Elementary Algebra

564 Pages·2010·7.39 MB·English

by  Jerome E. Kaufmann

Rectangle Triangle
w a h c
l
A = lw P = 2l + 2w
b
1
A area A = bh P = a + b + c
2
P perimeter
l length A area
w width P perimeter
b base
h altitude
a, c sides
Parallelogram Right Triangle
h
c
b
b
a
A = bh
Pythagorean theorem: a2 + b2 = c2
A area
a, b legs
b base
c hypotenuse
h altitude (height)
Trapezoid Circle
b
1
h
r
b
2
1
A = h(b + b )
2 1 2
A area
A = πr2 C = 2πr
b , b bases
1 2
h altitude A area
C circumference
r radius
Cube Rectangular Prism
b
s
s c
s
V = s3 S = 6s2 a
V volume
V = abc S = 2ac + 2ab + 2bc
S total surface area
s length of a side V volume
S total surface area
a width
b length
c height
Sphere
Right Circular Cylinder
r
r
h
4 V = πr2h S = 2πr2 + 2πrh
V = πr3 S = 4πr2
3
V volume
V volume
S total surface area
S total surface area
r radius
r radius
h altitude (height)
Pyramid Right Circular Cone
h
s
h
r
base
1
V = πr2h S = πr2 + πrs
3
1
V = Bh
3 V volume
V volume S total surface area
B area of base r radius
h altitude (height) h altitude (height)
s slant height
ELEMENTARY
ALGEBRA
N I N T H E D I T I O N
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ELEMENTARY
N I N T H
ALGEBRA
E D I T I O N
Jerome E. Kaufmann
Karen L. Schwitters
Seminole State College of Florida
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Elementary Algebra, Ninth Edition © 2011, 2007 Brooks/Cole, Cengage Learning
Jerome E. Kaufmann and Karen L. Schwitters
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CONTENTS
1 Some Basic Concepts of Arithmetic and Algebra 1
1.1 Numerical and Algebraic Expressions 2
1.2 Prime and Composite Numbers 8
1.3 Integers: Addition and Subtraction 14
1.4 Integers: Multiplication and Division 21
1.5 Use of Properties 26
Chapter 1 Summary 35
Chapter 1 Review Problem Set 37
Chapter 1 Test 39
2 Real Numbers 41
2.1 Rational Numbers: Multiplication and Division 42
2.2 Addition and Subtraction of Rational Numbers 50
2.3 Real Numbers and Algebraic Expressions 59
2.4 Exponents 69
2.5 Translating from English to Algebra 75
Chapter 2 Summary 82
Chapter 2 Review Problem Set 85
Chapter 2 Test 87
Chapters 1 – 2 Cumulative Review Problem Set 88
3 Equations, Inequalities, and Problem Solving 91
3.1 Solving First-Degree Equations 92
3.2 Equations and Problem Solving 97
3.3 More on Solving Equations and Problem Solving 103
3.4 Equations Involving Parentheses and Fractional Forms 111
3.5 Inequalities 120
3.6 Inequalities, Compound Inequalities, and Problem Solving 127
Chapter 3 Summary 135
Chapter 3 Review Problem Set 139
Chapter 3 Test 141
v
vi Contents
4 Formulas and Problem Solving 143
4.1 Ratio, Proportion, and Percent 144
4.2 More on Percents and Problem Solving 152
4.3 Formulas 158
4.4 Problem Solving 167
4.5 More about Problem Solving 172
Chapter 4 Summary 178
Chapter 4 Review Problem Set 181
Chapter 4 Test 182
Chapters 1 – 4 Cumulative Review Problem Set 183
5 Exponents and Polynomials 185
5.1 Addition and Subtraction of Polynomials 186
5.2 Multiplying Monomials 192
5.3 Multiplying Polynomials 197
5.4 Dividing by Monomials 204
5.5 Dividing by Binomials 208
5.6 Integral Exponents and Scientific Notation 212
Chapter 5 Summary 220
Chapter 5 Review Problem Set 223
Chapter 5 Test 225
Chapters 1 – 5 Cumulative Review Problem Set 226
6 Factoring, Solving Equations, and Problem Solving 229
6.1 Factoring by Using the Distributive Property 230
6.2 Factoring the Difference of Two Squares 236
6.3 Factoring Trinomials of the Form x2(cid:2)bx(cid:2)c 242
6.4 Factoring Trinomials of the Form ax2(cid:2)bx(cid:2)c 249
6.5 Factoring, Solving Equations, and Problem Solving 255
Chapter 6 Summary 264
Chapter 6 Review Problem Set 266
Chapter 6 Test 268
7 Algebraic Fractions 269
7.1 Simplifying Algebraic Fractions 270
7.2 Multiplying and Dividing Algebraic Fractions 274
7.3 Adding and Subtracting Algebraic Fractions 278
7.4 Addition and Subtraction of Algebraic Fractions and Simplifying Complex Fractions 284
Contents vii
7.5 Fractional Equations and Problem Solving 292
7.6 More Fractional Equations and Problem Solving 298
Chapter 7 Summary 307
Chapter 7 Review Problem Set 310
Chapter 7 Test 312
Chapters 1 – 7 Cumulative Review Problem Set 313
8 Coordinate Geometry and Linear Systems 315
8.1 Cartesian Coordinate System 316
8.2 Graphing Linear Equations and Inequalities 324
8.3 Slope of a Line 332
8.4 Writing Equations of Lines 340
8.5 Systems of Two Linear Equations 350
8.6 Elimination-by-Addition Method 360
Chapter 8 Summary 370
Chapter 8 Review Problem Set 375
Chapter 8 Test 377
9 Roots and Radicals 379
9.1 Roots and Radicals 380
9.2 Simplifying Radicals 385
9.3 More on Simplifying Radicals 391
9.4 Products and Quotients Involving Radicals 397
9.5 Solving Radical Equations 402
Chapter 9 Summary 409
Chapter 9 Review Problem Set 412
Chapter 9 Test 413
Chapters 1 – 9 Cumulative Review Problem Set 414
10 Quadratic Equations 417
10.1 Quadratic Equations 418
10.2 Completing the Square 426
10.3 Quadratic Formula 431
10.4 Solving Quadratic Equations—Which Method? 436
10.5 Solving Problems Using Quadratic Equations 440
Chapter 10 Summary 447
Chapter 10 Review Problem Set 449
Chapter 10 Test 450