Download Name: ___ Period: ____ Review for the 1st Semester Pre

Name: _____________________________
Period: ____
Review for the 1st Semester Pre-Algebra Final
Expressions and Variables
Write a variable expression to represent the phrase.
1. 6 decreased by a number
2. The sum of a number and 18
3. The product of a number and 12
4. The quotient of 4 and a number
Powers and Exponents
Evaluate the power.
5.)
6.)
7.)
8. Find the area of a square that has a side length of 12 feet.
9. Find the volume of a cube that has a side length of 5 meters.
10. What is the side length of a square if the area is 81
11. What is the side length of a cube if the volume is 27
?
?
Order of Operations
Evaluate the expression when a= 
12.) b(
1
, b= - 4, c= 6
2
+ 4)
13.) 6(a + 4c)
14.) – b(10a – a)
15.)  4 b  c  a
Comparing and Ordering Integers
16.) Graph the integers on a number line. Then, write the integers in order from least to
greatest.
2, -6, 4, -1, 0
Adding, Subtracting, Multiplying, or Dividing Integers
17.)
18.)
19.)
20.)
21.)
22.)
23.)
0 – 15
-15 – 15
-15 – (-15)
-22(3)
-3(-8)
- 15 – 75 – 100
118 – ( - 2) -315
Mean, Median, Mode, and Range
24.) Use the scores: 91, 76, 88, 92, 99, 88, and 77 to answer the following questions.
a.) What is the range?
b.) What is the mode?
c.) What is the mean? (Round to the nearest tenth)
d.) What is the median?
e.) What measure of central tendency would change if another score of 88 was added
to the set of values? Explain.
Coordinate Plane
Graph each ordered pair and describe the location (quadrant) of the point.
25.) (-8, 1)
26.) (2, 2)
27.) (1, -4)
28.) (-3, -5)
Properties and Operations
Identify the property that the statement illustrates.
29.) 11(3) = 3(11)
30.) ab + 0 = ab
31.) 2(a + b) = 2a + 2b
32.) -3a(1) = -3a
33.) (4+5) + 3 = 4 + (5+3)
Simplifying Variable Expressions
Simplify the expression.
34.) y + 2y – 3 + x -18
35.) a(3 + b) + a + 3b + 4ab – 7
36.) -(a + c) -3a + 15c – 3
37.) 12 – (8 + a) + 16 – 3a
Variables and Equations
Write the verbal sentence as an equation. Do not solve.
38.) The quotient of n and 4 is 12.
39.) The sum of 6 and m is -22
40.) The difference of a number and 16 is 4.
41.) The product of 16 and a number is 128.
Solving Equations Using Subtraction, Addition, Multiplication, or Division
42.) The advertised price of a DVD player is $155 after a $25 mail-in rebate. Write and
solve an equation to find the price of the DVD player before the rebate is applied.
Solve the equation. Check your answer.
43.) 21 + m = 4
44.) p – 24 = - 53
45.) -r = 38
46.) 17 =
47.) 3x= - 27
Decimal Operations and Equations with Decimals
Solve the equation. Check your answer.
48.) x + 3.8 = 5.2
49.)
= 0.4
Solving 2-Step Equations
Solve the equation. Check your answer.
50.) 6 – 2n = 8
51.) -2 = 5 – m
52.) 12=
53.)
+ 17
+ 4 = 12
54.) 56=17x – 29
55.) 18 – x = 42
Solving Equations Having Like Term and Parentheses
Solve the equation. Check your answer.
56.) - 5(3x + 5) = 20
57.) 12= 3(x -17)
58.) 2= 4(3x – 8) – 11x
59.) -5x – (8 – x) = 12
Solving Equations with Variables on Both Sides
Solve the equation. Check your answer.
60.) 10x = 5x + 60
61.) 19x + 26 = 41 + 14 x
Solving Inequalities Using Addition, Subtraction, Multiplication, or Division
Solve the inequality and graph the solution.
62.) 10 ≥ x + 3
63.) 18.1 ≤ p- 3
64.) x + 4 < 8
65.) m - 6 > 14.6
66.)
< 12
67) 12x ≤ - 60
68.)
-12x ≤ -60
Solving Multi-Step Inequalities
Solve the inequality and graph the solution.
69.) 6x – 3 ≤ - 9
70.) - 3 x -3 < 2x – 83
Factors and Prime Factorization
Tell whether the number is prime or composite. If it is composite, write its prime
factorization.
71.) 45
72.) 41
73.) 59
74.) 51
Greatest Common Factor
Find the greatest common factor of the numbers. Tell whether the numbers are
relatively prime.
75.) 120 and 960
76.) 54 and 89
77.) 64 and 144
Equivalent Fractions
Write the fractions in simplest form. Tell whether they are equivalent.
78.)
and
79.)
and
Least Common Multiple
Find the least common multiple of the numbers.
80.) 15, 30, and 50
81.) 55 and 15
82.) 30 and 36
Rules of Exponents
Find the product or quotient.
83.)
•
84.)
•
85.)
Negative and Zero Exponents
Write the expression using only positive exponents.
