Free Printable 8th Grade Module 1 Unit Review

1.

If the exponent on your power of 10 is positive, is your number larger or smaller than 10?

a)

Larger

b)

Smaller

2.

7.82 x 10⁸ is an example of scientific notation. The exponent of 8 tells you your number will be very ________

a)

Large

b)

Small

c)

Basic

3.

Change from standard form to scientific notation: 12,000,000

a)

12.0 x 10⁷

b)

0.12 x 10⁷

c)

1.2 x 10⁶

d)

1.2 x 10⁷

4.

Change from standard form to scientific notation: 450,000

a)

4.5 x 10⁵

b)

45 x 10⁵

c)

4.5 x 10⁴

d)

4.5 x 10⁶

5.

Change from standard form to scientific notation: 0.000398

a)

39.8 x 10^-5

b)

3.98 x 10^-5

c)

3.98 x 10^-4

d)

39.8 x 10^-6

6.

Change from standard form to scientific notation: 0.004078

a)

4.078 x 10^-3

b)

4.078 x 10³

c)

40.78 x 10^-4

d)

.4078 x 10^-2

7.

125,678,000: Change to scientific notation

a)

1.25678 x 10¹²

b)

.125678 x 10^-9

c)

12.5678 x 10⁸

d)

1.25678 x 10⁸

8.

Try to change the number back to standard form: 6.79 x 10⁴

a)

679,000

b)

6,790

c)

67,900

d)

6,790,000

9.

Try to change the number back to standard form: 3.97 x 10^-2

a)

0.000397

b)

0.0397

c)

0.0000397

d)

0.397

10.

The factor multiplied by a power of 10 in scientific notation needs to be greater than or equal to one but less than ___________?

a)

1

b)

10

c)

100

d)

1,000

11.

What is scientific notation?

a)

A long way to write really short numbers

b)

A short way to write really long numbers

c)

I don't know...

d)

None of the above

12.

How would you write 564,000,000 in scientific notation?

a)

5.64 x 10^-7

b)

5.64 x 10⁶

c)

5.64 x 10⁸

d)

56.4 x 10⁷

13.

How do you write
1001
in scientific notation?

a)

1.0001 x 10⁴

b)

1.01 x 10⁵

c)

1.001 x 10³

d)

10.1 x 10³

14.

Express the following in scientific notation:
.000457

a)

457 x 10⁶

b)

457 x 10^-6

c)

4.57 x10⁴

d)

4.57 x 10^-4

15.

When your exponent is negative, you move your decimal....

a)

to the right

b)

to the left

c)

to both sides

d)

nowhere.... the decimal goes nowhere

16.

ANY number raised to a power of 0 will be....

a)

10

b)

itself

c)

1

d)

0

17.

Which of the following is correct scientific notation?

a)

20.35 x 10⁴

b)

.2035 x 10⁴

c)

2035⁴

d)

2.035 x10⁴

18.

Convert this number to standard notation: 7.1 x 10⁴

(a)

19.

When using scientific notation, a positive exponent means ...

a)

the standard number is greater than one

b)

the standard number is less than one

c)

the negative sign doesn't have a meaning

d)

None of the above

20.

Convert this number to standard notation: 1.4 x 10^-2

(a)

21.

7.82 x 10^-⁶ is an example of scientific notation. The exponent of -6 tells you your number will be very ________.

a)

Large

b)

Small

c)

Basic

22.

Which number is the least in value

a)

5.0 x 10^-9

b)

5.0 x 10^-4

c)

5.0 x 10⁶

d)

0.5 x 10^-7

e)

0.05 x 10^-10

23.

Which value is the greatest

a)

5.0 x 10^-9

b)

5.0 x 10^-4

c)

5.0 x 10⁶

d)

5.0 x 10⁸

e)

0.005 x 10¹⁰

24.

Which of these numbers are NOT in scientific notation?

a)

1.2 x 10³

b)

5.3 x 10⁹

c)

2.0 x 10⁰

d)

10 x 10²

25.

How would you write 5.6 x 10^-3 in standard form?

a)

56,000

b)

5,600

c)

0.00056

d)

0.0056

26.

Express the following in standard notation:
8.025 x 10^-⁸

a)

.00000008025

b)

.000000008025

c)

802,500,000,000

d)

80,250,000,000

27.

What would the base number be if this number was written in scientific notation?

520,000,000

(a)

28.

Select the value equivalent to 10^-²?

a)

0.01

b)

0.001

c)

0.02

d)

0.002

29.

