Font size
S
M
L
XL
WorksheetsAlgebra SOL Review
Total questions: 150
Worksheet time: 13hrs 30mins
Name
Class
Date
1.
The quotient of a 15 and a number plus 1
a)
15 / g - 1
b)
15 / g + 1
c)
g / 15 + 1
d)
g + 1 / 15
2.
What is the difference between an expression and equation?
a)
Expressions have an equal sign and equations do not have an equal sign
b)
Expressions do not have an equal sign and equations do have an equal sign
c)
There is not a difference
d)
Expressions do not have variables and equations have variables
3.
Translate this phrase into an algebraic expression.
8 less than the product of 4 and a number
Use the variable m to represent the unknown number.
8 less than the product of 4 and a number
Use the variable m to represent the unknown number.
a)
8 - 4m
b)
8m - 4
c)
8m + 4
d)
4m - 8
4.
Write an algebraic expression for:
three times a number plus 16
three times a number plus 16
a)
3(16)+n
b)
16n+3
c)
3n+16
5.
Translate the sentence into an equation.
Seven subtracted from n is 18
Seven subtracted from n is 18
a)
n + 7 = 18
b)
7 - n = 18
c)
n - 7 = 18
d)
n + 7 = 18n
6.
Translate the sentence into an equation:
Four more than six times a number is 18.
Four more than six times a number is 18.
a)
4 + 6x = 18
b)
4x + 6 = 18
c)
6x + 4 = 18
d)
not enough info
7.
How would you translate
x - 5 = 12 into words?
x - 5 = 12 into words?
a)
x - 5 = 12
b)
The product of x and 5 is twelve
c)
x less than 5 is 12
d)
Five less than x is 12.
8.
Translate: Six fewer than twice a number is four.
a)
6 - 2x = 4
b)
2x - 6 = 4
c)
x2 - 6 = 4
d)
6 - x2 = 4
9.
Five times Mike's age, increased by nine
a)
5(x+9)
b)
9(5+x)
c)
9x+5
d)
5x+9
10.
Evaluate expression: 5a + b for a= 6 and b= 3
a)
33
b)
36
c)
30
d)
59
11.
Translate the statement into an equation:
10 more than twice a number is 18
10 more than twice a number is 18
a)
2n + 10 = 18
b)
10n + 2 = 18
12.
the quotient of 4 and a number increased by 10.
a)
4 - n + 10
b)
4n - 10
c)
4n + 10
d)
4 / n + 10
13.
Translate the sentence into an inequality.
Seven subtracted from n is greater than or equal to 18.
Seven subtracted from n is greater than or equal to 18.
a)
n - 7 > 18
b)
7 - n ≥ 18
c)
n - 7 ≥ 18
d)
n + 7 ≥ 18
14.
Write an inequality for the following statement.
n is less than 9
n is less than 9
a)
n < 9
b)
n > 9
c)
n ≤ 9
d)
n ≥ 9
15.
Translate this sentence into an equation.
72 is the product of 8 and a Steve's age.
Use the variable h to represent Steve's age.
72 is the product of 8 and a Steve's age.
Use the variable h to represent Steve's age.
a)
72 = 8 + h
b)
72 = 8h
c)
72 = 8 - h
d)
72 = 8/h
16.
m - 5 > 10
a)
m is less than 15
b)
m is greater than 5
c)
m is greater than 15
d)
m is less than 5
17.
Which phrase represents the following expression:
6x – 1
a)
The quotient of 6 and x minus 1.
b)
6 times x increased by 1.
c)
1 less than 6 times x.
d)
1 minus 6 multiplied by x.
18.
Write an inequality for the following statement.
n is less than 9
n is less than 9
a)
n < 9
b)
n > 9
c)
n ≤ 9
d)
n ≥ 9
19.
Translate the sentence into an inequality.
Seven subtracted from n is greater than or equal to 18.
Seven subtracted from n is greater than or equal to 18.
a)
n - 7 > 18
b)
7 - n ≥ 18
c)
n - 7 ≥ 18
d)
n + 7 ≥ 18
20.
The maximum score on the pilot's test is 95 points.
a)
p < 95
b)
p > 95
c)
p ≥ 95
d)
p ≤ 95
21.
