http://cnx.org/content
http://cnx.org/content/col10624/1.15
col10624
Advanced Algebra II: Conceptual Explanations
1.15
2008/11/11 16:57:22.652 US/Central
2010/05/04 12:18:56.857 GMT-5
Kenny
Felder
Kenny M. Felder
KFelder@RaleighCharterHS.org
kennyfelder
kennyfelder
kennyfelder
Creative Commons Attribution License 2.0
algebra
Algebra 2
conceptual
felder
Mathematics and Statistics
This is the Conceptual Explanations part of Kenny Felder's course in Advanced Algebra II. It is intended for students to read on their own to refresh or clarify what they learned in class. This text is designed for use with the "Advanced Algebra II: Homework and Activities" (http://cnx.org/content/col10686/latest/) and the "Advanced Algebra II: Teacher's Guide" (http://cnx.org/content/col10687/latest/) collections to make up the entire course.
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How to Use Advanced Algebra II
Functions
Function Concepts
Introduction to Functions Video
What is a Variable?
Defining Variables Video
What is a Function?
The Rule of Consistency
Four Ways to Represent a Function
Connecting Graphs, Tables, and Equations Video
Interpreting Graphs Video
Domain and Range
Domain and Range Video
Functions in the Real World
Function Notation
Function Notation Video
Algebraic Generalizations
Writing an Equation Video
Determining Whether a Relation is a Function Video
Graphing
Interpreting Graphs Video
Lines
Definition of Slope Video
Applications of Linear Equations Video
Writing an Equation Video
Writing an Equation to Describe a Table Video
Composite Functions
Inverse Functions
Definition of Inverse Video
Finding the Inverse Video
Graphing Inverse Functions Video
Proving Inverse Functions Video
Inequalities and Absolute Values
Inequalities
Solving Multi Step Inequalities Video
Compound Inequalities Video
Linear Inequalities Video
Solving Inequalities Using Multiplication Video
Absolute Value Equations
Absolute Value Equations Video
Absolute Value Video
Absolute Value Inequalities
Absolute Value Inequalities Video
Solving Absolute Value Inequalities Video
Graphing Absolute Values
Shifts in Absolute Value Graphs Video
Absolute Value Graphing Video
Graphing Inequalities
Graphing Inequalities with Two Variables Video
Solving and Graphing Inequalities Video
"Piecewise Functions" and Absolute Value
Piecewise Functions Video
Simultaneous Equations
Distance, Rate and Time
Simultaneous Equations by Graphing
Substitution
Elimination
Special Cases
Word Problems
Using Letters as Numbers
Quadratic Functions
Multiplying Binomials
Multiplying Binomials Video
Factoring
Solving Quadratic Equations by Factoring Video
Solving Quadratic Equations by Factoring
Solving Quadratic Equations by Completing the Square
Completing the Square Video
Solving Quadratic Equations by Completing the Square Video
The Quadratic Formula
Deriving the Quadratic Formula Video
The Quadratic Formula Video
Different Types of Solutions to Quadratic Equations
Graphing Quadratic Equations
Graphing Quadratic Inequalities Video
Graphing a Horizontal Parabola Video
Parabola Focus Video
Parabola Intercept Video
Parabola Vertex Video
Graph Dilations Video
Graph Shifts Video
Graphing Quadratic Equations Video
Quadratic Graphs Video
Solving Problems by Graphing Quadratic Functions
Quadratic Inequalities
Graphing Quadratic Inequalities Video
Exponents
Exponent Concepts
Laws of Exponents
Laws of Exponents Video
Multiplying Exponents Video
Simplifying Expressions with Exponents Video
Zero, Negative Numbers, and Fractions as Exponents
Negative and Zero Exponents Video
Exponential Curves
Graphing Exponential Functions Video
Exponential Growth and Decay Video
Compound Interest Video
Exponential Growth and Decay Video
Logarithms
Logarithm Concepts
Introduction to Logarithms Video
Simple Logarithmic Equations Video
Solving Logarithmic Equations Video
The Logarithm Explained by Analogy to Roots
Rewriting Logarithm Equations as Exponent Equations
Graphing Exponential Functions Video
