Chapter 1: Basic Algebraic Operations
- Algebra & Real Numbers
- Polynomials: Basic Operations
- Polynomials: Factoring
- Rational Expressions: Basic Operations
- Integer Exponents
- Rational Exponents
- Radicals
Chapter 2: Equations and Inequalities
- Linear Equations & Applications
- Systems of Linear Equations & Applications
- Linear Inequalities
- Absolute Value in Equations and Inequalities
- Complex Numbers
- Quadratic Equations & Applications
- Equations Reducible to Quadratic Form
- Polynomial & Rational Inequalities
Chapter 3: Graphs & Functions
- Basic Tools; Circles
- Straight Lines
- Functions
- Graphing Functions
- Combining Functions
- Inverse Functions
Chapter 4: Polynomial & Rational Functions
- Polynomial Functions and Graphs
- Finding Rational Zeros of Polynomials
- Approximating Real Zeros of Polynomials
- Rational Functions
- Partial Fractions
Chapter 5: Exponential & Logarithmic Functions
- Exponential Functions
- The Exponential Function With Base e
- Logarithmic Functions
- Common and Natural Logarithms
- Exponential & Logarithmic Equations
Chapter 6: Trigonometric Functions
- Angles and Their Measure
- Acute Angle Domains
- General Angle and Real Number Domains
- Exact Values for Special Angles and Real Numbers
- Circular Functions
- Graphing Basic Trigonometric Functions
- Graphing y= k + A sin(Bx+C) and y= k + A cos(Bx + C)
- Graphing More General Tangent, Cotangent, Secant and Cosecant
Functions
- Inverse Trigonometric Functions
Chapter 7: Trigonometric Identities and Conditional Equations
- Basic Identities and Their Use
- Sum, Difference, and Cofunction Identities
- Double-Angle and Half-Angle Identities
- Product-Sum and Sum-Product Identities
- Trigonometric Equations
Chapter 8: Additional Topics in Trigonometry
- Law of Sines
- Law of Cosines
- Geometric Vectors
- Algebraic Vectors
- Polar Coordinates and Graphs
- Complex Numbers in Rectangular and Polar Forms
- De Moivre’s Theorem
Chapter 9: Systems of Equations & Inequalities
- Systems of Linear Equations and Augmented Matrices
- Gauss-Jordan Elimination
- Systems Involving Second-Degree Equations
- Systems of Linear Inequalities in Two Variables
- Linear Programming
Chapter 10: Matrices and Determinants
- Matrices: Basic Operations
- Inverse of a Square Matrix
- Matrix Equations and Systems of Linear Equations
- Determinants
- Properties of Determinants
- Cramer’s Rule
Chapter 11: Sequences & Series
- Sequences and Series
- Mathematical Induction
- Arithmetic & Geometric Sequences
- Binomial Formula
- Multiplication Principle, Permutations, and Combinations
Chapter 12: Additional Topics in Analytic Geometry
- Conic Sections; Parabola
- Ellipse
- Hyperbola
- Translation of Axes
- Parametric Equations
