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Worksheets8th Grade Math Review
Total questions: 220
Worksheet time: 9hrs 49mins
To which real number set do the following real numbers belong?
Irrational Numbers
Natural Numbers
Rational Numbers
Integers
We know that π (Pi) is approximately equal to 3.141592654... To which subset of the real numbers does π belong?
Irrational Numbers
Rational Numbers
Integers
Natural Numbers
Simplify the expression using exponents.
818
915
98
8115
Write the decimal as a fraction in simplest form
Using exponents, what is the simplified form of the expression (24)7
23
1428
228
211
Using exponents, what is the simplified form of this expression?
59
15
514
55
What is the value of 180?
18
0
1
-18
How do you write the standard number 0.00095 in scientific notation?
9.5 x 10-3
9.5 x 10-5
9.5 x 10-4
9.5 x 10-6
Write the standard number 6,267,000 in scientific notation.
62.67 x 106
6.267 x 106
6.267 x 104
6.267 x 107
How do you write 8.7 x 10-1 in standard form?
0.87
8.7
87
0.087
What is the best estimate for the following.
9.3432...
6.782...
8.2326...
10.7638...
This is between which two integers?
12 and 13
13 and 14
45 and 46
91 and 92
Which integer is a perfect square?
169
24
10
212
0 is a Natural Number.
True
False
Which of the following has the greatest value?
3.5 x 104
2.1 x 106
7.2 x 107
9.9 x 105
How many times larger is 5 x 107 than 5 x 102?
1 x 106
1 x 104
1 x 105
1 x 109
Which statement is correct?
All integers are rational numbers.
All irrational numbers are whole numbers
A real number must be a rational number.
A repeating decimal is an irrational number.
Which number is equivalent to 5-1?
According to exponent rules, when we raise the power to a power we _______ the exponents.
Example: (d2)5
add
subtract
multiply
divide
According to exponent rules, when we multiply two power with the same base we _______ the exponents.
Example: c6 ⋅ c4
add
subtract
multiply
divide
According to exponent rules, when we divide two powers with the same base we _______ the exponents.
Example: h8 / h3
add
subtract
multiply
divide
3³ ⋅ 3
34
33
30
1 ⁄ 34
Express the following in scientific notation:
.000457
457 x 106
457 x 10-6
4.57 x104
4.57 x 10-4
How would you write 564,000,000 in scientific notation?
5.64 x 10-7
5.64 x 106
5.64 x 108
56.4 x 107
Which of the following is correct scientific notation?
20.35 x 104
.2035 x 104
2035 4
2.035 x104
Divide:
(6.9 x 107) / (2.3 x 10-3)
3 x 1010
3 x 104
3 x 10-4
3 x 10-11
Which is the smallest?
1.3 x 1020
2.9 x 1021
9.5 x 1032
8.4 x 1019
1.3 x 1020
2.9 x 1021
9.5 x 1032
8.4 x 1019
What is the solution?
(1, -1)
(-1, 1)
(0, -2)
(0, 1)
Give the solution to the system.
(3,1)
(1,3)
(-1,3)
(1, -3)
Numbers like -3, -2, -1, 0, 1, 2, 3 are called
whole numbers
integers
rational numbers
natural numbers
0.8 is a rational number
True
False
In the Pythagorean Theorem, c is always the ____ number.
largest
smallest
middle
first
The formula V=(1/3)∏r2h is used to find the volume for ______.
A cube
A cylinder
A sphere
A cone
In the equation y=mx+b, m is the ____.
Slope
Y-intercept
X-intercept
Origin
Slope, in basic terms, is simply...
Rise over run
Run over rise
Left over down
Right over up
Function
Not a Function
The Pythagorean Theorem is _____.
a2+b2=c2
a2+c2=b2
b2+c2=a2
a2-b2=c2
At a home improvement store, customers can rent a small cargo truck to transport any large items they purchase. The store charges $20 as a rental fee plus $7.50 per hour to rent the truck. Which equation best represents the situation?
y=7.5x - 20
y=7.5x + 20
y=20x - 7.5
y=20x + 7.5
Nicolas places his 30 foot ladder against a house he is painting. If the foot of the ladder is 8 feet from the base of the house, how high above the ground is the top of the ladder touching the house? Round to the nearest tenth.
22.0 ft
27.8 ft
28.9 ft
31.0 ft
Which scatter plot shows a linear relationship between x and y?
