Table of Contents
Real Numbers. Algebra Review. Geometry Review. Integer Exponents. Polynomials. Factoring Polynomials. Rational Expressions. Square Roots; Radicals. Rational Exponents.
1. Equations and Inequalities.
Equations. Setting up Equations: Applications. Quadratic Equations. Radical Equations; Equations Quadratic in Form. Solving Inequalities. Equations and Inequalities Involving Absolute Value.
Rectangular Coordinates. Graphs of Equations. Lines. Parallel and Perpendicular Lines; Circles. Scatter Diagrams; Linear Curve Fitting. Variation.
3. Functions and Their Graphs.
Functions. Properties of Functions. Library of Functions; Piecewise-Defined Functions. Graphing Techniques: Transformations. Operations on Functions; Composite Functions. Mathematical Models: Constructing Functions.
4. Polynomial and Rational Functions.
Quadratic Functions and Models. Polynomial Functions. Rational Functions I. Rational Functions II: Analyzing Graphs. Polynomial and Rational Inequalities.
5. The Zeros of a Polynomial Function.
Synthetic Division. The Real Zeros of a Polynomial Function. Complex Numbers; Quadratic Equations with a Negative Discriminant. Complex Zeros; Fundamental Theorem of Algebra.
6. Exponential and Logarithmic Functions.
One-to-One Functions; Inverse Functions.Exponential Functions. Logarithmic Functions. Properties of Logarithms; Exponential and Logarithmic Models. Logarithmic and Exponential Equations. Compound Interest. Growth and Decay; Newton's Law; Logistic Models. Logarithmic Scales.
7. The Conics.
Preliminaries. The Parabola. The Ellipse. The Hyperbola.
8. Systems of Equations and Inequalities.
Systems of Linear Equations: Two Equations Containing Two Variables. Systems of Linear Equations: Three Equations Containing Three Variables. Systems of Linear Equations: Matrices. Systems of Linear Equations: Determinants. Matrix Algebra. Partial Fraction Decomposition. Systems of Nonlinear Equations. Systems of Inequalities. Linear Programming.
9. Sequences; Induction; The Binomial Theorem.
Sequences. Arithmetic Sequences. Geometric Sequences; Geometric Series. Mathematical Induction. The Binomial Theorem.
10. Counting and Probability.
Sets and Counting. Permutations and Combinations. Probability.
Appendix: Graphing Utilities.
The Viewing Rectangle. Using a Graphing Utility to Graph Equations. Using a Graphing Utility to Locate Intercepts and Check for Symmetry. Using a Graphing Utility to Solve Equations. Square Screens. Using a Graphing Utility to Graph Inequalities. Using a Graphing Utility to Solve Systems of Linear Equations.