Free Printable Algebra II

1.

Solve 5^-2

a)

-10

b)

1/25

c)

1/(5)²

d)

-1/10

2.

3⁻⁴

a)

1 ⁄ 81

b)

-81

c)

81

d)

1 ⁄ 12

3.

What is 10⁰equivalent to?

a)

1

b)

10

c)

0

d)

100

4.

Solve (-8)^-2

a)

1/(-8)²

b)

1/8²

c)

1/64

d)

-64

5.

Simplify x^-7

a)

-7

b)

-7x

c)

1/x⁷

d)

-1/x⁷

6.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

7.

Are these two equivalent: 2² = (-2)²

a)

Yes

b)

No

8.

Which of the following is in exponential form?

a)

5 x 5 x 5

b)

125

c)

5³

9.

$m\cdot m^3$

a)

$m^2$

b)

$m^3$

c)

2m

d)

$m^4$

10.

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

a)

$4^6$

b)

$4^5$

c)

$\left(\frac{1}{4^6}\right)$

d)

4

11.

$\frac{m^{10}}{d^3}$

a)

Cannot combine

b)

$m^{10}$

c)

$d^{13}$

d)

$m^{13}$

12.

In order to multiply powers with the same base, we add their exponents.

a)

True

b)

False

13.

According to exponent rules, when we raise a power to another exponent we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

14.

When dividing powers with the same base, you _______________ the exponents.

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

15.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

16.

Negative Exponent Property: $\frac{1}{a^{-m}}=$

a)

$a^{-m}$

b)

$-a^m$

c)

$\frac{1}{a^m}$

d)

$a^m$

17.

m⁴ x 2m^-3

a)

2m^-12

b)

2m

c)

-2m^-12

d)

-2m

18.

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

a)

$y^8$

b)

$y^{-8}$

c)

$y^{-6}$

d)

$y^2$

19.

$\left(a^{2\ }b^{-7}\right)^3=$

a)

$a^6b^{-21}$

b)

$a^5b^{10}$

c)

$a^5b^{-10}$

d)

$a^6b^{-10}$

20.

$\left(3a^{-2}b^{-1}c^5b^{-2}\right)^2\cdot\left(\frac{a^{-2}b^3c^{4\ }}{4b^6}\right)^{\ ^{-2}}=$

a)

$12c^2$

b)

$144abc$

c)

$122a^2$

d)

$144c^2$

21.

Which of the following is correct?

a)

Root over Power

b)

Power over Root

22.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

23.

Which number is the BASE?
2³= 8

a)

2

b)

3

c)

8

24.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

25.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

26.

Write the following expression in exponential form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

27.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

28.

Write the following expression in exponential form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

29.

Simplify the following expression:

a)

5

b)

25

c)

125

d)

625

30.

Simplify the following expression:

a)

2

b)

4

c)

16

d)

64

31.

Simplify:

a)

6

b)

12

c)

36

d)

432

32.

In an exponential function, what does the 'a' represent?
f(x) = a ⋅ b^x

a)

A
Slope

b)

B
y -intercept

c)

C
x-intercept

d)

D
Common Ratio

33.

In an exponential function, what does the 'b' represent?
f(x) = a ⋅ b^x

a)

A
Slope

b)

B
y -intercept

c)

C
x-intercept

d)

D
Common Ratio

34.

In an exponential function, what is an interpretation of the y-intercept?

a)

A
initial amount

b)

B
ending amount

c)

C
growth factor

d)

D
decay factor

35.

a)

A
Growth

b)

B
Decay

c)

C
Both

d)

D
Neither

36.

Identify each function as representing exponential growth or decay.
f(x) = 5(1.09)^x

a)

A
growth

b)

B
decay

37.

a)

A
Growth

b)

B
Decay

c)

C
Both

d)

D
Neither

38.

Which function will show exponential behavior?
f(x) = (4.3)^xg(x) = 4.3x + 9

a)

A
f(x)

b)

B
g(x)

c)

C
both

d)

D
neither

39.

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

a)

300

b)

1.16

c)

.16

d)

x

40.

What is the Range of this function?

a)

y> 0

b)

x> 0

c)

All Real Numbers

d)

y= 1

41.

What is the Domain of the function?

a)

80 < y < 180

b)

0 < x < 6

c)

All Real Numbers

d)

x > 0

42.

Write an equation that models the following situation:

The current student count at John Jay is 6500, it is expected to grow at a rate of 14% next year.

a)

y= 6500(1+.14)^x

b)

y= 6500(1-.14)^x

c)

y= 6500(14)^x

d)

y= 14(6500)^x

43.

