Free Printable Unit 11 Test Review

1.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

2.

Simplify.

a)

A.

b)

B.

c)

C.

d)

D.

3.

Reduce, or simplify

the rational expression.

a)

( x + 5 )( x - 5 ) / ( x + 5 )( x - 2 )

b)

( x - 5 ) / ( x - 2 )

c)

( x + 5 ) / ( x - 2 )

d)

-25 / ( 3x - 10 )

4.

Simplify.

a)

(x+6)/(x+4)

b)

(x+6)(x+4)

c)

(x+6)

d)

(x+6)/(x-5)

5.

Divide

a)

1/6

b)

x+10/ 6x+60

c)

x+8/ 6x+60

d)

(x+10)(x+8)/ 6x+60

6.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

7.

simplify.

a)

a

b)

b

c)

c

d)

d

8.

a)

A

b)

B

c)

C

d)

D

9.

a)

A

b)

B

c)

C

d)

D

10.

a)

A

b)

B

c)

C

d)

D

11.

a)

b)

c)

d)

12.

a)

b)

c)

d)

13.

a)

b)

c)

d)

14.

a)

b)

c)

d)

15.

a)

b)

c)

d)

16.

Simplify the expression.

a)

b)

c)

d)

17.

Simplify the expression.

a)

b)

c)

d)

18.

Simplify the expression.

a)

b)

c)

d)

19.

$\frac{4x}{x-5}-\frac{3}{x-6}$ Simplify

a)

$\frac{4x^2-27x+15}{\left(x-6\right)\left(x-5\right)}$

b)

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

c)

$\frac{4x^2-27x+21}{\left(x-6\right)\left(x-5\right)}$

d)

$\frac{4x^2+21x+15}{\left(x-5\right)\left(x+6\right)}$

20.

Subtract the fractions

a)

a

b)

b

c)

c

d)

d

21.

Add or Subtract: $\frac{2x-1}{3x^2}-\frac{3x+2}{x^3}-\frac{4}{5x}$

a)

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

b)

$\frac{2\left(x^2-4x-1\right)}{15x^3},\ x\ne0$

c)

$\frac{10x^2-15x+9}{3x^3},\ x\ne0$

d)

$\frac{-2\left(x^2-2x-1\right)}{15x^3},\ x\ne0$

22.

What is the least common denominator for $\frac{2x-1}{3x^2}-\frac{3x+2}{x^3}-\frac{4}{5x}$ ?

a)

$3x^2$

b)

$5x^2$

c)

$15x^3$

d)

$x^3$

23.

Add/Subtract: $\frac{x+4}{5x+25}-\frac{2x-2}{15x-75}$

a)

$\frac{x^2-11x-50}{15\left(x-5\right)\left(x+5\right)},\ x\ne\pm5$

b)

$\frac{x^2+5x-70}{15\left(x+5\right)\left(x-5\right)},\ x\ne\pm5$

c)

$\frac{x^2+5x-10}{5\left(x+5\right)\left(x-5\right)},\ x\ne\pm5$

d)

It can't be subtracted :(

24.

Add/Subtract: $\frac{5}{x-3}-\frac{6}{3-x}$

a)

$\frac{11}{x-3}$

b)

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

c)

$-\frac{11}{3-x}$

d)

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

25.

What is the common denominator in the complex fraction $\frac{5}{\frac{10}{x+3}+\frac{5}{x}}$ ?

a)

x

b)

$x\left(x+3\right)$

c)

$x+3$

d)

$10x\left(x+3\right)$

26.

Simplify: $\frac{5}{\frac{10}{x+3}+\frac{5}{x}}$

a)

$\frac{x\left(x+3\right)}{3\left(x+1\right)},\ x\ne0,-1,-3$

b)

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

c)

$\frac{x+3}{x\left(x+1\right)},\ x\ne0,\ -1$

d)

$\frac{5\left(x+1\right)}{x\left(x+3\right)}x\ne0,-1,\ -3$

27.

Simplify

$\frac{2x^2}{x+1}\cdot\frac{x+1}{3x^5}$

28.

Simplify

a)

a

b)

b

c)

c

d)

d

29.

Simplify.

$\frac{x^2+11x+28}{x^2+14x+40}\cdot\frac{x^2-100}{8x+56}$

30.

Simplify

$\frac{3b^2-6b}{b^2+2b-3}\cdot\frac{b^2-8b+7}{b-2}$

a)

$\frac{1}{b\left(b-2\right)}$

b)

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

c)

$b-8$

d)

$\frac{3b\left(b-7\right)}{b+3}$

31.

