Free Printable Algebra 2 Honors Semester 2 Exam Review

1.

Solve: 9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

2.

81^3-x = (1/3)^5x-6

a)

6

b)

-6

c)

9/2

d)

3/2

3.

Solve for x:
(1/8)^x = 2³

a)

x=−3

b)

x=3

c)

x=−1

d)

x=1

4.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

5.

log(x+6)-log(x) =log(20)

a)

1/135

b)

27/4

c)

No solution

d)

6/19

6.

log(2x) - log(5) = log(30)

a)

6/5

b)

45/2

c)

75

d)

-3/8

7.

log₂(x + 2) + log₂x = 3

a)

-4, 2

b)

-2, 4

c)

2

d)

1

8.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

9.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

10.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

11.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

12.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

13.

Use the change of base rule to rewrite this problem:

log₃64

a)

log(64)/log(3)

b)

log(3)/log(64)

14.

Use the change of base rule to rewrite this problem:

log₅75

a)

log(75)/log(5)

b)

log(5)/log(75)

15.

Use the change of base rule to rewrite this problem:

log₆216

a)

log(6)/log(216)

b)

log(216)/log(6)

16.

The natural logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

17.

Use the change of base rule to rewrite this problem:

log₃64

a)

log(64)/log(3)

b)

log(3)/log(64)

18.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

19.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

20.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

21.

Solve.

a)

0.2560

b)

0.4926

c)

3.9069

d)

7.5

22.

Solve

a)

A

b)

B

c)

C

d)

D

23.

Solve each equation. Select the closest answer.

a)

-0.3

b)

-0.4

c)

-0.2

d)

No solution

24.

Solve each equation. Select the closest answer.

a)

-0.2

b)

0.2

c)

0.3

d)

0

25.

Solve each equation. Select the closest answer.

a)

4.5

b)

1.5

c)

1.8

d)

5

26.

Rewrite in simplified exponential notation:

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

a)

$\frac{1}{3^8}$

b)

$3^6$

c)

$3^8$

d)

$\frac{1}{3^6}$

27.

Simplify the following: $\left(\left(4a^3b^2c\right)^3\right)^0$

Assume that a, b, and c are not equal to zero.

a)

$64a^9b^6c^3$

b)

$4a^6b^5c^4$

c)

$1$

d)

$0$

28.

Evaluate:

a)

2

b)

4

c)

16

d)

64

29.

Identify whether the function, f(x) = 3(.5)^x has exponential growth or decay?

a)

growth

b)

decay

c)

cannot be determined

d)

both exponential growth and decay

30.

What is the equation of an exponential function that is shifted 5 units to the right and down 9 units?

a)

f(x) = 2^{x + 5} - 9

b)

f(x) = 2^{x - 5} - 9

c)

f(x) = 2^{x - 9} - 5

d)

f(x) = 2^{x + 9} - 5

31.

What are the transformations of f(x) = 2^{x + 7}+ 1

a)

left 7

down 1

b)

left 7

up 1

c)

right 7

down 1

d)

right 7

up 1

32.

What are the transformations of this graph from y = log₄x ?

a)

Right 1 Up 5

b)

Right 1 Down 5

c)

Left 1 Up 5

d)

Left 1 Down 5

33.

What transformation is occurring when y = log x is changed to y = log x - 6

a)

Horizontal shift left 6

b)

Horizontal shift right 6

c)

Vertical shift up 6

d)

Vertical shift down 6

34.

When the function y = log₅x is changed to y = log ₅(x + 1) + 1, select all the transformations that apply.

a)

Horizontal shift left 1

b)

Horizontal shift right 1

c)

Vertical shift up 1

d)

Vertical shift down 1

35.

Describe the transformation?

a)

shifted up 3 units

b)

shifted down 3 units

c)

shifted right 3 units

d)

shifted left 3 units

36.

Describe the transformation?

a)

shifted up 3 units

b)

shifted down 3 units

c)

shifted right 3 units

d)

shifted left 3 units

37.

Which is the reasonable graph of f(x) = log₂(x - 5)

a)

b)

c)

d)

38.

