Click to download the playlist as a pdf:  Algebra 2

Polynomial Functions
Determining the Characteristics of Polynomial Functions

Determine if a Function is a Polynomial Function
Degree, Leading Term, and Leading Coefficient of a Polynomial Function
Ex: Information about a Given Polynomial Function
Turning Points and X Intercepts of a Polynomial Function
Summary of End Behavior or Long Run Behavior of Polynomial Functions
Ex:  End Behavior or Long Run Behavior of Functions
Ex:  End Behavior of a Polynomial Function in Factored Form
Ex:  Find the Intercepts of a Polynomial Function in Factored Form
Ex:  Determine the Least Possible Degree of a Polynomial From the Graph
Ex:  Increasing / Decreasing / Relative Extrema from Analyzing a Graph
Ex 1: Determine the Local / Relative Extrema of a Cubic Function Using Desmos
Ex 2: Determine the Local / Relative Extrema of a Cubic Function Using Desmos (Challenging)
Determine the Maximum Volume of an Open Top Box Using a Graph Only
Ex:  Concavity / Points of Inflection by Analyzing a Graph (Algebra Topic)
Ex:  Concavity / Increasing / Decreasing Functions as Tables (Algebra Topic)
Ex:  Find the Intercepts of a Polynomial Function (Factorable)
Ex: Find the Intercepts of a Polynomial Function (Real Zero)
Ex 1: Find the Intercepts and the End Behavior of a Polynomial Function
Ex 2: Find the Intercepts and the End Behavior of a Polynomial Function
Ex 3: Find the Intercepts and the End Behavior of a Polynomial Function
Ex 1:  Solve a Cubic Function Graphically (One Solution)
Ex 2:  Solve a Cubic Function Graphically (Two Solutions)

Determining the Equations of Polynomial Functions

Ex 1:  Find a Degree 3 Polynomial Function Given Integer Zeros
Ex 2:  Find a Degree 3 Polynomial Function Given Fractional Zeros
Ex 3:  Find a Degree 3 Polynomial Function Given Imaginary Zeros
Ex 4:  Find a Degree 3 Polynomial Function Given Complex Zeros
Ex 1:  Find a Polynomial Function Given the Zeros or Roots with Multiplicity and a Point
Ex 2:  Find a Polynomial Function Given the Zeros or Roots with Multiplicity and a Point
Ex 1:  Find a Degree 4 Polynomial Function Given Integer and Complex Zeros
Ex 2:  Find a Degree 4 Polynomial Function Given Integer and Complex Zeros
Ex 3:  Find a Degree 4 Polynomial Function Given Fractional and Complex Zeros
Ex1:  Find an Equation of a Degree 4 Polynomial Function From the Graph of the Function
Ex2:  Find an Equation of a Degree 5 Polynomial Function From the Graph of the Function
Ex3:  Find an Equation of a Degree 6 Polynomial Function From the Graph of the Function
Ex 1: Cubic Regression on the TI84 – Natural Gas Consumption
Ex 2: Cubic Regression on the TI84 - Total Sales

Finding the Zeros of Polynomial Functions

Real Zeros, Factors, and Graphs of Polynomial Functions
Polynomial Function - Complex Factorization Theorem
Ex: Factor and Solve a Polynomial Equation
Ex: Solve a Basic Cubic Equation Using a Cube Root and Rational Exponent
Ex 1:  Find the Zeros of a Polynomial Function - Integer Zeros
Ex 2:  Find the Zeros of a Polynomial Function - Real Rational Zeros
Ex 3:  Find the Zeros of a Polynomial Function with Irrational Zeros
Ex 4:  Find the Zeros of a Polynomial Function with Imaginary Zeros
Ex 5:  Find the Zeros of a Polynomial Function with Complex Zeros
Ex 6:  Find the Zeros of a Degree 4 Polynomial Function
Ex 7:  Find the Zeros of a Degree 5 Polynomial Function
Ex 1:  Write a Degree 3 Polynomial Function as a Product of Linear Factors (2 Imaginary)
Ex 2:  Write a Degree 3 Polynomial Function as a Product of Linear Factors (2 Irrational)
Ex 3:  Write a Degree 5 Polynomial Function as a Product of Linear Factors
Ex 1:  The Zero Feature of the TI84 to Find Rational Zeros of a Polynomial
Ex 2:  The Zero Feature of the TI84 to Find Rational Zeros of a Polynomial
Ex 1:  The Intersection Feature of the TI84 to Find Rational Zeros of a Polynomial
Ex 2:  The Intersection Feature of the TI84 to Find Rational Zeros of a Polynomial

