1. Basic Concepts of Algebra.
The Real-Number System.
Exponential, Scientific, and Absolute-Value Notation.
Addition and Subtraction of Algebraic Expressions.
Multiplication of Algebraic Expressions.
Factoring.
Rational Expressions.
Radical Notation.
Rational Exponents.
Handling Dimension Symbols.
2. Equations, Inequalities, and Problem Solving.
Solving Equations and Inequalities.
Rational Equations.
Formulas and Problem Solving.
The Complex Numbers.
Quadratic Equations.
Formulas and Problem Solving.
Radical Equations.
Equations Reducible to Quadratic Variation.
3. Functions, Graphs, and Transformations.
Graphs of Equations.
The Distance Formula and Circles.
Functions.
Lines and Linear Functions.
Graphs and Applications of Functions.
Symmetry.
Combinations of Functions.
Transformations of Functions.
4. Polynomial and Rational Functions.
Quadratic Functions.
Sets, Sentences, and Inequalities.
Equations and Inequalities with Absolute Value.
Polynomial and Rational Inequalities.
Graphs of Polynomial Functions.
Division of Polynomials.
Theorems About Roots.
Further Help in Finding Roots.
Rational Functions.
5. Exponential and Logarithmic Functions.
Inverses of Relations and Functions.
Exponential Functions.
Logarithmic Functions.
Properties of Logarithmic Functions.
Finding Logarithmic Function Values on a Calculator.
Graphs of Exponential Functions with Base E, and Applications.
Solving Exponential and Logarithmic Equations.
Applications of Exponential and Logarithmic Functions.
Applications of Exponential and Natural Logarithmic Functions.
6. The Trigonometric Functions.
Trigonometric Functions of Acute Angles.
Applications of Right Triangles.
Trigonometric Functions of Any Angle.
Radians, Arc Length, and Angular Speed.
Graphs of Basic Circular Functions.
Graphs of Transformed Sine and Cosine Functions.
Transformed Graphs of Other Trigonometric Functions.
7. Trigonometric Identities, Inverse Functions, and Equations.
Trigonometric Manipulations and Identities.
Sum and Difference Identities.
Cofunction and Related Identities.
Some Important Identities.
Proving Trigonometric Identities.
Inverse of the Trigonometric Functions.
Composition of Trigonometric Functions and Their Inverses.
Trigonometric Equations.
Identities in Solving Trigonometric Equations.
8. Triangles, Vectors, and Applications.
The Law of Sines.
The Law of Cosines.
Vectors and Applications.
Polar Coordinates.
Complex Numbers.
Complex Numbers: DeMoivre's Theorem and nth Roots of Complex Numbers.
9. Systems and Matrices.
Systems of Equations in Two Variables.
Systems of Equations in Three or More Variables.
Special Cases of Systems.
Matrices.
