Free Printable 8th Grade Math Year Review

1.

Find the slope of the line.

a)

-2

b)

2

c)

-1

d)

1

2.

Find the slope of the line that passes through the points (2, 4) and (6, 12)

a)

1/2

b)

-1/2

c)

2

d)

-2

3.

Find the slope of the line.

a)

Undefined

b)

0

c)

1

d)

-1

4.

Find the slope of the line.

a)

1/2

b)

-1/2

c)

2/1

d)

-2/1

5.

Find the slope

a)

-5/3

b)

-3/5

c)

5/3

d)

3/5

6.

Which expression is equivalent to

\left(6^3\right)^{-4}

?

a)

$\frac{1}{6^{12}}$

b)

$\frac{1}{6}$

c)

$6^{-1}$

d)

$6^{12}$

7.

Which of these would be equivalent to

7^3\times7\times7^{-2}

?

a)

$\frac{1}{7}$

b)

$\frac{1}{7\times7}$

c)

$7\times7$

d)

$\frac{1}{7\times7\times7\times7\times7\times7}$

8.

Simplify:

\left(-7.647\right)^0

a)

-7.647

b)

0

c)

7.647

d)

1

9.

Pluto has a volume of

10^{10}\

cubic kilometers. Saturn has a volume of

10^{15}

cubic kilometers. How many times larger is Saturn than Pluto?

a)

$10^{150}$ times

b)

$5$ times

c)

$10^{25}$ times

d)

$10^5$ times

10.

Simplify. Your answer should contain only positive exponents.

$\frac{4x^2y^4}{6xy}$

a)

$\frac{2xy^3}{3}$

b)

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

c)

$\frac{3xy}{2}$

11.

Simplify. Your answer should contain only positive exponents.

$3\left(x^2+y\right)^0$

(a)

12.

Simplify. Your answer should contain only positive exponents.

$\left(6b^4c^2\right)^2$

a)

$6b^8c^4$

b)

$36b^4c^2$

c)

$6^2b^2c$

d)

$6^2b^8c^4$

13.

Write the equation in slope intercept form of a line that passes through the given pair of points: (-2, -3), (4, 3)

a)

y =x + 1

b)

y = x - 1

c)

y = -x + 1

d)

y = -x - 1

14.

Write the equation of the line.

a)

y=(3/5)x+1

b)

y=(3/5)x-1

c)

y=(5/3)x+1

d)

y=(3/5)x+1

15.

Determine the slope and y-intercept. y = 3/2x + 3

a)

slope: 5 y-intercept: (0,3)

b)

slope: 3/2 y-intercept: (0,3)

c)

slope: 4 y-intercept: (0,3/2)

d)

slope: 1/5 y-intercept: (0,5)

16.

Graph the line with the equation
$x\ =\ -3$

a)

b)

c)

d)

17.

Graph the line with the equation
$y\ =\ -\frac{2}{3}x\ +\ 4$

a)

b)

c)

d)

18.

Write the equation of the graph in slope-intercept form

a)

$y=-2x-4$

b)

$y=2x\ -\ 4$

c)

$y=\frac{1}{2}x-4$

d)

$y=-\frac{1}{2}x-4$

19.

Determine the missing value in the table.

a)

15

b)

3

c)

1/3

d)

9

20.

Is this table proportional?

a)

Yes

b)

No

21.

Does the graph show a proportional relationship?

a)

Yes

b)

No

22.

Which is the best explanation of why this graph shows a non-proportional relationship?

a)

The line is not straight.

b)

The line does not touch the origin.

c)

The line is at the wrong angle.

d)

The graph shows a proportional relationship.

23.

Which graph is a nonproportional relationship?

a)

b)

c)

d)

24.

Name the correlation in this graph

a)

Positive correlation

b)

Negative correlation

c)

No correlation

d)

Lots of correlation

25.

Name the correlation in this graph

a)

Negative correlation

b)

No correlation

c)

Lots of correlation

d)

Positive correlation

26.

As the age of the car increases, its value decreases. Which scatterplot represents this relationship?

a)

A

b)

B

c)

C

d)

D

27.

What type of relationship does this scatter plot show?

a)

Positive

b)

Negative

c)

No Relationship

d)

Constant

28.

What are the coordinates of the outlier?

a)

(1,9)

b)

(9,1)

c)

(2,2)

d)

y=x

29.

What is the equation of the line of best fit

a)

y= -2x + 10

b)

y= 10x+ 2

c)

y=2x+10

d)

y= 10

30.

What is the equation of the line of best fit?

a)

y= 2x+3

b)

y=3x+2

c)

y= $\frac{1}{2}x\ +3$

d)

y= $-\frac{1}{2}x\ +3$

31.

A can of chili has a radius of 5.25 cm and a height of 13 cm. Find the volume.

a)

1152.67 cubic cm

b)

1125.67 cubic cm

c)

281.48 cubic cm

d)

255.25 cubic cm

32.

Find the volume to the nearest whole number using 3.14 instead of Pi.

a)

151 ft³

b)

152 ft³

c)

150 ft³

d)

150.72 ft³

33.

