Elementary and Intermediate Algebra Book

TO THE STUDENT

PREFACE
1 Real Numbers and Their Properties
1.1 The Real Numbers
1.2 Fractions
1.3 Addition and Subtraction of Real Numbers
1.4 Multiplication and Division of Real Numbers
1.5 Exponential Expressions and the Order of Operations
1.6 Algebraic Expressions
1.7 Properties of the Real Numbers
1.8 Using the Properties to Simplify Expressions
Chapter 1 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 1 Test
• Critical Thinking
2 Linear Equations and Inequalities in One Variable
2.1 The Addition and Multiplication Properties of Equality
2.2 Solving General Linear Equations
2.3 More Equations
2.4 Formulas
2.5 Translating Verbal Expressions into Algebraic Expressions
2.6 Number, Geometric, and Uniform Motion Applications
2.7 Discount, Investment, and Mixture Applications
2.8 Inequalities
2.9 Solving Inequalities and Applications
Chapter 2 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 2 Test
• Making Connections: A review of Chapters 1-2
• Critical Thinking
3 Linear Equations and Inequalities in Two Variables
3.1 Graphing Lines in the Coordinate Plane
3.2 Slope
3.3 Equations of Lines in Slope-Intercept Form
3.4 The Point-Slope Form
3.5 Variations
3.6 Graphing Linear Inequalities in Two Variables
Chapter 3 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 3 Test
• Making Connections: a review of Chapters 1-3
• Critical Thinking
4 Exponents and Polynomials
4.1 The Rules of Exponents
4.2 Negative Exponents and Scientific Notation
4.3 Addition and Subtraction of Polynomials
4.4 Multiplication of Polynomials
4.5 Multiplication of Binomials
4.6 Special Products
4.7 Division of Polynomials
Chapter 4 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 4 Test
• Making Connections: a review of Chapters 1-4
• Critical Thinking
5 Factoring
5.1 Factoring Out Common Factors
5.2 Special Products and Grouping
5.3 Factoring the Trinomial ax² + bx + c with a = 1
5.4 Factoring the Trinomial ax² + bx + c with a ≠ 1
5.5 The Factoring Strategy
5.6 Solving Quadratic Equations by Factoring
Chapter 5 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 5 Test
• Making Connections: a review of Chapters 1-5
• Critical Thinking
6 Rational Expressions
6.1 Reducing Rational Expressions
6.2 Multiplication and Division
6.3 Finding the Least Common Denominator
6.4 Addition and Subtraction
6.5 Complex Fractions
6.6 Solving Equations with Rational Expressions
6.7 Applications of Ratios and Proportions
6.8 Applications of Rational Expressions
Chapter 6 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 6 Test
• Making Connections: a review of Chapters 1-6
• Critical Thinking
7 Systems of Linear Equations
7.1 Solving Systems by Graphing and Substitution
7.2 The Addition Method
7.3 Systems of Linear Equations in Three Variables
Chapter 7 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 7 Test
• Making Connections: a review of Chapters 1-7
• Critical Thinking
8 More on Inequalities
8.1 Compound Inequalities in One Variable
8.2 Absolute Value Equations and Inequalities
8.3 Compound Inequalities in Two Variables
8.4 Linear Programming
Chapter 8 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 8 Test
• Making Connections: a review of Chapters 1-8
• Critical Thinking
9 Radicals and Rational Exponents
9.1 Radicals
9.2 Rational Exponents
9.3 Adding, Subtracting, and Multiplying Radicals
9.4 Quotients, Powers, and Rationalizing Denominators
9.5 Solving Equations with Radicals and Exponents
9.6 Complex Numbers
Chapter 9 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 9 Test
• Making Connections: a review of Chapters 1-9
• Critical Thinking
10 Quadratic Equations and Inequalities
10.1 Factoring and Completing the Square
10.2 The Quadratic Formula
10.3 More on Quadratic Equations
10.4 Graphing Parabolas
10.5 Quadratic and Rational Inequalities
Chapter 10 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 10 Test
• Making Connections: a review of Chapters 1-10
• Critical Thinking
11 Functions
11.1 Functions and Relations
11.2 Graphs of Functions and Relations
11.3 Transformations of Graphs
11.4 Graphs of Polynomial Functions
11.5 Graphs of Rational Functions
11.6 Combining Functions
11.7 Inverse Functions
Chapter 11 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 11 Test
• Making Connections: a review of Chapters 1-11
• Critical Thinking
12 Exponential and Logarithmic Functions
12.1 Exponential Functions and Their Applications
12.2 Logarithmic Functions and Their Applications
12.3 Properties of Logarithms
12.4 Solving Equations and Applications
Chapter 12 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 12 Test
• Making Connections: a review of Chapters 1-12
• Critical Thinking
13 Nonlinear Systems and the Conic Sections
13.1 Nonlinear Systems of Equations
13.2 The Parabola
13.3 The Circle
13.4 The Ellipse and Hyperbola
13.5 Second-Degree Inequalities
Chapter 13 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 13 Test
• Making Connections: a review of Chapters 1-13
• Critical Thinking
14 Sequences and Series
14.1 Sequences
14.2 Series
14.3 Arithmetic Sequences and Series
14.4 Geometric Sequences and Series
14.5 Binomial Expansions
Chapter 14 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 14 Test
• Making Connections: A Review of Chapter 1-14
• Critical Thinking
Appendix A: Geometry Review Exercises
Appendix B: Sets
Appendix C: Chapters 1-6 Diagnostic Test
Appendix D: Chapters 1-6 Review
Answers to Selected Exercises
Index