86.)
87.)
88.) 3
89.)
•
Scientific Notation
Write the number in scientific notation.
90.) 4,320
91.) 41
92.) 0.0067
Write the number in standard form.
93.) 8.42 x
94.) 8.42 x
Real Numbers, Rational Numbers, Square Roots, & Cube Roots
95.) Write all of the names that describe the number.
(Real, rational, irrational, integer, whole number, natural or counting number)
3.14…
-4
96.)
is in between what two integers? ________ Graph it.
97.)
is in between what two integers? ________Graph it.
Find the square root of the number.
98.)
99.)
Find the cube root of the number.
100.)
101.)
Using Multiplicative Inverses to Solve Equations
Solve the equation. Check your answer.
102.) 10 +
x – 10 = 12
103.) x + 5 = 11
104.)
-
x=
0
4
Equations and Inequalities with Rational Numbers
Solve the equation. Check your answer.
105.)
x+
=
106.) -1.2x + 1.25 = 0.77
107)
≥
-
x
Ratios and Rates
Find the unit rate and round your answer to the nearest hundredth.
108.)
109.)
110.) Store A sells 40 pencils for $2.79, and store B sells 60 pencils for $3.59. Which
store has the better buy if you need 120 pencils? What is the unit rate for each store?
How much do you save?
Writing and Solving Proportions & Solving Proportions Using Cross Products
Solve the proportion.
111.)
=
112.)
=
Percents and Fractions
113.) Write the percent as a fraction in simplest form, or write the fraction as a percent.
49%
14%
Percents and Proportions
Use a proportion to answer the question.
114.) What percent of 56 is 16.8?
115.) What is 40% of 122?
116.) 22.32 is 36% of what number?
1%
Percents and Decimals
Find the percent of the number.
117.) 0.5% of 600
118.) 120% of 82
119.) 12% of 16
120.) Write the decimal as a percent or the percent as a decimal.
0.72
5.1
51%
102%
0.5%
121.) Write the fraction as a percent.
The Percent Equation
Use the percent Equation to answer the equation.
122.) What number is 60% of 22?
123.) 18 is 36% of what number?
Percent of Change
Find the percent of change.
124.) A shirt was $20 last week. Now, it is on clearance for $5.
125.) 150 students attended the 1st quarter dance. 183 students attended the 2nd
quarter dance.
Percent Applications
Use the given information to find the new price.
126.) Mary buys a shirt for $24. She wants to make a profit, so she marks the price up
120%.
127.) A sweater cost $48. What is the cost after 7.5% tax is added to it?
Simple Interest
128.) Bill’s account has a principal of $400 and he earns a simple annual interest of 5%
over 3 years. Find the interest and the balance of his account after 3 years.
129.) Lorraine has a balance of $563 in her account after 7 years. The principal was
$500 7 years ago. What is the simple annual interest rate?
Relations and Functions
130.) Identify the domain and range of the relation.
(3, 7), (0, 5), (1, 14), (-2, 14)
Tell whether the relation is a function. Explain why it is or is not a function. If so, is it a
linear function? Write a rule if it is a linear function.
131.)
132.)
x
-2
-1
0
1
-2
133.)
y
1
2
3
4
5
x
-2
-1
0
1
2
y
-2
-4
-6
-8
-10
x
-2
-1
0
1
2
y
8
4
0
4
8
134.)
x
-2
-1
0
1
2
y
2
4
6
8
10
Tell whether the relationship below is a function. If so, is it a linear function?
135.)
136.)
137.)
138.)
139.)
140.)
Make a sketch of the graph of the situation using time and distance.
141.) A tennis ball drops from a tree that is 15 feet tall.
142.) Sue drives at a constant speed for 7 minutes and travels 7 blocks. She stops at a
light for 1 min. She continues to drive at a constant speed for 7 more minutes and
travels 7 more blocks.
Linear Equations in Two Variables
143.) Tell whether the ordered pair (1, 0) is a solution of 2x+ 3y=2. Is (0, 1) a solution?
Graph the equation.
144.) y = 3x + 1
145.) y = 2x
146.) y = - 2x + 2
147.) y = x -1
148.)
y=1
149.)
x=1
Using Intercepts
Find the x-intercept and y-intercept of the equation and then graph it.
150.) y = 2x – 2
151.) x – 2y= 8
152.) 3x – 2y = - 12
The Slope of a Line
Find the slope of the line through the given points.
153.) (1, 2), (2, 10)
154.) (-1,-4), (8,12)
155.) 16, -1), (5, 15)
156.) (1, 2), (1, 4)
157.) (1, 2), (2, 2)
Slope-Intercept Form
Identify the slope and y-intercept of the line with the given equation.
158.) y= 15x – 12
159.) y=x
160.) y=2
Find the equation of the line in the graph.
161.)
162.)
163.)
Sequences
Tell whether the sequence is arithmetic or geometric. Then find the common difference
or common ratio, and write the next three terms.
164.) 16, 8, 4, 2, ___, ____, ____
164.) -7, -1, 5, 11, ____, ____, ____