Simplify

$x-5\cdot\frac{2x}{x^2-7x+10}$

32.

Simplify

$\frac{x+1}{x^2-25}\cdot\frac{x+5}{x^2+8x+7}$

a)

$\frac{x+1}{\left(x+5\right)\left(x+7\right)}$

b)

$\frac{1}{\left(x+5\right)\left(x+7\right)}$

c)

$\frac{1}{\left(x-5\right)\left(x+7\right)}$

d)

$\frac{1}{\left(x-5\right)\left(x-7\right)}$

33.

What are the restricted values?

a)

x = - 3 and x = 4

b)

x = 3 and x = - 4

c)

x = 3 only

d)

x = - 4 only

34.

Identify the restricted values

a)

x≠-6

b)

x≠-6, 3

c)

x≠3

d)

x≠-18

35.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

36.

Simplify. Leave answer factored.

$\frac{12x-36}{x+4}\div\frac{3x-9}{x^2-16}$

37.

Simplify

$\frac{5x+7}{3x-18}\div\frac{5x+7}{x-6}$

38.

Simplify

a)

A

b)

B

c)

C

d)

D

39.

Simplify
$\frac{x^2-4x-5}{x^2-3x+2}\div\frac{x^2-3x-10}{x^2-4}$

40.

Simplify
$\frac{3x-27}{x^2-36}\div\frac{x-9}{x^2-x-30}$

Leave your answer in factored form.

41.

Divide $\frac{\frac{3a^3b^3}{\left(a-b\right)}}{\frac{4ab}{\left(b-a\right)}}$

a)

$\frac{3a^3b^3}{\left(a-b\right)}\cdot\frac{\left(b-a\right)}{4ab}$

b)

$\frac{3a^3b^3}{\left(a-b\right)}\cdot\frac{4ab}{\left(a-b\right)}$

c)

$\frac{3a^2b^2}{4}$

d)

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

42.

Simplify: $\frac{2d}{5}\cdot\frac{10}{cd}$

a)

$\frac{20d}{5cd}$

b)

$\frac{20}{5c}$

c)

$\frac{4}{c}$

d)

4

43.

$\frac{n^2+10n+9}{80}\times\frac{8}{n^2+10n+9}$

a)

$64$

b)

$\frac{27n^3}{n+6}$

c)

$\frac{1}{10}$

d)

$\frac{7n\left(n+10\right)}{6}$

44.

Find the excluded value(s).

a)

n = 0

b)

n = 24

c)

n = -24

d)

n can be any real number

45.

Find the excluded value(s).

a)

v = 5

b)

v = 10

c)

v = -25

d)

v = -5

46.

What are the domain restrictions of the following rational expression:

a)

x ≠ 4

b)

x ≠ -4, 4

c)

x ≠ -16, 16

d)

x ≠ 0, 4

47.

Determine the excluded values.

a)

x = 5, -1

b)

x = -5, 1

c)

x = 5, 1

d)

x = -5, -1

48.

Find the excluded value(s). $\frac{x\left(x+4\right)}{\left(x^2-16\right)}$

a)

x = 4

b)

x = -4, 4

c)

x = -16, 16

d)

x = 0, 4

49.

What are the excluded values for this function? $h\left(x\right)=\frac{x}{x-2}$

(a)

50.

Select all of the excluded values: $\frac{\left(x+1\right)\left(x-3\right)}{\left(x-2\right)}\div\frac{\left(x+5\right)}{\left(x+8\right)\left(x-1\right)}$

a)

$x\ne3$

b)

$x\ne2$

c)

$x\ne-8$

d)

$x\ne1$

e)

$x\ne-5$

51.

What would be the common denominator (LCD) when adding these rational expressions: $\frac{ }{\left(x+3\right)}+\frac{ }{\left(x-7\right)}$

a)

$\frac{ }{\left(x+3\right)\left(x-7\right)}$

b)

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

c)

$\frac{ }{\left(x-7\right)}$

d)

$\frac{ }{\left(x-3\right)\left(x+7\right)}$

52.

Select all of the excluded values: $\frac{\left(x+1\right)\left(4x-1\right)}{\left(x-3\right)}\times\frac{\left(x-3\right)\left(x+5\right)}{2x\left(4x-1\right)}$

a)

$x\ne0$

b)

$x\ne-\frac{1}{4}$

c)

$x\ne\frac{1}{4}$

d)

$x\ne3$

e)

$x\ne-5$

53.

Select all of the excluded values/restrictions: $\frac{x-3}{x^2-9}$

a)

$x\ne3$

b)

$x\ne9$

c)

$x\ne-3$

d)

$x\ne-9$

54.

