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Table of Contents
PREFACE APPLICATIONS INDEX 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 and Functions 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 4.3 Scientific Notation 4.4 Addition and Subtraction of Polynomials 4.5 Multiplication of Polynomials 4.6 Multiplication of Binomials 4.7 Special Products 4.8 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 Difference and Sum of Cube and a 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 The Graphing Method 7.2 The Substitution Method 7.3 The Addition Method 7.4 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 Quadratic Functions 10.5 Quadratic 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 (Available online at www.mhhe.com/dugopolski) 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