Intermediate Algebra or Algebra II

• Real Number Properties
  Real Numbers
  Introduction to Real Numbers
  Analyzing Data
  Properties of Real Numbers

• Graphs of Linear Equations
  Coordinate System
  Rectangular Coordinate System
  Midpoint Formula
  
  The Slope of a Line
  Definition of Slope
  Finding the Slope of a Line from a Graph
  Finding the Slope of a Line from 2 Points
  Finding the Slope of a Line from an Equation
  
  Equation of a Line
  Slope-Intercept Form of a Line
  Point-Slope Form of a Line
  Standard Form of a Line
  Applications of Linear Equations
  
  

• Linear Equations & Applications
  Linear Equations
  Solving Linear Equations
  Solving for a Parameter in a Linear Equation
  Applied Linear Equations: Geometry Problem
  Applied Linear Equations: Mixture Problem
  
  Applied Linear Equations
  Applied Linear Equations: Investment Problem
  Applied Linear Equations: Tax Problem
  Applied Linear Equations: Distance Problem
  Applied Linear Equations: Collection or Coin Problem
  Applied Linear Equations: Consecutive Numbers

• Factoring & Synthetic Division
  Method of Factoring
  Review of the Methods of Factoring
  Factoring the Sum or Difference of Cubes
  Factoring Complicated Expressions
  
  Synthetic Division
  Using Synthetic Division to Factor
  Solving by Factoring
  Rational Roots Theorem
  Using Synthetic Division to Solve an Equation

• Exponents & Scientific Notations
  Exponents
  Rules of Exponents
  Multiplication & Division Properties of Exponents
  Zero & Negative Exponents
  Scientific Notation
  Simplifying Expressions with Exponents

• Quadratic Equations & Quadratic Formula
  Quadratic Equations
  Vocabulary of Quadratic Polynomials
  Solving Quadratic Equations by Factoring
  Solving Quadratic Equations Using Square Roots
  Solving a Quadratic by Completing the Square
  
  Quadratic Formula
  Deriving the Quadratic Formula
  Overview of the Different Methods of Solving a Quadratic Equation
  The Discriminant of a Quadratic Equation
  Solving Quadratic Equations in Disguise

• Parabolas & Quadratic Graphs
  Graphing Parabolas
  Introduction to Parabolas
  Finding the Vertex of a Parabola by Completing the Square
  Finding Intercepts, Domain, Range & Vertex of a Parabola
  Finding the Maximum or Minimum of a Quadratic
  
  Parabolas
  Graphing a Horizontal Parabola
  Dilations of Parabolas or Quadratic Graphs
  Focus & Directrix of a Parabola
  
  Quadratic Inequality
  Graphing a Quadratic Inequality
  Solving a Quadratic Inequality using a Sign Chart

• Linear Inequalities
  Solve Linear Inequalities
  Set Operation: Union
  Set Operation: Intersection
  Solving a Three-part Linear Inequality or Compound Inequality
  Applied Linear Inequalities
  
  

• Systems of Linear Equations
  Solve Systems of Equations
  Solve a System of Linear Equations in Two Variables
  Solve a Linear System in Three Variables with a Solution
  Solve a Linear System in Three Variables with no or Infinite Solutions
  
  

• Polynomials & Synthetic Division
  Polynomials Basics
  Introduction to Polynomials
  Polynomial Function
  
  Polynomial Graphs
  Basic Polynomial Graphs
  Basic Transformations
  
  Multiply & Divide Polynomials
  Multiplying Polynomials
  Multiplying Complicated Polynomials
  Dividing Polynomials using Long Division
  
  Synthetic Division
  Dividing Polynomials using Synthetic Division
  Using Synthetic Division to Evaluate Polynomials
  
  

• Binomial Theorem
  Pascal's Triangle & Binomial Theorem
  Pascal's Triangle
  Binomial Theorem

• Functions & Variation
  Functions
  Introduction to Functions
  Domain & Range
  Function Notation
  Composition of Functions
  
  Variation
  Direct Variation
  Indirect Variation
  Joint & Combined Variation

• Rational Expressions & Equations
  Rational Expressions
  Definition & Domain of a Rational Expression
  Multiplying & Dividing Rational Expressions
  Adding & Subtracting Rational Expressions
  Simplifying Complex Fractions
  
  Rational Equations
  Solving a Rational Equation
  Graphing a Rational Expression
  Solving a Rational Equation for a parameter

• Inverse, Exponential & Logarithmic Functions
  Functions & Inverse Functions
  Definition of One-to-One Functions
  Definition of Inverse
  Finding an Inverse Algebraically
  Proving Two Functions are Inverses
  Finding an Inverse Graphically
  
  Exponential & Logarithmic Functions
  Exponential Functions & their Graphs
  Solving Exponential Equations with the 'Same' Base
  Introduction to Logarithms
  Solving Simple Logarithmic Equations
  Function Notation with Logs & Exponentials
  Graph of Logarithmic Functions
  
  Properties of Logarithms
  Product Rule of Logarithms
  Quotient Rule of Logarithms
  Power Rule of Logarithms
  
  Evaluating Logarithms
  Expanding Logarithms
  Condensing Logarithms
  Evaluating a Logarithmic Expression in terms of Known Quantities
  
  Solve Exponential & Logarithmic Functions
  Common & Natural Logarithms
  Change of Base Formula
  Solve Exponential Equations with the Different Bases
  Solve a Logarithmic Equation
  Solve a Logarithmic Equation with Multiple Logs
  
  Applications of Exponential & Log Functions
  Compound Interest (Finite Number of Calculations)
  Compound Interest (Continuously)
  Exponential Growth & Decay

• Roots & Radicals
  Radicals
  Introduction to Radicals
  Radicals & Absolute Values
  
  Rational Exponents
  Rational Exponents
  Evaluating Rational Exponents
  Rational Exponents with Negative Coefficients
  Rules for Rational Exponents
  
  Radical Expressions & Equations
  Simplifying Radicals using Rational Exponents
  Multiplying Radicals of the Same Root
  Multiplying Radicals of Different Roots
  
  Rationalize Denominator
  Rationalizing the Denominator with Higher Roots
  Rationalizing a Denominator with a Binomial
  Solve an Equation with Radicals

• Complex Numbers
  Imaginary Numbers
  Introduction to Imaginary Numbers
  Adding & Subtracting Complex Numbers
  Multiplying Complex Numbers
  Dividing Complex Numbers
  Powers of i

• Matrices
  Matrices
  Introduction to Matrices
  Matrix Operations
  Matrix Multiplication
  Augmented Matrices

• Conic Sections
  Parabolas
  Introduction to Conic Sections
  The Parabola
  The Circle
  The Ellipse
  
  Hyperbolas
  The Hyperbola
  Transformations of a Hyperbola
  Conic Section Formulas & Equations

• Sequences & Series
  Sequences
  Introduction to Sequences
  Series & Summation Notation
  
  Arithmetic Sequences & Series
  Arithmetic Sequences
  Arithmetic Series
  
  Geometric Sequences & Series
  Geometric Sequences
  Geometric Series
  
  Recursion Sequences
  Recursion Sequences
  Mathematical Induction

• Additional Topics
  Step Functions etc.
  Step Functions
  Piecewise Functions
  Using the Calculator
  Common Algebra Mistakes

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