Free Printable Algebra 2 2nd Semester Final Review

1.

Given f(x) = $\frac{3x+2}{x-1}$ , what is the domain of f(x)?

a)

All real numbers greater than or equal to 1

b)

All real numbers except 1

c)

x = 1

d)

All real numbers

2.

Find the value of x for

5^{\left(2x+3\right)}=\frac{1}{125}.

a)

$x=-2$

b)

$x=-3$

c)

$x=2$

d)

$x=3$

3.

Describe the transformation of the equation below from the parent function of y = IxI
y = I x + 2 I - 5

a)

Left 2 up 5

b)

Right 2 up 5

c)

Left 2 down 5

d)

Right 2 down 5

4.

The area of a rectangular pool table is: x² + 14x +40.

The length is x + 4. What is the width?

a)

x + 8

b)

x + 14

c)

x + 10

d)

x +4

5.

What is the RANGE?

a)

All real numbers

b)

x > 2

c)

y > 2

d)

None of these

6.

a)

13√3

b)

10√30

c)

13√6

d)

11√3

7.

Factor completely:

3x² + 18x +15

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

8.

Write a polynomial function of least degree with integral coefficients and have zeros 2, 1, -1.

a)

x³ - 2x² - x + 2

b)

x³ + 2x² - x + 2

c)

x³ - 2x² - x - 2

d)

x³ - 2x² + x + 2

9.

Simplify the following radical: √32

a)

3√2

b)

4√8

c)

16√2

d)

4√2

10.

Add the polynomials.
(3x³ + 3x² – 4x + 5) + (x³ – 2x² + x – 4)

a)

4x³ + 1x² – 3x + 1

b)

2x³ + 1x² - 5x + 9

c)

6x³ + 1x - 1x² - 3

d)

3x⁵ +1x - 1x⁵ - 3x

11.

Simplify

(x³-x²+4) - (3x³-2x²+3)

a)

-2x³-3x²+7

b)

-2x³+x²+1

c)

2x³-3x³-1

d)

4x³-3x²+7

12.

What is the degree of the polynomial function
P(x)=3x⁴-7x²-2x⁷-x+4

a)

4

b)

7

c)

2

d)

11

13.

Simplify: (4x - 2x³) + (5x³ - 4x + 5)

a)

3x³ + 5

b)

3x³ + 8x + 5

c)

3x² + 5

d)

7x³ + 8x + 5

14.

Factor Completely:
x² - 36

a)

(x + 9)(x - 4)

b)

(x - 6)(x - 6)

c)

(x - 9)(x + 4)

d)

(x + 6)(x - 6)

15.

Solve a³- 9a²+ 14a=0.

a)

-7, -2

b)

7, 2

c)

0, -7, -2

d)

0, 7, 2

16.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect, and error occurs on the 2nd line!

c)

This is incorrect, and the error occurs on the 4th line!

d)

This is incorrect, and the error occurs on the 3rd line!

17.

$-2^2$

a)

4

b)

- 4

c)

22

d)

None of these

18.

Simplify:

$\frac{3x}{10x^2}+\frac{7}{5x^2}$

a)

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

b)

$\frac{3x+7}{10x^2}$

c)

$\frac{1}{x^2}$

d)

$\frac{3x+14}{10x^2}$

19.

If you were to factor using Synthetic Division, what should be the order of the polynomial coefficients if (3x - 4x³ + 6x⁴ + 1) / (x + 3)

a)

3 0 -4 6 1

b)

6 -4 0 1 3

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

20.

Calculate the zeros of the quadratic.

a)

x = 2 and -3

b)

x = 0 and 9/4

c)

x = 0 and 4/9

d)

x = 1/2 and 1/3

21.

Which is a zero of the graph?

a)

0

b)

-1

c)

1.5

d)

-3

22.

Simplify: $2\log_2x-\log_2\left(x+3\right)$

a)

$\log_2\left(x^3+3x^2\right)$

b)

$\log_2\left(2x^2+6x\right)$

c)

$\log_2\left(\frac{x^2}{x+3}\right)$

d)

$\log_2\left(\frac{2x}{x+3}\right)$

23.

$\left(-5\right)^4$

a)

625

b)

-625

c)

20

d)

-20

24.

The x-intercepts of a quadratic equation are known as the _____.

a)

vertices

b)

squares

c)

zeros

d)

formulas

25.

Solve

3^{\left(x+1\right)}=27.

a)

$x=2$

b)

$x=4$

c)

$x=-4$

d)

$x=-2$

26.

What is the value of 27^⅓?

a)

27

b)

9

c)

3

d)

1/3

27.

Simplify the following expression:

a)

5

b)

25

c)

125

d)

625

28.

