Course Contents at a Glance

an icon of a pair of binoculars

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