Free Printable Algebra 2 Semester Review

1.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(1 - 0.30)^x

b)

y=30(5000)^x

c)

y=5000(1 + 0.30)^x

d)

y=5000x^x

2.

The original value of a painting is $1400, and the value increases by 9% each year. Write an exponential growth function to model this situation.

a)

y=1400(1.09)^x

b)

y=1.09(1400)^x

c)

y=1400(.91)^x

d)

y=1.09^x

3.

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

a)

14327

b)

4309

c)

839

d)

7680

4.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

5.

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

a)

9766

b)

9006

c)

9765

d)

5433

6.

What is a, the starting term, for the function: f(x) = 300(1.16)^x?

a)

300

b)

1.16

c)

.16

d)

x

7.

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

a)

Growth

b)

Decay

8.

Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)³

a)

Growth

b)

Decay

9.

Is the pictured graph growth, decay, or linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

10.

Is this exponential growth or decay?

a)

Growth

b)

Decay

11.

What type of function is y = 7(5/4)^x?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None of the above

12.

Is this exponential growth or decay?

a)

Growth

b)

Decay

13.

Which equation is an exponential equation?

a)

y = a * b^x

b)

y = ln x

c)

y = mx + b

14.

The population of the United States was 248,718,301 in 1990 and was projected to grow at a rate of about 8% per decade. Predict the population, to the nearest hundred thousand, for the years 2018.

a)

978617180000 people

b)

248757647 people

c)

993883180 people

d)

55448350 people

15.

a)

A

b)

B

c)

C

d)

D

16.

Write in logarithmic form.
2^-4 = ¹/₁₆

a)

log₂(¹/₁₆) = -4

b)

log_-4(¹/₁₆) = 2

c)

log_-4 2 = ¹/₁₆

d)

log₂(-4) = ¹/₁₆

17.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

18.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

19.

Solve for x
5^x = 17

a)

x = log₁₇5

b)

x = log 5 + log 17

c)

x = log₅17

d)

x = (log 5)/(log 17)

20.

Expand

a)

A

b)

B

c)

C

d)

D

21.

Expand

a)

A

b)

B

c)

C

d)

D

22.

Expand

a)

log₈x + log₈y + log₈z

b)

5log₈x + 5log₈y + 5log₈z

c)

log₈xy + 5log₈z

d)

log₈x + log₈y + 5log₈z

23.

Write as a single logarithm:

log(30)-log(6)

a)

-6log(30)

b)

log(24)

c)

log(-24)

d)

log(5)

24.

Solve the equation for x.

a)

32

b)

25

c)

1.66

d)

512

25.

6^-3x=216

a)

x=3

b)

x=-1

c)

x=6

d)

x=-3

26.

ln(9x-2)=ln(x+14)

a)

x=2

b)

x=.156

c)

x=-3

d)

x=0

27.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

28.

log₄1 =

a)

0

b)

1

c)

4

d)

DNE

29.

Solve for x:

a)

1

b)

2

c)

.5

d)

4

30.

log₅(25) = y

a)

y = 2

b)

y = 0.5

c)

y = 5

d)

y = (1/2)

31.

log₃(1) = y

a)

y = 0

b)

y = 1

c)

y = (1/3)

d)

y = 2

32.

log₁₆(4) = y

a)

y = 2

b)

y = 4

c)

y = (1/2)

d)

y = (1/4)

33.

log₂(1/8) = y

a)

y = -3

b)

y = (1/3)

c)

y = 3

d)

y = 0

34.

log₃(4x) = 2

a)

x=4/9
x=4/9

b)

x=9/4

c)

x=3/2

d)

x=2/3

35.

log₂(x + 5) = 3

a)

3

b)

4

c)

5

d)

6

36.

Solve for x:
log₃3^x = 5

a)

5

b)

4

c)

3

d)

243

37.