Which sentence represents m > 41?
a)
Mary’s points, m, totaled more than 41
b)
Calvin ran no less than 41 miles, m
c)
The temperature, m, was less than 41°F
d)
The magazines’ cost, m, was not more than $41.
22.
a)
less than
b)
greater than
c)
less than or equal to
d)
greater than or equal to
23.
a)
less than
b)
greater than
c)
less than or equal to
d)
greater than or equal to
24.
You downloaded a video game to your computer. You have a 60 minute free trial of the game. It takes 5 minutes to set up the game and 7 minutes to play each level. Write an inequality to show how many levels you can play. DO NOT SOLVE
a)
5x-7 ≥ 60
b)
7x+5 ≤ 60
c)
7+5 ≤ 60x
d)
7x-5 ≥ 60
25.
Melissa wants to spend no more than $300 on school clothes. She spends $75 on a coat and then wants to buy some sweaters that are on special for $10 each. Write an inequality to show how many sweaters Melissa can buy. DO NOT SOLVE
a)
75x-10 ≥ 300
b)
75+10 ≤ 300x
c)
10x ≥ 300
d)
75+10x ≤ 300
26.
Translate this phrase into an algebraic expression.
the difference of 100 and the sum of 6 and w
the difference of 100 and the sum of 6 and w
a)
100 - 6 + w
b)
100 / (6 + w)
c)
100 - (6 + w)
d)
100 / 6 + w
27.
Translate this phrase into an algebraic expression.
35 multiplied by the quantity r less than 45
35 multiplied by the quantity r less than 45
a)
35(r - 45)
b)
35r - 45
c)
35(45 - r)
d)
45 - 35r
28.
Mike is 6 years younger than twice Iris's age. What expression can be used to find Mike’s age?
a)
6 + 2a
b)
6 - 2a
c)
2a - 6
d)
12 - a
29.
Simplify (-4r5)(2r8)
a)
-8r13
b)
-2r13
c)
-8r40
d)
-2y40
30.
Simplify
(-7y2)(5y4)
(-7y2)(5y4)
a)
-35y6
b)
-2y6
c)
-35y8
d)
-2y8
31.
a)
5-8
b)
52
c)
25-8
d)
252
32.
Evaluate this expression using the quotient rule.
a)
95
b)
99
c)
15
d)
9-5
33.
Evaluate the expression using the quotient rule.
a)
214 z13
b)
22/z7
c)
214/ z7
d)
22 z7
34.
Simplify the following:
(x2y)5
(x2y)5
a)
x7y5
b)
x2y5
c)
x10y5
d)
x5y5
35.
(2ab)3
a)
23a3b3
b)
2ab3
c)
6a3b3
d)
6ab
36.
Simplify the exponential expression.
a)
2x6y12
b)
2x5y7
c)
8x6y12
d)
8x5y7
37.
Anything raised to a power of zero is always:
a)
0
b)
1
c)
itself
d)
negative
38.
(53x2y4)0
a)
5xy
b)
1
c)
0
d)
5
39.
Make this negative exponent positive.
9-3
9-3
a)
93
b)
1/9-3
c)
1/93
d)
729
40.
a)
9-4
b)
9-45
c)
3-4
d)
3-45
41.
a)
49
b)
444
c)
421
d)
415
42.
a)
A
b)
B
c)
C
d)
D
43.
a)
A
b)
B
c)
C
d)
D
44.
a)
A
b)
B
c)
C
d)
D
45.
a)
A
b)
B
c)
C
d)
D
46.
a)
A
b)
B
c)
C
d)
D
47.
a)
A
b)
B
c)
C
d)
D
48.
a)
A
b)
B
c)
C
d)
D
49.
a)
A
b)
B
c)
C
d)
D
50.
a)
A
b)
B
c)
C
d)
D
51.
Add or Subtract to Simplify:
(5x + 2) + (4x + 5)
(5x + 2) + (4x + 5)
a)
9x -7
b)
-9x-11
c)
9x+7
d)
x+7
52.
Add or Subtract to Simplify:
(4x2+ x) - (x2+ 2x)
(4x2+ x) - (x2+ 2x)
a)
3x2 - x
b)
4x2 + 2x
c)
3x2 + 3x
d)
3x2 + 2x
53.
