Pre-Calculus / Trigonometry
Chapter P - Prerequisites
Real Numbers
Cartesian Coordinate System
Linear Equations and Inequalities
Lines in the Plane
Solving Equations Graphically, Numerically, and Algebraically
Complex Numbers
Solving Inequalities Algebraically and Graphically
Chapter 1 - Functions and Graphs
Modeling and Equation Solving
Functions and Their Properties
Twelve Basic Functions
Building Functions from Functions
Parametric Relations and Inverses
Graphical Transformations
Modeling with Functions
Chapter 2 - Polynomial, Power & Rational Functions
Linear and Quadratic Functions and Modeling
Power Functions with Modeling
Polynomial Functions of Higher Degree with Modeling
Real Zeros of Polynomial Functions
Complex Zeros and the Fundamental Theorem of Algebra
Graphs of Rational Functions
Solving Equations in One Variable
Chapter 3 - Exponential, Logistic, and Logarithmic Functions
Exponential and Logistic Functions
Exponential and Logistic Modeling
Logarithmic Functions and Their Graphs
Properties of Logarithmic Functions
Equation Solving and Modeling
Mathematics of Finance
Chapter 4 - Trigonometric Functions
Angles and Their Measures
Trigonometric Functions of Acute Angles
The Circular Functions
Graphs of Sine and Cosine
Inverse Trigonometric Functions
Solving Problems with Trigonometry
Chapter 5 - Analytic Trigonometry
Fundamental Identities
Proving Trigonometric Identities
Sum and Difference Identities
Multiple Angle Identities
The Law of Sines
The Law of Cosines
Area of a Triangle and Heron’s Formula
Chapter 6 - Applications of Trigonometry
Vectors in the Plane
Dot Product of Vectors
Polar Coordinates
De Moivre’s Theorem and nth Roots
Chapter 7 - Systems and Matrices
Solving Systems of Two Equations
Matrix Algebra
Multivariate Linear Systems and Row Operations