Match the parts of a division problem to their description.

a)

the number doing the dividing

(the number outside the house)

1.

Divisor

b)

the number being divided

(the number under the house)

2.

Dividend

c)

the answer to a division problem

(the number on top of the house)

3.

Quotient

d)

the portion of the dividend that cannot be fairly divided

4.

Remainder

55.

There is always a remainder in division.

a)

True

b)

False

56.

Divide.

$\left(8x^4+6x^3-10x^2\right)\div2x^2$

57.

Simplify using long division.

$\left(8x^2+6x-20\right)\div\left(4x-5\right)$

58.

After we subtract and bring down, the next step is to...

a)

divide $27x^2$ by $3x$

b)

divide $3x^{ }$ by $27x^2$

c)

Subtract $3x-3x=0$

d)

calculate the remainder

59.

Simplify using long division.

$\left(x^4-7x^2+8x-5\right)\div\left(x-2\right)$

60.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

61.

Simplify using long division.

$\left(8x^3-17x^2-x+2\right)\div\left(x-2\right)$

62.

Simplify using long division.

$\left(3x^3+5x-1\right)\div\left(x+1\right)$

63.

The equation
xy = 25 represents:

a)

direct variation

b)

inverse variation

c)

joint variation

d)

none of these

64.

Suppose y varies directly as x.
If y = 22.5 when x = 15, find y when x = 20.

a)

1.5

b)

337.5

c)

30

d)

16.875

65.

Suppose y varies inversely with x.
If y = 150 when x = 2, find y when x = 25.

a)

300

b)

75

c)

1,875

d)

12

66.

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

a)

y=1344x

b)

y=100x

c)

y=5.25x

d)

y=4/21x

67.

The width of a rectangle varies inversely with its length. If the width is 6 when the length is 24, give an equation that shows the relationship.

a)

y = 4x

b)

y = 144x

c)

y = 4/x

d)

y = 144/x

68.

Which table represents a direct variation?

a)

b)

c)

d)

69.

Write an equation for this relationship.

a)

y=4x

b)

y=1/8x

c)

y=1/4x

d)

y=8x

70.

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

a)

Yes; 1/4

b)

Yes; 4

c)

Yes; 2

d)

No

71.

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

a)

4

b)

5

c)

25

d)

100

72.

What kind of variation is shown in the graph?

a)

Direct

b)

Inverse

73.

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

74.

x and y are in inverse variation

x=6 and y=7

Given y=k/x... Find k

75.

a)

11

b)

5

76.

a)

-5

b)

5

77.

Solve for x.

a)

-1

b)

2

c)

6

d)

No solution

78.

a)

A

b)

B

c)

C

d)

D

79.

Solve!

a)

x = 36/7

b)

x = 6

c)

x = 44/7

d)

x = 0

80.

Solve for x

a)

2

b)

0, 3

c)

0, - 7/2

d)

0, 2

81.

a)

A

b)

B

c)

C

d)

D

82.

Solve. Don't forget to check for extraneous solutions. $\frac{x+1}{x+3}=\frac{1}{x+3}+\frac{1}{x^2+3x}$

a)

$A.\ \ \ x\ =-1$

b)

$B.\ \ \ x\ =\ 1$

c)

$C.\ \ \ x=-1,\ x=1$

d)

$D.\ \ x=1,\ x=2$

83.

7)

\frac{2x}{2x+4}\ =\ \frac{3x}{x+2}

a)

$x\ =\ 0,\ -2$

b)

$x=0$

c)

$x=\pm4$

d)

$x=8$

84.

What is the VERTICAL asymptote of this function? (click on the graph to enlarge)

a)

x=1

b)

x=-3

c)

y=1

d)

y= -3

85.

What is the equation of the rational function graphed?

a)

$f\left(x\right)=\frac{1}{x-2}$

b)

$f\left(x\right)=\frac{1}{x+2}$

c)

$f\left(x\right)=\frac{1}{x}+2$

d)

$f\left(x\right)=\frac{1}{x}-2$

86.

What is the HORIZONTAL asymptote of this function? (click on the graph to enlarge)

a)

x=1

b)

x=-3

c)

y=1

d)

y= -3

87.

What is the DOMAIN?

a)

$\left(-\infty,-3\right)U\left(-3,\infty\right)$

b)

$\left(-\infty,1\right)U\left(1,\infty\right)$

c)

$\left(-\infty,-3\right)U\ \left(-3,\ 1\right)\ U\left(1,\infty\right)$

d)

All Real Numbers

88.