What is the x-intercept of log₇(x)?

a)

Pizza

b)

-1

c)

0

d)

1

39.

What is the equation of the asymptote?

a)

x = -3

b)

x=3

c)

y= -3

d)

y=5

40.

Match the graph with its equation

a)

y = log₆(-x) + 1

b)

y = log₆(x − 2) + 1

c)

y = log₆(x + 2) - 1

d)

y = log(x-8) + 1

41.

Which graph matches the function

*remember the transformation has shifted it right 3 and down 3

a)

b)

c)

d)

42.

What is the first step in finding the equation of the inverse of a function?

a)

get x by itself

b)

switch x and y

c)

solve for y

d)

write the function in inverse function notation

43.

f(x) = {(3, 7), (4, -2), (5, -1), (8, 7)}
Is f^-1(x) a function?

a)

Yes

b)

No

c)

No way to tell

44.

What is the inverse of the points
(1,3)(2,4)(6,8)

a)

(3,1)(4,2)(8,6)

b)

(-3,-1)(-4,-2)(-8,-6)

c)

(1,3)(2,4)(6,8)

d)

(-1,-3)(-2,-4)(-6,-8)

45.

a)

9

b)

3

c)

5

d)

√15

46.

a)

9 - √17

b)

4

c)

2

d)

√8

47.

a)

-1

b)

1

c)

-1/3

d)

-5/3

48.

What is the value of x in the equation $\sqrt[3]{x+28}=4$ ?

a)

-16

b)

-12

c)

24

d)

36

49.

What is the inverse, $f^{-1}\left(x\right)$ , of the function $f\left(x\right)=5^{\left(x+2\right)}-1$ ?

a)

$f^{-1}\left(x\right)=\log_2\left(x+1\right)-5$

b)

$f^{-1}\left(x\right)=\log_5\left(x-2\right)+1$

c)

$f^{-1}\left(x\right)=\log_1\left(x+5\right)-2$

d)

$f^{-1}\left(x\right)=\log_5\left(x+1\right)-2$

50.

What is the value of $x$ in the equation? $\log_3 (x - 2) = 2$

a)

3

b)

10

c)

2

d)

11

51.

What is the inverse function of $y = \sqrt[3]{2x} + 7$ ?

a)

$y = 2(x - 7)^3$

b)

$y = \frac{(x + 7)^3}{2}$

c)

$y = 2(x + 7)^3$

d)

$y = \frac{(x - 7)^3}{2}$

52.

What are the x-intercepts?

a)

x= 2/3

b)

x= 4, x = -2

c)

x= -8, x = 1

d)

x= -4, x = 2

53.

What is the horizontal asymptote to this function?

a)

y=4

b)

y=0

c)

y=-2

d)

y=1

54.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1

d)

y = 9

55.

What is the Horizontal Asymptote?

a)

None

b)

y= 0

c)

y= 1

d)

y= 5/4

56.

Does this function have any vertical asymptotes? If so, what are their equations? $y=\frac{\left(x+3\right)\left(x-4\right)\left(x+7\right)}{\left(x-4\right)}$

a)

No vertical asymptotes.

b)

One vertical asymptote: x = 4

c)

Two vertical asymptotes: x = -3 and x = -7

d)

Three vertical asymptotes: x = -3, x = 4, and x = -7

57.

Which equations below state the asymptotes for the graph of the rational function?
$f(x)=\frac{x^2}{x^2-9}$

Check all that apply.

a)

$x=3$

b)

$x=-3$

c)

$x=9$

d)

$y=0$

e)

$y=1$

58.

Which of the following rational functions has the three attributes: vertical asymptote at x = -3, horizontal asymptote at y = 0, and a zero at -1?

a)

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

b)

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

c)

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

d)

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

59.

Which of the following functions has the given three attributes: no vertical asymptote, a horizontal asymptote at y = 3, and a y-intercept at 5.

a)

$g\left(x\right)=\frac{3x^2+10}{x^2+5}$

b)

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

c)

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

d)

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

60.

