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Worksheets

Math Reviewer

Total questions: 121

Worksheet time: 20hrs 10mins

Name
Class
Date
1.

What type of set is denoted as either { } or ∅?

a)

Superset

b)

Disjointed Set

c)

Empty (or Null) Set

d)

Subset

2.

Find n(A) when

A = {14, 16, 18, 20, 22, 24}

a)

6

b)

4

c)

12

d)

even numbers

3.

A = {x : x is a letter in the word SEAT}

B = {x : x is a letter in the word TASTE}


Determine if these two sets are equal or equivalent.

a)

Not equal because seat has 4 letters and taste has 5 letters.

b)

Equivalent because they have the same letters

c)

Equal because each set has the same cardinality and the same letters.

4.

If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∪ B?

a)

{3, 5, 7}

b)

{2, 3, 5, 7}

c)

{2, 3, 5, 7, 9}

d)

{1, 2, 3, 5, 7, 9}

5.

If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∩ B?

a)

{3, 5, 7}

b)

{2, 3, 5, 7}

c)

{2, 3, 5, 7, 9}

d)

{1, 2, 3, 5, 7, 9}

6.

The Universal Set = { -4, -3, -2, -1, 0, 1, 2, 3 ,4} and A = {0}.

What is the complement of A?

a)

{-4, -3, -2, -1, 0, 1, 2, 3}

b)

{-3, -2, -1, 1, 2, 3}

c)

{-4, -3, -2, -1, 1, 2, 3, 4}

d)

{-4, -3, -2, -1, 1, 2, 3}

7.

If

P = {0, 1, 2, 3, 4}, Q = {4, 6, 8}

R = {6, 12, 18} Then what is (P ∩ Q) ∪ (Q ∩ R)?

a)

{4}

b)

{4, 6}

c)

{4, 6, 8}

d)

{1, 2, 3, 4, 6, 8}

8.

If

A = {1, 3, 5, 15},

B = {2, 3, 5, 7}

C = {2, 4, 6, 8}

then what is (A U B) ∩ C ?

a)

{1,3,5}

b)

{1,2,3}

c)

{2,3,5}

d)

{2}

9.

From the above Venn diagram, what is the set S ∩ T?

a)

{casey, drew, jade, glen}

b)

{alex, casey, drew,hunter}

c)

{casey, drew}

d)

{drew, jade}

10.

From the above Venn diagram, what is the set (S ∪ T) ∩ V?

a)

{casey, drew, jade, glen}

b)

{alex, glen, hunter, jade}

c)

{casey, drew, glen}

d)

{drew, jade}

11.

From the above Venn diagram, what is the set S' ? Look at ALL of the Universal set called "U."

a)

{casey, drew}

b)

{blair, erin, francis, glen, jade, ira}

c)

{blair, erin, francis, ira}

d)

{jade, glen, blair, erin, francis, ira}

12.

Let A={1, 3, 4} and B={x|x is an even whole number less than 9}. Find A U B

a)

{1, 3, 4}

b)

{1, 2, 3, 4, 6,8}

c)

{1, 2, 3, 4, 5, 6, 7, 8}

d)

{1, 2, 3, 4, 5, 6, 7}

13.

Which of the following represents the shaded region?

a)

A union B

b)

A intersect B

c)

A ⊂ B

d)

B ⊂ A

14.

It is a collection of well-defined group of objects.

a)

Element

b)

Set

c)

Cardinality

d)

Universal Set

15.

What is the cardinal of the set, H = {w, o, n, d, e, r, f, u, l}

a)

10

b)

9

c)

8

d)

7

16.

Set D is the set of the distinct letters in the word mathematics. Write the set using the Roster method.

a)

D = {m, a, t, h, e, m, a, t, i, c, s}

b)

D = {m, a, t, h}

c)

D = {m, a, t, h, e, i, c, s}

d)

D = {m, a, t, h, i, c, s}

17.

Set C is the set of whole numbers less than 9. Write the set using the Roster method.

a)

C = {1, 2, 3, 4, 5, 6, 7, 8, 9}

b)

C = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

c)

C = {1, 2, 3, 4, 5, 6, 7, 8}

d)

C = {0, 1, 2, 3, 4, 5, 6, 7, 8}

18.
If every element in set A is also in set B, then...
a)
A is a subset of B
b)
B is a subset of A
c)
A = B
d)
A and B are disjoint
19.

