Algebra 2Algebra 2
Use these videos and readings to enhance your understanding of material that we cover in class. Note: These videos DO NOT cover everything we have covered in class. However, this is a REALLY good place to start if you are having trouble on an assignment.
Unit 1: Simplifying Polynomials
Dividing Monomials and Negative Exponents
The Distributive Property with Variables
Greatest Common Factor with Polynomials
Factoring Trinomials (but use the “clues” we discuss in class)
Recognizing a Perfect Square Quadratic
Sum/Difference of Perfect Cubes
Factoring Polynomials in Quadratic Form
Polynomial Division (Long Division Algorithm)
Polynomial Division (Synthetic Algorithm)
Unit 2: Systems
Special Systems with 0 or infinite number of solutions
Solving Systems with Three Variables
Finding the Determinant of a 2 by 2 Matrix
Finding the Determinant of a 3 by 3 Matrix (Diagonal Trick)
Cramer’s Rule to Solve a 2 Variable System
Cramer’s Rule to Solve a 3 Variable System (Used expansion of minors, not diagonal trick, to find determinant of matrix)
Unit 3: Inequalities and Coordinate Graphing
Solving and Graphing Inequalities
Solving Absolute Value Equations
Example of manipulating equations to put in different forms
Graphing Horizontal and Vertical Lines
Graphing a System of Inequalities
Graphing an Absolute Value Inequality
Unit 4: Roots and Radicals
Simplifying Radicals with Variables
Adding and Simplifying Radicals
Simplifying Cube Roots with Variables
Simplifying Radicals by Multiplying by the Conjugate
Simplifying Radicals with Polynomials
Radicals and the Distributive Property
Dividing Radicals and Rationalizing the Denominator
Solving Radical Solutions (including no solution and cube root. This is a VERY good video to watch)
Unit 5: Sequence and Series
Connecting Pascal’s Triangle and Binomial Theorem
Pascal’s Triangle for Binomial Expansion
Arithmetic Series and Summation Notation
Geometric Series and Summation Notation
Writing Arithmetic Series and Summation Notation
Writing Geometric Seres and Summation Notation
Unit 6: Rational Exponents and Complex Numbers
Converting a Rational Exponent to Radical Form
Zero, Negative, and Fractional Exponents
Multiplying and Dividing Fractional Exponents
Rationalizing Denominators with Fractional Exponents
Multiply by Conjugate to Rationalize Denominator with Radicals
Introduction to i and Imaginary Numbers
Complex Numbers (Longer video but VERY good. Includes FOIL, radicals, multiplying by conjugates, and rationalizing the denominator)
Solving Equations with Imaginary Solutions
Adding and Subtracting Complex Numbers
Unit 7: Quadratics
Completing the Square (where “a” is not 1)
Quadratic Formula with Complex Solutions
The Discriminant and How Many Real Solutions
Solving Equations in Quadratic Form
Graphing Quadratic Inequalities
Unit 8: Rational Expressions
Simplifying Rational Expressions Intro
Adding and Subtracting Rational Expressions
Multiplying and Dividing Rational Expressions
Direct and Inverse Variation (can use this equation or the one from class)
Direct Variation Real World Example
Inverse Variation Real World Example
Unit 9: Matrices
Adding and Subtracting Matrices
Multiplying Matrices by Constant
Solving Systems of Linear Equations Using Matrices
Solving 2nd Order Systems (Augmented Matrix Method)
Solving a 3 by 3 System using Matrix Multiplication (using inverses)
Unit 10: Logarithms
Exponent Rules Multiplication and Division of Exponents
Simplifying Exponential Expressions
Converting Between Exponential Form and Logarithmic Form
Solving Exponential Equations by Using Logs
Solving Exponential Equations and Logarithmic Equations
Use Logs to Solve Exponential Equations
Unit 11: Conics
Basics of Graphing Parabolas (Vertex, intercepts, which way it opens)
Graphing Horizontal and Vertical Ellipses
Completing the Square Ellipses
Given Vertices and Foci, Writing the Equation of an Ellipse
Graphing Horizontal and Vertical Hyperbolas
Completing the Square Hyperbolas
Writing Equations of Hyperbolas
Unit 12: Using Your TI Calculator
Unit 13: Graphing Polynomials
Introduction to Finding Inverses
Functions and the Vertical Line Test
Sketching a Cubic Function (do not worry about “true critical points” – you need to take the derivative of the function and set it equal to 0 to find it-that’s calc.)