Which of the followings functions shows an initial amout of $15 and an increase of 35% ?

a)

y=15(35)^x

b)

y=15(1.35)^x

c)

y=15(0.35)^x

d)

y=35(15)^x

44.

A new savings account is opened with $400 and gains 3% every year. What is the exponential function?

a)

f(x)=400(1+3)^x

b)

f(x)=400(1-0.03)^x

c)

f(x)=400(1+0.03)^x

d)

f(x)=400(0.03)^x

45.

Which is the correct standard form equation of an exponential function?

a)

$y=mx+b$

b)

$y=b+mx$

c)

$ax+by=c$

d)

$y=a\left(b\right)^x$

46.

Choose the correct equation for an exponential function that has a growth factor of 3 and starts at 1

a)

$y=a\left(1\right)^3$

b)

$y=3\left(a\right)^1$

c)

$y=3\left(1\right)^x$

d)

$y=1\left(3\right)^x$

47.

Oscar's mom agrees to a unique allowance plan for 2021. Oscar starts with $3 in January and his mom promises to double it each month. Choose the correct equation:

a)

$y=1\left(3\right)^x$

b)

$y=3\left(2\right)^x$

c)

$y=3\left(1\right)^x$

d)

$y=2\left(3\right)^x$

48.

To solve 36 = 6^x, re-write 36 as what base and exponent?

a)

3⁶

b)

6³

c)

6²

d)

3¹²

49.

To solve 8 = 2^5x+7, you would need to re-write 8 using what base?

a)

8

b)

4

c)

2

d)

Cannot be determined

50.

2^-m = 2^3m-3

a)

4/3

b)

3/4

c)

2

d)

1

51.

Solve: 2^x = 4^x+1

a)

x = -2

b)

x = 2

c)

x = -3

d)

x = 3

52.

Solve for p:
4^p+2 = 64

a)

p = -16/9

b)

p = 1

c)

p = 8

d)

p = 7/6

53.

Solve: 7^-x = 49

(a)

54.

Solve 8 = 2^5x+7

a)

x = ⅘

b)

x = ¼

c)

x = -⅘

d)

x = -¼

55.

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

(a)

56.

Solve for x:
$4^x=\frac{1}{4}$

a)

1

b)

2

c)

-1

d)

$-\frac{1}{2}$

e)

$\frac{1}{2}$

57.

Rewrite the following equation in exponential form:
$\log_636=2$

a)

$36^2=6$

b)

$2^6=36$

c)

$6^2=36$

d)

$2^{36}=6$

58.

Rewrite the following equation in exponential form:
$\log_381=4$

a)

$4^3=81$

b)

$3^4=81$

c)

$81^3=4$

d)

$4^{81}=3$

59.

Rewrite the equation in exponential form:
$\log_vu=4$

a)

$v^4=u$

b)

$4^v=u$

c)

$v^u=4$

d)

$u^4=v$

60.

Rewrite the equation in exponential form:
$\log_{289}17=\frac{1}{2}$

a)

$17^{\frac{1}{2}}=289$

b)

$\frac{1}{2}^{17}=289$

c)

$289^{17}=\frac{1}{2}$

d)

$289^{\frac{1}{2}}=17$

61.

Rewrite the equation in logarithmic form:
$8^b=a$

a)

$\log_a8=b$

b)

$\log_8a=b$

c)

$\log_ba=8$

d)

$\log_8b=a$

62.

Rewrite the equation in logarithmic form:
$9^{-2}=\frac{1}{81}$

a)

$\log_29=\frac{1}{81}$

b)

$\log_9\ \left(-2\right)=\frac{1}{81}$

c)

$\log_2\ \left(\frac{1}{81}\right)=9$

d)

$\log_9\ \frac{1}{81}=-2$

63.

Rewrite the equation in logarithmic form:
$12^2=144$

a)

$\log_{12}2=144$

b)

$\log_2144=12$

c)

$\log_{12}144=2$

d)

$\log_{144}12=2$

64.

Evaluate the following expression:
$\log_{343}7$

a)

3

b)

$\frac{1}{3}$

c)

$\frac{1}{7}$

d)

7

65.

Rewrite each expression with a negative exponent.
¹/_12⁴

a)

¹/_12^-4

b)

12⁴

c)

¹/_20,736

d)

12^-4

66.

Simplify.

a)

y⁶⁰

b)

¹/_y¹⁶

c)

y^-16

d)

y⁴

67.

