1.THE BASICS | |
Notation and Symbols | |
Real Numbers | |
Addition of Real Numbers | |
Subtraction of Real Numbers | |
Properties of Real Numbers | |
Multiplication of Real Numbers | |
Division of Real Numbers | |
Subsets of the Real Numbers | |
Addition and Subtraction with Fractions | |
Summary, Review, Projects, Test | |
2.LINEAR EQUATIONS AND INEQUALITIES | |
Simplifying Expressions | |
Addition Property of Equality | |
Multiplication Property of Equality | |
Solving Linear Equations | |
Formulas | |
Applications | |
More Applications | |
Linear Inequalities | |
Summary, Review, Projects, Test, Cumulative Review | |
3.GRAPHING AND LINEAR SYSTEMS | |
Paired Data and Graphing Ordered Pairs | |
Solutions to Linear Equations in Two Variables | |
Graphing Linear Equations in Two Variables | |
More on Graphing: Intercepts | |
Solving Linear Systems by Graphing | |
The Addition Method | |
The Substitution Method | |
Applications | |
Summary, Review, Projects, Test, Cumulative Review | |
4.EXPONENTS AND POLYNOMIALS | |
Multiplication With Exponents | |
Division With Exponents | |
Operations With Monomials | |
Addition and Subtraction of Polynomials | |
Multiplication With Polynomials | |
Binomial Squares and Other Special Products | |
Dividing a Polynomial by a Monomial | |
Dividing a Polynomial by a Polynomial | |
Summary, Review, Projects, Test, Cumulative Review | |
5. FACTORING | |
The Greatest Common Factor and Factoring by Grouping | |
Factoring Trinomials | |
More Trinomials to Factor | |
Special Factorings | |
Factoring: A General Review | |
Solving Equations by Factoring | |
Applications | |
Summary, Review, Projects, Test, Cumulative Review | |
6. RATIONAL EXPRESSIONS | |
Reducing Rational Expressions to Lowest Terms | |
Multiplication and Division of Rational Expressions | |
Addition and Subtraction of Rational Expressions | |
Equations Involving Rational Expressions | |
Applications | |
Complex Fractions | |
Proportions | |
Summary, Review, Projects, Test, Cumulative Review | |
7.TRANSITIONS | |
Review of Solving Equations | |
Equations With Absolute Value | |
Compound Inequalities and Interval Notation | |
Inequalities Involving Absolute Value | |
Factoring the Sum and Difference of Two Cubes | |
Review of Systems of Equations in Two Variables | |
Systems of Linear Equations in Three Variables | |
Summary, Review, Projects, Test, Cumulative Review | |
8.EQUATIONS AND INEQUALITIES IN TWO VARIABLES | |
The Slope of a Line | |
The Equation of a Line | |
Linear Inequalities in Two Variables | |
Introduction to Functions | |
Function Notation | |
Algebra With Functions | |
Variation | |
Summary, Review, Projects, Test, Cumulative Review | |
9. 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, Projects, Test, Cumulative Review | |
10. QUADRATIC FUNCTIONS | |
Completing the Square | |
The Quadratic Formula | |
Additional Items Involving Solutions to Equations | |
Equations Quadratic in Form | |
Graphing Parabolas | |
Quadratic Inequalities | |
Summary, Review, Projects, Test, Cumulative Review | |
11. 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, Projects, Test, Cumulative Review | |
12. SEQUENCES AND SERIES | |
Sequences | |
Series | |
Arithmetic Sequences | |
Geometric Sequences | |
The Binomial Expansion | |
Summary, Review, Projects, Test, Cumulative Review | |
13. CONIC SECTIONS | |
The Circle | |
Ellipses and Hyperbolas | |
Second-Degree Inequalities and Nonlinear Systems | |
Summary, Review, Projects, Test, Cumulative Review | |
Appendix: A: Synthetic Division | |
Appendix B: Introduction to Determinants | |
Appendix C: Cramers Rule | |
Appendix D: Matrix Solutions to Linear Systems | |
Appendix E: Answers to Odd-Numbered Problems, Reviews, Tests, and Cumulative Reviews | |
Index |
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