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Math 678 Mid-Term Review

Total questions: 126

Worksheet time: 8hrs 49mins

Name
Class
Date
1.
What type of number is π ?
a)
Rational
b)
Irrational
2.
Which number is irrational?
a)
9.6
b)
√45
c)
3/8
d)
3.4 x 10 ⁵
3.
Which number is a rational number ?
a)
1/4
b)
π
c)
√3
d)
∛25
4.

Identify 5.4 as rational or irrational

a)

Irrational number

b)

Rational number

5.
√7
a)
Rational 
b)
Irrational
6.
√25
a)
Rational
b)
Irrational
7.
-17.565
a)
Rational
b)
Irrational
8.
.141414141414...
a)
Rational 
b)
Irrational 
9.
The decimal of an irrational number doesn't repeat with a pattern.
a)
true
b)
false
10.
The √98 falls between what two numbers on a number line?
a)
10 and 11
b)
11 and 12
c)
9 and 10
d)
90 and 100
11.
A perfect square is which type of number?
a)
Rational 
b)
Irrational
12.
A fraction is which type of number?
a)
Rational
b)
Irrational
13.
A non-perfect square is which type of number?
a)
Rational
b)
Irrational
14.
The square root of 57 is ...
a)
rational 
b)
irrational 
15.
Zero
a)
Rational, Integer
b)
Rational
c)
Rational, Integer, Whole
d)
Rational, Integer, Whole, Natural
16.
Choose the best definition of the term WHOLE NUMBERS...
a)
Numbers that have holes in them (like 0, 4, 8, etc.)
b)
Any positive #s
c)
1 and then +1 after that (1, 2, 3, 4, 5, 6...)
d)
Zero and the positive numbers with decimals of with .0
17.
Choose the best definition of the term INTEGERS...
a)
Whole numbers
b)
Negative numbers
c)
Negative Numbers and Positive Numbers
d)
Positive whole #s and their opposites and zero
18.

Which number is real, rational, an integer, and a whole number?

a)

-15

b)

9.5

c)

-7

d)

12

19.

Which number is real and irrational?

a)

-5.785

b)

2.3

c)

8.4183969701...

d)

9.9725

20.

Which number is real, rational, and an integer?

a)

-7.5

b)

12

c)

4.75

d)

9.5938106...

21.

Which categories does the number 0 belong to?

a)

real, rational, integer, whole, natural

b)

real, rational, integer, whole

c)

real, irrational

d)

real, irrational, integer, whole

22.

Which categories does the number -7.25 belong to?

a)

real, irrational

b)

real, rational, integer

c)

real, rational, integer, whole, natural

d)

real, rational

23.

Which categories does the number 523 belong to?

a)

real, irrational, integer, whole, natural

b)

real, rational, integer, whole, natural

c)

real, rational, integer

d)

real, rational, integer, whole

24.

Which categories does the number -92 belong to?

a)

real, rational, integer

b)

real, irrational, integer

c)

real, rational, integer, whole, natural

d)

real, irrational

25.
Is the following number rational or irrational? (77/3)
a)
Rational
b)
Irrational
26.
Is the following number rational or irrational? (π / 2)
a)
Rational
b)
Irrational
27.
Once simplified, is this number rational or irrational? 10√2
a)
Rational
b)
Irrational
28.
Select the ONLY number that is RATIONAL 
a)
π
b)
π/4
c)
√2
d)
√49
29.
Select the ONLY number that is IRRATIONAL
a)
π / π
b)
0.1234567...
c)
3√4
d)
-0.74747474...
30.
Which is GREATER?
27 or 72
a)
27
b)
72
c)
Neither, they are equal
31.
34 is bigger than 43.
a)
True
b)
False
32.
Any number written to the 0 power is always 1
Example: 80=1
a)
True
b)
False
33.
A repeating decimal is what type of number?
a)
Rational 
b)
Irrational
34.
Write the following repeating decimal as a fraction in lowest terms  0.2̅7̅
a)
3/11
b)
27/100
c)
27/99
d)
5/11
35.
Order -5, -7, 0 and 4 from least to greatest
a)
4, 0, -5, -7
b)
0, 4, -5, -7
c)
4, 0, -7, -5
d)
-7, -5, 0, 4
36.
Which operation would you do first in the following equation?
10 - 4 ÷ 1 · 5
a)
Subtraction
b)
Division
c)
Multiplication
d)
Addition 
37.
Which operation would you do first?
( 12 + 10) ÷ 10 · 14 - 6
a)
Division
b)
Multiplication
c)
Addition
d)
Subtraction
38.
Evaluate the equation:
5 · 2 - (11 - 7)
a)
10
b)
4
c)
6
d)
11
39.
Evaluate the equation:
7 ÷ 1 - 6
a)
1
b)
5
c)
6
d)
7
40.
Which operation would you do first?
10 - 7 + 8 ÷ 1
a)
Subtraction
b)
Addition
c)
Division
d)
Multiplication
41.
Which operation would you do first?
10 - ( 9 + 3 ) ÷ 2
a)
Subtraction
b)
Addition
c)
Division
d)
Multiplication
42.
List in order from least to greatest.
5/4, 56%, 1.07, 4/5
a)
5/4, 56%, 1.07, 4/5
b)
1.07, 4/5, 5/4, 56%
c)
56%, 1.07, 4/5, 5/4
d)
56%, 4/5, 1.07, 5/4
43.