Solving Polynomial Inequality

Ex 1:  Solve a Polynomial Inequality in Factored Form
Ex 2:  Solve a Polynomial Inequality in Factored Form
Ex:  Solve a Polynomial Equation Using a Graphing Calculator (Approximate Solutions)
Ex: Solve a Polynomial Inequality Using Factor By Grouping (Degree 3)
Ex: Solve a Polynomial Inequality Using Factor Using GCF (Degree 3)
Ex: Solve a Polynomial Inequality Using Factor of a Trinomial (Degree 4)
Introduction to Odd and Even Functions
Ex 1:  Determine if a Function is Odd, Even, or Neither
Ex 2:  Determine if a Function is Odd, Even, or Neither

Radicals Expressions, Equations, and Functions

Introduction to Radical Expressions

Introduction to Square Root and Perfect Squares
Introduction to Radicals
Using Rational Exponents
Approximate a Square Root to Two Decimal Places Using Trial and Error

Simplifying Radicals

Simplifying Radicals
Simplify Square Roots (Perfect Square Radicands)
Simplify a Variety of Square Expressions (Simplify Perfectly)
Simplify Perfect Nth Roots
Simplify Square Roots (Not Perfect Square Radicands)
Simplify Square Roots with Variables
Simplify Cube Roots (Perfect Cube Radicands)
Simplify Cube Roots (Not Perfect Cube Radicands)
Simplifying Radical Expressions Without Fractions
Simplifying Radical Expressions With Fractions
Order of Operations with a Fraction Containing a Square Root
Ex:  Simplify Square Roots - Perfect Roots
Ex:  Simplify Perfect Nth Roots - Radicals
Ex:  Simplify Square Roots - Not Perfect Roots
Ex: Simplify Square Roots of Variable Expressions - Absolute Value Needed
Ex:  Simplify a Radical Expression containing Square Roots in the Numerator and Denominator
Ex:  Simplify Radicals with the Same Radicand and Different Indexes
Ex:  Simplify a Radical Containing a Fraction - Perfect Root
Ex:  Simplify Radicals with Variables - Perfect Roots
Simplify Nth Roots with Variables
Ex 1:  Simplifying Perfect Nth Roots Containing Variables
Ex 2:  Simplifying Perfect Nth Roots Containing Variables
Ex:  Simplify Radicals Containing Variables With Large Exponents - Not Perfect Roots
Ex:  Simplify Radicals with Negative Radicands and Odd Indexes
Ex:  Simplify Radicals with Variables - Not Perfect Roots
Evaluating Radical Expressions on the TI83/84

Multiplying Radicals

Introduction to Multiplying Radicals
Multiplying Radical Expressions with Variables Using Distribution
Multiplying Binomial Radical Expressions with Variables
Multiplying Radicals Containing Variables
Multiplying Binomials with Radicals
Multiplying Conjugates of Radical Expressions
Review of Multiplying Radicals
Ex:  Multiply Square Roots
Ex 1:  Multiply Radicals
Ex 2:  Multiply Radicals
Ex:  Multiply Radicals with Variables
Ex:  Radicals Raised to Powers
Ex:  Distribution with Square Roots
Ex: Multiply Binomials with Square Roots
Ex:  Square Binomials With Square Roots
Ex:  Multiply Radical Conjugates - Square Roots

