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