Write the logarithm expression as a single logarithm

log₄60 - log₄4 + log₄x

a)

log₄15

b)

log₄15x

c)

log₄56x

d)

xlog₄30

38.

Write the logarithm expression as a single logarithm

log₆25 - log₆5

a)

log₆125

b)

log₅20

c)

log₆5

d)

log₆30

39.

Write the logarithm expression as a single logarithm

log₅4 + log₅3

a)

log₅7

b)

log₅12

c)

log₇5

d)

3log₅4

40.

Write the logarithm expression as a single logarithm

2log 4 + log 2

a)

log 8

b)

log 16

c)

log 32

d)

log 8²

41.

Write as one logarithm. Simplify, if possible.

log₃9 + log₃27

a)

log₃3

b)

log₃243

c)

log₃1/3

d)

not possible

42.

Expand the logarithm expression

log 6x³y

a)

log 6x³ + log y

b)

log 6 + log x³ + log y

c)

3 log 6 + log x + log y

d)

log 6 + 3log x + log y

43.

Expand the logarithm expression

log 5x/4y

a)

log 5x + log 4y

b)

log 5x - 4log y

c)

(log 5 + log x) - (log 4 + logy)

d)

5log x - 4 logy

44.

Write as one logarithm. Simplify, if possible.

(log 3 - log 6) + log 2

a)

log 4

b)

log 2

c)

log 1

d)

log 6

45.

Expand the logarithm expression

log₅5x^-5

a)

-5(log₅5x)

b)

-5log₅5 + log₅x

c)

log₅25x

d)

log₅5 - 5log₅x

46.

Write as one logarithm. Simplify, if possible.
log₂800 - log₂100

a)

8

b)

3

c)

-3

d)

1

47.

Write as one logarithm. Simplify, if possible.
log₃9 + log₃27

a)

-1

b)

5

c)

4

d)

1

48.

Write as one logarithm. Simplify, if possible.
log₅125 - log₅25

a)

1

b)

0

c)

5

d)

-1

49.

Write as one logarithm. Simplify, if possible.
log₆3 + log₆2

a)

0

b)

log₆5

c)

log₆1

d)

1

50.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

51.

Evaluate.
log₆(¹/₂₁₆)

a)

3

b)

¹/₃

c)

-¹/₃

d)

-3

52.

$2m^2=-2m+12$
Solve using the quadratic formula.

a)

$x=2,-3$

b)

$x=3,-2$

c)

$x=1\pm\sqrt{13}$

d)

No Solution

53.

Use the quadratic formula to solve 2x² + 2x - 12.

a)

-2, 3

b)

2, 3

c)

2, -3

d)

-2, -3

54.

$w^2+7w+4=0$

a)

$\frac{-7\pm\sqrt{33}}{2}$

b)

$\frac{-7\pm\sqrt{65}}{2}$

c)

$\frac{7\pm\sqrt{33}}{2}$

d)

$\frac{-7\pm3\sqrt{11}}{2}$

55.

What letter usually represents an imaginary number?

a)

a

b)

i

c)

j

d)

x

56.

What is $\sqrt{-1}$ ?

a)

$i$

b)

$-1$

c)

$-i$

d)

$1$

57.

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

a)

2x²+ 3x +1

b)

-2x²- 11x -4

c)

2x² + 5x -7

d)

-2x² + 11x -4

58.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

59.

5x²+ 2x – 3x – 5x

a)

-3x

b)

5x² - 6x

c)

5x²

d)

5x² - 10x

60.

Which of the following are examples of like terms?

a)

2 and 2x

b)

y³and x³

c)

y and x

d)

-3x and 3x

61.

-4x - 10x

a)

-14

b)

6x

c)

-6x

d)

-14x

62.

Combine like terms
3x + 2x + 3y - 7y

a)

5x + 10y

b)

5x + 4y

c)

5x - 4y

d)

5x -10y

63.

