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.

 

Calculator for Trig Functions

 

Unit 1:  Simplifying Polynomials

Combining Like Terms

Dividing Monomials and Negative Exponents

Squaring a Binomial

FOIL Method

The Distributive Property with Variables

Greatest Common Factor with Polynomials

Difference of Perfect Squares

Factoring Trinomials (but use the “clues” we discuss in class)

Recognizing a Perfect Square Quadratic

Factoring by Grouping 

Sum/Difference of Perfect Cubes

Factoring Polynomials in Quadratic Form

Polynomial Division (Long Division Algorithm)

Polynomial Division (Synthetic Algorithm)

 

Unit 2:  Systems

Solving Systems Substitution

Solving Systems Elimination 

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

Compound Inequalities 

Absolute Value Inequalities

Slope

Slope Intercept Form

Standard Form

Point-Slope Form

Example of manipulating equations to put in different forms

Graphing Horizontal and Vertical Lines 

Graphing an Inequality

Graphing a System of Inequalities

Graphing an Absolute Value Inequality

 

Unit 4:  Roots and Radicals

Simplifying Radicals

Simplifying Radicals with Variables

Adding and Simplifying Radicals

Finding Cube Roots

Simplifying Cube Roots with Variables

Multiplying Radicals 

Simplifying Radicals by Multiplying by the Conjugate

Simplifying Radicals with Polynomials

Radicals and FOIL

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

Pascal’s Triangle

Binomial Theorem

Connecting Pascal’s Triangle and Binomial Theorem

Pascal’s Triangle for Binomial Expansion

Arithmetic Series

Arithmetic Series and Summation Notation

Geometric Series

Geometric Series and Summation Notation

Writing Arithmetic Series and Summation Notation

Writing Geometric Seres and Summation Notation

 

Unit 6:  Rational Exponents and Complex Numbers

Rational Exponents

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

Multiplying Complex Numbers

 

Unit 7:  Quadratics

Zero Product Property

Completing the Square

Completing the Square (where “a” is not 1)

Quadratic Formula

Quadratic Formula with Complex Solutions

The Discriminant and How Many Real Solutions

Solving Equations in Quadratic Form

Graphing Quadratic Functions

Graphing Quadratic Inequalities

 

Unit 8:  Rational Expressions

Simplifying Rational Expressions Intro

Adding and Subtracting Rational Expressions

Multiplying and Dividing Rational Expressions

Simplifying Complex Fractions

Solving Rational Equations

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)

Row Reduced Echelon Form

Solving a 3 by 3 System using Matrix Multiplication (using inverses)

Multiplying Matrices

Inverse of 2 by 2 Matrix

Inverse of 3 by 3 Matrix

 

Unit 10:  Logarithms

Exponent Rules Multiplication and Division of Exponents

Raising a Power to a Power

Simplifying Exponential Expressions

Solving Exponential Equations

Converting Between Exponential Form and Logarithmic Form

Solving Exponential Equations by Using Logs

Logarithmic Properties

Solving Exponential Equations and Logarithmic Equations

Nested Logarithms

Use Logs to Solve Exponential Equations

 

Unit 11:  Conics

Basics of Graphing Parabolas (Vertex, intercepts, which way it opens)

Parabolas Focus and Directrix

Graphing Horizontal Parabolas

Graphing and Writing Circles

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

Basics to TI-83 Calculator

 

Unit 13: Graphing Polynomials

Introduction to Finding Inverses

Graphing Inverse Functions

Functions and the Vertical Line Test

Graphing on the TI 83

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

Holes of a Rational Function

Example of a Rational Function with a Hole (and Asymptotes)

Graphing Irrational Functions

 

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

Hyperbola Review

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).

Linear Equations

Parabolas

Ellipses

Circles

Hyperbolas

Using the Discriminant to Identify the Conic Section

Absolute Value Equations

Exponential Functions

Logarithmic Functions

Cubic Functions

Quartic Functions

Rational Functions

Irrational Functions

Finding x and y intercepts

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

Quadratics in the Real World

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

Combined Variation Functions

Composite Functions

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.