Find the vertical asymptote(s) of the following rational function. Select all that apply.

$f\left(x\right)=\frac{x^2-3x-10}{x^2+2x-15}$

a)

x = 3

b)

x = 5

c)

x = -5

d)

x = -2

61.

Find the horizontal asymptote of the following rational function.

$f\left(x\right)=\frac{x^2-3x-10}{x^2+2x-15}$

a)

y = 0

b)

y = 1

c)

y = 2

d)

y = 3

62.

Find the x-intercept(s) of the following rational function. Select all that apply.

$f\left(x\right)=\frac{x^2-3x-10}{x^2+2x-15}$

a)

-5

b)

5

c)

-2

d)

3

63.

Find the y-intercept(s) of the following rational function. Select all that apply.

$f\left(x\right)=\frac{x^2-3x-10}{x^2+2x-15}$

a)

2/3

b)

1

c)

-2

d)

5

64.

Find the y-intercept

a)

(0, -3.5)

b)

(0, -5)

c)

(0, 7)

d)

(0, -2)

65.

Find the horizontal asymptote

a)

y = 1

b)

y = -1

c)

y = 2

d)

y = -2

66.

Find the x-intercept

a)

(0, 6)

b)

(6, 0)

c)

(0, 4)

d)

(4, 0)

e)

(1.5, 0)

67.

Find the y-intercept

a)

(6, 0)

b)

(0, -2)

c)

(3, 0)

d)

(0, -3)

68.

Is the function even, odd, or neither?

f(x) = x² + 2

a)

Even

b)

Odd

c)

Neither

69.

Is the graph an even, odd, or neither function
f(x) = (x+4)² - 1

a)

Even

b)

Odd

c)

Neither

70.

Is the graph an even, odd, or neither function
f(x) = 4x³

a)

Even

b)

Odd

c)

Neither

71.

Which of the following best describes this sequence?

\left\{2,\ -4,\ \ 8,\ -16,\ 32,\ ...\right\}

a)

Arithmetic

b)

Geometric

c)

Neither

d)

Both

72.

Which of the following best describes this sequence?

\left\{32,\ 20,\ 8,\ -4,\ ...\right\}

a)

Arithmetic

b)

Geometric

c)

Neither

d)

Both

73.

Which of the following best describes this sequence?

\left\{1,\ 3,\ 6,\ 10,\ 15,\ 21,\ ...\right\}

a)

Arithmetic

b)

Geometric

c)

Neither

d)

Both

74.

Which explicit formula describes the sequence?

-1,\ 3,\ 7,\ 11,\ ...

a)

$a_n=-4+\left(n-1\right)\left(-1\right)$

b)

$a_n=\left(-4\right)\left(-1\right)^{\left(n-1\right)}$

c)

$a_n=-1+\left(n-1\right)\left(-4\right)$

d)

$a_n=\left(-1\right)\left(-4\right)^{\left(n-1\right)}$

75.

The diagrams represent the first three terms of a sequence. Assuming the pattern continues, how many shaded squares are in the 6th term?

a)

26

b)

28

c)

30

d)

32

76.

What is the formula for the nth term of the sequence 3, -6, 12, -24, 48, ...?

a)

$a_n=-2\left(3\right)^n$

b)

$a_n=3\left(-2\right)^n$

c)

$a_n=-2\left(3\right)^{\left(n-1\right)}$

d)

$a_n=3\left(-2\right)^{\left(n-1\right)}$

77.

Which of the following best describes this sequence?

\left\{5,\ 8,\ 11,\ 14,\ ...\right\}

a)

An arithmetic sequence with a common ratio of 3.

b)

A geometric sequence with a common difference of 3.

c)

An arithmetic sequence with a common difference of 3.

d)

A geometric sequence with a common ratio of 3.

78.

Which of the following best describes this sequence?

\left\{135,\ 45,\ 15,\ 5,\ ...\right\}

a)

An arithmetic sequence with a common ratio of $\frac{1}{3}$

b)

A geometric sequence with a common difference of 3.

c)

An arithmetic sequence with a common difference of 3.

d)

A geometric sequence with a common ratio of $\frac{1}{3}$

79.