Add or Subtract to Simplify:
(x2 + 6x - 8) + (7 - 5x + 9x2)
(x2 + 6x - 8) + (7 - 5x + 9x2)
a)
10x2 - x - 1
b)
10x2 + x - 1
c)
8x2 + 11x - 1
d)
10x2 - 11x - 1
54.
Add or Subtract to Simplify:
(4x2+ x) - (x2+ 2x)
(4x2+ x) - (x2+ 2x)
a)
3x2 - x
b)
4x2 + 2x
c)
3x2 + 3x
d)
3x2 + 2x
55.
Add or Subtract to Simplify:
(4n4 - 8n + 4) - (8n2 + 4n4 + 1)
(4n4 - 8n + 4) - (8n2 + 4n4 + 1)
a)
-8n2 - 8n + 3
b)
-7n2 - 8n + 3
c)
-6n2 - 8n + 3
d)
-7n2 - 4n + 3
56.
Add or Subtract to Simplify:
(4x - 2x3) + (5x3 - 4x + 5)
(4x - 2x3) + (5x3 - 4x + 5)
a)
3x3 + 5
b)
3x3 + 8x + 5
c)
3x2 + 5
d)
7x3 + 8x + 5
57.
(4x+1)(5x−2)
a)
20x2 + 3x − 2
b)
20x2 − 11x + 5
c)
20x2 − 18x + 2
d)
20x2 − 3x − 2
58.
(3x − 6)(7x + 7)
a)
21x2 − 63x + 42
b)
21x2 − 21x − 42
c)
21x2 − 42
d)
21x2 + 63x + 42
59.
Simplify the expression.
x3(2x2+3x)
x3(2x2+3x)
a)
2x5+3x4
b)
2x6+3x3
c)
5x9
d)
5x
60.
-5x6(3x2 - 12x + 30)
a)
-15x8 + 60x7 - 150x6
b)
15x8 - 60x7 - 150x6
c)
8x6 - 17x + 35
d)
-8x6 + 17x - 35x2
61.
(x-3)(x2+2x+7)
a)
x3-x2+x-21
b)
x3+5x+13x-21
c)
x3-3x2+7x-21
d)
x2+2x-3
62.
Simplify
(p − 8)2
Hint: (p − 8)2 = (p − 8)(p − 8)
(p − 8)2
Hint: (p − 8)2 = (p − 8)(p − 8)
a)
p 2 − 16p − 64
b)
p 2 + 16p + 64
c)
p 2 − 16p − 8
d)
p 2 − 16p + 64
63.
What is the degree of the following polynomial?
3x4 + 4x + 1
3x4 + 4x + 1
a)
First Degree
b)
Second Degree
c)
Third Degree
d)
Fourth Degree
64.
which binomial product would produce this as an answer?
x2 - 100
x2 - 100
a)
(x - 10)(x +10)
b)
(x - 2)(x + 50)
c)
(x - 4)(x + 25)
d)
(x - 1)(x + 100)
65.
a)
5p2 - 16p
b)
5p + 4
c)
5p - 4
d)
5p + 4p
66.
Divide the polynomial by the monomial.
a)
15x9 - 8x3
b)
3x6 - 8x3
c)
-5x12
d)
3x6 - 40x3
67.
Divide the polynomial by the monomial.
a)
2x8-8x2-28x
b)
2x8-2x2-7x
c)
8x7-8x-28x
d)
2x7 -2x -7
68.
Divide 8x2 -4x + 12 by 2x
a)
4x+2
b)
4x - 2 + 6/x
c)
4x-2
d)
4x-2+12/2x
69.
What is the GCF of 18 and 24?
a)
3
b)
6
c)
8
d)
9
70.
Factor Completely:
x2 - 36
x2 - 36
a)
(x + 9)(x - 4)
b)
(x - 6)(x - 6)
c)
(x - 9)(x + 4)
d)
(x + 6)(x - 6)
71.
What do you call a polynomial that cannot be factored?
a)
FOIL
b)
Simplified
c)
Prime
d)
Proper
72.