Dividing Radicals

Dividing Radicals
Dividing Radicals without Variables (Basic with no rationalizing)
Dividing Radicals with Variables (Basic with no rationalizing)
Ex 1: Rationalize The Denominator of a Fraction (Basic)
Ex 2: Rationalize The Denominator of a Fraction
Ex 3: Rationalize The Denominator of a Fraction
Ex 1:  Rationalize the Denominator of a Radical Expression
Ex 2:  Rationalize the Denominator of a Radical Expression
Ex:  Rationalize the Denominator of a Radical Expression - Conjugate

Performing Operations with Rational Exponents

Ex:  Write a Radical in Rational Exponent Form
Write Basic Expression in Radical Form and Using Rational Exponents
Write Expressions Using Radicals and Rational Exponents
Simplify Radicals Using Rational Exponents
Ex: Simplify Exponential Expressions with Fraction Exponents (Power Property of Exponents)
Ex: Simplify Exponential Expressions with Fraction Exponents (Quotient Property of Exponents)
Ex: Simplify Expressions with Rational Exponents
Ex: Simplify an Expression with Rational Exponents and Write in Radical Form
Ex: Simplify an Expression with Negative Rational Exponents and Write in Radical Form
Ex 1: Simplify an Expression with a Negative Rational Exponent
Ex 2: Simplify an Expression with a Negative Rational Exponent
Multiply Square Roots
Multiple Cube Roots
Simplify Basic Quotients of Square Roots
Ex:  Multiply and Divide Radicals with Different Indexes Using Rational Exponents - Same Radicand
Ex: Multiply Radicals with Different Indexes Using Rational Exponents - Different Radicand
Ex:  Evaluate an Expression with Rational Exponents Using Radicals
Ex: Simplify an Expression with Rational Exponents and Write in Radical Form
Ex: Simplify an Expression with Negative Rational Exponents and Write in Radical Form

Adding and Subtracting Radicals

Adding Radicals (Basic With No Simplifying)
Adding Radicals That Requires Simplifying
Subtracting Radicals (Basic With No Simplifying)
Subtracting Radicals That Requires Simplifying
Adding and Subtracting Radicals
Ex:  Evaluate the Square Root of a Sum and the Sum of Square Roots on a Calculator
Ex:  Add and Subtract Square Roots - No Simplifying
Ex:  Add and Subtract Square Roots
Ex:  Add and Subtract Square Roots Containing Variables

Solving Radical Equations

Solving Radical Equations with One Radical
Solving Radical Equations with Two Radicals
Ex 1:  Solve a Basic Radical Equation - Square Roots
Ex 2:  Solve Radical Equations - Square Roots
Ex 3:  Solve Radical Equations - Square Roots
Ex 4:  Solve Radical Equations - Square Roots
Ex 5:  Solve Radical Equations - Two Square Roots
Ex 6:  Solve Radical Equations - Two Square Roots
Ex 7:  Solve Radical Equations - Two Square Roots
Ex: Solve a Radical Equation with One Radical:  Factoring and Extraneous Solution
Ex: Solve a Radical Equation with Two Radicals:  a*sqrt(b)=sqrt(d)
Ex:  Solve Radical Equations - Cube Roots / Fourth Roots
Ex: Solving an Equation with Rational Exponents Using Reciprocal Powers

Radical Equation Applications

Radical Equation Application - Vehicle Speed from Skid Mark Length
Ex:  Radical Equation Application - Obesity Percentage
Ex: Radical Function Application Finding Inputs and Outputs (Speed and Length of Skids)
Ex:  Radical Function Outputs and Inputs Application - BMI
Ex:  Radical Function Outputs and Inputs Application - Pendulum
Ex:  Rational Function Outputs and Inputs Application - Average Cost
Kinetic Energy - Radical Equation Application
Volume of a Cone -Radical Equation Application
Volume of a Cone -Radical Equation Application (Special Formula)