Graph A
Graph B
Graph C
Graph D
Order the following from greatest to least:
0.35, ⅜, 42%, ⅘, 0.2
⅘, 42%, ⅜, 0.35, 0.2
⅜, 42%, ⅘, 0.2, 0.35
⅘, 0.35, ⅜, 42%, 0.2
0.2, 0.35, ⅜, 42% ⅘,
What type of slope does the following graph have?
Postive
Negative
Zero Slope
Undefined
Function
Not a Function
.
Function
Not a Function
.
Function
Not a Function
When you dilate, you ______ x and y by a number.
Multiply
Add
Subtract
Divide
What do you do to find the side length of a square?
Find the square Root
Divide by 4
Divide by 2
Nothing
What is the solution?
(1, -1)
(-1, 1)
(0, -2)
(0, 1)
Give the solution to the system.
(3,1)
(1,3)
(-1,3)
(1, -3)
Which way do you rotate if you turn to the right?
Clockwise
Counter-clockwise
upside down
flip-flop
Identify the transformation from ABCD to A'B'C'D'.
Translation
Reflection across the x-axis
Reflection across the y-axis
90o counter clockwise rotation
How is Quadrilateral EFGH translated to E'F'G'H'?
6 down
6 down, 1 right
6 down, 3 left
8 down, 1 right
What is the definition of function?
Has inputs and outputs
Every input has only ONE output
Inputs have different outputs every time
x-values and y-values
Josh is thinking of two numbers. Their sum is -10 and their difference is -2. Which system of equations represents the situation?
x - y = -10
x + y = -2
x = -2
y = 5
x + y = -2
x - y = -10
x + y = -10
x - y = -2
The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?
S + A = 530
3S + 4A = 1740
S + A = 530
4S + 3A = 1740
S + A = 1740
3S + 4A = 530
S + A = 1740
4S + 3A = 530
Y= -3x+4, which graph represents this equation
what is the square root of 81
18
9
62
41
find the approximate volume of the cylinder
24
302
75
4
Which graph does NOT illustrate a Function?
A
B
C
D
What is the value of the expression shown?
-1
7
71
79
What is the value of:
9
18
21
39
Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?
17 miles
32 miles
37 miles
40 miles
Identify the transformation from C to D.
90o Counter Clockwise Rotation
180o Rotation
270o Counter clockwise Rotation
360o Rotation
Enlargement or reduction? Find the scale factor!
It's a reduction; the scale factor is 2.
It's an enlargement; the scale factor is 2.
It's an enlargement; the scale factor is 1/2.
It's a reduction; the scale factor is 1/2.
x - 8 = -5
13
-13
3
-3
Which line has the equation
y = 2x + 1
Which line has the equation
y = x + 2
Identify the slope and y -intercept in the equation:
y = 2x - 2
y = -2x + 2
y = -2x + 4
y = 2x + 4
Which is the equation of the line with y-intercept -2 and slope 6.
y = -2x + 6
y = 3x
y = -2x - 6
y = 6x - 2
What is the equation of this line?
x=5
y=5
y=5x
x=-5
-4(8r + 3)
-32r - 12
32r - 12
-32r + 12
32r + 12
-30x+15
30x-15
30x+15
-30x+15
Which statement describes the relationship between the data sets displayed on the scatterplot?
The number of pets owned by a student increases as the student’s science test score increases.
The number of pets owned by a student decreases as the student’s science test score increases.
The number of pets owned by a student remains the same as the student’s science test score increases.
There is no relationship between the number of pets owned by a student and the student’s science test score.
Which statement is true about the scatter plots?
Graph 1 shows a strong relationship, and Graph 2 shows a weak relationship.
Graph 2 shows a strong relationship, and Graph 1 shows a weak relationship
Graph 1 shows a negative correlation, and Graph 2 shows a positive correlation.
Graph 2 shows a negative correlation, and Graph 1 shows a positive correlation.
The scatterplot below suggests which of the following types of data relationship?
Weak, negative
weak, positive
strong, negative
strong, positive
What percentage of girls have blonde hair?
30%
32%
29%
40%
According to the two-way table, a person who plays an instrument is most likely to:
Not play an instrument
Not play a team sport
Play a team sport
All of the above
What percentage of the students have brown hair?
25%
60%
45%
50%
A survey explored the relationship between gender and band class. Which is a reasonable conclusion?
