\frac{2}{x+5}$

a)

$x=-5$

b)

$x=5$

c)

$\frac{5}{\left(x+5\right)\left(x-5\right)}$

d)

No Solution

103.

Solve for x: $x-8=-\frac{15}{x}$

a)

x = 5, x = 3

b)

x = −5, x = −3

c)

x = 5

d)

x = −3

104.

Solve for x: $\frac{2}{x+2}+\frac{5}{x-2}=\frac{6}{x^2-4}$

a)

x = 7

b)

x = 6

c)

x = 14

d)

x = 0

105.

Solve for x: $\frac{1}{x}=\frac{1}{5x}-\frac{x-1}{5x}$

a)

x = 5

b)

x = -3

c)

x = 3

d)

x = -5

106.

Solve for x: $\frac{6x+18}{x^2}+\frac{1}{x}=\frac{3}{x}$

a)

x = 4.5

b)

x = -4.5

c)

x = 3

d)

x = -3

107.

State the domain restrictions.

a)

x ≠ -2

b)

x ≠ 2, 1

c)

x ≠ 2, -1

d)

x ≠ -2, 2, 1

108.

Solve for v

a)

v = - 7/6

b)

v = - 9/5

c)

v = 9/5

d)

v = -3

109.

Solve for r

a)

r = 5

b)

r = - 5, 4

c)

r = - 5

d)

r = 5, 4

110.

Solve and check for extraneous solutions

a)

x=5

b)

x= -5

c)

No Solution

111.

Solve and check for extraneous solutions

a)

x= - 3 &x= -8

b)

x= -3 & -8 is extraneous

c)

No Solution

d)

x= -8 & -3 is extraneous

Alg 2 Ch. 7 Multiple Choice Part

Total questions: 111

Worksheet time: 8hrs 1mins

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