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Preface to the Instructor | |
Preface to the Student | |
1. BASIC PROPERTIES AND DEFINITIONS | |
Fundamental Definitions and Notation | |
The Real Numbers | |
Properties of Real Numbers | |
Arithmetic with Real Numbers | |
Recognizing Patterns | |
Summary | |
Review | |
Test | |
Projects | |
2. LINEAR EQUATIONS AND INEQUALITIES IN ONE VARIABLE | |
Linear Equations in One Variable | |
Formulas | |
Applications | |
Linear Inequalities in One Variable | |
Equations with Absolute Value | |
Inequalities Involving Absolute Value | |
Summary | |
Review | |
Cumulative Review | |
Test | |
Projects | |
3. EQUATIONS AND INEQUALITIES IN TWO VARIABLES | |
Paired Data and the Rectangular Coordinate System | |
The Slope of a Line | |
The Equation of a Line | |
Linear Inequalities in Two Variables | |
Introduction to Functions | |
Function Notation | |
Algebra and Composition with Functions | |
ariation | |
Summary | |
Review | |
Cumulative Review | |
Test | |
Projects | |
4. SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES | |
Systems of Linear Equations in Two Variables | |
Systems of Linear Equations in Three Variables | |
Introduction to Determinants | |
Cramer's Rule | |
Applications | |
Systems of Linear Inequalities | |
Summary | |
Review | |
Cumulative Review | |
Test | |
Projects | |
5. EXPONENTS AND POLYNOMIALS | |
Properties of Exponents | |
Polynomials, Sums, and Differences | |
Multiplication of Polynomials | |
The Greatest Common Factor and Factoring by Grouping | |
Factoring Trinomials | |
Special Factoring | |
Factoring: A General Review | |
Solving Equations by Factoring | |
Summary | |
Review | |
Cumulative Review | |
Test | |
Projects | |
6. RATIONAL EXPRESSIONS AND RATIONAL FUNCTIONS | |
Basic Properties and Reducing to Lowest Terms | |
Division of Polynomials | |
Multiplication and Division of Rational Expressions | |
Addition and Subtraction of Rational Expressions | |
Complex Fractions | |
Equations Involving Rational Expressions | |
Applications | |
Summary | |
Review | |
Cumulative Review | |
Test | |
Projects | |
7. RATIONAL EXPONENTS AND ROOTS | |
Rational Exponents | |
More Expressions Involving Rational Exponents | |
Simplified Form for Radicals | |
Addition and Subtraction of Radical Expressions | |
Multiplication and Division of Radical Expressions | |
Equations with Radicals | |
Complex Numbers | |
Summary | |
Review | |
Cumulative Review | |
Test | |
Projects | |
8. QUADRATIC FUNCTIONS | |
Completing the Square | |
The Quadratic Formula | |
Additional Items Involving Solutions to Equations | |
Equations Quadratic in Form | |
Graphing Parabolas | |
Quadratic Inequalities | |
Summary | |
Review | |
Cumulative Review | |
Test | |
Projects | |
9. EXPONENTIAL AND LOGARITHMIC FUNCTIONS | |
Exponential Functions | |
The Inverse of a Function | |
Logarithms are Exponents | |
Properties of Logarithms | |
Common Logarithms and Natural Logarithms | |
Exponential Equations and Change of Base | |
Summary | |
Review | |
Cumulative Review | |
Test | |
Projects | |
10. CONIC SECTIONS | |
The Circle | |
Ellipses and Hyperbolas | |
Second-degree Inequalities and Nonlinear Systems | |
Summary | |
Review | |
Cumulative Review | |
Test | |
Projects | |
11. SEQUENCES AND SERIES | |
Sequences | |
Series | |
Arithmetic Sequences | |
Geometric Sequences | |
he Binomial Expansion | |
Summary | |
Review | |
Cumulative Review | |
Test | |
Projects | |
Appendix A: Synthetic Division | |
Appendix B: Matrix Solutions to Linear Systems | |
Appendix C: Conditional Statements | |
Answers to Odd-Numbered Problems, Chapter Reviews, Chapter Tests, and Cumulative Reviews | |
Index |