Free Printable 8 HW 15

1.

-1 x 1 x -1 x 1 x 1 x -1 x -1

2.

Which of the following numbers is an example of an irrational number?

a)

$\frac{3}{4}$

b)

$\sqrt{2}$

c)

$0.75$

d)

$1.5$

3.

True or false?

$\sqrt{5}>\frac{5}{7}$

a)

True

b)

False

4.

True or false?

$3\pi>3\sqrt{3}$

a)

True

b)

False

5.

Which numbers fall between 3 and 4 on a number line? Select all that apply.

a)

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

b)

$\frac{8\pi}{4+1}$

c)

$\frac{3^2\pi}{9+1}$

d)

$\frac{\sqrt{8}}{1+3}$

e)

$\frac{\sqrt{24}+2}{2}$

6.

a)

A

b)

B

c)

C

d)

D

7.

Which numbers are irrational? Select all that apply.

a)

$\frac{3}{44}$

b)

$\sqrt{2}$

c)

$3.14$

d)

$\frac{22}{7}$

e)

$\pi$

8.

Which statement explains why $\sqrt{30}$ is considered an irrational number?

a)

When evaluated, $\sqrt{30}$ results in a repeating decimal, which is considered an irrational number

b)

When evaluated, $\sqrt{30}$ results in a terminating decimal, which is considered an irrational number

c)

When evaluated, $\sqrt{30}$ results in a nonterminating and nonrepeating decimal, which is considered an irrational number

d)

When evaluated, $\sqrt{30}$ results in a whole, which is considered an irrational number

9.

Select the answer choices that are irrational

a)

$\frac{1}{\sqrt{9}}$

b)

$\sqrt{17}$

c)

$-1\frac{2}{3}$

d)

$0.423$

10.

Which values are irrational? Select all that apply.

a)

$-4\pi$

b)

$-5.56\overline{45}$

c)

$-\frac{1}{3}$

d)

$\sqrt{2}$

e)

$2.2578$

11.

Select the boxes that identify the numbers that are rational.

a)

$\frac{13}{90}$

b)

$\sqrt{84}$

c)

$\frac{4}{11}$

d)

$12\pi$

e)

$4.\overline{63}$

12.

Which values are irrational? Select all that apply.

a)

$-4\pi$

b)

$-5.56\overline{45}$

c)

$-\frac{1}{3}$

d)

$\sqrt[]{2}$

e)

2.2578

13.

a)

A

b)

B

c)

C

d)

D

14.

A list of numbers is shown.

$7.6,\ \sqrt[]{50},\ \sqrt[]{65},\ \sqrt[]{78},\ 8.2$

To plot the numbers on a number line, which list is ordered from least to greatest?

a)

$\sqrt[]{50},\sqrt[]{65},\sqrt[]{78},7.6,\ \ 8.2$

b)

$\sqrt[]{78},8.2,\ \sqrt[]{65},\ 7.6,\ \sqrt[]{50}$

c)

$7.6,\ 8.2,\sqrt[]{50},\sqrt[]{65},\ \sqrt[]{78}$

d)

$\sqrt[]{50},7.6,\sqrt[]{65},\ 8.2,\sqrt[]{78}$

15.

a)

Point K and point L

b)

Point K and point J

c)

Point M and Point K

d)

Point M and point L

16.

Between which two consecutive rational numbers is the irrational number? Choose two consecutive rational numbers for each irrational number.

$\pi$

a)

1

b)

2

c)

3

d)

4

e)

5

17.

Between which two consecutive rational numbers is the irrational number? Choose two consecutive rational numbers for each irrational number.

$\sqrt{5}$

a)

1

b)

2

c)

3

d)

4

e)

5

18.

Between which two consecutive rational numbers is the irrational number? Choose two consecutive rational numbers for each irrational number.

$\sqrt{17}$

a)

2

b)

3

c)

4

d)

5

e)

6

19.

