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8th Grade Math Milestones Review for Algebra Students

Total questions: 80

Worksheet time: 5hrs 20mins

Name
Class
Date
1.

Match the following

a)
1.

one solution

b)
2.

no solution

c)
3.

infinitely many solutions

2.

Solve the system by substitution

a)

(1,1)

b)

(-1,1)

c)

(-1,0)

d)

(1,-1)

3.

Solve the system by elimination

a)

(8,-3)

b)

(3,8)

c)

(16,3)

d)

(8,3)

4.

The system has ​ ​ (a)  

Choose from the below words
infinitely many solutions
no solutions
one solution
5.

The store sold ​ (a)   regular towels and ​ (b)   beach towels

Choose from the below words
33
9
51
50
2
10
6.

What distance do you need to run until you catch up to your opponent?

a)

144 meters

b)

256 meters

c)

(80, 144)

d)

80 seconds

7.

You record the heights of two plants each month for three months. In what month with Plant A be as tall as Plant B.

a)

Month 5

b)

Month 16

c)

Month 32

d)

Month 24

8.

I collect ​ (a)   coins and ​ (b)   stamps.

My friend collects ​ (c)   coins and ​ (d)   stamps.

Choose from the below words
25
45
5
90
30
40
3
92
9.

Match the following

a)

System of linear equations

1.

a set of two or more linear equations in the same variable

b)

solution of a system of linear equations

2.

point of intersection

c)

parallel lines

3.

lines that have the same slope but different y intercepts

d)

infinitely many solutions

4.

the lines are the same

e)

one solution

5.

lines that have different slopes

10.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

11.

What side(s) will always be the longest on a right triangle?

a)

The Hypotenuse

b)

Leg A

c)

Leg B

d)

The Right Angle

12.
The legs form what type of angle?
a)
Acute
b)
Obtuse
c)
Reflex
d)
Right
13.

What is the relationship between the sides in the Pythagorean Theorem shown?


Hint: Think about when the hypotenuse is missing!

a)

a + b = c

b)

a2 + b2 = c2

c)

a2 – b2 = c2

d)

a – b = c

14.
Do three squares with side lengths of 6, 12, and 13 form a right triangle?
a)
Yes
b)
No
15.
If three sides of a right triangle are 9, 40, and 41, which side is the hypotenuse?
a)
9
b)
40
c)
41
16.
Do the segment lengths 9, 12, and 15 form a right triangle?
a)
Yes
b)
No
17.
Do these 3 side lengths form a right triangle?
13, 80, and 81?
a)
yes
b)
no
18.

If the sides of a triangle are 7, 24, and 25, is it a right triangle?

a)
yes
b)
no
19.
a = 2.1, b = 7.2,
c = 7.5
Is this a right triangle?
a)
yes 
b)
no
20.
Isabella has sticks that are 10cm, 11cm, and 13cm long.  Can she place the sticks together to form a right triangle?  Justify your answer.
a)
No, because 10+11 does not equal 13
b)
No, because 100+121 does not equal 169
c)
Yes, because there is a small side, medium side and long side
d)
Yes, because a triangle has 3 sides
21.
Find the missing side
a)

9

b)

41

c)

6.4

d)

3

22.

Level 2

Solve for the value of y

a)

13

b)

5

c)

23

d)

10

23.

Find the missing side.

a)

18

b)

16

c)

17

d)

19

24.

Find the missing side.

25.

For the area of a triangle the formula is - 



A= 12bh\frac{1}{2}bh  , which of the following is the same as multiplying by  12\frac{1}{2}  ?

a)

multiplying by 2

b)

dividing by 2

26.

How would you write 4.3756 x 104 in standard form?

(a)  

27.

How would you write 4.3756 x 104 in standard form?

(a)  

28.

How would you write 0.0005 in scientific notation?

a)

50 x 10-5

b)

5 x 10-4

c)

5 x 103

d)

.5 x 103

29.

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

(a)  

30.

How do you write 8.317 x 106 in standard form?

(a)  

31.

Which of the following numbers is written in scientific notation?

a)

20.35 x 104

b)

.2035 x 104

c)

2035 4

d)

2.035 x104

32.

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

33.