What is the range of the exponential function?

a)

all real numbers

b)

y > -3

c)

y < -3

d)

x > -3

29.

Solve

8^x=4.

a)

$x=-\frac{2}{3}$

b)

$x=\frac{2}{3}$

c)

$x=\frac{3}{2}$

d)

$x=\frac{1}{2}$

30.

Solve

3^x=\frac{1}{27}.

a)

$x=-2$

b)

$x=3$

c)

$x=-3$

d)

$x=9$

31.

Solve

\left(\frac{1}{2}\right)^x=8^{\left(x-2\right)}.

a)

$x=-3$

b)

$x=3$

c)

$x=-\frac{3}{2}$

d)

$x=\frac{3}{2}$

32.

Find the solution for

5^{\left(x+7\right)}=25^x.

a)

$x=2$

b)

$x=-2$

c)

$x=-7$

d)

$x=7$

33.

What is the Domain of this exponential function?

a)

y=1

b)

x=0

c)

All Real Numbers

d)

x>0

34.

What is the Range?

a)

All Real Numbers

b)

x > 0

c)

y < 0

d)

None

35.

What is the transformation?

a)

Vertical Translation up 2 and Horizontal translation right 1

b)

Vertical Translation down 2 and Horizontal Translation left 1

c)

Horizontal Translation left 2 and Vertical Translation up 1

d)

Horizontal Translation right 2 and Vertical Translation down 1

36.

Simplify: $\frac{1}{4}\log_281+\frac{1}{2}\log_249$

a)

$\log_221$

b)

$\log_210$

c)

$\log_2\left(\frac{3}{7}\right)$

d)

$\log_244.75$

37.

(x²)⁰

a)

1

b)

2

c)

x²⁰

d)

x²

38.

(2x²)^-4

a)

16x⁸

b)

1
---
16x⁸

c)

1
-----
2x⁸

d)

1
----
8x⁸

39.

(3x⁴y³z⁵)³

a)

12x¹²y⁹z¹⁵

b)

9x¹²y⁹z¹⁵

c)

3x¹²y⁹z¹⁵

d)

27x¹²y⁹z¹⁵

40.

3m^-4
^--------m³

a)

3
---
m⁷

b)

3
---
m¹

c)

3
---
m^-1

d)

3m⁷

41.

Convert 16 = 2^x to a Log

a)

Log₂(x) = 16

b)

Log₂(16) = x

c)

Log₁₆(x) = 2

d)

Log_x(16) = 2

42.

log(x+6) = 1

a)

4

b)

4.222

c)

-5

d)

-9.550

43.

Solve for x: log_x 3 = 1

a)

3

b)

1

c)

0

d)

x

44.

Convert Log₂(16) = y to an exponent

a)

64^y = 2

b)

2⁶⁴ = y

c)

16² = y

d)

2^y = 16

45.

Simplify: $\log_73+\log_76$

a)

$\log_736$

b)

$\log_7\left(\frac{1}{2}\right)$

c)

$\log_718$

d)

undefined

46.

Simplify: $\log_4\left(x+4\right)-\log_4\left(x-5\right)$

a)

$\log_49$

b)

$\log_4\left(2x-1\right)$

c)

$\log_4\left(x^2-x-20\right)$

d)

$\log_4\left(\frac{x+4}{x-5}\right)$

47.

When you have a log expression with a number in front of it, we really need to ___________ .

a)

make the number an exponent at the end of the log expression.

b)

multiply it with the log expression.

c)

add it to the log expression.

d)

subtract it from the log expression.

48.

Simplify: $\log_4\left(x+4\right)-\log_4\left(x-5\right)$

a)

$\log_49$

b)

$\log_4\left(2x-1\right)$

c)

$\log_4\left(x^2-x-20\right)$

d)

$\log_4\left(\frac{x+4}{x-5}\right)$

49.

Simplify: $\frac{1}{4}\log_516+3\log_5x$

a)

$\log_5\left(4x^3\right)$

b)

$\log_5\left(2x^3\right)$

c)

$\log_5\left(6x\right)$

d)

$\log_5\left(\frac{2}{x^3}\right)$

50.

Simplify: $\frac{1}{2}\log_964+\log_9x$

a)

$\log_9\left(32x\right)$

b)

$\log_9\left(\frac{32}{x}\right)$

c)

$\log_9\left(\frac{8}{x}\right)$

d)

undefined

51.

Solve:
3^x-2= 27^4x

a)

-2/11

b)

-2/3

c)

2/11

d)

2/3

52.

Multiply:
2x(3xy²+ 4x³y)=

a)

6xy² + 8x⁴y

b)

6x²y + 8x³y

c)

6x²y² + 4x⁴y

d)

6x²y² + 8x⁴y

53.

Solve:
16^x-3 = 8^x-3

a)

9

b)

-3

c)

0

d)

3

54.