Performing Operations with Complex Numbers

Complex Numbers
Ex: Determine a Real, Imaginary, and Complex Number
Simplify Square Roots to Imaginary Numbers
Write Number in the Form of Complex Numbers
Complex Number Operations
Ex: Simplify Complex Numbers
Ex :  Simplify Imaginary and Complex Numbers
Ex:  Simplify, Add, and Subtract Imaginary and Complex Numbers
Ex 1:  Adding and Subtracting Complex Numbers
Ex 2:  Adding and Subtracting Complex Numbers
Ex 1:  Simplify and Multiply Complex Numbers
Ex 2:  Multiply Complex Numbers
Ex 3:  Multiply Complex Numbers
Ex: Multiplying Complex Conjugates
Ex:  Subtract and Multiply Complex Number
Ex:  Raising the imaginary unit i to powers
Ex:  Dividing Complex Numbers
Complex Number Operations on the TI-84

Using the Pythagorean Theorem

The Pythagorean Theorem
Ex:  Determine if a Triangle is a Right Triangle Given the Length of 3 Sides
Ex:  Determine the Length of the Hypotenuse of a Right Triangle
Ex:  Determine the Length of the Leg of a Right Triangle
Ex: Pythagorean Theorem App - Find the Width of a Laptop
Ex: Determine the Distance Between Two Points Using the Pythagorean Theorem
Ex: Find the Shortest Distance Between Two Locations North and West

Using the Distance Formula / Midpoint Formula

The Distance Formula
Ex:  Midpoint of a Segment
Ex: Find the Endpoint of a Segment Given the Midpoint and One Endpoint
Ex:  Determine the Distance Between Two Points (length of segment)

Graphing the Square Root Function with Transformations

Graphing the Basic Square Root Function
Ex: Domain and Range of Square Root Functions
Ex: Domain and Range of Radical Functions
Ex: Domain of a Square Root Function with a Quadratic Radicand
Reflections of the Square Root Function
Horizontal and Vertical Shifts of the Square Root Function
Horizontal and Vertical Stretches and Compressions of the Square Root Function
Ex:  Match the Graph of a Horizontal and Vertical Shifted Graph to the Function
Ex:  Match the Graph of a Reflected or Horizontally Compressed or Stretched Graph to a Function
Function Transformation Summary - The Square Root Function
Summary of Function Transformations
Ex 1:  Find the Equation of a Transformed Square Root Function from the Graph
Ex 2:  Find the Equation of a Transformed Square Root Function From the Graph
Ex 3: Find the Equation of a Transformed Square Root Function From a Graph
Ex 4: Find the Equation of a Transformed Square Root Function From a Graph
Ex 1:  Graphing a Transformation of the Square Root Function
Ex 2:  Graphing a Transformation of the Square Root Function

Rational Expressions, Equations, and Functions

Simplifying Rational Expressions

Simplifying Rational Expressions
Simplify and Give the Domain of Rational Expressions
Ex 1:  Simplifying Rational Expressions – Monomials
Ex 2:  Simplifying Rational Expressions
Ex 3:  Simplifying Rational Expressions
Ex 4:  Simplifying Rational Expressions
Ex: Find Values Where a Rational Expression is Undefined