Convert to scientific notation:


520,000,000

a)

52 x 107

b)

5.2 x 10-7

c)

5.2 x 108

d)

0.52 x 109

34.

What is scientific notation?

a)

A long way to write really short numbers

b)

A short way to write really large or really small numbers

c)

I don't know...

d)

None of the above

35.

If the exponent is a positive number the original number was...

a)

a really big number.

b)

a really small number.

36.

If the exponent is a negative number the original number was...

a)

a really large number.

b)

a really small number.

37.

Convert this number to standard notation:


7.1 x 104

(a)  

38.

Convert this number into scientific notation:


0.068

a)

6.9 x 106

b)

6.8 x 10-9

c)

6.8 x 10-2

d)

None of the above

39.

Convert this number to standard notation:


1.4 x 10-2

(a)  

40.

Convert this number into scientific notation:


950,000

a)

9.5 x 105

b)

9.5 x 10-9

c)

9.5 x 102

d)

None of the above

41.

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

42.

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)

5.0 x 108

43.
Is the red line a radius or diameter of the circle?
a)
Radius
b)
Diameter
44.
Is the red line a radius or diameter of the circle?
a)
Radius
b)
Diameter
45.
What is this formula used to find?
V=πr2h
a)
The volume of a cylinder
b)
The volume of a cone
c)
The volume of a sphere
d)
The area of a circle
46.
Find the volume of the cylinder.
a)
4239
b)
1696
c)
1130
d)
565
47.
Given a cylinder with the height of 10cm and the base radius of 9cm. Find the volume of this cylinder to the nearest tenth.  
a)
810 cm3
b)
2543.4 cm3
c)
847.8 cm3
d)
2826 cm3
48.
Find the volume of the figure. Round to the nearest tenth.
a)
128.6 units³
b)
1,286.1 units³
c)
401.9 units³
d)
5,144.6 units³
49.
Soda is sold in aluminum cans that measure 6 inches in height and 2 inches in diameter.  How many cubic inches of soda are contained in a full can?
a)
12.0
b)
24.0
c)
75.4
d)
18.8
50.
Find the volume of the cylinder. Round your answers to the nearest tenth if necessary. Use 3.14 for π.
a)
16.4 cm3
b)
31.7 cm3
c)
31.4 cm3
d)
22.0 cm3
51.
Find the volume of the right cylinder?
a)
6516 units3
b)
2276 units3
c)
1693 units3
d)
9923 units3
52.
Estimate the volume.
a)
163in3
b)
18in3
c)
283in3
d)
324in3
53.

Find the volume of the given sphere.

a)

418.7 cubic ft

b)

3,984.6 cubic ft

c)

4,188.8 cubic ft

d)

4,319.8 cubic ft

54.

Find the volume of the given sphere.

a)

3,817.9 cubic mm

b)

2,506.2 cubic mm

c)

2,000.8 cubic mm

d)

2,144.7 cubic mm

55.

Find the volume of the given sphere.

a)

904.8 cubic yd

b)

856.2 cubic yd

c)

994.5 cubic yd

d)

883.5 cubic yd

56.

Find the volume of the given sphere.

a)

1,563.5 cubic in.

b)

1,325.5 cubic in.

c)

1,129.9 cubic in.

d)

1,819.6 cubic in.

57.

Find the volume of the sphere.

a)

904.32 ft3

b)

7,234.56 ft3

c)

150.72 ft3

58.
When a sphere has a volume of 972π, what is the radius of the sphere?
a)
9
b)
7
c)
18
d)
21
59.
A sphere has the volume of 905 cm. What is the radius of the sphere rounded to the nearest whole number?
a)
6
b)
9
c)
3
d)
12
60.

A sphere has volume of   256π3 units3\frac{256\pi}{3}\ units^3 . What is the length of the DIAMETER? Hint: Determine the radius and use the relationship between radius and diameter to determine the diameter!  

a)

2 units 

b)

4 units 

c)

6 units 

d)

8 units

61.

Find the volume to the nearest tenth.

a)

5575.3 cm3

b)

506.8 cm3

c)

1774.7 cm3

d)

1393.11 cm3

62.

The radius of a basketball is 4.7 inches. What is the volume of the basketball?

a)

400.6 cubic in.

b)

398.8 cubic in.

c)

434.9 cubic in.

d)

500.3 cubic in.