$\log_4x^2=\log_43+\log_4\left(x+6\right)$

Which quadratic equation would you wind up solving when solving the log equation?

a)

$x^2-3x-18=0$

b)

$x^2+3x+6=0$

c)

$x^2-3x-6=0$

d)

$x^2-x-9=0$

55.

Solve:

log (x - 1) - log (x - 2) = log 5

a)

7

b)

4/9

c)

9/4

d)

1/7

56.

log₅x - log₅(x+4)=log₅38

a)

-152/37, -8

b)

1/2

c)

-152/37

d)

No Solution

57.

log7+log(x²-4)=log35

a)

1, -1

b)

2, -2

c)

3, -3

d)

4, -4

58.

Expand the Logarithim $\ln\left(\frac{2x^2y}{z^4}\right)$

a)

ln2+2lnx+lny+4lnz

b)

ln2+2lnx+lny-4lnz

c)

2ln(2xy)-4lnz

d)

2ln2x+lny-4lnz

59.

The equation
xy = 25 represents:

a)

direct variation

b)

inverse variation

c)

joint variation

d)

none of these

60.

The value of y varies directly with x. Which function represents the relationship between x and y if y = 14 when x = 6.

a)

y=20x

b)

y=84x

c)

y=7/3x

d)

y=3/7x

61.

Simplify:

$\frac{3}{x-1}+\frac{5}{6x}$

a)

$\frac{23x-5}{6x\left(x-1\right)}$

b)

$\frac{13x-5}{6x\left(x-1\right)}$

c)

$\frac{13x-5}{6x^2}$

d)

$17x-6$

62.

Simplify:

$\frac{4x}{2x+8}-\frac{12}{x}$

a)

$\frac{4x^2+24x-96}{x\left(2x+8\right)}$

b)

$\frac{4x^2-24x+96}{x\left(2x+8\right)}$

c)

$\frac{4x^2-24x-96}{x\left(2x+8\right)}$

d)

$\frac{4x^2+24x+96}{x\left(2x+8\right)}$

63.

Simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

64.

Divide and Simplify

a)

1/6

b)

x+10/ 6x+60

c)

x+8/ 6x+60

d)

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

65.

Solve

a)

x = 1

b)

x = -3

c)

x = 0

d)

x = 3

66.

What is the correct ratio you would use to solve for "w"?

a)

sin 40 = w/28

b)

cos 40 = w/28

c)

tan 40 = w/28

d)

sin 40 = 28/w

67.

What is the acronym to help you remember the ratios to use in trigonometry?

a)

RIGHTANG

b)

SOHCAHTOA

c)

SHOCHATOA

d)

SAHCOHTOA

68.

Roger bowled 7 games last weekend. His scores are: 155, 165, 138, 172, 127, 193, 142. What is the range of Roger's scores?

a)

193

b)

127

c)

60

d)

66

69.

At Donald's Donuts the number of donut holes in a bag can vary. Help Donald find the MODE.

12,10,10,10,13,12,11,13,10

a)

10

b)

12

c)

10 and 12

d)

No Mode

70.

Find the mean (average).

18, 2, 0, 0, 0

a)

4

b)

5

c)

10

d)

20

71.

Find the median.

7, 1, 1, 7, 1, 4, 1

a)

4

b)

7

c)

1

d)

5

72.

What is the range?

a)

The sum of the largest and smallest number

b)

The number in the middle

c)

The difference between the largest and smallest number

d)

The number that appears most often

73.

Is there an outlier? If so, what is it?

17, 36, 45, 98, 25, 34, 19, 45, 36

a)

outlier: none

b)

outlier: 98 and 17

c)

outlier: 98

d)

outlier: 17

74.

What is the minimum value?

a)

64

b)

58

c)

66

d)

60

75.

What is the maximum value?

a)

58

b)

66

c)

64

d)

60

76.

What is the median of the data?

a)

200

b)

100

c)

90

d)

140

77.

The first step to creating a box and whisker plot is...

a)

immediately cross numbers off to find the median

b)

find the average

c)

find the number that appears the most

d)

ordering the data from least to greatest

78.

What is the interquartile range?

a)

4

b)

6

c)

2

d)

8

79.

When finding the median, what do you do if there are TWO numbers in the middle?

a)

You write both numbers for your answer.

b)

You choose the larger number.

c)

You cross them out-- there is no median.

d)

You add them together and divide by 2.

80.

What percent of students have a height between 58 inches and 60 inches?

a)

25%

b)

50%

c)

75%

d)

100%

81.

What percentage of the data is between 90 and 140?

a)

25 %

b)

50%

c)

75%

d)

100%

82.