6v(2v + 3)

a)

12v+18

b)

15v² + 8v

c)

12v² + 18v

d)

12v² + 18v²

64.

(2n + 2)(6n + 1)

a)

12n + 2

b)

12n² + 2

c)

12n² + 12n + 2

d)

12n² + 14n + 2

65.

(x − 3)(6x − 2)

a)

6x² − 20x + 6

b)

6x² + 20x - 6

c)

6x² +6

d)

6x + 6

66.

(x+10)(x-10)

a)

x² - 100

b)

x² + 100

c)

x² + 20x - 100

d)

x² -20x + 100

67.

Simplify the expression.

(4n² - 8n + 4) - (8n² + 4n + 1)

a)

-4n² - 12n + 3

b)

-12n² - 12n + 5

c)

-4n²- 4n + 3

d)

-12n² - 4n + 3

68.

Simplify:
2x ( -2x -3)

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

69.

Identify the end behavior: $f\left(x\right)=5-2x+x^2+3x^3$

a)

$x\ \rightarrow\ -\infty,\ \ y\ \rightarrow\ \infty$
$x\ \rightarrow\ \infty,\ \ y\ \rightarrow\ \infty$

b)

$x\ \rightarrow\ -\infty,\ \ y\ \rightarrow\ \infty$

$x\ \rightarrow\ \infty,\ \ y\ \rightarrow\ -\infty$

c)

$x\ \rightarrow\ -\infty,\ \ y\ \rightarrow\ -\infty$

$x\ \rightarrow\ \infty,\ \ y\ \rightarrow\ \infty$

d)

$x\ \rightarrow\ -\infty,\ \ y\ \rightarrow\ -\infty$

$x\ \rightarrow\ \infty,\ \ y\ \rightarrow\ -\infty$

70.

Identify the end behavior: $f\left(x\right)=-3x^3+4x^6-2x^2-1+5x^4$

a)

$x\ \rightarrow\ -\infty,\ \ y\ \rightarrow\ \infty$
$x\ \rightarrow\ \infty,\ \ y\ \rightarrow\ \infty$

b)

$x\ \rightarrow\ -\infty,\ \ y\ \rightarrow\ \infty$

$x\ \rightarrow\ \infty,\ \ y\ \rightarrow\ -\infty$

c)

$x\ \rightarrow\ -\infty,\ \ y\ \rightarrow\ -\infty$

$x\ \rightarrow\ \infty,\ \ y\ \rightarrow\ \infty$

d)

$x\ \rightarrow\ -\infty,\ \ y\ \rightarrow\ -\infty$

$x\ \rightarrow\ \infty,\ \ y\ \rightarrow\ -\infty$

71.

Identify the end behavior: $f\left(x\right)=5x^7-3x^4-9x+1$

a)

$x\ \rightarrow\ -\infty,\ \ y\ \rightarrow\ \infty$
$x\ \rightarrow\ \infty,\ \ y\ \rightarrow\ \infty$

b)

$x\ \rightarrow\ -\infty,\ \ y\ \rightarrow\ \infty$

$x\ \rightarrow\ \infty,\ \ y\ \rightarrow\ -\infty$

c)

$x\ \rightarrow\ -\infty,\ \ y\ \rightarrow\ -\infty$

$x\ \rightarrow\ \infty,\ \ y\ \rightarrow\ \infty$

d)

$x\ \rightarrow\ -\infty,\ \ y\ \rightarrow\ -\infty$

$x\ \rightarrow\ \infty,\ \ y\ \rightarrow\ -\infty$

72.