Multiplying and Dividing Rational Expressions

Multiplying and Dividing Rational Expressions
Multiply Rational Expressions and Give the Domain
Divide Rational Expressions and Give the Domain
Ex 1:  Multiply Rational Expressions – Monomials
Ex 2:  Multiply Rational Expressions
Ex 3:  Multiply Rational Expressions
Ex 4:  Multiply Rational Expressions
Ex 1:  Dividing Rational Expressions – Monomials
Ex 2:  Dividing Rational Expressions
Ex 3:  Dividing Rational Expressions
 Ex 1:  Simplify a Complex Fraction (No Variables)
Ex 2:  Simplify a Complex Fraction (Variables)
Ex 3:  Simplify a Complex Fraction (Variables)
Ex 4:  Simplify a Complex Fraction (Variables)
Ex 5:  Simplify a Complex Fraction (Variables)
Ex 6:  Simplify a Complex Fraction (Variables)
Ex 7:  Simplify a Complex Fraction (Variables)
Ex 1: Simplify a Complex Fraction with Variables (Basic)
Ex 2: Simplify a Complex Fraction with Variables (Basic)
Ex: Simplify a Complex Fraction with Variables (Factoring)
Ex: Simplify a Complex Fraction with Addition and Subtraction and Constant Denominators
Ex: Simplify a Complex Fraction Subtraction and Variable Denominators
Ex: Simplify a Complex Fraction Subtraction and Variable Denominators with Factoring
Ex: Simplify a Complex Fraction with Addition and Constant and Variable Denominators
Ex: Simplify a Complex Fraction with Addition and Subtraction and Binomial Denominators

Adding and Subtracting Rational Expressions

Adding and Subtracting Rational Expressions
Add and Subtract Rational Expressions with Like Denominators and Give the Domain
Ex 1:  Add and Subtract Rational Expressions - Like Denominators
Ex 2:  Add and Subtract Rational Expressions - Like Denominators
Ex 3:  Add and Subtract Rational Expressions - Like Denominators
Ex:  Add and Subtract Rational Expressions - Opposite Denominators
Add Rational Expressions with Unlike Denominators and Give the Domain (Mono Denom)
Subtract Rational Expressions with Unlike Denominators and Give the Domain
Subtract Rational Expressions with Unlike Denominators - 3 Expressions
Add and Subtract Rational Expressions with Unlike Denominators - 3 Expressions
Ex 1:  Add and Subtract Rational Expressions - Unlike Denominators
Ex 2:  Add and Subtract Rational Expressions - Unlike Denominators
Ex 3:  Add and Subtract Rational Expressions - Unlike Denominators
Ex 4:  Add and Subtract Rational Expressions - Unlike Denominators
Ex: Add and Subtract Rational Expressions with Unlike Monomial Denominators
Ex: Add Rational Expressions with Unlike Denominators
Ex: Subtract Rational Expressions with Unlike Denominators
Ex: Subtracting Rational Expressions (Factoring With A Not 1)

Solving Rational Equations

Solving Rational Equations
Solve Basic Rational Equations
Solve  Rational Equations with Like Denominators
Ex 1: Solve Rational Equations Algebraically by Clearing Fractions and  Solve Graphically
Ex 2: Solve Rational Equations Algebraically by Clearing Fractions and Solve Graphically
Ex 1:  Solving Rational Equations
Ex 2:  Solving Rational Equations
Ex 3:  Solving Rational Equations
Ex 4:  Solving Rational Equations
Ex 5:  Solving Rational Equations
Ex:  Solve a Rational Equation
Ex:  A Rational Equation with No Solution
Ex 1: Solve Equations with Fractions (Alternative Method)
Ex 2: Solve Equations with Fractions (Alternative Method)
Ex 1:  Solve a Rational Equation (Alternative Method)
Ex 2:  Solve a Rational Equation (Alternative Method)
Ex:  Solve a Rational Equation - Alternative Method

Solving Applications using Rational Equations

Ex:  Rational Function Outputs and Inputs Application - Time, Distance, Rate
Rational Equation Applications I
Rational Equation Applications II
Ex 1:  Rational Equation Application - Painting Together
Ex 2:  Rational Equation Application - Fill a Pool with Drain Open
Ex 3:  Rational Equation Application - Plane and Car Travelling the Same Time
Ex 4:  Rational Equation Application - Two Bikers Riding Different Distances
Ex: Rational Equation App - Find Individual Working Time Given Time Working Together
Ex: Rational Equation App - Find a Number Given the Sum of Reciprocals
Ex: Find How Faster Than the Speed Limit Is Needed Given a Travel Time