Which of the following means proper subset?

a)

 ⊂\subset  

b)

 ⊆\subseteq  

c)

 ∈\in  

d)

=

20.

Which of the following is the symbol for element of?

a)

∅

b)

 ⊂\subset  

c)

 ∈\in  

d)

 ⊄\not\subset  

21.

Equivalent sets have

a)

the same number of elements

b)

the exact same elements

c)

the opposite elements

d)

nothing

22.

Equal sets have

a)

the same number of elements

b)

the exact same elements

c)

the opposite elements

d)

nothing

23.

The objects inside the set are called (a)  

24.

A set whose elements are countable.

a)

finite

b)

infinite

c)

equal

d)

equivalent

25.

What is the cardinality of a null set?

a)

0

b)

1

c)

infinite

d)

undefined

26.

Which of the following statements are true for the Venn diagram shown?

a)

A is a subset of B

b)

B is a subset of A

c)

A = B

d)

A and B are disjoint sets

e)

B is a superset of A

27.

Which of the following means any subset?

a)

 ⊂\subset  

b)

 ⊆\subseteq  

c)

 ∈\in  

d)

=

28.

How do you write "the complement of A"?

a)

n(A)

b)

(A)

c)

∀\forall

d)

A'

29.
What statement does the shaded region represent?
a)
A or B
b)
A and B
c)
A
d)
B
30.
What statement does the shaded region represent?
a)
A or B
b)
A and not B
c)
Not A
d)
Not A or B
31.
How many senior boys play football but do not wrestle?
a)
9
b)
12
c)
18
d)
104
32.

Which of the following operations on sets describe the given Venn diagram?

a)

A−B

b)

B−A

c)

A′−B′

d)

B′−A′

33.

Tell what type of set is illustrated in the given statement.


Students in the seventh grade.

a)

Well-defined

b)

Not well-defined

c)

Empty or Null

34.

Tell what type of set is illustrated in the given statement.


Colors of the rainbow.

a)

Well-defined

b)

Not well-defined

c)

Empty or Null

35.

Tell what type of set is illustrated in the given statement.


Girl members of BTS.

a)

Well-defined

b)

Not well-defined

c)

Empty or Null

36.

Tell what type of set is illustrated in the given statement.


Tourist spots in Cavite.

a)

Well-defined

b)

Not well-defined

c)

Empty or Null

37.
What are the terms in the expression?
-4x + 6y - 2
a)
-4x, 6y, -2
b)
x, y
c)
4x, 6y
d)
-2
38.
What are the variables in the expression?
-4x + 6y - 2
a)
-4x, 6y, -2
b)
x, y
c)
4x, 6y
d)
-2
39.
What are the coefficients in the expression?
-4x + 6y - 2
a)
-4x, 6y, -2
b)
x, y
c)
4x, 6y
d)
-4, 6
40.
Which of the following best describes the algebraic expression 3(x - 5)?
a)
Three times a number minus five
b)
Three times the quantity of a number minus five
c)
Three times the quantity of a number plus five
d)
Three times a number plus five
41.
Which of the following best describes the algebraic expression 6x + 1?
a)
Six times more than the quantity of a number plus one
b)
Six times the quantity of a number plus one
c)
One more than the product of six and a number
d)
One more than the quantity of six and a number
42.
Match this word expression with the correct algebraic expression:
a number decreased by 9
a)
n + 9
b)
n - 9
c)
9n
d)
n/9
43.
17 less than the product of 3 and m
a)
3m - 17
b)
17 - 3m
c)
17m -3
d)
17-3 + m
44.
2 less than the quotient of d and 6
a)
d - 6  + 2
b)
6d - 2
c)
d/6 - 2
d)
2 - d/6
45.

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.

a)

8 − 4m

b)

8m − 4

c)

8m + 4

d)

4m − 8

46.

Translate: two times the sum of a number and five

a)

2 + y + 5

b)

2y + 5

c)

2(y + 5)

d)

2 − y + 5

47.
b2 + 4
when b = 3
a)
10
b)
12
c)
13
d)
11
48.
6a - 3d
when a = 1, d = 2
a)
3
b)
12
c)
1
d)
0
49.
3(2x + z) when x=8 and z=2
a)
12
b)
30
c)
54
d)
60
50.