Identify the end behavior: $f\left(x\right)=4x^2-3x^5+4x-1$

a)

$x\ \rightarrow\ -\infty,\ \ y\ \rightarrow\ \infty$
$x\ \rightarrow\ \infty,\ \ y\ \rightarrow\ \infty$

b)

$x\ \rightarrow\ -\infty,\ \ y\ \rightarrow\ \infty$

$x\ \rightarrow\ \infty,\ \ y\ \rightarrow\ -\infty$

c)

$x\ \rightarrow\ -\infty,\ \ y\ \rightarrow\ -\infty$

$x\ \rightarrow\ \infty,\ \ y\ \rightarrow\ \infty$

d)

$x\ \rightarrow\ -\infty,\ \ y\ \rightarrow\ -\infty$

$x\ \rightarrow\ \infty,\ \ y\ \rightarrow\ -\infty$

73.

Identify the end behavior: $f\left(x\right)=-x^6-3x^5+4x^3-x^2+5$

a)

$x\ \rightarrow\ -\infty,\ \ y\ \rightarrow\ \infty$
$x\ \rightarrow\ \infty,\ \ y\ \rightarrow\ \infty$

b)

$x\ \rightarrow\ -\infty,\ \ y\ \rightarrow\ \infty$

$x\ \rightarrow\ \infty,\ \ y\ \rightarrow\ -\infty$

c)

$x\ \rightarrow\ -\infty,\ \ y\ \rightarrow\ -\infty$
$x\ \rightarrow\ \infty,\ \ y\ \rightarrow\ \infty$

d)

$x\ \rightarrow\ -\infty,\ \ y\ \rightarrow\ -\infty$

$x\ \rightarrow\ \infty,\ \ y\ \rightarrow\ -\infty$

74.

Identify the missing term to complete the solution.

a)

28

b)

38

c)

48

d)

58

75.

Identify the missing term to complete the solution.

a)

4

b)

-4

c)

5

d)

-5

76.

Identify the missing term to complete the solution.

a)

-7

b)

7

c)

-57

d)

57

77.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

Use synthetic division

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.

78.

What is the quotient when (10n²- 37n - 12) is divided by (n - 4)?

a)

(10n - 3)

b)

(3n - 10)

c)

(10n + 3)

d)

(3n + 10)

79.

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.

80.

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

81.

Solve using long division. $\left(x^2+2x\ -\ 63\right)\div\left(x+9\right)$

a)

$x-7$

b)

$x^2-7$

c)

$x+7$

d)

$x^2+3x-54$

82.

Identify the missing term to complete the solution.

a)

-2

b)

2

c)

-3

d)

3

83.

Use long division for the following

$\left(x^2+2x-63\right)\div\left(x+9\right)$

(a)

84.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

85.

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

a)

0

b)

1

c)

2

d)

3

86.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

87.

x³-3x²-10x+24 ÷ x+3

a)

x²-7x+5

b)

x-8

c)

x²-6x+8

d)

x+9

88.

-2x²+4x+48 ÷ x+4

a)

-2x+12

b)

2x+12

c)

-4x+9

d)

4x+9

89.

x²-6x+8 ÷ x-2

a)

x-6

b)

x-9 R=2

c)

x-4

d)

x-8 R=3

90.

State the solutions of the equation $x^2\ +2x\ -8\ =\ 0$

a)

4 and 2

b)

-4 and -2

c)

4 and -2

d)

-4 and 2

91.

Solve.
n² - 2n = 0

a)

n = 2 and 0

b)

n = -2 and 0

c)

n = 2

d)

n = 0

92.

What are the zeros of $x^2+9x=-14$

a)

2, 7

b)

-2, -7

c)

2, -7

d)

-2, 7

93.

Solve by factoring: x² + 3x - 18 = 0

a)

x = -3 and x = 6

b)

x = 3 and x = -6

c)

x = -9 and x = 2

d)

x = 9 and x = -2

94.

x² + 15x + 44 = 0

a)

{-8, 2}

b)

{-7, 5}

c)

{-11, -4}

d)

{-11}

95.

What are the factors AND solutions of x² + 2x – 3 = 0

a)

(x - 2)(x + 1); x=2, x=-1

b)

(x + 1)(x - 3); x=-1, x=3

c)

(x + 2)(x - 1); x=-2, x=1

d)

(x - 1)(x + 3); x=1, x=-3

96.

