1. ALGEBRA: THE FUNDAMENTALS | |
The Real Numbers | |
Operations with Real Numbers | |
Polynomials | |
Rational Expressions | |
Exponents and Radicals | |
The Complex Numbers | |
Chapter Summary | |
Review Exercises | |
Practice Test | |
2. EQUATIONS AND INEQUALITIES | |
First-Degree Equations and Inequalities in One Variable | |
Absolute Value Equations and Inequalities | |
Quadratic Equations | |
Radical Equations: Equations Reducible to Quadratic Form | |
Quadratic and Rational Inequalities | |
Substitution | |
Chapter Summary | |
Review Exercises | |
Practice Test | |
3. FUNCTIONS AND GRAPHS: PART I | |
The Cartesian Coordinate System: Graphing Straight Lines Functions and Circles | |
Slope | |
Equations of a Line | |
Relations and Functions | |
Function Notation | |
Relating Equations to Their Graphs | |
Introduction to Graph Sketching: Symmetry | |
Chapter Summary | |
Review Exercises | |
Practice Test | |
4. FUNCTIONS AND GRAPHS: PART II | |
Basic Graphing Principles | |
More Graphing Principles: Types of Functions | |
Mathematical Modeling: Extracting Functions from Real-Life Situations | |
Quadratic Functions | |
Operations on Functions | |
Inverse Functions | |
Chapter Summary | |
Review Exercises | |
Practice Test | |
5. POLYNOMIAL, RATIONAL AND RADICAL FUNCTIONS | |
Polynomial Functions | |
More Polynomial Functions and Mathematical Models | |
Polynomial Division, Roots of Polynomials; The Remainder and Factor Theorems | |
More on Roots of Polynomial Equations; The Rational Root Theorem and Descartes's Rule of Signs | |
ational Functions | |
Radical Functions | |
Variation | |
Chapter Summary | |
Review Exercises | |
Practice Test | |
6. EXPONENTIAL AND LOGARITHMIC FUNCTIONS | |
Exponential Functions | |
Logarithmic Functions | |
Properties of Logarithms: Logarithmic Equations | |
Common and Natural Logarithms: Exponential Equations and Change of Base | |
Applications | |
Chapter Summary | |
Review Exercises | |
Practice Test | |
7. SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES | |
Elimination and Substitution: 2 X 2 Linear Systems | |
Elimination and Gaussian Elimination: 3 X 3 Linear Systems | |
Solving Linear Systems Using Augmented Matrices | |
The Algebra of Matrices | |
Solving Linear | |
Systems Using Matrix Inverses | |
Determinants and Cramer's Rule: 2 X 2 and 3 X 3 Systems | |
Properties of Determinants | |
Systems of Linear Inequalities | |
An Introduction to Linear Programming: Geometric Solutions | |
Chapter Summary | |
Review Exercises | |
Practice Test | |
8. CONIC SECTIONS AND NONLINEAR SYSTEMS | |
Conic Sections: Circles | |
The Parabola | |
The Ellipse | |
The Hyperbola | |
Identifying Conic Sections: Degenerate Forms | |
Nonlinear Systems of Equations and Inequalities | |
Chapter Summary | |
Review Exercises | |
Practice Test | |
9. SEQUENCE, SERIES AND RELATED TOPICS | |
Sequences | |
Series and Sigma Notation | |
Arithmetic Sequences and Series | |
Geometric Sequences and Series | |
Mathematical Induction | |
Permutations and Combinations | |
Probability | |
The Binomial Theorem | |
Chapter Summary | |
Review Exercises | |
Practice Test |
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