Kalia buys 5 items that cost d dollars each. She gives the cashier $60. Which expression represents the change she should receive?

a)

60 − 5d

b)

60 − d

c)

60 + 5d

d)

5d − 60

51.
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.
a)
72 = 8 + h
b)
72 = 8h
c)
72 = 8 - h
d)
72 = 8/h
52.
Twice a number is 24.
a)
2n = 24
b)
2/n = 24
c)
2 + n = 24
d)
2 - n = 24
53.
Translate this phrase intoan Algebraic expression.
57 more than 3 times Kate's score
Use the variable g to represent Kate's score.
a)
57g + 3
b)
3g - 57
c)
3g + 57
d)
57 - 3g
54.
x - 62 = 123
How should you show your work to isolate the variable and solve the equation?
a)
Add 62 to each side. 
b)
Subtract 62 from each side.
c)
Multiply each side by 62.
d)
Add 123 to each side.
55.
Solve the equation below:
a)
k = 152
b)
k = 176
c)
k = 5
d)
k = 27
56.
What is the formula for Area?
a)
L = A x W
b)
W = L X A
c)
A = L X W
57.
Jordan's teacher, Mr. Langdon, is eight years younger than five times his age. The sum of their ages is 64. Which equation can be used to find Jordan's age? 
a)
6x - 8 = 64
b)
5x - 8 = 64
c)
4x - 8 = 64 
d)
5x + 8 = 64
58.
The sum of three consecutive integers is 147. Which equation can be used to find the first integer? 
a)
3x = 147
b)
x + 3 = 147 
c)
x + x + 1 + x + 2 = 147 
d)
x ⋅ x ⋅ x = 147 
59.
Rewrite the expression by combining like terms.
3xy + 8x2 + 4y + 2y – 5x2
a)
3x2 + 3xy + 6y
b)
6y2 + 2xy + 2x
c)
7x2 + 35x
d)
3x2 + 6y + y
60.
Rewrite the expression by combining like terms.
8y2 + 7xy – 2y2  - 5xy + 2x
a)
3x2 + 3xy + 6y
b)
6y2 + 2xy + 2x
c)
7x2 + 35x
d)
3x2 + 6xy + y
61.
Which of these is the correct use of the distributive property for the following expression?
5(2x - 8)
a)
10x - 8
b)
10x + 40
c)
7x - 3
d)
10x - 40
62.
Simplify the following expression by combining like terms:
(3b - 4) - (4b + 6)
a)
-b + 2
b)
-b - 10
c)
7b - 10
d)
7b + 2
63.
Simplify the following expression by combining like terms:
(3b - 4) - (4b + 6)
a)
-b + 2
b)
-b - 10
c)
7b - 10
d)
7b + 2
64.
Factor the following expression:
3a + 12b + 6b2
a)
3b(a + 4 + 2b)
b)
3(ab + b + 2b2)
c)
b(13ab)
d)
3(a + 4b + 2b2)
65.
Factor the following expression:
4x2 - 8x + 10xy
a)
2x(2x - 4 + 5y)
b)
4x(x - 2x + 2y)
c)
x(4x - 8 + 10y)
d)
2(x2 - 4x + 5xy)
66.

What is the degree classification of this polynomial?

x2 + 4x -8

a)

binomial

b)

trinomial

c)

quadratic

d)

cubic

67.

What is the term classification of the following polynomial?

x3 - 7x2 +3

a)

monomial

b)

binomial

c)

trinomial

d)

polynomial

68.

Which is an example of a linear polynomial?

a)

x2 - 5

b)

6x + 4

c)

5x5

d)

2x3 - 9x2

69.

Which is an example of a cubic binomial?

a)

x3 + 5

b)

x2 + 3

c)

x2 + 5x - 6

d)

5x3

70.

Solve. (x+2) (x+3)

a)

x2 + 5x + 6

b)

x2 + x + 6

c)

x2 + 6x + 6

d)

x2 + 5x + 5

71.

Simplify 2x (-2x - 3)

a)

-4x - 3

b)

x2 - 3

c)

-4x2 - 6x

d)

-4x - 6

72.