Solve.

x² + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

97.

Solve by Factoring X²+10X+24=0

a)

x= - 4, x= - 6

b)

x=4, x=6

c)

x=4, x= - 6

d)

x= - 4, x = 6

98.

Factor by Grouping

7r³-8r²+42r-48

a)

(r²+6)(7r+8)

b)

(r²+6)(7r-8)

c)

(r²+6)(r²+8)

d)

(r²+6)(7r+6)

99.

Factor by grouping:
5n³-10n²+3n-6

a)

(5n²+3)(n-2)

b)

(5n²-3)(n-2)

c)

(5n³+3)(n-2)

d)

10n(n²-6)

100.

Factor by grouping:
4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

101.

Use the Zero Product Property to solve for the values of x.

$\left(x+2\right)\left(x-3\right)=0$

a)

2 and 3

b)

-2 and -3

c)

2 and -3

d)

-2 and 3

102.

Solve using the Zero Product Property:
$\left(3x+2\right)\left(x+1\right)=0$

a)

$x=1,\ x=\frac{2}{3}$

b)

$x=-1,\ \ x=-\frac{2}{3}$

c)

$x=2,\ x=1$

d)

$x=-1,\ \ x=\frac{2}{3}$

103.

Factor: x³+ 1

a)

(x + 1)³

b)

(x+1)(x²- x + 1)

c)

(x - 1) (x² + x - 1)

d)

(x + 1)(x² - 2x + 1)

104.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

105.

Factor
27x³-64

a)

(3x-4)(9x²+12x+16)

b)

(3x-4)(9x²-12x+16)

c)

(3x+4)(9x²-12x+16)

d)

(3x+4)(9x²+12x+16)

106.

Fully Factor the Following
8x³-27

a)

(2x+3)(4x²-6x+9)

b)

(2x-3)(4x²+6x+9)

c)

(2x-3)(4x²+6x-9)

d)

(2x-3)(2x²+6x+9)

107.

x³ - 1000

a)

(x + 10)(x² - 10x + 100)

b)

(x - 10)(x² + 10x + 100)

c)

(x - 1)(x² + 1x + 1)

d)

(x - 5)(x² + 5x + 25)

108.

f(x) = 9-3x
g(x) = 5x-7
Find f(x)+g(x).

a)

14x-10

b)

-8x+2

c)

2x+2

d)

2x-2

109.

f(x) = x²+9
g(x) = x-9
Find f(x)-g(x).

a)

x²+x+9

b)

x²-x+9

c)

x²-x

d)

x²-x+18

110.

f(x)=x²+1
g(x)=2x-5
Find f(x)-g(x)

a)

x²-2x+6

b)

-x²+2x+4

c)

-x²-2x-6

d)

x²-2x-4

111.

f(x) = 4x+8
g(x) = x+3,
Find f(x) * g(x)

a)

4x²+24

b)

4x²+20x+24

c)

4x²+12x+24

d)

4x²+4x+24

112.

f(x)=2x+4
g(x)=3x²-1
Find f(x)*g(x)

a)

6x⁴+12x³-4x²-8x

b)

-6x³+12x²+2x-4

c)

6x³+12x²-2x-4

d)

5x²-18x+20

113.