Which is ordered from least to greatest order?

a)

1/4, -3/7, 1/2

b)

-3/7, 1/2, 1/4

c)

1/2, 1/4, -3/7

d)

-3/7, 1/4, 1/2

44.
Put the rational numbers in order from least to greatest.
-4.2, -4 1/2, -4, 0, 4 
a)
0, -4 1/2, -4.2, 4, -4
b)
-4 1/2, -4.2, -4, 0, 4
c)
-4 1/2, -4.2, -4, 4, 0
45.

Which is ordered from least to greatest?

a)

-12.3, -12.75, -12, -12.25

b)

-12.75, -12.3, -12.25, -12

c)

-12.3, -12.75, -12.25, -12

46.
What is the opposite of 3?
a)
-3
b)
0
c)
3
d)
1/3
47.
The number -4 is classified as:
I. Whole Number
II. Integer
III. Rational Number
a)
II and III only
b)
II only
c)
I, II, and III
d)
III only
48.

Gail's dad has tools in his garage. They're labeled for the size of the tool. Which of these are listed from greatest to least?

a)

1/4, 1/3, .20, .75, 1.25, 2 1/2

b)

2 1/2, 1.25, .75, 1/3, 1/4, .20

c)

.20, 1/4, 1/3, .75, 1.25, 2 1/2

d)

2 1/2, 1.25, .75, .20, 1/3, 1/4

49.
Fractions are shown.  
1/3, 1/4, 5/8 
Order the fractions from least to greatest.
a)
1/4, 5/8, 1/3
b)
1/4, 1/3, 5/8 
c)
5/8, 1/3, 1/4
d)
1/3, 1/4, 5/8
50.
Put the following in order LEAST to GREATEST:
54%, 2/5, .45
a)
2/5, .45, 54%
b)
54%, 2/5, .45
c)
54%, .45, 2/5
d)
.45, 2/5, 54%
51.

Solve: 4 = 2(x + 3)

a)

1/2

b)

7/2

c)

-1

d)

5

52.
Solve: 5x - 14 = 8x + 4
a)
6
b)
-6
c)
-18/13
d)
10/3
53.
What is the first step to solve this equation:
11 - 3x = 44
a)
Add 3 to both sides
b)
Subtract 11 from both sides
c)
Add 11 to both sides
d)
Divide 3 on both sides.
54.

Solve: 3y+6+4y-7=-8

a)

y=-1

b)

y=-8

c)

y=1

d)

y=7

55.

Solve: -2x-7+3x=10

a)

x=-2

b)

x=3

c)

x=10

d)

x=17

56.

Solve: 12+5w-4w=15

a)

w=1

b)

w=3

c)

w=5

d)

w=4

57.

Solve: 10(h+1)-4=76

a)

h=10

b)

h=4

c)

h=7

d)

h=76

58.

Solve: 3y+4y+6 = 20

a)

y=2

b)

y=-2

c)

y=4

d)

y=3

59.