Which is the correct exponent ? 0.000001 = 10^?

a)

6

b)

5

c)

-6

d)

5

30.

Write 0.216 in scientific notation.

a)

216 x 10³

b)

216 x 10^-3

c)

2.16 x 10¹

d)

2.16 x 10^-1

31.

Write 0.0003 in scientific notation.

a)

3 x 10⁴

b)

3 x 10^-4

c)

0.3 x 10³

d)

0.3 x 10^-3

32.

Write 2.07 x 10⁵in standard notation.

a)

20,700,000

b)

0.00000207

c)

0.0000207

d)

207,000

33.

Write 7,000,000 in scientific notation.

a)

0.7 x 10⁷

b)

7 x 10^-6

c)

7 x 10⁶

d)

70 x 10⁵

34.

What would the base number look like if this number was written in scientific notation, 6,081,000,000,000?

(a)

35.

Write 5.43 x 10^-7in standard notation.

a)

0.000000543

b)

0.0000000543

c)

5,430,000,000

d)

54,300,000

36.

What is the correct symbol we should put for:

90,000,000 ____ 9.6 x 10⁷

a)

<

b)

>

c)

=

37.

What is the correct symbol we should put for:

5.9 x 10⁴ ____ 0.58 x 10⁶

a)

<

b)

>

c)

=

38.

What is the correct symbol we should put for:

6.8 x 10³____ 4.3 x 10³

a)

<

b)

>

c)

=

39.

How many zeros would be in this number if written in standard form?
6.47 x 10¹¹

a)

11

b)

9

c)

10

d)

12

40.

How would you write 4.3756 x 10⁵in standard form?

(a)

41.

Which is the smallest?
1.3 x 10²⁰2.9 x 10²¹9.5 x 10³²8.4 x 10¹⁹

a)

1.3 x 10²⁰

b)

2.9 x 10²¹

c)

9.5 x 10³²

d)

8.4 x 10¹⁹

42.

What is the standard form?

1.245 x 10³

(a)

43.

How would you write -5.6 x 10^-3 in standard form?

(a)

44.

Write 9.2 x 10⁴in standard notation

(a)

45.

Write 2.8 x 10^-4 in standard notation

(a)

46.

Give the sum of (2.6 x 10⁶) + (4.2 x 10⁶)

a)

6.8 x 10⁶

b)

6.8 x 10¹²

c)

8.4 x 10⁶

d)

3.2 x 10¹²

47.

Write the answer in scientific notation.
5 x 10⁸ - 3.4 x 10⁸ =

a)

2.4 x 10⁸

b)

2.4 x 10⁰

c)

1.6 x 10⁰

d)

1.6 x 10⁸

48.

Give the difference of (6.4 x 10^-6) - (5.7 x 10^-7)

a)

5.83 x 10^-6

b)

7 x 10^-7

c)

1.23 x 10^-13

d)

1.3 x 10^-6

49.

Subtract the within the scientific notation.
(2 x 10³) - (1.9 x 10²)

a)

1.81 x 10⁵

b)

1.81 x 10³

c)

1.81 x 10⁶

d)

1.81 x 10⁴

50.

Write the answer in scientific notation.
4.1 x 10⁵ + 5.5 x 10⁶ =

a)

5.91 x 10⁶

b)

9.6 x 10⁵

c)

9.6 x 10¹¹

d)

4.65 x 10⁵

51.

Simplify

x³⋅x²

a)

x⁶

b)

x⁵

c)

x

d)

x⁴

e)

x³

52.

Simplify

x⁴⋅x³⋅x

a)

x⁸

b)

x¹²

c)

x⁷

d)

x¹⁰

e)

x⁹

53.

Simplify

(x²)³

a)

x³

b)

x⁵

c)

x⁶

d)

x⁴

e)

x⁸

54.

Simplify

y⁸⋅y³

a)

y²⁴

b)

y¹¹

c)

y⁵

d)

y¹⁵

e)

y³⁵⁶

55.

Simplify

(y³)⁴

a)

y⁷

b)

y¹²

c)

y^-1

d)

y⁸

e)

y⁶⁴

56.

Simplify

a)

y²

b)

y³⁵

c)

y¹²

d)

y¹⁴

e)

y³

57.

Simplify

a)

x¹²

b)

x¹⁷

c)

x⁶

d)

x²³

e)

z¹⁸

58.

Simplify

a)

z

b)

z¹²

c)

1

d)

z¹⁴

e)

z^-1

59.

Simplify

a)

z¹⁵

b)

z⁸

c)

z³

d)

z¹¹

e)

z^-3

60.