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

114.

f(x)=2x + 4

g(x)=3x²- 1

Find f(x) ⋅ g(x)

a)

6x⁴+ 12x³- 4x²- 8x

b)

-6x³+ 12x²+ 2x - 4

c)

6x³+ 12x²- 2x - 4

d)

5x²- 18x + 20

115.

f(x) = 4x + 8

g(x) = x + 3,

Find f(x) ⋅ g(x)

a)

4x²+ 24

b)

4x²+ 20x + 24

c)

4x²+ 12x + 24

d)

4x²+ 4x + 24

116.

f(x)= x³- 3x

g(x)= - 4x + 1

Find f(x) ⋅ g(x)

a)

-4x³-5x²- 3

b)

-4x³+ 2x²- 3x

c)

-4x⁴+ x³+ 12x²- 3x

d)

-4x⁴-x³+ 12x²+3x

117.

f(n)= n²+ 4n

g(n)= - n - 5

Find f(n) + g(n)

a)

n²+ 3n - 5

b)

-n³+ 2n - 7

c)

n³+ 3n - 3n

d)

n²- 3n - 5

118.

f(x) = 6x-8
g(x) = -3x+2
Find f(x)-g(x).

a)

9x-6

b)

9x-10

c)

3x-6

d)

3x+6

119.

p(x) = 3x + 4
q(x) = 2x²
Find p(q(x))

a)

10x²

b)

18x² + 4

c)

6x² + 4

120.

g(x)=3x+4
h(x)=3x-1
Find g(h(x))

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

121.

g(x)=3x+4
h(x)=3x-1
Find g(h(x))

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

122.

f(g(x))

a)

3x - 16

b)

3x - 2

c)

3x - 26

d)

4x - 2

123.

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

a)

16

b)

4

c)

-4

d)

None of these.

124.

√128

a)

64√2

b)

16

c)

2√8

d)

8√2

125.

√200

a)

14

b)

20√8

c)

5√3

d)

10√2

126.

Simplify:

a)

A

b)

B

c)

C

d)

D

127.

Simplify. $\sqrt{5}\left(2+3\sqrt{5}\right)$

a)

A.) $4\sqrt{5}-40$

b)

B.) $25\sqrt{2}+2$

c)

C.) $2\sqrt{5}+15$

d)

D.) $2\sqrt{3}+5$

128.

Simplify. $\left(2\sqrt{5}+\sqrt{2}\right)\cdot\left(-5\sqrt{5}+3\sqrt{2}\right)$

a)

A.) $-44$

b)

B.) $-8$

c)

C.) $-4\sqrt{5}+2\sqrt{3}$

d)

D.) $-44+\sqrt{10}$

129.

Simplify. $\sqrt{3a^2}\cdot\sqrt{15a^2}$

a)

A.) $3a^2\sqrt{5}$

b)

B.) $5a^2\sqrt{3}$

c)

C.) $3a\sqrt{5a}$

d)

D.) $\sqrt{18a^4}$

130.

$2\sqrt{150}+3\sqrt{175}+4\sqrt{24}$

a)

$2\sqrt{6}+15\sqrt{7}$

b)

$18\sqrt{6}+15\sqrt{7}$

c)

$17\sqrt{13}$

131.

A radical has a radicand of 6 and an index of 5. What does the radical look like?

a)

$\sqrt{65}$

b)

$^6\sqrt{5}$

c)

$^5\sqrt{6}$

d)

$6\sqrt{5}$

132.

What is the index of this radical? $^4\sqrt{18}$

a)

Square Root

b)

Fourth Root

c)

Cube Root

d)

Quartic Root

133.

If a radical has no listed index, what would the index be?

(a)

134.

2√3(√6 - √3)

a)

6√2 - 6

b)

3√2 + 3

c)

6 - √3

d)

√3 - √2

135.

√8 - 6√2

a)

-4√2

b)

2√2

c)

-6√6

d)

-6√10

136.

∛8

(a)

137.

Evaluate ∛27

(a)

138.

Which is equivalent to ∛54 in simplest form?

a)

3∛6

b)

9∛2

c)

3∛2

d)

3∛3

139.

a)

7²

b)

7^1/2

c)

7^-2

d)

7^-1/2

140.

a)

4^4/3

b)

4^3/4

c)

2^4/3

d)

2^3/4

141.

a)

2^3/5

b)

-2^3/5

c)

2^5/3

d)

8⁵

142.