Factor Completely:
x4-9x2
Hint: Factor GCF first.
x4-9x2
Hint: Factor GCF first.
a)
x2(x+3)(x-3)
b)
(x2+3x)(x2-3x)
c)
(x2+9)(x-3)(x+3)
d)
x2(x2-9)
73.
Factor
x2 + 9x - 36
x2 + 9x - 36
a)
(x + 12)(x - 3)
b)
(x + 9)(x - 4)
c)
(x - 12)(x + 3)
d)
(x - 9)(x - 4)
74.
What is the GCF of the trinomial?
3x2 - 9x -120
3x2 - 9x -120
a)
3
b)
2
c)
6
d)
9
75.
Factor:
x2 + 4xy + 4y2
x2 + 4xy + 4y2
a)
(x + y)(4x + 4y)
b)
(x + 2y)(x + 2y)
c)
(2x + y)(2x + y)
d)
(x + 2)(x + 2)
76.
Factor
3a2 + 4a + 1
3a2 + 4a + 1
a)
(7a-10)(a-8)
b)
Not factorable
c)
(3a+1)(a+1)
d)
(3a-1)(a-1)
77.
Factor completely.
2n2 + 13n + 15
2n2 + 13n + 15
a)
(5n - 9)(n - 3)
b)
(3n + 7)(n + 4)
c)
(2n + 3)(n + 5)
d)
Not factorable
78.
What number can be written under the radical to make a true statement?
a)
405
b)
18,225
c)
3,645
d)
45
79.
Identify each expression that is in simplest radical form.
a)
∛27
b)
∛50
c)
∛3
d)
∛81
e)
∛96
80.
Which is equivalent to ∛375 in simplest form?
a)
3∛5
b)
5∛25
c)
3∛125
d)
5∛3
81.
Solve for t.
D= rt
D= rt
a)
D/r = t
b)
Dr = t
c)
D/t = r
d)
Dt = r
82.
pV = nRT
solve for R
solve for R
a)
R= pV/nT
b)
R= p/n + V/T
c)
R= pV - nT
d)
R= (pV-n)/T
83.
What should we do first to solve for x?
y=mx+b
y=mx+b
a)
Add
b)
Subtract
c)
Multiply
d)
Divide
84.
a)
b = 3A - a - c
b)
b = -3A + a - c
c)
b = -3A - a - c
d)
b = 2A - c
85.
Solve:
V = πr²h , for h
V = πr²h , for h
a)
V/(πr²) = h
b)
V - πr² = h
c)
V + πr² = h
d)
V/π = h
86.
Solve:
12x - 4y = 20 , for y
12x - 4y = 20 , for y
a)
y = 3x - 5
b)
y = -3x + 5
c)
y = -3x - 5
d)
y = 3x + 5
87.
10(h+1)-4=76
a)
h=10
b)
h=4
c)
h=7
d)
h=76
88.
Solve for v.
a)
60
b)
-3
c)
15
d)
3
89.
Solve for x.
a)
55
b)
60
c)
15
d)
35
90.
7(1 - y) = -3(y - 2)
a)
y = 1/4
b)
y = 4
c)
y = 5
91.
6x + 2 + 6x < 14
a)
x < 1
b)
x > 1
c)
x < -1
d)
x > -1
92.
-138 ≥ -6(6b − 7)
a)
b ≤ 5
b)
b ≤ -5
c)
b ≥ 5
d)
b ≥ -5
93.
-2(5 + 6n) < 6(8 − 2n)
a)
no solution
b)
infinite solution
c)
x < 0
d)
x > 0
94.
The graph of a quadratic function is called
a)
a line
b)
a hyperbola
c)
a parabola
d)
a cubic
95.
Standard form of a quadratic equation
a)
y=x²
b)
y=ax²+bx+c
c)
y=mx+b
d)
y=x
96.
What are the green dots called?
a)
axis of symmetry
b)
vertex
c)
parabola
d)
roots or x-intercepts
97.
What is the equation for axis of symmetry?
a)
y=3
b)
x=3
c)
x=5
d)
x=1
98.
Determine the values of
a, b, and c for
the quadratic equation:
4x2 – 8x = 3
a, b, and c for
the quadratic equation:
4x2 – 8x = 3
a)
a = 4, b = -8, c = 3
b)
a = 4, b =-8, c =-3
c)
a = 4, b = 8, c = 3
d)
a = 4, b = 8, c = -3
99.