What is the 16th term of the following sequence?

\left\{10,\ 12,\ 14,\ 16,\ 18,\ ...\right\}

a)

36

b)

38

c)

40

d)

42

80.

What is the 12th term of the following sequence?

\left\{3,-6,\ 12,\ -24,\ 48,\ ...\right\}

a)

$6,411$

b)

$-6,411$

c)

$354,294$

d)

$-354,294$

81.

A plumber charges $55 for 1 hour of work, $90 for 2 hours, and $125 for 3 hours. Which function represents the sequence of hourly charges?

a)

a_n = 55 + 35n

b)

a_n = 55(35)^n-1

c)

a_n = 35 + (n-1)55

d)

a_n = 55 + (n-1)35

82.

An arithmetic sequence has a₁=2 and d=4. What is the Explicit Rule for a_n and use it to find the 20^th term.

a)

a_n = 2 - 4(n-1)

a₂₀ = 82

b)

a_n = 2 + 4(n-1)

a₂₀ = 78

c)

a_n = 2(4)^n-1

a₂₀ = 2199023255552

d)

a_n = 4 + 2(n-1)

a₂₀ = 42

83.

A geometric sequence has a₁ = 3 and r = 2. What is the Explicit Rule for a_n and use it to find the 10th term.

a)

a_n = 3 + 2(n-1)

a₁₀ = 21

b)

a_n = 2(3)^n-1

a₁₀ = 39366

c)

a_n = 3(2)^n-1

a₁₀ = 1536

d)

a_n = 2 + 3(n-1)

a₁₀ = 29

84.

Identify the inverse variation relationship from the following equations:

a)

$y=2x$

b)

$y=5x^2$

c)

$y=\frac{x}{6}$

d)

$y=\frac{4}{x}$

85.

Solve the inverse variation equation: $y=\frac{6}{x}$ for x when y = 3

a)

5

b)

7

c)

4

d)

2

86.

Apply inverse variation to a real-life scenario: If the number of workers is inversely proportional to the time taken to complete a task, and 8 workers can complete the task in 6 hours, how long will it take for 12 workers to complete the same task?

a)

10 hours

b)

4 hours

c)

5 hours

d)

2 hours

87.

Apply inverse variation to a real-life scenario: If the speed of a car is inversely proportional to the time taken to reach the destination, and a car traveling at 60 mph reaches the destination in 4 hours, how long will it take for a car traveling at 80 mph to reach the same destination?

a)

2 hours

b)

3 hours

c)

4 hours

d)

5 hours

88.

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

a)

$1,225,54

b)

$2,225.54

c)

$22,255.40

d)

$225.54

89.

Willie invests $8,515 in a retirement account with a fixed annual interest rate of 5% compounded continuously. What will the account balance be after 20 years?

a)

$22,017.32

b)

$23,146.17

c)

$20,021.95

d)

$20,943.52

90.

Mark invests $3,285 in a retirement

account with a fixed annual interest rate of

7% compounded continuously. What will

the account balance be after 18 years?

a)

$12,420.73

b)

$13,321.33

c)

$12,671.64

d)

$11,581.01

91.

Sumalee invests $6,227 in a savings account with a fixed annual interest rate of 8% compounded continuously. What will the account balance be after 6 years?

a)

$10,685.57

b)

$11,011.00

c)

$10,369.77

d)

$10,063.30

92.

Adam invests $5,208 in a savings account with a fixed annual interest rate of 8% compounded continuously. What will the account balance be after 8 years?

a)

$9,876.87

b)

$10,699.49

c)

$9,489.59

d)

$8,803.91

93.

Chelsea invests $2,709 in a savings account with a fixed annual interest rate of 8% compounded continuously. What will the account balance be after 6 years?

a)

$4,248.56

b)

$3,941.57

c)

$4,377.95

d)

$4,041.35

94.

In the formula A= Pe^rt

T is time in ...

a)

Months

b)

Years

c)

Days

d)

Weeks

e)

Decades

95.