Between which two consecutive rational numbers is the irrational number? Choose two consecutive rational numbers for each irrational number.

$\sqrt{30}$

a)

2

b)

3

c)

4

d)

5

e)

6

20.

Which of the following equations are true? Select all that apply.

a)

$3^{-2}\times3^5=3^2$

b)

$3^6\times3^{-2}=3^{-3}$

c)

$3^4\times3^2=3^6$

d)

$3^{-2}\times3^{-2}=\frac{1}{81}$

e)

$3^2\times3^2=3^0$

21.

All 8th grade students at a school answered Yes or No to the two survey questions:

Have you ridden on a city bus in the last year?

Have you taken a taxi in the last year?

The same students responded to both questions. Complete the two-way frequency table by dragging the correct answers where they belong. REMEMBER THAT IN A TWO WAY TABLE, ALL THE NUMBERS ADD UP TOGETHER.

a)

120

b)

400

c)

275

d)

95

1

2

3

4

1)

2)

3)

4)

22.

Solve this multi-step equation.

Remember:

1) Distributive Property if its there

2) Combine like terms

3) Isolate the variable by doing inverse operations

4) What you do to one side, do to the other

23.

Solve this multi-step equation.

Remember:

1) Distributive Property if its there

2) Combine like terms

3) Isolate the variable by doing inverse operations

4) What you do to one side, do to the other

24.

Remember:

.1111111 = 1/9

.22222 = 2/9

.55555 = 5/9

25.

Determine for each number whether it is rational or irrational.

Rational numbers CAN be written as fractions.

Irrational numbers CANNOT be written as fractions.

Remember: Anything with pi in it is irrational.

Anything with an imperfect square root is also irrational.

Categorize the following

Rational

Irrational

26.

?

a)

About 4.5

b)

About 2.5

c)

About 7.5

d)

About 9.5

27.

?

a)

Between 6.6 and 6.8

b)

Between 11.1 and 11.3

c)

Between 21.9 and 22.1

d)

Between 33.7 and 33.9

28.

Organize these options into the right categories. REMEMBER THAT PI IS JUST A LITTLE BIGGER THAN 3.

Categorize the following

True

False

29.

Triangle ABC is rotated 180 degree clockwise to create A'B'C'.

Select all the equivalent transformations that could create triangle A'B'C'.

HINT: Translation = slide

Rotation = turn

Reflection = Flip

Dilation = Bigger or Smaller

a)

A dilation of a scale factor of 2.

b)

A reflection across the x axis.

c)

A rotation of 180 degrees counter clock-wise.

d)

A translation of 3 units up and 3 units right.

30.

?

a)

b)

c)

d)

31.

Hint: Make a table for each...

Liquid 16.9 14.6 12.3 etc. etc.

Solid 30.7 23.8 16.9 etc. etc.

32.

$Enter\ the\ approximate\ value\ of\ \ 2\ \sqrt[]{29}\ to\ the\ nearest\ tenth.$

33.

$Enter\ the\ approximate\ value\ of\ \ \sqrt[]{\left(13\ +\ 5\right)}\ \ to\ the\ nearest\ tenth.$

34.

All 8th grade students at a school answered Yes or No to the two survey questions:

Have you ridden on a city bus in the last year?

Have you taken a taxi in the last year?

The same students responded to both questions. Complete the two-way frequency table by dragging the correct answers where they belong. REMEMBER THAT IN A TWO WAY TABLE, ALL THE NUMBERS ADD UP TOGETHER.

a)

120

b)

400

c)

275

d)

95

1

2

3

4

1)

2)

3)

4)

35.

Determine for each number whether it is rational or irrational.

Rational numbers CAN be written as fractions.

Irrational numbers CANNOT be written as fractions.

Remember: Anything with pi in it is irrational.

Anything with an imperfect square root is also irrational.

Categorize the following

Rational

Irrational

36.

Remember:

.1111111 = 1/9

.22222 = 2/9

.55555 = 5/9

37.