Solving Exponential Equations Video
The Logarithm Defined as an Inverse Function
Definition of Inverse Video
Finding the Inverse Video
Graphing Inverse Functions Video
Proving Inverse Functions Video
Properties of Logarithms
Condensing Logarithms Video
Evaluating Logarithms Video
Expanding Logarithms Video
Properties of Logarithms Video
Logarithmic Functions Video
Common Logarithms
Common Logarithm Video
Graphing Logarithmic Functions
Graphing Logarithmic Functions Video
Rational Expressions
Rational Expression Concepts
Rational Functions Video
Rational Expressions Video
Simplifying Rational Expressions
Simplifying Complex Fractions Video
Simplifying Rational Functions Video
Multiplying Rational Expressions
Multiplying Rationals Video
Adding and Subtracting Rational Expressions
Adding and Subtracting Rational Expressions Video
Rational Equations
Solving a Rational Equation Video
Solving Equations with Rational Numbers Video
Solving Rational Equations Video
Solving Rational Equations with Unlike Denominators Video
Dividing Polynomials
Dividing Rationals Video
Dividing Polynomials Video
Radicals
Radical Concepts
Cube Roots Video
Estimating Square Roots Video
Math Radicals Video
Properties of Radicals
Simplifying Radicals
Adding and Subtracting Radical Expressions Video
Dividing Radicals Video
Multiplying Radicals Video
Simplifying Radical Expressions Video
Simplifying Radicals Video
Evaluating Rational Exponents Video
How to Multiply Radicals Video
Multiplying Radical Expressions Video
Radical Equations
Solving Radical Equations Video
Solving Radicals Video
Imaginary Numbers
Imaginary Numbers Concepts
Playing with i
Powers of i Video
Imaginary Numbers Video
Complex Numbers
Imaginary Numbers Video
Radical Expressions Video
Adding Complex Numbers Video
Dividing Complex Numbers Video
Multiplying Complex Numbers Video
Equality and Inequality in Complex Numbers
Quadratic Equations and Complex Numbers
Complex Quadratic Equations Video
The Discriminant Video
Quadratic Equation Discriminant Video
A Few “Extra for Experts” Thoughts on Imaginary Numbers
Properties of Real Numbers Video
Imaginary Numbers Video
Real Numbers Video
Complex Number Roots Video
Matrices
Matrices
Introduction to Matrices Video
Multiplying Matrices
Matrix Multiplication Video
Matrix Operations Video
The Identity Matrix
The Identity Matrix Video
The Inverse Matrix
Square Matrix Inverse Video
Invertible Square Matrix Video
Matrices on a TI-83 or TI-84 Calculator
Determinants
Simplifying Determinants Video
2x2 Determinant Video
3x3 Determinant Video
Area Determinant Video
Solving Linear Equations
Matrix Algebra Video
Modeling Data with Functions
Data Modeling Concepts
Direct and Inverse Variations
Inverse Variation Video
Direct Variation Video
Joint Variation Video
Finding a Linear Function for any Two Points
Finding a Parabolic Function for any Three Points
Regression on the Calculator
Conics
Conic Concepts
Conic Sections Video
Conic Section Formulas Video
A Mathematical Look at Distance
Circles
Circle Conic Section Video
Parabolas
Parabola Video
Parabola Focus Video
Parabola Intercepts Video
Vertex of a Parabola Video
Ellipses
Ellipse Video
Hyperbolas
Hyperbola Video
Hyperbola Graphs Video
A Brief Recap: How Do You Tell What Shape It Is?
Sequences and Series
Sequences
Recursion Sequences Video
Introduction to Sequences Video
Arithmetic Sequences Video
Geometric Sequences Video
Series
Arithmetic Series Video
Series and Summation Video
Geometric Series Video
Proof by Induction
Mathematical Induction Video
Probability
Probability
Introduction to Probability Video
Conditional Probability Video
Calculating Probability Video
Fundamental Counting Principal Video
Probability of Dependent Events Video
Probability of Independent Events Video
Probability of Multiple Events Video
Permutations
Permutations Video
Combinations and Permutations Video
Combinations
Statistics Combination Video
Combinations and Permutations Video
(Untitled)