Simplify

a)

1

b)

x²

c)

x¹⁸

d)

x¹¹

e)

x

61.

Simplify

a)

x⁴

b)

x⁶

c)

x²⁹

d)

x²⁰

e)

x⁸

62.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

63.

56¹= ?

a)

56

b)

0

c)

1

d)

65

64.

Which is equivalent to 3^{4 ?}

a)

27

b)

9

c)

81

d)

12

65.

Which is equivalent to 5 x 5 x 5 x 5

a)

5³

b)

5⁴

c)

4⁵

d)

5⁵

66.

Which is equivalent to 4 x 4 x 4 x 4 x 4

a)

4⁶

b)

5⁴

c)

4⁴

d)

4⁵

67.

Which is equivalent to 2⁴

a)

8

b)

20

c)

16

d)

12

e)

24

68.

How would you represent 8⁶ ?

a)

8 x 6

b)

8 x 8 x 6

c)

8 x 8 x 8 x 8 x 8 x 8

d)

6 x 6 x 6 x 6 x 6 x 6 x 6 x 6

69.

Which number is the BASE?
2³= 8

a)

2

b)

3

c)

8

d)

not here

70.

Which number is the EXPONENT?
4^{2 =}16

a)

4

b)

2

c)

16

d)

not here

71.

Find the value (standard form) of the power.

Eleven to the power of 3

a)

1331

b)

121

c)

33

d)

333

e)

9

72.

Simplify to an equivalent expression BUT leave in exponent form. (use product rule)

4³⋅4⁵

a)

4⁸

b)

16⁸

c)

4¹⁵

d)

16¹⁵

e)

8⁸

73.

simplify (-4)³

a)

64

b)

-64

c)

12

d)

-12

e)

81

74.

simplify (-3)⁴

a)

81

b)

-81

c)

12

d)

-12

e)

120

75.

simplify -(2)⁴

a)

8

b)

16

c)

-8

d)

-16

e)

-24

76.

simplify -(-5)³

a)

15

b)

125

c)

-15

d)

-125

e)

25

77.

Write the following in expanded form.
10³

a)

10+10+10

b)

10x10x10

c)

3x10

d)

1,000

78.

Simplify (2⁴)(2⁵)

a)

2²⁰

b)

4⁹

c)

4²⁰

d)

2⁹

79.

Simplify m¹²/ m³

a)

m^12-3 = m⁹

b)

m^12/3= m⁴

c)

m^-9

d)

-m⁹

80.

Which expression has the largest value?

a)

6²

b)

2⁶

c)

1¹⁰

d)

10¹

81.

Which expressions are not equivalent to 81?

a)

3⁴

b)

9²

c)

81¹

d)

27³

e)

4⁴

82.

What is the missing exponent in 4^x = 1024?

a)

2

b)

3

c)

10

d)

256

e)

5

83.

Which is GREATER?
2⁷ or 7²

a)

2⁷

b)

7²

c)

Neither, they are equal

84.

When there is no exponent connected to the base it means the power is 0?
Ex: x= x⁰

a)

True

b)

False

85.

Simplify the following expression:

r⁶⋅ r²⋅ r³

a)

r⁶²³

b)

r¹¹

c)

11r

d)

r³⁶

e)

3r¹¹

86.

What special word do you use for the exponent of 3?

a)

squared

b)

cubed

c)

triangled

d)

boxed

87.

Simplify

c¹² ∗ c¹³

a)

c²⁵

b)

c¹⁵⁶

c)

c¹²³

d)

2c²⁵

88.

$\frac{\ \ \ x^{15}\ \ \ }{y^{12}}$

a)

$xy^3$

b)

$x^{27}$

c)

Not like bases, laws of exponents can not be applied

d)

$y^3$

e)

$x^3$

89.

Simplify the expression.

a)

1

b)

g¹⁰

c)

g²⁵

d)

g

e)

g¹

90.

Simplify the expression.

a)

7⁶

b)

7^-5

c)

1/7⁵

d)

7⁵

e)

7¹

91.

(4³)³

a)

4⁶

b)

4

c)

7³

d)

4⁹

92.

(9xyz)⁸

a)

72xyz⁸

b)

72x⁸y⁸z⁸

c)

9⁸x⁸y⁸z⁸

d)

9xyz⁸

e)

43,046.721 xyz⁸

93.

Evaluate the expression using the quotient rule.

a)

1²²

b)

1³⁰

c)

6²²

d)

6³⁰

94.

a)

0

b)

1

c)

3

d)

31

e)

3a

95.