?

a)

7

b)

8

c)

25

d)

26

38.

?

a)

About 4.5

b)

About 2.5

c)

About 7.5

d)

About 9.5

39.

?

a)

Between 6.6 and 6.8

b)

Between 11.1 and 11.3

c)

Between 21.9 and 22.1

d)

Between 33.7 and 33.9

40.

Organize these options into the right categories. REMEMBER THAT PI IS JUST A LITTLE BIGGER THAN 3.

Categorize the following

True

False

41.

Organize these options into the right categories

Categorize the following

True

False

42.

HINT: Pi has a value approximately equal to 3.14

a)

b)

c)

d)

43.

?

a)

b)

c)

d)

44.

$\sqrt[3]{8}$

45.

$\sqrt[3]{27}$

46.

$\sqrt[3]{64}$

47.

$\sqrt[3]{125}$

48.

$\sqrt[3]{216}$

49.

$\sqrt[3]{343}$

50.

$\sqrt[3]{512}$

51.

$\sqrt[3]{729}$

52.

$\sqrt[3]{1000}$

53.

$13^2$

54.

$14^2$

55.

$15^2$

56.

Simplify the expression: $(2^3) \cdot (2^4)$

a)

$2^7$

b)

$2^{12}$

c)

$2^{1}$

d)

$2^{6}$

57.

Evaluate the expression: $5^0$

a)

$0$

b)

$1$

c)

$5$

d)

$10$

58.

Simplify the expression: $\frac{3^5}{3^2}$

a)

$3^3$

b)

$3^7$

c)

$3^2$

d)

$3^1$

59.

What is the value of $10^{-2}$ ?

a)

$100$

b)

$0.01$

c)

$0.1$

d)

$10$

60.

Simplify the expression: $(4^2)^3$

a)

$4^5$

b)

$4^6$

c)

$4^8$

d)

$4^{12}$

61.

Evaluate the expression: $(-2)^3$

a)

$-8$

b)

$8$

c)

$-6$

d)

$6$

62.

Simplify the expression: $x^5 \cdot x^{-3}$

a)

$x^2$

b)

$x^8$

c)

$x^{-8}$

d)

$x^{-2}$

63.

What is the value of $7^{-1}$ ?

a)

$7$

b)

$-7$

c)

$\frac{1}{7}$

d)

$-1$

64.

(5³)⁴

a)

1/5¹

b)

5⁷

c)

(5x5x5)(5x5x5)(5x5x5)

d)

5¹²

65.

Which expression is equivalent to the expression in the picture?

a)

6 / 9

b)

2

c)

8 / 27

d)

4 / 9

66.

Evaluate the expression using the quotient rule.

a)

2¹⁴ z¹³

b)

2²/z⁷

c)

2¹⁴/ z⁷

d)

2²z⁷

67.

x⁻⁶

a)

1 ⁄ x⁶

b)

x⁶

c)

-x⁶

d)

-1 ⁄ x⁶

68.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

69.

(2x⁷)³

a)

6x²¹

b)

8x²¹

c)

6x¹⁰

d)

8x¹⁰

70.

Re-write the expression with a positive exponent

a)

1/6³

b)

6³

c)

1³/6

d)

6/1³

71.

3^-2 = 1/9

a)

True

b)

False

72.

Which is a reasonable estimate for $\sqrt[]{22}$ ?

a)

4.7

b)

4.1

c)

3.9

d)

5.6

73.

Between which two square roots does the √51 fall?

a)

√16 and √25

b)

√25 and √36

c)

√36 and √49

d)

√49 and √64

74.

In between what two integers is $\sqrt[]{44}$

a)

3 and 4

b)

4 and 5

c)

5 and 6

d)

6 and 7

75.

Between which two whole numbers does the √115 fall?

a)

9 and 10

b)

10 and 11

c)

9 and 11

d)

11 and 12

76.

Which number is closest to √76?

a)

8.7

b)

8.2

c)

7.8

d)

9.1

77.

