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## Chapter 1 – Prerequisites

- Real Numbers: Algebra Essentials
- Exponents and Scientific Notation
- Radicals and Rational Exponents
- Polynomials
- Factoring Polynomials
- Rational Expressions

## Chapter 2 – Equations and Inequalities

- The Rectangular Coordinate Systems and Graphs
- Linear Equations in One Variable
- Models and Applications
- Complex Numbers
- Quadratic Equations
- Other Types of Equations
- Linear Inequalities and Absolute Value Inequalities

## Chapter 3 – 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

## Chapter 4 – Linear Functions

- Linear Functions
- Modeling with Linear Functions
- Fitting Linear Models to Data

## Chapter 5 – Polynomial and Rational Functions

- Quadratic Functions
- Power Functions and Polynomial Functions
- Graphs of Polynomial Functions
- Dividing Polynomials
- Zeros of Polynomial Functions
- Rational Functions
- Inverses and Radical Functions
- Modeling Using Variation

## Chapter 6 – 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

## Chapter 7 – 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

## Chapter 8 – Analytic Geometry

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

## Chapter 9 – Sequences, Probability, and Counting Theory

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