Simplify
(z⁴)³⋅z⁴

a)

z¹¹

b)

z¹⁶

c)

z⁵

d)

z²⁸

96.

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

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

e)

Do nothing

97.

Simplify (6x⁷)²

a)

12x¹⁴

b)

36x¹⁴

c)

6x¹⁴

d)

6x⁹

e)

36x⁹

98.

5⁴=

a)

20

b)

625

c)

1024

d)

9

e)

125

99.

Which of the following are a PERFECT SQUARES?

a)

121

b)

10

c)

140

d)

300

e)

400

100.

Simplify

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

d)

ab

e)

ab⁶

101.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

102.

Side a on a right triangle is ALWAYS the longest side.

a)

true

b)

false

103.

If a right triangle has side lengths 6, 6.7 and 3, which side is the hypotenuse?

a)

6

b)

6.7

c)

3

d)

15.7

e)

None of them

104.

Sides a and b are called legs.

a)

true

b)

false

105.

Which equation can be used to solve for "x"?

a)

15² – x² = 21²

b)

x² – 15² = 21²

c)

15² + 21² = x²

d)

21² – 15² = x²

106.

Name the longest side of a right triangle.

a)

leg a

b)

leg b

c)

leg

d)

hypotenuse

107.

Determine the length of the missing side.

a)

7

b)

8

c)

17

d)

23

108.

Find the length of the missing side.

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

109.

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

110.

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the corner diagonally across. What is this distance?

a)

210 m

b)

180 m

c)

150 m

d)

79 m

111.

What is the longest side of a right triangle called?

a)

Leg A

b)

Leg B

c)

Hypotenuse

d)

Pythagoras' Big Buddy

112.

_{^{Find the missing side}}

a)

36

b)

76.8

c)

12

d)

40

113.

_{^{Find the missing side}}

a)

29.2

b)

20

c)

400

d)

10

114.

a= 12, b= 35, c= ? Find c

a)

32

b)

37

c)

19

d)

20

115.

c= 97, b= 72, a=?

a)

35

b)

75

c)

65

d)

55

116.

Do the lengths form a right triangle? 6, 8, 10

a)

yes

b)

no

117.

How long is the hypotenuse of this triangle?

(a)

118.

Is a triangle with side lengths of 12, 9, and 15 a right triangle?

a)

Yes

b)

No

119.

Is this a right triangle?

a)

Yes

b)

No

120.

A triangle has legs that are 7 inches and 24 inches long. How long is the hypotenuse?

a)

23

b)

26

c)

28

d)

25

121.

In between what two integers is the square root of 77?

a)

5 and 6

b)

6 and 7

c)

7 and 8

d)

8 and 9

122.

In between what two integers is the square root of 44?

a)

3 and 4

b)

4 and 5

c)

5 and 6

d)

6 and 7

123.

√100

a)

15

b)

10

c)

11

d)

12

124.

√16

a)

4

b)

8

c)

2

d)

9

125.

√64

a)

3

b)

8

c)

7

d)

6

126.

Level 2: Which number has a square root that is between 5 and 6?

a)

48

b)

81

c)

28

d)

36

127.

Level 3: Estimate the square root.

a)

Between 4 and 5 and closer to 5

b)

Between 5 and 6 and closer to 5

c)

Between -4 and -5 and closer to -5

d)

Between -5 and -6 and closer to -6

128.

Level 3: Estimate the square root.

a)

Between 3 and 4 and closer to 3

b)

Between 2 and 3 and closer to 3

c)

Between 3 and 4 and closer to 4

d)

Between 2 and 3 and closer to 2

129.

Level 3: Which point best represents √47?

a)

A

b)

D

c)

E

d)

F

130.

Level 2

Identify the letter that best estimates the following square root on the following number line.

√156

a)

d

b)

b

c)

c

d)

e

131.

Round to the Nearest tenth: √7

a)

3.5

b)

2.6

c)

2.8

d)

14

132.

Round to the Nearest Tenth: √13

a)

5.6

b)

2.6

c)

3.9

d)

3.6

133.

Round to the Nearest Hundredth: √28

a)

5.6

b)

5.9

c)

5.3

d)

8

134.

Between which two whole numbers is the
√20 ?

a)

5 and 6

b)

10 and 2

c)

4 and 5

d)

3 and 4

135.

Find the best estimate for √18 .
Look at the number line.

a)

4.2

b)

4.4

c)

5.1

d)

4

136.

a)

9

b)

3

c)

1/3

d)

1

137.

a)

8

b)

9

c)

10

d)

11

138.