63.

What is the formula for a sphere.

a)

V = πr2hV\ =\ \pi r^2h

b)

V= 13πr2V=\ \frac{1}{3}\pi r^2

c)

V = 43πr3V\ =\ \frac{4}{3}\pi r^3

d)

V = πr2V\ =\ \pi r^2

64.

Kayla has two spherical gazing balls in her yard.

(see picture). Which statement about their volumes is true?

a)

The volume of Ball 2 is twice the volume of Ball 1.

b)

The volume of Ball 1 is 8 times the volume of Ball 2.

c)

The volume of Ball 1 is twice the volume of Ball 2.

d)

The volume of Ball 2 is 8 times the volume of Ball 1.

65.

Find the radius of a sphere with a volume of  3,053.63 in3.3,053.63\ in^3.  Use 

a)

9 in.9\ in.  

b)

6.2 in.6.2\ in.  


c)

31.2 in.31.2\ in.  

d)

18 in.18\ in.  

66.

The volume of a sphere is  113.04 ft3113.04\ ft^3 .  Solve for the radius. Use 

a)

r=9 ftr=9\ ft  

b)

r=3 ftr=3\ ft  

c)

r=5.2 ftr=5.2\ ft  

d)

r=12 ftr=12\ ft  

67.

Which of the following has the greatest volume?

a)

a cube with a side length of 5cm and a height of 5cm

b)

a cone with a radius of 5cm and a height of 5cm

c)

a rectangular prism with a length of 5cm, a width of 5cm and a height of 5cm

d)

a sphere with a radius of 5cm

68.

A table tennis (ping-pong) ball has a volume of 33,510.3 cubic millimeters. What is the approximate length of the diameter of the table tennis ball? Use the  π\pi   button.

a)

49.4 mm

b)

24.7 mm

c)

40 mm

d)

20 mm

69.

 A sphere has volume of  288π cm3288\pi\ cm^3   .  What is the radius? Write an equation and solve, show your work on a sheet of paper!

a)

6 cm 

b)

2 cm 

c)

3 cm 

d)

12 cm

70.

 A sphere has volume of  27π cm327\pi\ cm^3   .  What is the radius? Write an equation and solve, show your work on a sheet of paper!

a)

6 cm 

b)

2 cm 

c)

3 cm 

d)

12 cm

71.

What is the formula for Volume of a Cone?

a)

V=π r3h

b)

V=π r2h

c)

V= 13\frac{1}{3} π r2r^2 h

d)

V= 43\frac{4}{3} π r3r^3

72.

Find the volume of the conical figure. Round to the nearest hundredth.

a)

14.13 in3

b)

56.55 in3

c)

169.65 in3

d)

113.10 in3

73.
a)
8.4 ft3
b)
100.5 ft3
c)
25 ft3
d)
16.8 ft3
74.

Find the volume of the figure.

a)

150.8 cm³

b)

48 cm³

c)

452.4 cm³

d)

339 cm³

75.
a)
42.4 in3
b)
169.6 in3
c)
56.5 in3
d)
14.13 in3
76.
a)

1,767 ft3

b)

7,068.5 ft3

c)

589 ft3

d)

2,356.2 ft3

77.

A styrofoam model of a volcano is in the shape of a cone. The model has a circular base with a diameter of 48 centimeters and a height of 12 centimeters. Find the volume of foam in the model to the nearest tenth.

a)

7,238.2 cm3

b)

28,952.9 cm3

c)

1,809.6 cm3

d)

21,714.7 cm3

78.

Mike has a large plastic cup that he is going to fill with water. The plastic cup is in the shape of a cone as shown. Which is closest to the volume of Mike’s cup?

a)

21 cubic inches

b)

63 cubic inches

c)

66 cubic inches

d)

198 cubic inches

79.
A cone has a height of 6 centimeters and a radius of 5 centimeters. What is the volume of this shape? Round to the nearest hundredth. 
a)
471.24
b)
565.49
c)
188.5
d)
157.08
80.

An ice cream cone that is 4 inches tall has a diameter that is 8 inches across. Find the volume of the cone.

a)

201.06 inches3

b)

67.02 inches3

c)

268.08 inches3

d)

50.27 inches3

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