Select ALL values that are excluded from the DOMAIN.

a)

x=1

b)

x=-1

c)

y=1

d)

x=0

89.

What is the RANGE?

a)

$\left(-\infty,-3\right)U\left(-3,\infty\right)$

b)

$\left(-\infty,1\right)U\left(1,\infty\right)$

c)

$\left(-\infty,-3\right)U\ \left(-3,\ 1\right)\ U\left(1,\infty\right)$

d)

All Real Numbers

90.

What is the vertical asymptote?

a)

x = 2

b)

y = 2

c)

x = 1

d)

y = 1

91.

What is the y-intercept for f(x) = (2x - 18)/(2x + 6)

a)

(-9,0)

b)

(-3,0)

c)

(0,-3)

d)

(0,1)

92.

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

a)

vertical

b)

horizontal

c)

end behavior

d)

none

93.

What are the asymptotes of the following function:
y = x / (2x - 6)

a)

y = 1/2, x = 3

b)

y = 2, x = 6

c)

y = 1/2, x = 6

d)

y = 2, x = 3

94.

Which is the graph of the rational equation:

a)

b)

c)

d)

95.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

96.

What is the domain and range?

a)

D:\ \left(-\infty,2\right)\cup\left(2,\infty\right)

R:\ \left(-\infty,1\right)\cup\left(1,\infty\right)

b)

$D:\ \left(-\infty,1\right)\cup\left(1,\infty\right)$
$R:\ \left(-\infty,2\right)\cup\left(2,\infty\right)$

c)

$null$
$R:\ \left(-\infty,\frac{1}{2}\right)\cup\left(\frac{1}{2},\infty\right)$

d)

$D:\ \left(-\infty,-2\right)\cup\left(-2,\infty\right)$
$R:\ \left(-\infty,-1\right)\cup\left(-1,\infty\right)$

97.

Identify the domain and range of the function:

$f\left(x\right)=\frac{4}{x+1}+1$

a)

Domain: $\left(-\infty,1\right)U\left(1,\infty\right)$

Range:

$\left(-\infty,4\right)U\left(4,\infty\right)$

b)

Domain: $\left(-\infty,4\right)U\left(4,\infty\right)$

Range:

$\left(-\infty,-1\right)U\left(-1,\infty\right)$

c)

Domain: $\left(-\infty,1\right)U\left(1,\infty\right)$

Range:

$\left(-\infty,-1\right)U\left(-1,\infty\right)$

d)

Domain: $\left(-\infty,-1\right)U\left(-1,\infty\right)$

Range:

$\left(-\infty,1\right)U\left(1,\infty\right)$

98.

Identify the domain and range of the function:

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

a)

Domain: $\left(-\infty,-2\right)U\left(-2,\infty\right)$

Range:

$\left(-\infty,2\right)U\left(2,\infty\right)$

b)

Domain: $\left(-\infty,3\right)U\left(3,\infty\right)$

Range:

$\left(-\infty,-2\right)U\left(-2,\infty\right)$

c)

Domain: $\left(-\infty,2\right)U\left(2,\infty\right)$

Range:

$\left(-\infty,2\right)U\left(2,\infty\right)$

d)

Domain: $\left(-\infty,-3\right)U\left(-3,\infty\right)$

Range:

$\left(-\infty,2\right)U\left(2,\infty\right)$

99.

Identify the domain and range of the function:

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

a)

Domain: $\left(-\infty,-3\right)U\left(-3,\infty\right)$

Range:

$\left(-\infty,0\right)U\left(0,\infty\right)$

b)

Domain: $\left(-\infty,3\right)U\left(3,\infty\right)$

Range:

$\left(-\infty,0\right)U\left(0,\infty\right)$

c)

Domain: $\left(-\infty,0\right)U\left(0,\infty\right)$

Range:

$\left(-\infty,3\right)U\left(3,\infty\right)$

d)

Domain: $\left(-\infty,0\right)U\left(0,\infty\right)$

Range:

$\left(-\infty,-3\right)U\left(-3,\infty\right)$

100.

Find the domain of
$y=\frac{2}{x-7}+4$

a)

$\left(-\infty,-7\right)\cup\left(-7,\infty\right)$

b)

$\left(-\infty,4\right)\cup\left(4,\infty\right)$

c)

$\left(-\infty,-4\right)\cup\left(-4,\infty\right)$

d)

$\left(-\infty,7\right)\cup\left(7,\infty\right)$

Unit 11 Test Review - Optional

Total questions: 100

Worksheet time: 7hrs 24mins

Similar Resources on Wayground