There are more band members than non-band members
There are more boys in the class than girls
There are more boys in band than not in band
More than half of the bands members in the class are girls
Solve for the variable x in the following equation:
3x=12
x=9
x=3
x=15
x=4
Solve for the variable x in the following equation:
x−1.7=2.5
x=0.8
x=1.2
x=4.2
x=3.2
Solve for the variable the variable H in the formula:
V=LWH
(Formula for the volume of a prism)
H=V−LW
H=VLW
H=VLW
H=LWV
Erik took out a loan for $8400 for 6 years at a compound interest rate of 5.5%. How much interest does Erik owe from the loan?
$2,772
$11,582.28
$3,182.28
$108,084.86
Which rule would dilate shows a scale factor of 4?
(x, y) → (y, x)
(x, y) → (x + 4, y + 4)
(x, y) → (x, -y)
(x, y) → (4x, 4y)
Which of the following sentences would belong in the proof that describes this image?
The sum of the areas of the two smaller squares is equal to the area of the large square.
The sum of the side lengths of the two smaller squares is equal to the side length of the large square.
The difference of the areas of the two smaller squares is equal to the area of the large square.
The differences of the side lengths of the two smaller squares is equal to the side length of the large square.
What is the y-intercept?
0.25
4.5
5
4
What is the y-intercept?
7
5/2
3
-4
What is the y-intercept?
-34
-24
0
-3
What is the slope?
-1/3
-3
-4
5
What is the slope of the table?
-2/1
-1/2
2/1
1/2
What is the slope of the table?
-2/5
5/-2
5/2
2/5
What are vertical angles?
Angles that are adjacent to each other
Angles that add up to 180°
Angles that are opposite of each other when lines intersect
Angles that add up to 90°
Solve for x.
71
-3
35
-19
Find the value of x.
A
B
C
D
Slope is ________.
Positive
Negative
Zero
Undefined
Slope is ________.
Positive
Negative
Zero
Undefined
The image shows what type of transformation
Rotation
Translation
Reflection
Which rule would result in a translation of 2 units left and 3 units up?
(x, y) → (2x, 3y)
(x, y) → (x - 2, y + 3)
(x, y) → (-x, -y)
(x, y) → (x + 2, y - 3)
Solve the equation for x:
8x + 2 - 5x = 32
x = 8
x = 9
x = 10
x = 11
What type of slope does the graph have?
Positive
Negative
Zero Slope
Undefined
What would be the best first step to solving the equation?
-3=x+5
add 3 to both sides
subtract 5 from both sides
add 5 to both sides
subtract -5 from both sides
What would be the best first step to solving the equation?
multiply both sides by 3
multiply both sides by 4
divide both sides by 3
divide both sides by 4
What would be the best first step to solving the equation?
-6x=-24
multiply both sides by -6
divide both sides by -6
add 6 to both sides
subtract -6 from both sides
What would be the best first step to solving the equation?
multiply both sides by 10
divide both sides by 10
multiply both sides by 5
divide both sides by 5
What would be the best first step to solving the equation in one step?
multiply both sides by 3/2
divide both sides by 3
multiply both sides by 3
subtract 2/3 from both sides
Solve the equation:
20.5 = x + 4
16.5
16.05
24.5
24.05
Solve the equation:
0 = 4h
h = 4
g = 1
g = -4
g = 0
Solve the following equation
X + 8 = 15
23
-7
7
-23
Solve the following equation
8 = m - 12
4
0.5
5.0
20
3 = c -1
3
4
-3
2
Solve the following equation
14m = 28
2
14
32
1/2
3c + 5 = 23
c = 3
c = 6
c = 7
c = 18
Solve 2x - 3 = 1
3
2
1
-2
2x + 6 = 12
(a)
x - 10 = 3
(a)
Solve for x:
x = 20
x = 7
x = 10
x = 3
Solve the following equation
4−b=8
(a)
Solve the following equation
15 - 8g = 39
(a)
Solve the following equation
c / 4 = 4
(a)
Solve the following equation
18 = 3b
15
6
21
54
1/2
1/10
1/100
1/9
3/10
1/3
1/9
30/99
7/50
14/9
7/45
14/99
2 23/100
2 23/10
2 23/9
2 23/99
77/25
77/250
308/9
308/999
Identify the fraction equivalent to the decimal below.
2 4/99
2 4/9
2 2/5
2 4/10
2/3
-2/3
3/5
-3/5
What is 92 as a decimal?
0.29292
0.2
0.222...
0.29
Rewrite 6/11 as a decimal
0.05454...
