Fractions

• Before You Start
• Reminder
• Simple Fractions
• Complex Fractions
• Compound Fractions
• Converting Decimals to Fractions
• Converting Percentages to Fractions or Decimals
• Summary of Rules

Units of Conversion

Complex Numbers

• Basic Definitions and Arithmetic
• The Complex Plane
• The Polar Form of a Complex Number
• Euler's Formula

Quadratic Equations

• Basic Definitions
• Solutions or Roots of Quadratic Equations
• Completing the Square
• Quadratic Formula
• Solutions by Factoring
• Sign of Quadratic Functions: Application to Inequalities

Factorization and Roots of Polynomials

• Polynomial Long Division
• An Introduction: Factoring and Roots of Polynomials
• Finding Roots of Polynomials Graphically and Numerically
• The Fundamental Theorem of Algebra
• Factoring: Some Special Cases
• Quadratic Polynomials: Factoring by Guessing
• Quadratic Polynomials: Completing the Square
• Quadratic Polynomials: The Quadratic Formula
• Factoring over the Complex Numbers
• Rational Zeros of Polynomials
• The "Cubic Formula"
• The Geometry of the Cubic Formula
• The "Quartic Formula"

Solving Equations

• Linear Equations
• Equations Containing Radicals
• Equations Containing Absolute Value(s)
• Quadratic Equations
• Equations Involving Fractions
• Exponential Equations
• Logarithmic Equations
• Trigonometric Equations

Systems of Equations

• Systems of linear equations in Two variables.
• Systems of linear equations in Three variables.

Inequalities

• Basic Rules
• The Real Number Line, Interval Notation and Set Notation
• Absolute Value Inequalities
• Solving Polynomial Inequalities by Graphing
• Solving Polynomial Inequalities Analytically
• Solving Rational Inequalities Analytically

Inverse Functions

• Introduction
• Inverse Functions With No Domain Restriction
• Composition of Functions
• Inverse Functions With Domain Restriction

Logarithms and Exponential Functions

• Equivalence
• Exponential Shortcuts
• Exponential Rules
• Exponential Functions
• Logarithmic Functions
• Properties of Logarithms
• Graphs of Logarithms
• Change of Base
• Rules of Logarithms
• Logarithmic Inverse Functions
• Solving Exponential Equations
• Solving Logarithmic Equations
• Solving word problems related to exponential and logarithmic functions

Rational Functions

• The Method of Partial Fractions