A can of chili has a radius of 5.25 cm and a height of 13 cm. Find the volume.

a)

1152.67 cubic cm

b)

1125.67 cubic cm

c)

281.48 cubic cm

d)

255.25 cubic cm

34.

Find the volume to the nearest hundredth using 3.14 instead of Pi.

a)

5572.45 cm³

b)

506.59 cm³

c)

126.65 cm³

d)

1393.11 cm³

35.

You have a globe that has a radius of 11 inches. Find the volume of your globe.

a)

523 in³

b)

16,717 in³

c)

5,575 in³

d)

7,235 in³

36.

Volume = ?

a)

1,356 m³

b)

1,734 m³

c)

377 m³

d)

590 m³

37.

Russell is filling a cylinder-shaped swimming pool that has a diameter of 20 feet. He fills it with water to a depth of 3 feet. What is the volume of the water in the pool, to the nearest cubic foot?

a)

377 cubic feet

b)

942 cubic feet

c)

2,958 cubic feet

d)

3,768 cubic feet

38.

What is the radius of a sphere that has a volume of 17,157.3cm³ ?

a)

24cm

b)

16cm

c)

64cm

d)

34cm

39.

What is the radius of a cone that has a volume of 2375 in³ and a height of 7 inches?

a)

12in

b)

22in

c)

28in

d)

18in

40.

Find the length of the missing side.

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

41.

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

42.

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

43.

What is the longest side of a right triangle called?

a)

Leg A

b)

Leg B

c)

Hypotenuse

d)

Pythagoras' Big Buddy

44.

Determine if the following set of numbers are Pythagorean Triples.
15, 20, 25

a)

Yes

b)

No

45.

a² + b² = c^{2
b = 35 c = 37}

a)

a = 12

b)

a = 11

c)

a = 18

d)

a = 14

46.

solve for y

a)

7

b)

6.3

c)

2.5

d)

9

47.

An airplane flies 56 miles due north and then 33 miles due east. How many miles is the plane from its starting point?

a)

65 miles

b)

89 miles

c)

45.4 miles

d)

We don't have enough information.

48.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

a)

25 feet

b)

26 feet

c)

27 feet

d)

28 feet

49.

Are these triangles congruent, similar, both, or neither?

a)

Similar

b)

Congruent

c)

Both

d)

Neither

50.

Which transformation(s) create(s) similar figures?

a)

Dilation

b)

Translation, Reflection, and Rotation

c)

Translation and Reflection

d)

Reflection and Rotation

51.

Are these triangles similar?

a)

Yes

b)

No, they are congruent

c)

There is not enough information to determine this

d)

No, they are not similar nor congruent

52.

Triangle ABC is going to be translated. How is ABC being translated if the rule (x,y) --> (x+3, y-2) is used?

a)

3 up and 2 left

b)

3 right and 2 down

c)

3 left and 2 up

d)

3 right and 2 up

53.

Which answer represents a reflection across the x-axis, using the algebraic rule (x,y) --> (x, -y)?

a)

d

b)

c

c)

b

d)

a

54.

Identify the transformation from ABC to A'B'C'.

a)

90^o clockwise rotation

b)

90^o counter clockwise rotation

c)

Reflection across the y-axis

d)

Reflection across the x-axis

55.

Identify the transformation from ABCD to A'B'C'D'.

a)

Translation

b)

Reflection across the x-axis

c)

Reflection across the y-axis

d)

90^o counter clockwise rotation

56.

How is triangle ABC being translated to triangle A'B'C'?

a)

(x, y) --> (x - 8, y + 3 )

b)

(x, y) -->(x - 4, y - 9)

c)

(x, y) --> (x + 8, y - 3)

d)

(x, y) --> (x+ 4, y - 9)

57.

Determine where T' would be if you translated T three units to the right and six units up.

a)

(5, 1)

b)

(2, -5)

c)

(-1, 1)

d)

(8, -2)

58.

You plan to go snowboarding. The resort charges $15 an hour in addition to $25 to rent a board. Write an equation that represents the cost to go snowboarding for the day.

a)

y=15x-25

b)

15x+25y=100

c)

25x+y=15

d)

y=15x+25

59.

A dog walker earns $10 plus $3 per dog. What equation represents this model?

a)

y=3x + 10

b)

y=10x + 3

c)

y=13x

d)

y=10x - 3

60.

Is the following equation proportional or non proportional:
y= 4x

a)

Proportional

b)

Non Proportional

61.

Is the following equation proportional or non proportional:
y= 4x - 5

a)

Proportional

b)

Non Proportional

62.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(0, 1)

63.

If a system of equations has no solution, what does the graph look like?

a)

intersecting lines

b)

parallel lines

c)

skew lines

d)

intersecting lines

64.

There are 50 donkeys and chickens on a far. There are a total of 174 legs. Which system below can be used to figure out how many of each animal the farm has?

a)

d + c = 174
4d + 2c = 50

b)

d + c = 50
4d + 2c = 174

c)

d + c = 50
2d + 4c = 174

d)

d + c = 174
2d + 4c = 50

65.