Graphing Rational Functions (Just Asymptotes)
Finding Asymptotes of a Rational Function
Example of a Rational Function with a Hole (and Asymptotes)
Unit 14: Conics (Again) Emphasis on Solving Systems of Quadratics and Recognizing Equations of Conic Sections
Solving a System of Quadratics using Substitution
Solving a System of Quadratics using Elimination
Writing the Equation of a Circle given the Center and a Tangent Line
Writing the Equation of a Parabola given the Focus and Directrix
Writing the Equation of an Ellipse given Vertices and Foci
Finding the Asymptotes of a Hyperbola
Using the Discriminant to Identify the Conic Section
Identify an Ellipse from an Equation
Identify Circles and Parabolas from an Equation
Identifying a Hyperbola from an Equation
Unit 15: Identifying Graphs and Their Equations. Examining the Equations of Rational Expressions (This is primarily a review unit of every type of graph you have seen plus a couple of new ones).
Using the Discriminant to Identify the Conic Section
Vertical and Horizontal Asymptotes
Asymptotes vs. Holes in Graphs
Unit 16: Introduction to Graphic Representations of Real World Situations (Constructing Models for Linear and Quadratic Relationships)
Independent vs. Dependent Variables
Using Graphs and Tables to Model Real Wold Relationships
Modeling Real World Scenarios (Linear)
Modeling Real World Scenarios (Parabolas)
Calculating a Linear Regression using a TI 83
Constructing a Mathematical Model for a Quadratic Relationship (the example is at the bottom)
Unit 17: Constructing Models for Exponential Relationships, Direct Variation, Indirect Variation, and Higher Depress Polynomial Functions
Constructing an Exponential Function
Exponential Growth and Decay Models
Recall Direct vs. Indirect Variation
Direct and Indirect Word Problems
Modeling with Composite Functions
Higher Order Polynomial Functions
Use these videos and readings to enhance your understanding of material that we cover in class. Note: These videos DO NOT cover everything we have covered in class. However, this is a REALLY good place to start if you are having trouble on an assignment.
Unit 1: Simplifying Polynomials
Dividing Monomials and Negative Exponents
The Distributive Property with Variables
Greatest Common Factor with Polynomials
Factoring Trinomials (but use the “clues” we discuss in class)
Recognizing a Perfect Square Quadratic
Sum/Difference of Perfect Cubes
Factoring Polynomials in Quadratic Form
Polynomial Division (Long Division Algorithm)
Polynomial Division (Synthetic Algorithm)
Unit 2: Systems
Special Systems with 0 or infinite number of solutions
Solving Systems with Three Variables
Finding the Determinant of a 2 by 2 Matrix
Finding the Determinant of a 3 by 3 Matrix (Diagonal Trick)
Cramer’s Rule to Solve a 2 Variable System
Cramer’s Rule to Solve a 3 Variable System (Used expansion of minors, not diagonal trick, to find determinant of matrix)
Unit 3: Inequalities and Coordinate Graphing
Solving and Graphing Inequalities
Solving Absolute Value Equations
Example of manipulating equations to put in different forms
Graphing Horizontal and Vertical Lines
Graphing a System of Inequalities
Graphing an Absolute Value Inequality
Unit 4: Roots and Radicals
Simplifying Radicals with Variables
Adding and Simplifying Radicals
Simplifying Cube Roots with Variables
Simplifying Radicals by Multiplying by the Conjugate
Simplifying Radicals with Polynomials
Radicals and the Distributive Property
Dividing Radicals and Rationalizing the Denominator
Solving Radical Solutions (including no solution and cube root. This is a VERY good video to watch)
Unit 5: Sequence and Series
Connecting Pascal’s Triangle and Binomial Theorem
Pascal’s Triangle for Binomial Expansion
Arithmetic Series and Summation Notation
Geometric Series and Summation Notation
Writing Arithmetic Series and Summation Notation
Writing Geometric Seres and Summation Notation
Unit 6: Rational Exponents and Complex Numbers
Converting a Rational Exponent to Radical Form