5.45454...
0.545454...
1.83333...
Which of the following is a repeating decimal?
2.451836248702165064513549452
7.1245454545...
8.125
12.55
What is 23/99 as a decimal?
0.23
0.222222222222
0.2323232323.....
0.3232323232.......
7/9 is an example of a(n):
Repeating decimal
Rational number
Integer
Terminating decimal
What is the solution?
(1, -1)
(-1, 1)
(0, -2)
(0, 1)
Give the solution to the system.
(3,1)
(1,3)
(-1,3)
(1, -3)
Is this a function?
Function
Not a Function
How many solutions will this system have?
No solution
One Solution
I Don't Know
Infinitely Many Solutions
When you graph the exact same equation twice,
you will have no solution.
you will have one solution.
you will have infinite solutions.
you will graph a giraffe.
When you translate, (x-4,y) will move _____.
4 units right
4 units left
4 units up
4 units down
When you translate, (x+2,y) will move _____.
2 units right
2 units left
2 units up
2 units down
The vertical axis is the _____.
X-axis
Y-axis
Origin
Slope
-30x+15
30x-15
30x+15
-30x+15
-4(8r + 3)
-32r - 12
32r - 12
-32r + 12
32r + 12
What is the equation of this line?
x=5
y=5
y=5x
x=-5
Which is the equation of the line with y-intercept -2 and slope 6.
y = -2x + 6
y = 3x
y = -2x - 6
y = 6x - 2
Which line has the equation
y = x + 2
Simplify: 3x3 ⋅ 3x
32x4
3 ⋅ x ⋅ x ⋅ x ⋅3 ⋅ x
9x4
3x4
Simplify: (6x2)(-3x5)
18x7
-18x7
18x7
3x7
Evaluate using the quotient rule:
a8b13
a2b7
a15b30
Is this a function?
Function
Not a Function
Is this table a function?
Function
Not a Function
What is the definition of function?
Has inputs and outputs
Every input has only ONE output
Inputs have different outputs every time
x-values and y-values
Which set of values is a function?
(9,5) (10,5) (9,-5) (10,-5)
(3,4) (4,-3) (7,4) (3, 8)
(6,-5) (7, -3) (8, -1) (9, 1)
(2, -2) (5, 9) (5, -7) (1, 4)
Which set of values is a function?
(9,5) (10,5) (9,-5) (10,-5)
(3,4) (4,-3) (7,4) (3, 8)
(6,-5) (7, -3) (8, -1) (9, 1)
(2, -2) (5, 9) (5, -7) (1, 4)
Is this set of ordered pairs a function or not a function?
Function
Not a Function
Which two functions have a graph that is a line?
y = 3/x + 2
y = 2x2– 9x
y = –3x
y = 2x – 9
y = –6x/7
Select all of the following equations which define linear functions.
y = 3/5
y = x2 – 7
y = 6 – 5x
y = 9x
y = 4/x + 1
Which sets of ordered pairs are functions?
Choose all that apply.
(9, -1), (8, -2), (7, -3), (6, -4)
(5, -1), (5, -2,), (5,12), (5, 0)
(4, 2), (-4, 2), (2, 4), (-2, -4)
(1, -4), (2, -4,), (3, -4), (4, -4)
(5, 8), (4, 9), (5, 9), (4, 8)
Dave owns a lawn business. He charges $10 per hour and a $25 dollar disposal fee. What is the correct equation Dave would use to find out how much to charge his customers?
y = 25x + 10
x = 25y + 10
y = 10x +25
x = 10y + 25
Who has the greater rate of change?
Hunter has the greater rate of change.
Casey has the greater rate of change
They have the same rate of change
Who has the greater rate of change?
Tyler has the greater rate of change with 2/3
Aubri has the greater rate of change with 3/2
Tyler has the greater rate of change with 3/2
They have the same rate of change.
What's the initial value of the equation y = 2x + 4
4
-4
2
2x
What are the rate of change and initial value?
Rate of Change = 3 Initial Value = 8
Rate of Change = 1/3 Initial Value = 8
Rate of Change = 8 Initial Value = 3
Rate of Change = 8 Initial Value = 1/3
Function
Not a Function
Is this graph a function or not a function?
Function
Not a Function
Is this graph a function or not a function?