Solve: 9c - 3c = 48

a)

c=9

b)

c=3

c)

c=4

d)

c=8

60.
Solve for v.
a)
60
b)
-3
c)
15
d)
3
61.
Solve for x.
a)
55
b)
60
c)
15
d)
35
62.
Which of the following is an equation?
a)
4x - 7
b)
3 - 7t
c)
7x = 49
d)
43x - 9
63.
What is the inverse operation you would use to solve:
6x = 36
a)
Multiply
b)
Divide
c)
Add
d)
Subtract
64.
Laney pays $0.99 for each song she downloads from the Internet. In total, she paid $24.75 for songs from the Internet. How many songs does Laney download? 
a)
20 songs
b)
25 songs
c)
30 songs
d)
35 songs
65.
What is the inverse operation of multiplication? 
a)
multiplication
b)
addition
c)
subtraction 
d)
division 
66.
Translate: 
Four times a number plus six IS 30.
a)
4 + 6 = 30
b)
4x + 6 = 30
c)
x + 4 times 6 = 30
d)
30 = 4x
67.

Solve: 7(1 - y) = -3(y - 2)

a)

x = 1/4

b)

x = 4

c)

x = 5

d)

x = 1/5

68.

Simplify: -4(-4d - 5)

a)

-16d+20

b)

16+20

c)

16d+20

d)

16s-20

69.

Simplify: -8(6x + 3)

a)

48X+3

b)

-48X-3

c)

14x+3

d)

-48x-24

70.

Simplify: -3(3 - 8j)

a)

-6-11j

b)

9+24j

c)

-9+24j

d)

9-24j

71.

Simplify: - (6 - 4p)

a)

6-4p

b)

6+4p

c)

-6+4p

d)

6p-4

72.

Simplify: 2(4k + 7)

a)

4k-9

b)

4K+9

c)

8k-14

d)

8k+14

73.

Simplify: 9 + 5m - 4

a)

5m-5

b)

10m

c)

5m+5

d)

5m+13

74.

Simplify: 7 - 8c + 3 - 6c

a)

-10+14c

b)

-25

c)

10-14c

d)

25c

75.

Simplify: -9(14p - 8) - 4p

a)

130p - 72

b)

122p - 72

c)

-130p - 18

d)

-130p + 72

76.

Simplify: 3 + 5x + 8 - 2x

a)

-3x2 - 11

b)

3x2 + 11

c)

11 - 3x

d)

11 + 3x

77.

Simplify: -7x +5 (1 - 8x)

a)

-33x + 5

b)

5 + 33x

c)

47x + 5

d)

5 - 47x

78.

Simplify: x + 4 - 7(x - 5)

a)

-33x + 19

b)

-47x2 + 21

c)

33x - 19

d)

-6x + 39

79.

Simplify: -6x + 4(-x - 3)

a)

-2x - 12

b)

10x + 12

c)

-10x - 12

d)

-2x + 12

80.

Solve: 6(5x - 3) + 2 = 14

a)

2

b)

.5

c)

-1

d)

1

81.

Solve: -2(7 - 4x) = 10

a)

x = 3

b)

x = -3

c)

x = 6

d)

x = -5

82.

Solve: -24 = 6(2 - x)

a)

x = 6

b)

x = -6

c)

x = 36

d)

x = 8

83.

Solve: 6x - 4(x - 1) = 14

a)

x = 5

b)

x = -5

c)

x = 1.4

d)

x = 3

84.

Solve: 5x - 14 = 8x + 4

a)

x = 6

b)

x = -6

c)

x = -18/13

d)

x = 10/3

85.

Solve: 4(1-x)+3x=-2(x+1)

a)

x = -6

b)

x = 6

c)

x = 3

86.

Solve: -8x - 8 +3(x - 2) = -3x + 2

a)

x = -8

b)

x = 8

c)

x = 2

d)

x = -2

87.

Solve for n:

a)

n = 10

b)

n = -40

c)

n = 10/-4

d)

n = 6

88.

Solve for n

a)

n = 9

b)

n = 3

c)

n = 27

d)