Mei invests $6,285 in a savings account with a fixed annual

interest rate of 4% compounded continuously. How many years will it take for the account balance to reach $7,989.80? (Type answer in WHOLE number of years NO Decimals)

(a)

96.

Julio invests $3,853 in a savings account with a

fixed annual interest rate of 4% compounded continuously. How long will it take for the account balance to reach $5,098.02? Type answer in WHOLE years NO decimals)

(a)

97.

Eduardo invests $3,071 in a savings account with a

fixed annual interest rate of 7% compounded continuously. How long will it take for the account balance to reach $7,113.56?

a)

12

b)

13

c)

14

d)

15

98.

Which of these equations shifts a radical equation right 5 times and down once?

a)

$f\left(x\right)=\sqrt{x-5}-1$

b)

$f\left(x\right)=\sqrt{x+5}-1$

c)

$f\left(x\right)=\sqrt{x-5}+1$

d)

$f\left(x\right)=\sqrt{x+5}+1$

99.

Which of these equations shifts a radical equation left 3 times?

a)

$f\left(x\right)=\sqrt{x}+3$

b)

$f\left(x\right)=\sqrt{x}-3$

c)

$f\left(x\right)=\sqrt{x+3}$

d)

$f\left(x\right)=\sqrt{x-3}$

100.

Describe the transformation

a)

Left 4 units, up 1 unit

b)

Right 4 units, up 1 unit

c)

Left 4 units, down 1 unit

d)

Right 4 units, down 1 unit

101.

Solve for x.

$-3\sqrt[\ ]{x-2}+1=-11$

a)

144

b)

121

c)

16

d)

18

102.

Solve for x.

$2\sqrt[\ ]{x+3}\ -5=3$

a)

4

b)

9

c)

13

d)

16

103.

a)

x = -6

b)

x = 3

c)

x = -3

d)

x = 5±

104.

Solve for x. $\sqrt{9x-2}=\sqrt{3x+10}$

a)

x = 2

b)

x = -2

c)

x = 4

d)

No Solution

105.

Solve

a)

102

b)

12

c)

98

d)

7

106.

Given
f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

a)

11x² - 1

b)

5x⁴ + 6x² - 1

c)

5x² + 6x - 1

d)

5x² + 8x - 1

107.

f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f - g)(x).

a)

x² + 8x + 1

b)

x² + 6x - 1

c)

5x² + 8x - 1

d)

x² + 8x -1

108.

Given f(x) = 3x² - 2x + 1 and g(x) = x - 4, find (f*g)(x).

a)

3x³ - 10x² - 7x - 4

b)

3x³ - 14x² + 9x - 4

c)

3x² - x - 3

d)

3x³ + 14x² - 9x - 4

109.

f(x)= x+3

g(x)= x-2

Find (g(x) / f(x))

Be careful!!

a)

(x + 3)/(x - 2)

b)

(x - 2)/(x + 3)

c)

-2/3

d)

3/2

110.

Given f(x) = 2x and
g(x) = x²+3 , find f(g(x)).

a)

x²+2x+3

b)

4x²+3

c)

2x²+3

d)

2x²+6

111.

Given f(x)= -3x+7 and g(x)=2x² - 8, find f(g(x)).

a)

f(g(x))= -6x²+31

b)

f(g(x))= -6x²+24

c)

f(g(x))=18x²-84x+6

d)

f(g(x))=9x²-42x-1

112.

Given f(x)= -3x + 7 and g(x)=2x² - 8, find g(f(x)).

a)

g(f(x))= -6x²+ 31

b)

g(f(x))= -6x²+ 24

c)

g(f(x))=18x²- 84x + 90

d)

g(f(x))=9x²- 42x - 41

113.

f(x) = 3x + 10
g(x) = x - 2
Find g(f(-10))

a)

-42

b)

-26

c)

-18

d)

None of these.

114.

f(x) = 3x + 10
g(x) = x - 2
Find (f∘g)(0)

a)

16

b)

4

c)

-4

d)

None of these.