What is the equation for this parabola in factored form?
a)
y=(x+2)(x-1)
b)
y=(x-2)(x+1)
c)
y=(x-2)(x-1)
d)
y=(x+2)(x+1)
100.
The discriminant finds the
a)
number of solutions
b)
x-intercepts
c)
y-value of vertex
d)
y-intercept
101.
If the discriminant is greater than zero, the equation has
a)
1 solution
b)
2 solutions
c)
no solutions
102.
Find the roots of this equation
x2 + x - 6 = 0
x2 + x - 6 = 0
a)
4, -1
b)
3, -2
c)
-6, 1
d)
2, -3
103.
The equation
y = x2 -12x + 36 has
y = x2 -12x + 36 has
a)
1 solution
b)
2 solutions
c)
no solutions
104.
If the discriminant is less than zero, the equation has
a)
1 solution
b)
2 solutions
c)
no solutions
105.
What is the domain?
a)
x = 2
b)
−∞ < x < ∞
c)
y = 2
d)
none of these
106.
What is the RANGE?
a)
{-3, 3]
b)
all real numbers
c)
[-4, 5]
d)
[-4, ∞)
107.
What is the DOMAIN?
a)
(4, ∞)
b)
(-4, ∞)
c)
[-3, 3)
d)
(-3, 3]
108.
What is the RANGE?
a)
(-∞, 0)
b)
(0, ∞)
c)
All real numbers
d)
{0, 1, 2, 3, 4,...}
109.
a)
F
b)
G
c)
H
d)
J
110.
For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.
a)
D: {1, -3, -4,}
R: {0, 1, 2, -4}
R: {0, 1, 2, -4}
b)
D:{0, 1, 2, -4}
R:{1, -3, -4}
R:{1, -3, -4}
c)
D:{0, 1, 2, 3, 4}
R:{1, -3, -4}
R:{1, -3, -4}
111.
What is the range of the following graph?
a)
-5, -1, 0 , 1, 5
b)
-4, -2, 0, 3, 6
c)
(-4, 1) ( 6, 0)
d)
(6, 0)
112.
A set of ordered pairs is called what?
a)
Coordinates
b)
Relation
c)
Function
d)
Vertical Line Test
113.
a)
{-2, 3, 7}
b)
[-2, 3]
c)
{1, 2, 2, 3, 4}
d)
[1, 4]
114.
Does this table represent a function?
a)
Yes!
b)
No!
c)
I Don't Know
115.
Does this Mapping Diagram repersent a function?
a)
Function
b)
No Function
c)
I Don't Know
116.
Is this relation a Function?
a)
Yes
b)
No
c)
I Don't Know
117.
A graph is presented. What are the domains for this graph?
a)
-4,-1,4,5,8
b)
-6,0,2,3,4
c)
1,0,9,-4,5
d)
-6,0,4,5,8
118.
An equation is shown.
y=−3x−12
When the value of the range is −18, what is the value of the domain?
y=−3x−12
When the value of the range is −18, what is the value of the domain?
a)
-2
b)
2
c)
5
d)
36
119.
The graphs given show the functions f and g.
What is the difference between f and g at x=6?
What is the difference between f and g at x=6?
a)
6
b)
3
c)
-2
d)
4
120.
The value of y varies directly with x. Which function represents the relationship between x and y if y = 14 when x = 6.
a)
y=20x
b)
y=84x
c)
y=7/3x
d)
y=3/7x
121.
The interest received on a savings account varies directly with the amount deposited. Daniel received $55.35 in interest on $1230 he deposited. How much interest would Daniel have received if he had deposited $2000 into his account?
a)
34.04
b)
90.00
c)
1,285.35
d)
44,444.44
122.
Is this a direct variation?
y=2x
y=2x
a)
yes
b)
no
123.
Is this a direct variation? y =2x + 1
a)
Yes
b)
No
124.