Solve for x and y
3x + 2y = 16
7x + y = 19

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

66.

This system has _____ solutions

a)

0

b)

1

c)

2

d)

Infinitely many

67.

If a system of linear equations has one solution, what does this mean about the two lines?

a)

Parallel lines

b)

the same line

c)

Intersecting lines

68.

Solve the following system of equations using the elimination method:

a)

(-2, 1)

b)

no solutions

c)

(-2, 0)

d)

(-1, -3)

69.

Solve the following system of equations using the elimination method.

a)

infinite solutions

b)

(0, -2)

c)

no solutions

d)

(0, 2)

70.

Solve the system of equations by substitution.
y = -4x + 5
y = 3x - 16

a)

(-3, -25)

b)

(3,-7)

c)

(11, 17)

d)

(21, 47)

71.

8v - 4(v + 8) = 8

a)

2

b)

10

c)

4

d)

-4

72.

2x - 3 + 4x = 27

a)

12

b)

4

c)

5

d)

15

73.

3x + 2(4x - 4) = 3

a)

4

b)

3

c)

2

d)

1

74.

2x + 3(5x - 7) = 47

a)

1

b)

2

c)

3

d)

4

75.

4x + 10 = -26

a)

4

b)

-4

c)

-9

d)

9

76.

What is the solution?

a)

x = 4

b)

x = 6

c)

x = 96

d)

x = 144

77.

Solve for x.

a)

55

b)

60

c)

15

d)

35

78.

.141414141414...

a)

Rational

b)

Irrational

79.

pi - 3.141592....

a)

Rational

b)

Irrational

80.

√2

a)

Rational

b)

Irrational

81.

√7

a)

Rational

b)

Irrational

82.

√25

a)

Rational

b)

Irrational

83.

-√4

a)

rational
irrational

b)

rational

84.

a)

D, C, A, B

b)

D, A, B, C

c)

D, B, C, A

d)

A, C, B, D

85.

What is the exponent form for the factors
5 x 5 x 5?

a)

3⁵

b)

5³

86.

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

87.

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

88.

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

89.

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

90.

Divide:
(6.9 x 10⁷) / (2.3 x 10^-3)

a)

3 x 10¹⁰

b)

3 x 10⁴

c)

3 x 10^-4

d)

3 x 10^-11

91.

Multiply:
(9.4 x 10⁶)(3.2 x 10⁵)

a)

30.08 x 10¹¹

b)

3.8 x 10¹

c)

3.008 x 10¹²

d)

2.9375 x 10¹

92.

Multiply:
(3.4 x 10⁵)(1.2 x 10^-3)

a)

4.08 x 10^-8

b)

4.8 x 10²

c)

4.08 x 10²

d)

4.08 x 10^-15

93.

Which of the following is correct scientific notation?

a)

20.35 x 10⁴

b)

.2035 x 10⁴

c)

2035⁴

d)

2.035 x10⁴

94.

A bag contains 5 blue marbles, 4 red marbles, and 3 orange marbles. Mrs. Cox picks one without looking, replaces it and picks another one. What is the probability that she picks two that are not orange?

a)

9/16

b)

3/4

c)

9/144

d)

5/16

95.

In the game that Tony is playing, there is a 1/8 chance the spinner will land on red and a 3/8 chance that the spinner will land on yellow. What is the probability that Tony will NOT spin red, then will spin red?

a)

7/64

b)

7/16

c)

Other

96.

A number cube is rolled twice. What is the probability of getting a 6 on the first roll, then a number less than 5 on the second roll?

a)

2/3

b)

5/36

c)

1/9

d)

1/36

97.

Lucy has the spinner pictured and spins it twice in a row. What is the probability that she lands on blue first and then on yellow or green?

a)

1 / 16

b)

1 ⁄ 6

c)

1 ⁄ 8

d)

3 ⁄ 4

98.

When using a 6-sided number cube, what is the probability or rolling a 3, then not rolling a 3, and then rolling an even number?

a)

1/12

b)

1/2

c)

5/6

d)

5/72

99.

A chorus has 50 girls and 35 boys. If two are chosen at random to sing a duet, what is the probability that both will be boys? HINT: You can not have the same person twice in a duet

a)

1/6

b)

7/17

c)

3/8

d)

13/25

100.

A coin and a number cube with the numbers 1 through 6 are tossed. What is the probability of the coin showing tails and the number cube showing the number 3?

a)

1/12

b)

1/4

c)

1/8

d)

1/2

101.

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

102.

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

103.

Which is the best estimate for: √15

a)

5.6

b)

2.6

c)

3.9

d)

3.6

104.

Which is the best estimate for: √119

a)

10.9

b)

10.7

c)

11.1

d)

19

105.

Which is the best estimate for: √28

a)

5.6

b)

5.9

c)

5.3

d)

8

106.

Which number has a square root that is between 7 and 8?

a)

48

b)

81

c)

60

d)

36

107.

Which number is a perfect square?

a)

225

b)

132

c)

99

d)

110

8th Grade Math Year Review

Total questions: 107

Worksheet time: 6hrs 13mins

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