Solving Direct and Inverse Variation Problems

Direct Variation
Ex: Direct Variation Application - Aluminum Can Usage
Inverse Variation
Direct and Inverse Variation
Ex 1:  Inverse Variation
Ex 2:  Inverse Variation - Change of Variables
Ex 3:  Inverse Variation - Fractional Variation Constant
Ex:  Inverse Variation Application - Number of Workers and Job Time
Ex:  Inverse Variation Application - Loudness and Distance
Joint Variation: Determine the Variation Constant (Volume of a Cone)

Determining Key Components of Rational Functions

Ex: Rational Function Values
Ex: Determine Rational Function Outputs and Inputs
Ex:  The Domain of Rational Functions
Determining Vertical and Horizontal Asymptotes of Rational Functions
Determining Slant Asymptotes of Rational Functions
Ex 1: Determine Asymptotes and Graph a Rational Function
Ex 2: Determine Asymptotes and Graph a Rational Function
Ex 3: Determine Asymptotes and Graph a Rational Function
Ex 4: Determine Asymptotes and Graph a Rational Function (Slant)
Ex:  Determine Horizontal Asymptotes of Rational Functions
Ex:  Find the Intercepts and Asymptotes of a Rational Function
Ex:  Find the Intercepts, Asymptotes, and Hole of a Rational Function
Ex:  Find a Rational Function Given the Vertical Asymptotes and Intercepts
Ex 1: Determine the Vertical and Slant Asymptotes of a Rational Function
Ex 2: Determine the Vertical and Slant Asymptotes of a Rational Function
Ex 1: Domain, Range, Asymptotes of a Basic Rational Function Using Translations
Ex 2: Domain, Range, Asymptotes of a Basic Rational Function Using Translations
Ex 1: Domain, Range, Asymptotes of a Basic Rational Function Using a Graph and Procedure
Ex 2: Domain, Range, Asymptotes of a Basic Rational Function Using a Graph and Procedure
Ex:  Match Equations of Rational Functions to Graphs

Graphing Rational Functions

Graphing the Basic Rational Function f(x)=1/x
Graphing Rational Functions
Ex 1:  Graphing Rational Functions
Ex 2:  Graphing Rational Functions
Ex 3:  Graphing Rational Functions
Ex 4:  Graphing Rational Functions
Ex 5:  Graphing Rational Functions
Ex 6:  Graphing Rational Functions
Graphing Reflections of the Basic Rational Function f(x)=1/x
Graphing Translations of the Basic Rational Function f(x)=1/x
Ex 1: Graph Two Translations of the Basic Rational Function f(x)=1/x
Ex 2: Graph Two Translations of the Basic Rational Function f(x)=1/x

 

Determining Equations of Rational Functions

Ex 1:  Find the Equation of Rational Function From a Graph with a Hole
Ex 2:  Find the Equation of Rational Function From a Graph with a Hole
Ex 3:  Find the Equation of Rational Function From a Graph
Ex 4:  Find the Equation of Rational Function From a Graph (Squared Intercept)
Ex 5:  Find the Equation of Rational Function From a Graph (Squared VA)
Ex 6:  Find the Equation of Rational Function From a Graph (Squared Intercept / VA)
Rational Function Application - Concentration of a Mixture

Solving Rational Inequalities

Solving Rational Inequalities
Ex 1:  Solving Rational Inequalities
Ex 2:  Solving Rational Inequalities
Ex 3:  Solving Rational Inequalities
Ex 4:  Solving Rational Inequalities
Ex 5:  Solve a Rational Inequality