Estimate 7/8

a)

0

b)

1/2

c)

1

78.

Which number is closest to √90?

a)

10.2

b)

9.4

c)

9.9

d)

10.4

79.

What is the most reasonable estimate of $\frac{5}{6}+5.89$ ?

a)

2

b)

9

c)

5

d)

7

80.

What is the most reasonable estimate for $3\sqrt[]{10}$ ?

a)

12

b)

30

c)

9

d)

3

81.

Estimate 5/6

a)

0

b)

1/2

c)

1

82.

What is the most reasonable estimate for the following? $3.9\ +\ 5.68\ +\ \frac{12}{5}$

a)

12

b)

10

c)

15

d)

27

83.

Estimate $5\sqrt[]{30}$

a)

25

b)

40

c)

15

d)

35

84.

Estimate $6\ \frac{5}{6}$

a)

6

b)

7

c)

6 1/2

85.

1. Which statement best describes

-√8 ?

a)

Between 2 and 3

b)

Exactly 3

c)

Exactly -3

d)

Between -2 and -3

86.

The sum of π and 2.4 is best described as:

a)

Irrational

b)

Integer

c)

Natural

d)

Rational

87.

If x²=121, which of the following is true?

a)

x = 11 or x = -11

b)

x = 242 or x = -242

c)

x = 14561 or x = -14561

d)

x = 60.5 or x = -60.5

88.

Look at the number line below – which point best represents √18?

a)

W

b)

X

c)

Y

d)

Z

89.

John built a deck with an area of 55 square feet. What is the approximate length of one side of the deck?

a)

Less than 7 feet

b)

Between 7 feet and 8 feet

c)

Between 6 feet and 7 feet

d)

More than 7 feet

90.

Which classifications of the real number system correctly describe all numbers in the set shown?

a)

Rational

b)

Irational

c)

Integers

d)

Whole

e)

Natural

91.

Which pair of numbers are both between 4 and 5 on the number line?

a)

√15 and √25

b)

√14 and √23

c)

√8 and √10

d)

√17 and √24

92.

Which set of real numbers below does not contain a rational number?

a)

A

b)

B

c)

C

d)

D

93.

The sum/product of two rational numbers is

a)

rational

b)

irrational

94.

The sum/product of pi and an integer would be

a)

a rational number

b)

an irrational number

95.

The sum/product of two irrational numbers is

a)

rational

b)

irrational

96.

Evaluate the expression if x = 3 and y = -4.

|3x - 5| + y

a)

0

b)

3

c)

-3

d)

8

97.

Evaluate the expression if x = -5.

|-2x - 12|

a)

2

b)

-2

c)

22

d)

-22

98.

-|9| + |-5|

a)

-14

b)

14

c)

-4

d)

4

99.

What approximation is the most reasonable for the following: $\sqrt[]{126}$

a)

11.1 or 11.2

b)

11.4 or 11.5

c)

11.6 or 11.7

d)

11.8 or 11.9

100.

19² = (a)

101.

√196 = ______

a)

14

b)

14²

c)

15

d)

15²

102.

a)

9

b)

3

c)

1/3

d)

1

103.

Order the following numbers from smallest to largest: $-3, 0, \frac{1}{2}, -\frac{1}{4}$

a)

$-3, -\frac{1}{4}, 0, \frac{1}{2}$

b)

$-3, 0, -\frac{1}{4}, \frac{1}{2}$

c)

$-\frac{1}{4}, -3, 0, \frac{1}{2}$

d)

$-3, -\frac{1}{4}, \frac{1}{2}, 0$

104.

Between which two whole numbers is the
√5?

a)

1 and 2

b)

2 and 3

c)

3 and 4

d)

4 and 5

105.

Which of the following numbers is irrational?

a)

√8

b)

¾

c)

2

d)

-1.325

8 HW 15

Total questions: 105

Worksheet time: 7hrs 50mins

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