115.

f(x)= x²- 1

g(x)= x - 1

Find (f(x)/g(x))

Then simplify using x = 10

a)

9

b)

11

c)

90

d)

110

116.

Solve for r

a)

5

b)

- 5, 4

c)

- 5

d)

5, 4

117.

Solve and check for extraneous solutions

a)

x=5

b)

x= -5

c)

No Solution

118.

Solve by cross-multiplying.

a)

x = -1, 5

b)

No Solution

c)

x = -4, 5

d)

x= -4

119.

Solve for x

a)

4

b)

2

c)

-2

d)

-4

120.

Solve!

a)

x = 2

b)

x = 6

c)

x = 4

d)

x = 8

121.

Solve by cross-multiplying.

a)

x = 2

b)

No Solution

c)

x = -10

d)

x = 10

122.

a)

x = 8.9

b)

x = 16

c)

x = 9

d)

x = 12

123.

a)

3/5

b)

3/4

c)

1/4

d)

4/5

124.

a)

2

b)

1

c)

-1

d)

-4

125.

Simplify this rational expression:

\frac{\left(x+2\right)\left(x-1\right)}{\left(x+10\right)\left(x+2\right)\ }

a)

$\frac{\left(x-1\right)}{\left(x+10\right)}$

b)

$\frac{\left(x+2\right)}{\left(x+10\right)}$

c)

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

d)

$\left(x+2\right)\$

126.

Simplify this rational expression:

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

a)

1

b)

Does not simplify

c)

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

d)

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

127.

Simplify this rational expression:

\frac{\left(x+5\right)\left(x-3\right)\left(x+1\right)}{\left(x+1\right)\ \left(x-6\right)\ \left(x-3\right)\ }

a)

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

b)

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

c)

$\frac{\left(x+5\right)\left(x+1\right)\ }{\left(x-6\right)\ \left(x-3\right)\ }$

d)

$\frac{\left(x+5\right)\left(x-3\right)\ }{\left(x-6\right)\left(x+1\right)\ }$

128.

Simplify this rational expression:

\frac{x^2+2x-15}{\left(x+5\right)\left(x+7\right)}

a)

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

b)

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

c)

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

d)

Does not simplify

129.

Simplify this rational expression:

\frac{x^2-x-12}{x^2+8x+15}

a)

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

b)

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

c)

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

d)

Does not simplify

130.

Simplify

a)

A

b)

B

c)

C

d)

D

131.

Simplify by cancelling

a)

1

b)

-1

c)

Can't be simplified

132.

Simplify the following

a)

b)

c)

d)

133.

a)

A.4x³/(x+2)

b)

B.4x³/(x+10)

c)

C.2x³/(5x+1)

d)

D. 2x³/(x+5)

134.

simplify.

a)

a

b)

b

c)

c

d)

d

135.

Simplify

a)

A

b)

B

c)

C

d)

D

136.

Simplify

a)

A

b)

B

c)

C

d)

D

137.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

138.

Simplify

a)

A

b)

B

c)

C

d)

D

139.

Simplify

a)

A.(x+7)/(x-4)

b)

B.-3/4

c)

C.(x+3)/(x+4)

d)

D.(x+3)/(x-4)

140.

a)

A

b)

B

c)

C

d)

D

141.

a)

A

b)

B

c)

C

d)

D

142.

$\frac{a^2-5a-14}{a-7}\div\frac{a^2-a-6}{5a^3+30a^2}$

a)

$\frac{a+9}{15a}$

b)

$\frac{5a^2\left(a+6\right)}{a-3}$

c)

$\frac{1}{a-1}$

d)

$\frac{9a}{a+9}$

143.

$\frac{b-4}{b^2+14b-40}\div\frac{b^2+6b+8}{b^2-3b-70}$

a)

$\frac{b-3}{6}$

b)

$\frac{2b}{9}$

c)

$\frac{5b\left(b-6\right)}{7}$

d)

$\frac{b+7}{\left(b+4\right)\left(b+2\right)}$

144.