Classify the polynomial and given degree 5x3y2

a)

Monomial, 3

b)

Uninomial, 3

c)

Uninomial, 5

d)

Monomial, 5

73.

Which is an example of a quadratic monomial?

a)

x3 + 5

b)

x2 + 3

c)

x2 + 5x - 6

d)

-5x2

74.

Simplify (3x2) (3x4y3)

a)

9x6y3

b)

3x6y3

c)

6x8y3

d)

6x8y6

75.

Terms in a polynomial are separate by what?

a)

A. Parenthesis

b)

B. multiplication/division

c)

C. constant

d)

D. addition/ subtraction

76.
Which polynomial is written in standard form?
a)
-3x + 8x2 + 9x3 - 11
b)
9x3 + 8x2 - 3x - 11
c)
8x2 + 9x3 -11 - 3x
d)
-11 - 3x + 8x2 + 9x3
77.
Add the following polynomials:
(6n2 - 7n4+8) +  (6 + 8n + 4n4)
a)
-3n4+ 6n2+8n+14
b)
-n4-2n2+8n+7
c)
-n4 + 6n2+8n+7
d)
-3n4+ 6n2+8n+7
78.
Use the FOIL method to multiply:
(x-7)2
a)
x2-49
b)
x2+49
c)
x2-14x+49
d)
x2-14x-49
79.
What is the Area?
a)
2x2 - 3x - 18 inches2
b)
2x2 + 3x + 18 inches2
c)
2x2 + 9x - 18 inches2
d)
2x2 - 9x - 18 inches2
80.
Subtract the following polynomials:
(2x³+6x²+4x-2)-(x³+4x²-x)
a)
x³+2x²+5x-2
b)
x³+10x²+3x-2
c)
3x³+2x+4x-3
d)
3x³+10x²-3x-2
81.
Subtract the following polynomials:
(3x²-3x+2)-(x²-2x+1)
a)
2x²+x+1
b)
2x²-5x+3
c)
2x²-x+1
d)
4x²-5x+3
82.

Find the factors of

x2 + x - 6

a)

(x - 6)(x - 9)

b)

(x + 3)(x + 2)

c)

(x + 3)(x - 2)

d)

(x + 2)(x + 4)

83.

Find the factors of

x2 - 5x - 36

a)

(x + 4)(x - 9)

b)

(x - 4)(x + 9)

c)

(x - 9)(x + 6)

d)

(x + 4)(x + 9)

84.
Find the product:
(x + 12)(x - 12)
a)
x2 - 144
b)
x2 + 144
c)
x2 + 12x - 144
d)
x2 - 12x + 144
85.
Multiply:
(3a + 4)2
a)
6a2+12a+16
b)
9a2+24a+16
c)
9a2+12a+16
d)
9a2+16
86.
(n2 + 6n − 4)(2n − 4)
a)
2n3 + 16n2 − 32n + 16
b)
2n3 + 8n2 − 32n + 16
c)
2n3 + 8n2 − 12n + 16
d)
2n3 + 8n2 − 32n - 16
87.
(4p − 1)(4p - 1)
a)
16p2 + 1
b)
16p2 − 1
c)
16p2 − 8p + 1
d)
16p2 + 8p + 1
88.
Find the area of a rectangle with length (x-5) and width (3x+1).
a)
3x2+16x-5
b)
3x2-14x+5
c)
3x2-14x-5
89.
(4x+1)(5x−2)
a)
20x2 + 3x − 2
b)
20x2 − 11x + 5
c)
20x2 − 18x + 2
d)
20x2 − 3x − 2
90.
(2x − 3)(2x + 3)
a)
4x2 − 12x + 9
b)
4x2 − 9
c)
4x2 + 9
d)
4x2 + 6x − 9
91.
Simplify the expression.
-3x2( 7x2 - x + 4)
a)
-21x4 + 3x3 -12x2
b)
7x2 - x + 4 (-3x2)
c)
21x4 + 3x3 + 12x2
d)
-12x2 + 3x3 -21x4
92.
(x-3)(x2+2x+7)
a)
x3-x2+x-21
b)
x3+5x+13x-21
c)
x3-3x2+7x-21
d)
x2+2x-3
93.
a)
5p2 - 16p
b)
5p + 4
c)
5p - 4
d)
5p + 4p
94.
Divide:
(9x2 + 6x)  ÷ 3x
a)
3x + 2
b)
3x2 + 2x
c)
5x2
d)
3x + 6
95.
a)
4y6
b)
4y22
c)
30y6
d)
30y22
96.
Divide the polynomial by the monomial.
a)
15x9 - 8x3
b)
3x6 - 8x3
c)
-5x12
d)
3x6 - 40x3
97.