 

Calculator for Trig Functions

 

Unit 1:  Simplifying Polynomials

Combining Like Terms

Dividing Monomials and Negative Exponents

Squaring a Binomial

FOIL Method

The Distributive Property with Variables

Greatest Common Factor with Polynomials

Difference of Perfect Squares

Factoring Trinomials (but use the “clues” we discuss in class)

Recognizing a Perfect Square Quadratic

Factoring by Grouping 

Sum/Difference of Perfect Cubes

Factoring Polynomials in Quadratic Form

Polynomial Division (Long Division Algorithm)

Polynomial Division (Synthetic Algorithm)

 

Unit 2:  Systems

Solving Systems Substitution

Solving Systems Elimination 

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

Compound Inequalities 

Absolute Value Inequalities

Slope

Slope Intercept Form

Standard Form

Point-Slope Form

Example of manipulating equations to put in different forms

Graphing Horizontal and Vertical Lines 

Graphing an Inequality

Graphing a System of Inequalities

Graphing an Absolute Value Inequality

 

Unit 4:  Roots and Radicals

Simplifying Radicals

Simplifying Radicals with Variables

Adding and Simplifying Radicals

Finding Cube Roots

Simplifying Cube Roots with Variables

Multiplying Radicals 

Simplifying Radicals by Multiplying by the Conjugate

Simplifying Radicals with Polynomials

Radicals and FOIL

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

Pascal’s Triangle

Binomial Theorem

Connecting Pascal’s Triangle and Binomial Theorem

Pascal’s Triangle for Binomial Expansion

Arithmetic Series

Arithmetic Series and Summation Notation

Geometric Series

Geometric Series and Summation Notation

Writing Arithmetic Series and Summation Notation

Writing Geometric Seres and Summation Notation

 

Unit 6:  Rational Exponents and Complex Numbers

Rational Exponents

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

Multiplying Complex Numbers

 

Unit 7:  Quadratics

Zero Product Property

Completing the Square

Completing the Square (where “a” is not 1)

Quadratic Formula

Quadratic Formula with Complex Solutions

The Discriminant and How Many Real Solutions

Solving Equations in Quadratic Form

Graphing Quadratic Functions

Graphing Quadratic Inequalities

 

Unit 8:  Rational Expressions

Simplifying Rational Expressions Intro

Adding and Subtracting Rational Expressions

Multiplying and Dividing Rational Expressions

Simplifying Complex Fractions

Solving Rational Equations

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)

Row Reduced Echelon Form

Solving a 3 by 3 System using Matrix Multiplication (using inverses)

Multiplying Matrices

Inverse of 2 by 2 Matrix

Inverse of 3 by 3 Matrix

 

Unit 10:  Logarithms

Exponent Rules Multiplication and Division of Exponents

Raising a Power to a Power

Simplifying Exponential Expressions

Solving Exponential Equations

Converting Between Exponential Form and Logarithmic Form

Solving Exponential Equations by Using Logs

Logarithmic Properties

Solving Exponential Equations and Logarithmic Equations

Nested Logarithms

Use Logs to Solve Exponential Equations

 

Unit 11:  Conics

Basics of Graphing Parabolas (Vertex, intercepts, which way it opens)

Parabolas Focus and Directrix

Graphing Horizontal Parabolas

Graphing and Writing Circles

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

Basics to TI-83 Calculator

 

Unit 13: Graphing Polynomials

Introduction to Finding Inverses

Graphing Inverse Functions

Functions and the Vertical Line Test

Graphing on the TI 83

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

Holes of a Rational Function

Example of a Rational Function with a Hole (and Asymptotes)

Graphing Irrational Functions

 

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

Hyperbola Review

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).

Linear Equations

Parabolas

Ellipses

Circles

Hyperbolas

Using the Discriminant to Identify the Conic Section

Absolute Value Equations

Exponential Functions

Logarithmic Functions

Cubic Functions

Quartic Functions

Rational Functions

Irrational Functions

Finding x and y intercepts

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

Quadratics in the Real World

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

Combined Variation Functions

Composite Functions

Modeling with Composite Functions

Higher Order Polynomial Functions

 

 

 

 

 

 

 

 

 

 

 

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