For synthetic division, what should be the order of the polynomial coefficients to find

(3x - 4x³+ 6x⁴ + 1) / (x + 3)?

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

83.

For synthetic division, what would be the number in the left hand box?

a)

-2

b)

1

c)

2

d)

-1

84.

4x⁴+4x³-9x²-x+2 ÷ x-1

a)

4x³+8x²-7x-2

b)

4x³+19x²-x-2

c)

4x³+8x²-x-9

d)

4x³+8x²-x-2

85.

Is (x-2) a factor of

f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

86.

Use synthetic division:
(2x³ - 5x - 7) ÷ (x - 2)

a)

2x³ - 4x² + 3x - 13

b)

2x³ + 4x² +3x - 1

c)

2x² - 4x + 3 - 13/x-2

d)

2x² + 4x + 3 - 1/x-2

87.

What shape is a normal distribution curve?

a)

Half curve

b)

Round curve

c)

Bell curve

d)

Square curve

88.

What type of distribution is pictured?

a)

Right skewed

b)

Left skewed

c)

Random

d)

Normal

89.

Which interval has 400 employees?

a)

33-43

b)

0-10

c)

77-87

d)

66-76

90.

Type of Data arrangement

a)

Symmetrical

b)

Hairline

c)

Skewed Right

d)

Skewed Left

91.

What is the shape of the distribution?

a)

Skewed Left

b)

Skewed Right

c)

Symmetric

d)

Bimodal

92.

Find the outlier in the set of data
92, 88, 106, 169, 76, 72, 67, 10, 115, 73, 111, 59

a)

169

b)

115, 169

c)

111, 169

d)

10, 169

93.

How many students have more than 1,000 songs on their MP3 player?

a)

5

b)

16

c)

10

d)

4

94.

A florist recorded the number and cost of flower bouquets that were sold daily and recorded the data below. What is the frequency of a bouquet that cost at least $40?

a)

2

b)

15

c)

22

d)

37

95.

Which statement best describes the data shown in the dot plot?

a)

The peak of the data is at 35

b)

The data are clustered from 30 to 32

c)

The data distribution has gaps

d)

The data distribution is symmetrical

96.

Solve for r

a)

5

b)

- 5, 4

c)

- 5

d)

5, 4

97.

Solve for x

a)

1/3

b)

-5.5

c)

5.5

d)

2.5

98.

Solve.

a)

x = 5

b)

x = -3

c)

x = 3

d)

x = -5

99.

Solve the equation for x.

a)

6

b)

12

c)

0

d)

3

100.

Solve!

a)

x = 2

b)

x = 6

c)

x = 4

d)

x = 8

101.

Solve by cross-multiplying.

a)

x = 2

b)

No Solution

c)

x = -10

d)

x = 10

102.

a)

x = 8.9

b)

x = 16

c)

x = 9

d)

x = 12

103.

Simplify the expression.

a)

b)

c)

d)

104.

Simplify the expression.

a)

b)

c)

d)

105.

Find the excluded value(s). $\frac{45}{10x-10}$

a)

a = 0

b)

a = 10

c)

a = 1

d)

a = -1

106.

Find the excluded value(s). $\frac{x}{x^2+x-12}$

a)

x = - 3 and x = 4

b)

x = 3 and x = - 4

c)

x = 3 only

d)

x = - 4 only

107.

Solve. Remember to check for extraneous solutions.

a)

{-3}

b)

{6}

c)

{-5,6}

d)

{-5}

108.

a)

x = -6

b)

x = 3

c)

x = -3

d)

x = 5±

109.

Solve for x. $4\sqrt{x+9}+11=7$

a)

x = -8

b)

x = -10

c)

x = -1

d)

No Solution

110.

a)

36

b)

18

c)

-18

d)

27

111.

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

a)

Yes; 1/4

b)

Yes; 4

c)

Yes; 1/2

d)

No

112.

Which of the following represents indirect variation?

a)

y = kx

b)

y = k/x

c)

y = x/k

d)

y = mx + b

113.

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

a)

Yes; 1/3

b)

Yes; 3

c)

Yes; 5

d)

No

114.

Determine if the relationship between the two quantities is a direct variation. Explain your reasoning.

a)

yes, the constant of variation is 8.

b)

no, there is no constant of variation

c)

yes, the constant of variation is 1/8

115.

Given: y varies directly with x. If y = -4 when x = 2, find y when x = -6.

Find the value of k.

(a)

116.

If y varies inversely as x, and y = 23 when x = 8, find y when x = 4.

a)

26

b)

46

c)

52

d)

92

117.

Which equation represents an inverse variation?

a)

y = 40/x

b)

y = 40x

c)

y/x = 40

d)

x = y/40

Algebra 2 2nd Semester Final Review

Total questions: 117

Worksheet time: 21hrs 47mins

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