The width of a rectangle varies inversely with its length. If the width is 6 when the length is 24, give an equation that shows the relationship.
a)
y = 4x
b)
y = 144x
c)
y = 4/x
d)
y = 144/x
125.
a varies inversely as the square of b. If a is 1 when b is 3, find a when b is 5.
a)
0.36
b)
9
c)
25
d)
36
126.
Check to see if (-2,1) is a solution to the following system:
x+2y=0
4x+3y=1
x+2y=0
4x+3y=1
a)
yes
b)
no
127.
A system of equations that looks like this has ....
a)
infinite solutions
b)
no solution
c)
one solution
128.
Solve using any method:
2x+3y=10
-2x+y=14
2x+3y=10
-2x+y=14
a)
(6,-4)
b)
(-4,6)
c)
(4,6)
d)
(6,4)
129.
When you come across a solution that reads 3=4, your answer would be.....
a)
no solution
b)
all real numbers
c)
3 pizzas = 4 hungry hungry hippos
d)
one solution
130.
When you come across a solution that reads 4=4, your answer is...
a)
no solution
b)
all real numbers
c)
4
131.
Pick the following inequality that relates to this graph:
a)
y<-2x+2
b)
y≤-2x+2
c)
y>-2x+2
d)
y≥-2x+2
132.
You have a total of 17 coins. All of your coins are nickels and dimes. The total value of the coins is $1.35. Which system of equations represents this situation?
a)
n+d=17
.05n+.10d=1.35
.05n+.10d=1.35
b)
.05n+.10d=17
n+d=1.35
n+d=1.35
c)
.25n+.10d=1.35
n+d=17
n+d=17
133.
Is (3,2) a solution to
3x-4y=1
x-y=0
3x-4y=1
x-y=0
a)
yes
b)
no
134.
Solve the following equations for x and y:
-6x+6y=6
6x-3y=12
-6x+6y=6
6x-3y=12
a)
6,5
b)
5,6
c)
4,4
d)
2,4
135.
The relationship of birthdays to candles
a)
Positive correlation
b)
Negative correlation
c)
No correlation
d)
all of the above
136.
Which of the following could be a possible line of best fit for the data?
a)
y = -5/2x + 20
b)
y = -x + 19
c)
y = x + 20
d)
y = 2/3x + 15
137.
Use the line of best fit to approximate rate of change relative to the scatter plot above.
a)
7/5
b)
5/7
c)
-7/5
d)
-5/7
138.
What is the equation of the line of best fit?
a)
y = -25x + 170
b)
y = -5/8x + 170
c)
y = 25x + 170
d)
y = 5/8x + 170
139.
a)
1/3
b)
-1/3
c)
-2/3
d)
3/2
140.
a)
1/3
b)
-1/3
c)
-2/3
d)
3/2
141.
a)
2
b)
-2
c)
6
d)
-6
142.
a)
4/3
b)
-4/3
c)
6
d)
-6
143.
Find the slope between the two points.
(3, 7) and (-4, 2)
(3, 7) and (-4, 2)
a)
7/5
b)
5/7
c)
2/3
d)
2
144.
Find the slope between the two points.
(4, 2) and (3, 8)
(4, 2) and (3, 8)
a)
-1/6
b)
-6
c)
1/6
d)
6
145.
Identify the slope and y-intercept of:
y = 1/5x + 5
y = 1/5x + 5
a)
slope: 1/6 y-intercept: 4
b)
slope: 1/5 y-intercept: 5
c)
slope: 5/1 y-intercept: 5
d)
slope: 1 y-intercept: 5
146.
What is the y-intercept of the line graphed below?
a)
3
b)
4
c)
-3
d)
4/3
147.
Write an equation for the graph
a)
y = -1/2x + 2
b)
y = -2x + 2
c)
y = 1/2x - 2
d)
y = 2x + 2
148.
Write an equation for the table
a)
y = 6x + 4
b)
y = 4x - 2
c)
y = 4x + 2
d)
y = 4x + 6
149.
Write an equation that has a slope of 10 and passes through the point (2,5)
a)
y = 2x + 10
b)
y = 10x + 2
c)
y = 10x - 5
d)
y = 10x - 15
150.
Write an equation given the two points
a)
y = 6x - 43
b)
y = 12x - 43
c)
y = 1/2x + 5
d)
y = 2x - 7
Reset