$\frac{x^2+3x-18}{3x+18}\div\frac{x^2+7x-30}{x^2+x-90}$

a)

$3x^2\left(x-9\right)$

b)

$\frac{x-9}{3}$

c)

$\frac{x+7}{60}$

d)

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

145.

$\frac{8n}{10n^2+40n}\div\frac{n^2+10n+16}{10n^2+20n}$

a)

$\frac{8n}{\left(n+4\right)\left(n+8\right)}$

b)

$80n^2$

c)

$\frac{n-4}{7\left(n-10\right)}$

d)

$\frac{32n^2}{n-3}$

146.

$\frac{10m-20}{10m+70}\times\frac{m^2+8m+7}{m+1}$

a)

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

b)

$\frac{3}{20}$

c)

$m-2$

d)

$\frac{m+4}{m+7}$

147.

$\frac{16n-56}{n^2-11n+30}\div\frac{10n-35}{n^2-11n+30}$

a)

$\frac{n+7}{n+8}$

b)

$10$

c)

$\frac{8}{5}$

d)

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

148.

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

a)

$64$

b)

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

c)

$\frac{1}{10}$

d)

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

149.

Divide the Rational Expression
$\frac{x^2-4x-5}{x^2-3x+2}\div\frac{x^2-3x-10}{x^2-4}$

a)

$\frac{x-5}{x-1}$

b)

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

c)

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

d)

$x+1$

150.

$\frac{3x+12}{x^25x+6}\div\frac{x+4}{5x+15}$

a)

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

b)

$\frac{x+2}{15}$

c)

$\frac{15}{x+2}$

d)

$\frac{5}{x+2}$

151.

Simplify $\frac{x-8}{x^2-18x+80}\div\frac{x+1}{x^2-7x-8}$

a)

$\frac{x-8}{x-10}$

b)

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

c)

$\frac{5x}{x+7}$

d)

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

152.

a)

b)

c)

d)

153.

a)

b)

c)

d)

154.

Simplify the expression

a)

6x / 20xy

b)

3 / 10y

c)

(6x+1) / (20xy)

d)

3 / 20xy

155.

Simplify the expression

a)

n / 2m

b)

n / 3m

c)

(m²+ 4n²) / 12m

d)

n / 4m

156.

a)

A

b)

B

c)

C

d)

D

157.

a)

A

b)

B

c)

C

d)

D

158.

Factor 4x²-9

a)

(4x-9)(4x+9)

b)

(2x-3)(2x+3)

c)

2x-3

d)

(2x-4.5)(2x+4.5)

159.

Fully Factor the Following
25x²-81

a)

(5x-9)²

b)

(5x+9)(5x-9)

c)

25(x-9)²

d)

(9x+5)(9x-5)

160.

3x²- 75

a)

3( x + 5 ) ( x - 5 )

b)

Prime

c)

( x + 5 ) ( x - 5 )

d)

3( x - 5 ) ( x - 5 )

161.

9n² + 1

a)

(3n + 1) (3n - 1)

b)

(3n - 1) (3n - 1)

c)

(n + 3) (n - 3)

d)

Can't factor using Diff. of Squares

162.

Which of these can factor using difference of two squares?

a)

144x² - 49y²

b)

x² + 4x - 12

c)

100x² + 20x + 1

d)

14x - 16

163.

Factor
k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

164.

Factor
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

165.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

166.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

167.

factor x²+ 7x - 30

a)

PRIME

b)

(x + 10)(x + 3)

c)

(x - 10)(x + 3)

d)

(x + 10)(x - 3)

168.

what is the equation that best matches the graph?

a)

A

b)

B

c)

C

d)

D

169.

What is/are the vertical asymptote(s)?

a)

There are no vertical asymptotes

b)

x=5

c)

x=-5

d)

x=-1/2

170.

Simplify

a)

A

b)

B

c)

C

d)

D

171.

Simplify the expression:

a)

A

b)

B

c)

C

d)

D

172.

Simplify

a)

A

b)

B

c)

C

d)

D

173.