For the following problem, what operation will you use on the exponents?

a)

Multiply

b)

Add

c)

Subtract

d)

Nothing

143.

Simplify:

a)

a²

b)

a³

c)

a⁴

d)

a⁵

144.

Simplify:

a)

5⁴ = 625

b)

5³ = 125

c)

5² = 25

d)

5

145.

For the following problem, what operation will you use on the exponents?

a)

Multiply

b)

Add

c)

Subtract

d)

Nothing

146.

Simplify:

a)

4¹ = 4

b)

4² = 16

c)

4³ = 64

d)

4^-1 = 1/4

147.

For the following problem, what operation will you use on the exponents?

a)

Multiply

b)

Add

c)

Subtract

d)

Nothing

148.

Simplify:

a)

2

b)

4

c)

8

d)

16

149.

Simplify:

a)

25

b)

125

c)

625

d)

1/5

150.

Add

a)

11 8
-4 2

b)

3 2
-6 -6

c)

-3 2
-4 -6

d)

10 8
-6 2

151.

Subtract

a)

-5
-8
3
10

b)

-9
8
3
2

c)

5
-8
3
10

d)

-5
8
3
2

152.

Find A-B

a)

-3 1
7 -1

b)

1 0
1 -4

c)

-4 0
6 -1

d)

not possible because rows do not match columns

153.

What are the dimensions of this matrix?

a)

2 x 3

b)

3 x 2

c)

6 x 1

d)

1 x 6

154.

Find the answer using substitution: Please list your answer as a coordinate (x,y)

(a)

155.

Find the answer to the systems using substitution: List the solution as a coordinate (x,y):

(a)

156.

Solve the given systems of equations using elimination: Write you answer as a coordinate (x,y).

(a)

157.

Find the answer to the systems using elimination: List the answer as a coordinate (x,y):

(a)

158.

a)

A

b)

B

c)

C

d)

D

159.

a)

A

b)

B

c)

C

d)

D

160.

a)

A

b)

B

c)

C

d)

D

161.

Find the solution(s) to the system.

a)

(0,-3)(-1,-2)

b)

(0,-3)

c)

(-2,0)(2,0)

d)

No solution

162.

Find the solution.

a)

(2,3) and (3,4)

b)

(-3,-15) and (4,-8)

c)

(-3,10) and (8,4)

d)

(-8,3) and (-4,10)

163.

What are the solutions to the system:
y = x² + 3x - 5
y = x + 3

a)

(-4, 2) and (-1, 5)

b)

(-4, -1) and (2, 5)

c)

(2, -1 and (-4, 5)

d)

(-4, 1) and (2, -1)

164.

Which of the following represents the first step in solving:

y = x² + 3x - 5

y = x + 3

a)

x² - 3x + 5 = x - 3

b)

x² + 3x - 5 = x + 3

c)

x² + 3x - 5 + x + 3 = 0

d)

x² + 3x - 5 = 0

165.

Solve the system of linear and quadratic equations using substitution:
y = 5
y = 2x² - 16x + 29

a)

(6, 5) and (2, 5)

b)

(2, 6)

c)

(6, 2)

d)

(5, 6) and (5, 2)

166.

Which of the following is not a solution to this system of inequalities?

a)

(0,-1)

b)

(0,3)

c)

(4,0)

d)

(6,-2)

167.

Which system of inequalities matches the graph?

a)

y > 2x - 4
y < 2

b)

y < 2x - 4
y < 2

c)

y > 2x - 4
y < 2

d)

y < 2x - 4
y < -2

168.

Match the system to the graph (solution set is on the left)

a)

y ≤ 3x and y ≤ -2x + 4

b)

y > 3x and y > -2x + 4

c)

y < 3x and y > -2x + 3

d)

y > 3x and y < -2x + 4

Algebra 2 Semester Review

Total questions: 168

Worksheet time: 27hrs 56mins

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