Intermediate Algebra

A series of free Intermediate Algebra Video Lessons from Brightstorm online Algebra series.

The 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

Solving Linear Equations
Solving for a Parameter in a Linear Equation
Applied Linear Equations: Geometry Problem
Applied Linear Equations: Mixture Problem
Applied Linear Equations: Investment Problem
Applied Linear Equations: Tax Problem
Applied Linear Equations: Distance Problem
Applied Linear Equations: Collection Problem
Applied Linear Equations: Consecutive Numbers

Factoring

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

Exponents

Introduction to Exponents - Rules of Exponents
Multiplication and Division Properties of Exponents
Zero and Negative Exponents
Scientific Notation
Simplifying Expressions with Exponents

Quadratic Equations and Inequalities

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
Introduction to Parabolas
Finding the Vertex of a Parabola by Completing the Square
Finding Intercepts, Domain, Range and Vertex of a Parabola
Finding the Maximum or Minimum of a Quadratic
Graphing a Horizontal Parabola
Dilations of Parabolas or Quadratic Graphs
Focus and Directrix of a Parabola

Quadratic Inequality
Graphing a Quadratic Inequality
Solving a Quadratic Inequality using a Sign Chart

Linear Inequalities

Solving Linear Inequalities
Set Operation: Union
Set Operation: Intersection
Solving a Three-part Linear Inequality or Compund Ineqaulity
Applied Linear Inequalities

Systems of Linear Equations

Solving a System of Linear Equations in Two Variables
Solving a Linear System in Three Variables with a Solution
Solving a Linear System in Three Variables with no or Infinite Solutions

Polynomials

Polynomials Basics
Introduction to Polynomials
Polynomial Function

Polynomial Graphs
Basic Polynomial Graphs
Basic Transformations

Multiplying and Dividing 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

Functions and Variation

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

Rational Expressions and Functions

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

Inverse, Exponential and Logarithmic Functions

Functions and 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 and Logarithmic Functions
Exponential Functions and their Graphs
Solving Exponential Equations with the 'Same' Base
Introduction to Logarithms
Solving Simple Logarithmic Equations
Function Notation with Logs and 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

Solving Exponential and Logarithmic Functions
Common and Natural Logarithms
Change of Base Formula
Solving Exponential Equations with the Different Bases
Solving a Logarithmic Equation
Solving a Logarithmic Equation with Multiple Logs

Applications of Exponential and Log Functions
Compound Interest (Finite Number of Calculations)
Compound Interest (Continuously)
Exponential Growth and Decay

Roots and Radicals

Radicals
Introduction to Radicals
Radicals and Absolute Values

Rational Exponents
Rational Exponents
Evaluating Rational Exponents
Rational Exponents with Negative Coefficients
Rules for Rational Exponents

Radical Expressions and Equations
Simplifying Radicals using Rational Exponents
Multiplying Radicals of the Same Root
Multiplying Radicals of Different Roots
Rationalizing the Denominator with Higher Roots
Rationalizing a Denominator with a Binomial
Solving an Equation with Radicals

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

Matrices

Introduction to Matrices
Matrix Operations
Augmented Matrices
Matrix Multiplication

Conic Sections

Introduction to Conic Sections
The Circle
The Ellipse
The Hyperbola
Transformations of a Hyperbola
Conic Section Formulas

Sequences and Series

Sequence and Series
Introduction to Sequences
Series and Summation Notation

Arithemtic Sequences and Series
Arithmetic Sequences
Arithmetic Series

Geometric Sequences and Series
Geometric Sequences
Geometric Series

Recusion Sequences
Recursion Sequences
Mathematical Induction

Additional Topics

Step Functions
Piecewise Functions
Using the Calculator
Common Algebra Mistakes

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