Simplify

a)

A

b)

B

c)

C

d)

D

174.

a)

A

b)

B

c)

C

d)

D

175.

a)

A

b)

B

c)

C

d)

D

176.

a)

A

b)

B

c)

C

d)

D

177.

a)

A

b)

B

c)

C

d)

D

178.

a)

A

b)

B

c)

C

d)

D

179.

Expand the expression using the Binomial Theorem.

(2x+5)⁴

a)

2x⁴ + 40x³+ 300x² + 1000x +625

b)

16x⁴+ 160x³ +600x² +1000x + 625

c)

16x⁴ + 1000x³ + 600x²+ 160x +625

180.

Expand: $\left(a-b\right)^5$

a)

$a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5$

b)

$a^5-5a^4b+10a^3b^2-10a^2b^3+5ab^4-b^5$

c)

$a^5-5a^4b+10a^2b^3-10a^3b^2+5ab^4-b^5$

d)

$a^5-5a^4b-10a^3b^2-10a^2b^3-5ab^4-b^5$

181.

What would be the 5th term of the expansion of (n+4)⁴?

a)

257

b)

256

c)

n⁴

d)

259

182.

What would be the 2nd term of the expansion of (y+4)⁴?

a)

253y

b)

16y³

c)

64y

d)

96y²

183.

What would be the 4th term of the expansion of (a+3)⁴?

a)

108a

b)

12a³

c)

81

d)

27a

184.

What would be the 6th term of the expansion of (m-3)⁵?

a)

m⁵

b)

-243

c)

-244

d)

405m

185.

Simplify:

a)

a

b)

a²

c)

a³

d)

a⁴

186.

$yx^{\frac{1}{3}}\cdot xy^{\frac{3}{2}}$

a)

$x^{\frac{4}{3}}y^{\frac{5}{2}}$

b)

$x^{\frac{2}{3}}y^{\frac{1}{2}}$

c)

$x^{\frac{1}{3}}y^{\frac{3}{2}}$

d)

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

187.

$Evaluate\ \log_28$

(a)

188.

$Evaluate\ \log_864$

(a)

189.

$Evaluate\ \log_77$

(a)

190.

$Evaluate\ \log_381$

(a)

191.

$Evaluate\ \log_{10}1000$

(a)

192.

$Evaluate\ \log_61$

(a)

193.

$Evaluate\ \log_8\frac{1}{8}$

(a)

194.

$Evaluate\ \log_7\frac{1}{49}$

(a)

195.

$Evaluate\ \log_5\sqrt{5}$

(a)

196.

$Evaluate\ \log_93$

(a)

197.

a)

3

b)

1/3

c)

-3

d)

-1/3

198.

Which shows the log expression completely expanded correctly
$\log_6\left(\frac{5}{4y}\right)$

a)

$\log_65\ +\ \log_64\ +\ \log_6y$

b)

$\log_65\ -\ \log_64\ +\ \log_6y$

c)

$\log_65\ -\ \log_64\ -\ \log_6y$

d)

$\log_65\ -\ \log_64y$

e)

None of these

199.

Which shows the log expression completely expanded correctly

$\log_4\left(a^2+b^5\right)$

a)

$2\log_4\left(a\right)+5\log_4\left(b\right)$

b)

$2\log_4\left(a\right)\cdot5\log_4\left(b\right)$

c)

$\log_4\left(2a\right)+\log_4\left(5b\right)$

d)

$\log_4\left(2a\right)\cdot\log_4\left(5b\right)$

e)

None of these

200.

Which shows the log expression completely expanded correctly

$\log_4\left(a^2b^5\right)$

a)

$2\log_4\left(a\right)+5\log_4\left(b\right)$

b)

$\log_4\left(2a\right)+\log_4\left(5b\right)$

c)

$a\log_4\left(2\right)+b\log_4\left(5\right)$

d)

$\log\left(4\right)+2\log\left(a\right)+5\log\left(b\right)$

e)

None of these

Algebra 2 Honors Semester 2 Exam Review

Total questions: 200

Worksheet time: 12hrs 59mins

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