Divide:


(4x2 - 24x + 35) / (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

98.
Is this division problem worked correctly?
a)
This is correct!
b)
This is incorrect!
99.

The area of a rectangular pool table is: x2 + 14x +40.

The length is x + 4. What is the width?

a)

x + 8

b)

x + 14

c)

x + 10

d)

x +4

100.

 x2+12x+27x+9\frac{x^2+12x+27}{x+9}  

a)

x+3

b)

x+9

c)

x-3

d)

x-9

101.
Factor:
x2 - 49
a)
(x + 7)(x - 7)
b)
(x + 7)2
c)
(x - 7)2
d)
(x+7)(x-1)
102.
Factor the polynomial. 
x2-4x-32
a)
(x-8)(x+4)
b)
(x-4)(x-32)
c)
(x+3)(x-4)
d)
x+2)(x+5)
103.
x + 12 = 20
a)
x = 32
b)
x = -32
c)
x = 8
d)
x = -8
104.
Solve for x:
a)
x = 20
b)
x = 7
c)
x = 10
d)
x = 3
105.
Solve the equation 4x + 5 = 3x + 9
a)
2
b)
4
c)
7
d)
14
106.
Lisa went to the mall to do her back-to-school shopping.  When she returned, she noticed that the number of shirts (s) she purchased was 3 more than twice the number of pants (p) she bought.  What is an equation that can be used to represent the number of shirts Lisa purchased? 
a)
p=3 + 2s
b)
s + 2p =3
c)
s = 3 + 2p
d)
2p = s + 3
107.
What inequality does the number line graph represent?
a)
x ≥ 3
b)
x > 3
c)
x < -3
d)
x ≤ -3
108.
Four times a number increased by  7 is at least 19. 
a)
4x > 19
b)
4x + 7 ≥ 19
c)
4x < 19
d)
4x + 7 ≤ 19
109.
Erin can read at least 80 words per minute. Write an inequality to show this situation. 
a)
x > 80
b)
x < 80
c)
x ≥ 80
d)
x ≤ 80
110.
-13t > 26
a)
t > -2
b)
t > 2
c)
t < 2
d)
t < -2
111.
Solve:
6x+10>5x-12
a)
x>2
b)
x<2
c)
x<-22
d)
x>-22
112.
3(x-2)<2(x+9)
a)
x<24
b)
x>-24
c)
x<12
d)
x>18
113.
Does the sign need to flip when solving?
-2x ≥ 22
a)
YES
b)
NO
114.
a)
A)
b)
B)
c)
C)
d)
D)
115.
a)
A)
b)
B)
c)
C)
d)
D)
116.

What inequality does the number line graph represent?

a)

x ≤ 4

b)

x ≥ -4

c)

x < -4

d)

x < 4

117.

Select the inequality shown

a)

1 < x < 4

b)

1 ≤ x < 4

c)

1 < x ≤ 4

d)

1 ≤ x ≤ 4

118.

Select the inequality shown

a)

-3 < x < 4

b)

-3 ≤ x < 4

c)

-3 < x ≤ 4

d)

-3 ≤ x ≤ 4

119.

Select the inequality shown

a)

-3 < x < 4

b)

-3 ≤ x < 4

c)

-3 < x ≤ 4

d)

-3 ≤ x ≤ 4

120.

Match the sentence to the correct inequality


Two times the sum of a number and 28 is at least 21

a)

2(x + 28) ≥212\left(x\ +\ 28\right)\ \ge21

b)

2x + 28 ≥212x\ +\ 28\ \ge21

c)

2x + 28 >> 21

d)

2 ( x + 28) < 21

121.

Match the scenario to the correct inequality

The distance from my mother to the remote control is less than 10 feet.

Use d to represent the distance in feet to the remote control

a)

 d =10d\ =10  

b)

 d≤10d\le10  

c)

 d ≥10d\ \ge10  

d)

d < 10

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