The following list shows a summary of the topics covered in this course. To see all of the course pages, visit the Table of Contents.

Module 1: Introduction to Functions

• Functions and Function Notation
• Domain and Range
• Rates of Change and Behavior of Graphs
• Composition of Functions
• Transformation of Functions
• Absolute Value Functions
• Inverse Functions

Module 2: Linear Functions

• Linear Functions
• Graphs of Linear Functions
• Modeling with Linear Functions
• Fitting Linear Models to Data

Module 3: Polynomial and Rational Functions

• Complex Numbers
• Quadratic Functions
• Power Functions and Polynomial Functions
• Graphs of Polynomial Functions
• Dividing Polynomials
• Zeros of Polynomial Functions
• Rational Functions
• Inverse Functions
• Modeling Using Variation

Module 4: Exponential and Logarithmic Functions

• Exponential Functions
• Graphs of Exponential Functions
• Logarithmic Functions
• Graphs of Logarithmic Functions
• Logarithmic Properties
• Exponential and Logarithmic Equations
• Exponential and Logarithmic Models
• Fitting Exponential Models to Data

Module 5: Systems of Equations and Inequalities

• Systems of Linear Equations: Two Variables
• Systems of Linear Equations: Three Variables
• Systems of Nonlinear Equations and Inequalities: Two Variables
• Partial Fractions
• Matrices and Matrix Operations
• Solving Systems with Gaussian Elimination
• Solving Systems with Inverses
• Solving Systems with Cramer’s Rule

Module 6: Sequences, Probability, and Counting Theory

• Sequences and Their Notations
• Arithmetic Sequences
• Geometric Sequences
• Series and Their Notations
• Counting Principles
• Binomial Theorem
• Probability

Module 7: Trigonometric Functions

• Introduction to Trigonometric Functions
• Angles
• Unit Circle: Sine and Cosine Functions
• The Other Trigonometric Functions
• Right Triangle Trigonometry

Module 8: Periodic Functions

• Graphs of the Sine and Cosine Function
• Graphs of the Other Trigonometric Functions
• Inverse Trigonometric Functions

Module 9: Trigonometric Identities and Equations

• Solving Trigonometric Equations With Identities
• Sum and Difference Identities
• Double Angle, Half Angle, and Reduction Formulas
• Sum-to-Product and Product-to-Sum Formulas
• Solving Trigonometric Equations
• Modeling with Trigonometric Equations

Module 10: Further Applications of Trigonometry

• Non-right Triangles: Law of Sines
• Non-right Triangles: Law of Cosines
• Polar Coordinates
• Polar Coordinates: Graphs
• Polar Form of Complex Numbers
• Parametric Equations
• Parametric Equations: Graphs
• Vectors

Module 11: Analytic Geometry


• The Ellipse
• The Hyperbola
• The Parabola
• Rotation of Axes
• Conic Sections in Polar Coordinates

Module 12: Introduction to Calculus


• Finding Limits: Numerical and Graphical Approaches
• Finding Limits: Properties of Limits
• Continuity
• Derivatives