Function
Not a Function
Simplify the expression:
(58) ÷ (52)
56
510
54
516
Simplify the expression in exponential form:
(54)3
Hint: Expand it out
51
57
512
Simplify the expression in exponential form:
1340
0
134
1
Simplify (c5)(c2)(c2)
c20
c9
c11
3c45
(6x2)(-3x5)
18x7
-18x7
18x7
3x7
Simplify the expression.
214 z13
22/z7
214/ z7
22 z7
Simplify the expression.
214 z13
22/z7
214/ z7
22 z7
a8b13
a2b7
a15b30
If (2x)5=215, what does x equal?
x = 3
x = 5
x = 10
Simplify:
(5ab2)2
25a2b4
10a2b4
5a2b4
25ab2
CHALLENGE:
3x3y * 2x8y5
5x11y6
6x11y6
6x24y5
3x112y5
Simplify:
(5ab2)2
25a2b4
10a2b4
5a2b4
25ab2
Simplify (7x4)(9x3)
16x12
79 x12
63x4+3 = 63x7
63x12 noooo oh nooooo
Simplify
(2a2b4z)(6a3b2z5)
8a5b6z6
12a6b8z5
12a5b6z6
8a6b8z5
Simplify (2x4y7)3
6x7y10
6xy32
8x12y21
6xy21
How many solutions does the equation have
6x + 3 = 6x + 3
One Solution
No Solution
Infinite Solutions
How many solutions does the equation have
4p + 1 = 49 - 7
One Solution
No Solution
Infinite Solutions
How many solutions does the equation have
3t + 5 = 4t + 7
One Solution
No Solution
Infinite Solutions
How many solutions does the equation have
-2 ( -4x + 7 ) = -2 + 4x
One Solution
No Solution
Infinite Solutions
How many solutions does the equation have
3x + 7 + 2x = 5x + 7
One Solution
No Solution
Infinite Solutions
How many solutions does the equation have
3c -3 = 4c - 2
One Solution
No Solution
Infinite Solutions
How many solutions does the equation have
4y + 10 = 10 + 4y
One Solution
No Solution
Infinite Solutions
The goal of solving a one, two, or multi-step equations is to:
Find the value of the variable
Find the constant
Be confused
Find the coefficient
What is the solution to this equation?
one solution
no solution
infinite solutions
none of these
What is the definition of one solution?
no matter what constant is substituted in for the variable, the equation is ALWAYS true
no matter what constant is substituted in for the variable, the equation will NEVER be true
only this ONE solution will make the equation true
What is the definition of no solution?
no matter what constant is substituted in for the variable, the equation is ALWAYS true
no matter what constant is substituted in for the variable, the equation will NEVER be true
only this ONE solution will make the equation true
What is the definition of infinite solutions?
no matter what constant is substituted in for the variable, the equation is ALWAYS true
no matter what constant is substituted in for the variable, the equation will NEVER be true
only this ONE solution will make the equation true
What is the solution to the equations?
one solution
no solution
infinite solutions
none of these
How many solutions would this system of equations have?
No Solution
One Solution
Infinite Solutions
How many solutions would this system of equations have?
No Solution
One Solution
Infinite Solutions
How many solutions would this system of equations have?
No Solution
One Solution
Infinite Solutions
How many solutions would this system of equations have?
No Solution
One Solution
Infinite Solutions
How many solutions would this system of equations have?
No Solution
One Solution
Infinite Solutions
How many solutions will this system have?
No solution
One Solution
I Don't Know
Infinitely Many Solutions
Intersecting lines have how many solutions?
One solution
No solutions
Infinite solutions
4d + 2c = 50
4d + 2c = 174
2d + 4c = 174
2d + 4c = 50
3x + 2y = 16
7x + y = 19
y = -4x + 5
y = 3x - 16
x-2y=1
x+4y=7
3x - y = 7
2x + y = 3
y=-4x
y = 2x + 1
y = 4x - 1
3x - y = 7
2x + y = 3
y = 2/3x - 2
y = -x + 3
y = 2x + 1
y = 4x - 1
y = -3x - 4
y = 4x + 1
y = 8
y = 2x + 1
y = 4x - 1
Is (1,10) a solution to
y=7x+5
y=x+9
yes
no
Is (1,7) a solution for
y=3x+4
y=x+6
yes
no
HOW is a coordinate pair ordered?
(big number, small number)
(small number, big number)
(y, x)
(x, y)
y=8x+1
y=6x+3
Solve y=-x+4 and y=2x+4
(0,4)
(2,4)
(-1,3)
(4,0)