Simplify.
s^-5⋅ s^-2

a)

s^-3

b)

¹/_s⁷

c)

s^-7

d)

¹/_s³

68.

Which graph matches the function

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

a)

b)

c)

d)

69.

Which graph matches the logarithmic equation

a)

b)

c)

d)

70.

Which graph is logarithmic

a)

b)

c)

d)

71.

Describe domain of the function shown: y=log₂(x+1)

a)

(-∞,∞)

b)

(-1,∞)

c)

(-1,3)

d)

(∞, -1)

72.

Describe range of the function shown: y=log₂(x+1)

a)

(-∞,∞)

b)

(-1,∞)

c)

(-1,3)

d)

(∞, -1)

73.

Write the equation of the function f(x)=log₃x after the following transformations:

Translate 6 units left and 4 units up.

a)

g(x)=log₃(x+6)+4

b)

g(x)=log₃(x+4)-6

c)

g(x)=log₃(x-6)+4

d)

g(x)=3log(x+6)+4

74.

a)

A

b)

B

c)

C

d)

D

75.

a)

A

b)

B

c)

C

d)

D

76.

a)

A

b)

B

c)

C

d)

D

77.

a)

A

b)

B

c)

C

d)

D

78.

Condense

a)

logxyz³

b)

log(xy/z³)

c)

logx+logy+logz³

d)

logx³y³z³

79.

Expand

a)

log₈x+log₈y+log₈z

b)

5log₈x+5log₈y+5log₈z

c)

log₈xy+5log₈z

d)

log₈x+log₈y+5log₈z

80.

Condense

a)

log₈(a¹⁸/b³)

b)

log₈(a¹⁸b³)

c)

log₈(a/b³)

d)

15log₈(a/b³)

81.

Expand

a)

A

b)

B

c)

C

d)

D

82.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

83.

Expand the following logarithm:
log₂ 5x.

a)

log₂ 5 - log₂ x

b)

log₂ 5 + log₂ x

c)

2log 5 + 2log x

d)

log5 2 + log_x 2

84.

Expand the following logarithm:
log₃ 10z

a)

log₃ 10 - log₃ z

b)

log₃ 10 + log₃ z

c)

zlog₃ 10

d)

log₃ z¹⁰

85.

Evaluate: $\log_x1024=5$

a)

4

b)

5

c)

8

d)

$\frac{1}{4}$

86.

Evaluate: $\log_{11}x=5$

a)

1

b)

8694

c)

161051

d)

55

87.

Evaluate: $\log_3\left(0\right)=x$

a)

0

b)

1

c)

-1

d)

No solution

88.

Rewrite: $11^x=121$

a)

$\log_{11}x=121$

b)

$\log_{121}x=11$

c)

$\log_{11}121=x$

d)

$\log_x11=121$

89.

$2\left(7^x\right)=686$

What would you do first to solve?

a)

Rewrite $7^x$ in logarithmic form

b)

Multiply both sides by 2

c)

Take the square root of both sides

d)

Divide both sides by 2

90.

$2\left(7^x\right)=686$

Evaluate

a)

3

b)

13

c)

11

d)

-13

91.

log₂32=3x

a)

5/3

b)

3/5

c)

5

d)

3

92.

log₄(3x-1)=log₄(2x+3)

a)

4

b)

3

c)

1

d)

8

93.

log₈₁x = 3/4

a)

2

b)

3

c)

27

d)

81

94.

Write the equation in logarithmic form.
$e^3=x$

a)

$\ln x=3$

b)

$\ln3=x$

95.

Write the equation in logarithmic form.
$e^x=36$

a)

$\ln36=x$

b)

$\ln x=36$

96.

Write the equation in logarithmic form.
$e^{\left(x-9\right)}=74$

a)

$\ln\left(x-9\right)=74$

b)

$x-9=\ln74$

97.

Write the equation in exponential form.
$\ln53=x$

a)

$e^{53}=x$

b)

$e^x=53$

98.

Write the equation in exponential form.
$\ln x=18$

a)

$x^{18}=e$

b)

$e^{18}=x$

99.

Write the equation in exponential form.
$\ln87=x+4$

a)

$e^{\left(x+4\right)}=87$

b)

$e^{87}=x+4$

100.

Condense the expression as a single logarithm.

$\ln4+\ln3x$

a)

$\ln7x$

b)

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

c)

$\ln12x$

101.

Solve the equation. Round your answer to four decimal places.
$3e^x+1=5$
$x=$ (a)

Algebra II - Unit 4 Review

Total questions: 101

Worksheet time: 4hrs 52mins

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