What is the cube root of 125?

a)

5

b)

-5

c)

25

d)

-25

139.

What is the cube root of 8?

a)

4

b)

2

c)

-2

d)

-4

140.

What is the cube root of 1000?

a)

10

b)

100

c)

500

d)

20

141.

What is the cube root of 64?

a)

2

b)

4

c)

8

d)

16

142.

∛216

a)

6

b)

72

c)

108

d)

4

143.

∛64

a)

4

b)

32

c)

8

d)

2

144.

∛27

a)

3

b)

9

c)

14

d)

6

145.

∛1

a)

1

b)

3

c)

4

d)

2

146.

∛-8

a)

2

b)

-2

c)

4

d)

-4

147.

9³

a)

689

b)

709

c)

729

d)

749

148.

7³

a)

313

b)

323

c)

333

d)

343

149.

3³

a)

89

b)

27

c)

42

d)

100

150.

Find the cube root.

a)

-4

b)

4

c)

8

d)

-8

151.

Find the cube root. Use your chart!

a)

-5/6

b)

5/6

c)

25/36

d)

-25/36

152.

The solution of the equation is between...

a)

−50 and −40

b)

−20 and −10

c)

−30 and −20

d)

−40 and −30

153.

a)

x = 49

b)

x = 53

c)

x = 45

d)

x = 18

154.

x² = 121

a)

11,-11

b)

11

c)

-11

d)

10,-10

155.

x² = 36

a)

6

b)

18

c)

6, -6

d)

-6

156.

x² = 225

a)

5,-5

b)

15

c)

-15,15

d)

-5

157.

a)

x = 12

b)

x = 24

c)

x = 144

d)

x = 121

158.

How do you solve the equation: $x^2\ =\ 100$

a)

Take $100^2$

b)

Take $\sqrt{100}$

c)

Multiply 100 by 2

159.

How do you solve the equation: $\sqrt{x}=\ 25$

a)

Take $25^2$

b)

Multiply 25 by 2

c)

Take $\sqrt{25}$

160.

Solve: $\sqrt{h}=\ 9$

a)

3

b)

-3

c)

81

d)

-81

161.

How many solutions do Squared Equations have? Example: $m^2=16$

a)

1

b)

2

c)

3

162.

How many solutions do Square Root Equations have? Example: $\sqrt{b}=\ 11$

a)

1

b)

2

c)

3

163.

Solve $\sqrt{w}=\ 4$

a)

2

b)

-2

c)

16

d)

-16

164.

$6\sqrt{9}+18$

a)

36

b)

54

c)

72

165.

Solve for x

$\sqrt[]{x-7}=6$

a)

$x=-9$

b)

$x=-29$

c)

$x=36$

d)

$x=43$

166.

Solve for x

$\sqrt[]{2x-10}=2$

a)

$x=21$

b)

$x=14$

c)

$x=7$

d)

$x=4$

167.

Which of the following is a rational number?

a)

$\frac{5}{6}$

b)

$\sqrt{68}$

c)

1.1462543

d)

$\sqrt{100}$

168.

Which of the following is an irrational number?

a)

0.3

b)

$\sqrt{49}$

c)

$\sqrt{8}$

d)

$\frac{5}{22}$

169.

Between what 2 whole numbers is $\sqrt{35}$ ?

a)

2 and 3

b)

3 and 4

c)

4 and 5

d)

5 and 6

170.

Estimate the square root.

a)

9.8

b)

9

c)

9.3

d)

10

171.

Label the decimals as terminating or repeating

a)

terminating

b)

repeating

c)

repeating

d)

repeaing

1

2

3

4

1)

2)

3)

4)

172.

Convert 0.444... to a fraction.

a)

4/10

b)

4.4/99

c)

4/9

d)

2/5

173.

Which of the following is a rational number?

a)

$\frac{5}{6}$

b)

$\sqrt{68}$

c)

1.1462543

d)

$\sqrt{100}$

174.

Select ALL the perfect squares below

a)

$\sqrt[]{7}$

b)

$\sqrt[]{144}$

c)

$\sqrt[]{4}$

d)

$\sqrt[]{13}$

e)

$\sqrt[]{49}$

175.

Select all the RATIONAL numbers

a)

-78

b)

$\sqrt[]{2}$

c)

4.5

d)

$\pi$

e)

$\frac{6}{8}$

8th Grade Module 1 Unit Review

Total questions: 175

Worksheet time: 8hrs 19mins

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