Zero, Negative, and Fractional Exponents
Multiplying and Dividing Fractional Exponents
Rationalizing Denominators with Fractional Exponents
Multiply by Conjugate to Rationalize Denominator with Radicals
Introduction to i and Imaginary Numbers
Complex Numbers (Longer video but VERY good. Includes FOIL, radicals, multiplying by conjugates, and rationalizing the denominator)
Solving Equations with Imaginary Solutions
Adding and Subtracting Complex Numbers
Unit 7: Quadratics
Completing the Square (where “a” is not 1)
Quadratic Formula with Complex Solutions
The Discriminant and How Many Real Solutions
Solving Equations in Quadratic Form
Graphing Quadratic Inequalities
Unit 8: Rational Expressions
Simplifying Rational Expressions Intro
Adding and Subtracting Rational Expressions
Multiplying and Dividing Rational Expressions
Direct and Inverse Variation (can use this equation or the one from class)
Direct Variation Real World Example
Inverse Variation Real World Example
Unit 9: Matrices
Adding and Subtracting Matrices
Multiplying Matrices by Constant
Solving Systems of Linear Equations Using Matrices
Solving 2nd Order Systems (Augmented Matrix Method)
Solving a 3 by 3 System using Matrix Multiplication (using inverses)
Unit 10: Logarithms
Exponent Rules Multiplication and Division of Exponents
Simplifying Exponential Expressions
Converting Between Exponential Form and Logarithmic Form
Solving Exponential Equations by Using Logs
Solving Exponential Equations and Logarithmic Equations
Use Logs to Solve Exponential Equations
Unit 11: Conics
Basics of Graphing Parabolas (Vertex, intercepts, which way it opens)
Graphing Horizontal and Vertical Ellipses
Completing the Square Ellipses
Given Vertices and Foci, Writing the Equation of an Ellipse
Graphing Horizontal and Vertical Hyperbolas
Completing the Square Hyperbolas
Writing Equations of Hyperbolas
Unit 12: Using Your TI Calculator
Unit 13: Graphing Polynomials
Introduction to Finding Inverses
Functions and the Vertical Line Test
Sketching a Cubic Function (do not worry about “true critical points” – you need to take the derivative of the function and set it equal to 0 to find it-that’s calc.)
Graphing Rational Functions (Just Asymptotes)
Finding Asymptotes of a Rational Function
Example of a Rational Function with a Hole (and Asymptotes)
Unit 14: Conics (Again) Emphasis on Solving Systems of Quadratics and Recognizing Equations of Conic Sections
Solving a System of Quadratics using Substitution
Solving a System of Quadratics using Elimination
Writing the Equation of a Circle given the Center and a Tangent Line
Writing the Equation of a Parabola given the Focus and Directrix
Writing the Equation of an Ellipse given Vertices and Foci
Finding the Asymptotes of a Hyperbola
Using the Discriminant to Identify the Conic Section
Identify an Ellipse from an Equation
Identify Circles and Parabolas from an Equation
Identifying a Hyperbola from an Equation
Unit 15: Identifying Graphs and Their Equations. Examining the Equations of Rational Expressions (This is primarily a review unit of every type of graph you have seen plus a couple of new ones).
Using the Discriminant to Identify the Conic Section
Vertical and Horizontal Asymptotes
Asymptotes vs. Holes in Graphs
Unit 16: Introduction to Graphic Representations of Real World Situations (Constructing Models for Linear and Quadratic Relationships)
Independent vs. Dependent Variables
Using Graphs and Tables to Model Real Wold Relationships
Modeling Real World Scenarios (Linear)
Modeling Real World Scenarios (Parabolas)
Calculating a Linear Regression using a TI 83
Constructing a Mathematical Model for a Quadratic Relationship (the example is at the bottom)
Unit 17: Constructing Models for Exponential Relationships, Direct Variation, Indirect Variation, and Higher Depress Polynomial Functions
Constructing an Exponential Function
Exponential Growth and Decay Models
Recall Direct vs. Indirect Variation
Direct and Indirect Word Problems
Modeling with Composite Functions
Higher Order Polynomial Functions