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Tables of Contents for Introductory, Intermediate and College Algebra
Chapter/Section Title
Page #
Page Count
Preface
xi
To the Student: Success in Algebra
xxi
Introduction to the Graphics Calculator
xxiii
The Real Numbers
1
40
Basic Terms
2
11
Operations on Real Numbers
13
13
Properties of Real Numbers
26
15
Summary
33
1
Key Terms
33
1
New Symbols
33
1
Quick Review
33
2
Review Exercises
35
4
Test
39
2
Linear Equations and Inequalities
41
82
Linear Equations in One Variable
42
8
Formulas and Topics from Geometry
50
10
Applllications of Linear Equations
60
12
More Applications of Linear Equations
72
9
Linear Equations in One Variable
81
10
Set Operations and Compound Inequalities
91
7
Absolute Value Equations and Inequalities
98
25
Summary: Solving Linear and Absolute Value Equations and Inequalities
108
1
Summary
109
1
Key Terms
109
1
New Symbols
109
1
Quick Review
110
3
Review Exercises
113
6
Test
119
1
Cumulative Review (Chapters 1-2)
120
3
Exponents and Polynomials
123
78
Integer Exponents
124
7
Further Properties of Exponents
131
9
Addition and Subtraction of Polynomials
140
9
Multiplication of Polynomials
149
8
Greatest Common Factors: Factoring by Grouping
157
7
Factoring Trinomials
164
7
Special Factoring
171
6
General Methods of Factoring
177
5
Solving Equations by Factoring
182
19
Summary
190
1
Key Terms
190
1
New Symbols
190
1
Quick Review
190
2
Review Exercises
192
5
Test
197
1
Cumulative Review (Chapters 1-3)
198
3
Rational Expressions
201
120
Multiplication and Division of Rational Expressions
202
10
Addition and Subtraction of Rational Expressions
212
6
Complex Fractions
218
6
Division of Polynomials
224
5
Synthetic Division
229
5
Equations with Rational Expressions
234
6
Applications
240
22
Summary
250
1
Key Terms
250
1
Quick Review
250
3
Review Exercises
253
4
Test
257
1
Cumulative Review (Chapter 1-4)
258
4
Roots and Radicals
Rational Exponents and Radicals
262
7
More About Rational Exponents and Radicals
269
5
Simplifying Radicals
274
8
Adding and Subtracting Radical Expressions
282
5
Multiplying and Dividing Radical Expressions
287
8
Equations with Radicals
295
7
Complex Numbers
302
19
Summary
310
1
Key Terms
310
1
New Symbols
310
1
Quick Review
310
3
Review Exercises
313
4
Test
317
1
Cumulative Review (Chapters 1-5)
318
3
Quadratic Equations and Inequalities
321
52
Completing the Square
322
8
The Quadratic Formula
330
10
Equations Quadratic in Form
340
8
Formulas and Applications
348
9
Nonlinear Inequalities
357
16
Summary
363
1
Key Terms
363
1
Quick Review
363
3
Review Exercises
366
3
Test
369
1
Cumulative Review (Chapters 1-6)
370
3
The Straight Line
373
78
The Rectangular Coordinate System
374
15
The Slope of a Line
389
14
Linear Equations
403
10
Linear Inequalities
413
8
Introduction to Functions
421
12
Variation
433
18
Summary
442
1
Key Terms
442
1
New Symbols
442
1
Quick Review
442
2
Review Exercises
444
3
Test
447
2
Cumulative Review (Chapters 1-7)
449
2
Graphing Relations and Functions
451
84
Combining Functions: The Algebra of Functions
452
9
Quadratic Functions; Parabolas
461
10
More About Parabolas and Their Applications
471
11
Symmetry; Increasing/Decreasing Functions
482
8
The Circle and the Ellipse
490
11
The Hyperbola; Square Root Functions
501
14
Other Useful Functions
515
20
Summary
524
1
Key Terms
524
1
New Symbols
524
1
Quick Review
524
4
Review Exercises
528
4
Test
532
1
Cumulative Review (Chapters 1-8)
533
2
Polynomial and Rational Functions and Their Zeros
535
60
Poynomial Functions and Their Graphs
536
11
Zeros of Polynomial Functions
547
7
Rational Zeros of Polynomial Functions
554
6
Real Zeros of Polynomial Functions
560
9
Rational Functions
569
26
Summary
584
1
Key Terms
584
1
Quick Review
584
3
Review Exercises
587
5
Test
592
1
Cumulative Review (Chapters 1-9)
593
2
Inverse, Exponential, and Logarithmic Functions
595
62
Inverse Functions
596
9
Exponential Functions
605
9
Logarithmic Functions
614
8
Properties of Logarithms
622
7
Evaluating Logarithms
629
9
Exponential and Logarithmic Equations and Their Applications
638
19
Summary
646
1
Key Terms
646
1
Quick Review
646
3
Review Exercises
649
4
Test
653
1
Cumulative Review (Chapter 1-10)
654
3
Systems of Equations and Inequalities
657
62
Linear Systems of Equations in Two Variables
658
11
Linear Systems of Equations in Three Variables
669
8
Applications of Linear Systems of Equations
677
20
Nonlinear Systems of Equations
687
32
Summary
708
1
Key Terms
708
1
Quick Review
708
4
Review Exercises
712
3
Test
715
1
Cumulative Review (Chapters 1-11)
716
3
Matrices and Determinants
719
42
Matrices and Determinants
720
8
Properties of Determinants
728
9
Solution of Linear Systems of Equations by Determinants--Cramer's Rule
737
6
Solution of Linear Systems of Equations by Matrices
743
18
Summary
753
1
Key Terms
753
1
New Symbols
753
1
Quick Review
753
3
Review Exercises
756
2
Test
758
1
Cumulative Review (Chapter 1-12)
759
2
Further Topics in Algebra
761
Sequences and Series
762
7
Arithmetic Sequences
769
6
Geometric Sequences
775
8
The Binomial Theorem
783
6
Mathematical Induction
789
6
Permutations and Combinations
795
9
Probability
804
Summary
812
1
Key Terms
812
1
New Symbols
812
1
Quick Review
813
3
Review Exercises
816
2
Test
818
2
Cumulative Review (Chapters 1-13)
820
3
Answers to Selected Exercises
823
54
Index
877
APPENDIX A
A-1
1
A.1 The Addition and Multiplication Properties of Equality
A-3
1
Exercises
A-9
1
A.2 More on Solving Linear Equations
A-11
1
Exercises
A-17
1
APPENDIX B
B-1
1
B.1 The Quotient of a Polynomial and a Monomial
B-3
1
Exercises
B-5
1
B.2 The Quotient of Two Polynomials
B-7
1
Exercises
B-10
1
APPENDIX C
C-1
1
C.1 Basic Properties of Matrices
C-3
1
Exercises
C-7
1
Matrix Products
C-9
1
Exercises
C-15
1
Multiplicative Inverses of Matrices
C-17
1
Exercises
C-26
1
APPENDIX D ANSWERS TO SELECTED EXERCISES FOR APPENDICES A, B, AND C
D-1
1
A.1 Answers
D-3
1
A.2 Answers
D-3
1
B.1 Answers
D-4
1
B.2 Answers
D-4
1
C.1 Answers
D-5
1
C.1 Answers
D-5
1
C.2 Answers
D-6