n = 15

89.
Jason says that 10 less than one third of his age is 11 years old.  How old is Jason?
a)
3 years old
b)
7 years old
c)
57 years old
d)
63 years old
90.
 Erika sold half of her comic books and then bought sixteen more. She now has 36. How many did she begin with?
a)
36
b)
40
c)
20
d)
10
91.
Todd caught three times as many fish this year than last year. He caught 63 fish by the end of the year. Which algebraic equation represents how many fish he caught last year? 
a)
3f = 63
b)
63 - 3 = f
c)
63/3 = f
d)
3 + f = 63
92.
The difference of a and b is 3. The sum of the variables is 13. Find the numbers.
a)
a = 7
b = 10
b)
a = 8
b = 5
c)
a = 10
b = 13
93.
Logan asked his 20 coworkers whether they own a car or a truck. There were 6 more car owners than truck owners.  How many people owned a car?   
a)
7 people
b)
9 people
c)
11 people
d)
13 people
94.
The length of a rectangle is 3 times the width. The perimeter of the rectangle is 72 feet. What is the area of the rectangle?
a)
243
b)
36
c)
9
d)
24
95.
Each of the equal sides of an isosceles triangle is 4 times the third side. The perimeter of the triangle is 114 inches. What would you label the three sides using the same variable. 
a)
x, x , 4x 
b)
x + 4, x+ 4, x 
c)
x, x, x + 4 
d)
x, 4x, 4x
96.
Eight times a number increased by 9 is the same as 15 more than 7 times the number.  Find the number.
a)
6
b)
-7
c)
1
d)
2
97.
What THREE consecutive ODD integers have a sum of 141?
a)
45, 47 and 49
b)
32, 21 and 32
c)
50, 50 and 41
d)
35, 35, and 71
98.
Two consecutive ODD integers have a sum of 88? Find the numbers.
 
a)
35 and 53
b)
44 and 44
c)
51 and 37
d)
43 and 45
99.
Simplify the expression. 
(6x2)(-3x5)
a)
18x7
b)
-18x7
c)
18x7
d)
3x7
100.
Simplify   (2m4)(5m2)
a)
10m6
b)
10m8
c)
7m6
d)
7m8
101.
(x5)4
a)
x9
b)
x20
c)
x
d)
x54
102.
(ab)2
a)
ab2
b)
a2b2
c)
a2b
103.
Simplify:
(5ab2)2
a)
25a2b4
b)
10a2b4
c)
5a2b4
d)
25ab2
104.
(2ab)3
a)
8a3b3
b)
2ab3
c)
6a3b3
d)
6ab
105.
(52c3)5
a)
105c5
b)
57c8
c)
510c15
d)
510/c15
106.
Simplify (-3x4y5)2
a)
9x8y10
b)
6x8y10
c)
3x8y10
d)
-9x8y10
107.
54 means multiplying 5 by itself how many times?
a)
5
b)
1
c)
4
d)
0
108.
Which is greater,  26540 or 50?
a)
26540
b)
50
c)
They are the same
d)
Zero is greater
109.
Which is GREATER?
27 or 72
a)
27
b)
72
c)
Neither, they are equal
110.

What is 71?

a)

1

b)

7

c)

0

d)

14

111.
Anything raised to a power of zero is always: 
a)
0
b)
1
c)
itself
d)
negative
112.
Which number is the BASE?
23 = 8
a)
2
b)
3
c)
8
113.

What is 1/4 squared?

a)

1/16

b)

1/4

c)

1/8

d)

1/2

114.
Solve.
(1/2)3
a)
1/8
b)
3/6
c)
3/8
d)
Answer Not Given
115.
Which number is the EXPONENT?
42 = 16
a)
4
b)
2
c)
16
116.
What is the LCM of 45 and 72?
a)
72
b)
3,240
c)
360
d)
260
117.
What is the LCM of 12 and 18?
a)
18
b)
36
c)
24
d)
54
118.

Use a factor tree or upside down birthday cake to find the prime factorization of 48

a)

4x2x6

b)

4x2x2x3

c)

3x2x2x2x2

d)

12x4

119.

Use a factor tree or upside down birthday cake to find the prime factorization of 105

a)

7x5x3

b)

11x5x3

c)

7x5x2x1

d)

7x5x3x2

120.
Is 5 prime or composite? 
a)
Prime
b)
Composite
121.
All of these are prime except
a)
3
b)
9
c)
2
d)
13
122.
What is the GCF of 72, 96, and 84?
a)
2
b)
7
c)
12
d)
4
123.
Jane has 18 juice boxes, 24 bags of peanuts and 36 apples.  She wants to make snack bags with the same number of each thing in each bag.  What is the greatest number of snack bags Jane can make.
a)
4
b)
6
c)
8
d)
10
124.
What is the greatest factor of 28 and 49?
a)
1
b)
2
c)
7
d)
12
125.
What is the LCM of 18k and 15k3 ?
a)
3k2
b)
3k3
c)
90k3
d)
5k
126.
Find and explain the error.    
 5 - 3 + 2
     5 - 5
        0
a)
There is no error.
b)
Addition was done first and you should have subtracted first
c)
There is a subtraction error

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