Foundations of Algebra Midterm Review
Name__________________________
Part 1. Perform the following operations for #s 1-25 WITHOUT a calculator.
1.)
Simplify: 8 − (−7) − 3
2.)
Simplify: 2(15 − 21)
3.)
Simplify:
4.)
Simplify: (6)(2) + (3)(−2)(−5)
5.)
Simplify:
6.)
Simplify:
7.)
Simplify:
8.)
Simplify:
9.)
Simplify: |2| ∙ |12| + −3|−10|
10.)
Simplify: 55|4| + |−1 − 3|
11.)
Simplify:
12.)
Simplify: 2 ∙ 32 ÷ 6 ∙ 3
13.)
Simplify: 5 − 2 + [6 ∙ (10 + 2) − 2]
14.)
Evaluate the expression 3xy - 4x + 10y for x = -1 and y = 5.
15.)
Evaluate the expression xyz for x = 2, y = -3, and z = -9.
−65 + 20𝑥 + 3𝑥 − 4
( -2) ( -2) ( -2)( -2)
28
7
+ 23
−15
3
21
+ −7
120 ÷ (−6) − 6 + (−3)
|53|−3
|−3|+|−2|
16.) Simplify: −4(−𝑥 − 8)
17.) Combine Like Terms: −2𝑥 + 5 − 9 + 9𝑥
18.)
Write the number in words: 603
19.)
Write the number in words: 3,409,587
Foundations of Algebra Midterm Review
20.)
Write as a number: eight hundred nine thousand, five hundred seventy-one
21.)
Write as a number: two hundred nine billion, four hundred eighty-five million, three
hundred forty-eight thousand, seven hundred ninety-five
22.)
Write as a decimal: ten and three hundred seventy-two thousandths
23.)
Write as a decimal: twenty-four and two hundredths
24.)
Simplify: |10 − 22|
25.) Simplify: -2 |−2 + 4 × 10|
____________________________________________________________________
Part 2. Perform the following operations for #s 26-95 WITH a calculator.
26.)
Simplify: 22 + [2 + (1 – 2)3]
27.)
Simplify:
16  2 2  3
2 + (8)

28.)
Simplify: 15 − [8 ÷ (6 + (−2))]
29.)
Simplify: -4 [(2 - 9) + 32]
30.)
Simplify: 2|3 − 10| + (−3)|6 − 3|
31.)
Evaluate using the given values, x = 3, y = -5, z = 2: 𝑥 2 − 𝑦 3 − 2
32.)
Evaluate using the given values, x = -2, y = 10, z = 1: −𝑥 + 3𝑦 + 4𝑧 2
33.)
Evaluate using the given values, x = 5, y = -1, z = -3:
34.)
Evaluate using the given values, x = 6, y = -2, z = -4:
35.)
Solve: 16 − 𝑥 = 10
5𝑥−10
2𝑦−3𝑧
𝑦−(4𝑧+2)
10+𝑥−4𝑦
Foundations of Algebra Midterm Review
2
3
3
4
𝑥− =
36.)
Solve:
37.)
Write the inequality of the graph below:
38.)
Solve: -x + 2 > 6
2
Simplify:  6   
3
39.)
1 4
− ∙
5 7
40.)
Simplify: -3x + x – 2y + 4x
41.)
Simplify: 4y – 3(2x + 4) - 10
42.)
Simplify: 4𝑥 2 +3𝑥13
43.) Solve the following inequality: x + 6 < -19
44.) Simplify the expression: −3(−𝑥 + 3) − 4𝑥
45.)
Simplify the expression: −2𝑥(3 + 4) − 8𝑥 + 1
46.)
Solve:
47.)
Solve:
48. )
Add:
49.)
Evaluate the expression if a = 5 and b = -2: |𝑎| − |−𝑏|
50.)
Evaluate the expression if x = -5, y = 2 and z = -13: 𝑥 − 𝑦 + 𝑧
51.)
Compare: .625 ____ 5/8
52.)
Compare:
1
3
10x = 65
𝑥
2
= 12
+
1
6
2
3
______ .68
Foundations of Algebra Midterm Review
1
The area of a triangle is times base times height. What is the area of a triangle
2
1
2
measuring meters high by meters at the base?
4
3
53.)
54.)
Simplify: 2(x - y)
55.)
Order the values from greatest to least:
56.)
Order the values from least to greatest: − 3 , −.335, − 4 , 34%, −1
57.)
Compare: −|−5| _______ − 3
58.)
Translate the verbal expression into an algebraic equation and solve:
The sum of a number and fifteen is twenty-six.
59.)
Translate the verbal expression into an algebraic equation and solve:
The difference of a number and four is sixty-seven.
60.)
Translate the verbal expression into an algebraic equation and solve:
The product of a number and seven is twenty-eight.
61.)
Translate the verbal expression into an algebraic equation and solve:
The quotient of a number and four is twenty-five.
62.)
Round to the nearest tens place: 324,204
63.)
Round to the nearest hundredths place: 3487.8049
64.)
Round to the nearest thousands place: 58,309,583.1938
65)
John bought a pizza for $10.99 and a bottle of soda for $1.09. What is the BEST way
to estimate the total cost of the purchase?
66.)
Find the Least Common Multiple (LCM) of 6 and 24.
67.)
Find the Least Common Multiple (LCM) of 4 and 14.
68.)
Find the Least Common Multiple (LCM) of 5, 6, and 8.
69.)
Add:
70.)
Multiply:
17
4
,
35
8
1
, 4.24, 4 5 , 4.23̅
1
1
3
1
1
4
5
+ +
3 5
∙
2 3
1
Foundations of Algebra Midterm Review
2
−
1
71.)
Subtract:
72.)
Divide:
73.)
Solve: 𝑥 + 4 < 10
74.)
Solve: −3𝑥 > 15
75.)
What is 3 raised to the fourth power?
76.)
Which of the following equals 625?
a) 55
b) 252
c) 53
77.)
3
4
4 2

3 5
d) 253
6
What is the value of a when a = -2?
78.)
Which mathematical operation is performed on x and y to simplify the expression
ax  ay ?
79.)
Simplify: (84 ∙ 82 )
80.)
Simplify: 106
81.)
4
3
Which of the following is equivalent to 8a 5a ?
82.)
6 2
5 2 6
After the expression, 2a b c  5a b c is simplified, to what power is c raised?
83.)
84.)
( )



  is simplified?
What is the value of the expression t  when t = 3?
6
To what power is the 4 raised when 4
2
3 3
85.)
When raising a power to a power, what operation is performed on the
exponents?
86.)
What operation is performed on the exponents to simplify the expression
a 10
?
a4
5 29
What is the value of 27 ?
5
87.)
88.)
Simplify: 𝑝10 ∙ 𝑝15
Foundations of Algebra Midterm Review
89.)
 3 x 15 y 8
When the expression
is simplified, what is true about the exponent of x
2x8 y
compared to the exponent of y?
90.)
What is the value of (2) 2 ?
91.)
2
7
What is x  x when x = 2?
92.)
What is true about any number raised to a zero power?
93.)
How is the number 6,520,000 written using scientific notation?
94.)
x
If 0.00000000000249 = 2.4910 , what is the value of x?
95.)
8
Which number correctly expresses 5.38 10 in decimal notation?