Performing Partial Fraction Decomposition

Ex: Setting Up Partial Fraction Decomposition
Ex 1: Partial Fraction Decomposition (Linear Factors)
Ex 2: Partial Fraction Decomposition (Linear Factors)
Ex 3: Partial Fraction Decomposition (Repeated Linear Factors)
Ex 4: Partial Fraction Decomposition (Repeated Linear Factors)
Ex 5: Partial Fraction Decomposition (Linear and Quadratic Factors)
Ex 6: Partial Fraction Decomposition (Repeating Quadratic Factors)
Ex: Partial Fraction Decomposition - Degree 2 / Degree 3

Exponential and Logarithmic Expressions, Equations, and Functions

Determining Composite Functions and Composite Function Values

Composite Functions
Ex: Evaluate Functions and Composite Function in Context of a Story (Graphing Calculator)
Ex:  Intro Composite Function Notation Application Problem
Ex:  Evaluate Composite Functions Using Tables of Values
Ex:  Evaluate Composite Functions from Graphs
Ex 1: Determine Composite Function Values Using Table, Graph, and Function Rule
Ex 2: Determine Composite Function Values Using Table, Graph, and Function Rule
Ex:  Find and Evaluate a Composition of Three Functions
Ex:  Decompose Functions
Ex 1:  Composite Function Values
Ex 2:  Composite Function Values
Ex 1:  Composition of Functions
Ex 1:  Find Composite Function Values
Ex 2:  Find Composite Function Values With Fractions
Ex 1: Determine Composite Function Values Using Table, Graph, and Function Rule
Ex 2: Determine Composite Function Values Using Table, Graph, and Function Rule
Composite Function Values on the TI-84
Ex 1:  Domain of a Composite Function
Ex 2:  Domain of a Composite Function
Ex 3:  Domain of a Composite Function
Ex 4:  Domain of a Composite Function
Ex:  Find a Composition of Functions Involving Rational Functions
Ex:  Domain of a Quotient and Composite Functions
Ex:  Domain of Composite Function From Graphs
Ex:  Inverse Function Notation and Reciprocal of a Function

Introduction to Exponential Functions

Graphing by Plotting Points - Exponential
Graphing by Plotting Points - Exponential (6.3)
Graphing by Plotting Points - Exponential
Determine Exponential Function Values and Graph the Function
Graph a Basic Exponential Function Using a Table of Values
Graph an Exponential Function Using a Table of Values
Evaluate a Given Exponential Function to Predict a Future Population
Introduction to Exponential Functions in the Form f(x)=ab^x - Part 1
Introduction to Exponential Functions in the Form f(x)=ab^x - Part 2
Introduction to Exponential Functions in the Form f(x)=ae^(kx) - Part 1
Introduction to Exponential Functions in the Form f(x)=ae^(kx) - Part 2
Comparing Forms of Exponential Functions:  y = ab^x and y = ae^(kx)
Graphing Exponential Functions
Ex:  Determine Exponential Graphs that Have Specific Characteristics - y = ab^x
Ex:  Match Exponential Functions to Graphs
Ex: Exponential Application Solved Using a Graphing Calculator
Determine if a Table Represents a Linear or Exponential Function
Ex:  End (Long Run) Behavior of Exponential Functions
Ex:  Find the Equation of a Transformed Exponential Function From a Graph
Ex: Match the Graphs of Translated Exponential Function to Equations
Ex: Match the Graphs of Reflected Exponential Functions to Equations
Ex 1: Determine if a Table of Value Represents a Linear or Exponential Function
Ex 2: Determine if a Table of Value Represents a Linear or Exponential Function
Ex 1: Determine if a Table of Value Represents a Linear or Exponential Function (Fractions/Decimals)
Ex 2: Determine if a Table of Value Represents a Linear or Exponential Function (Fractions/Decimals)
Ex 1: Determine if a Table Represents a Linear or Exponential Function and Find Equation  (Linear)
Ex 2: Determine if a Table Represents a Linear or Exponential Function and Find Equation  (Linear)
Ex 1: Determine if a Table Represents a Linear or Exponential Function and Find Equation  (Exponential)
Ex 2: Determine if a Table Represents a Linear or Exponential Function and Find Equation  (Exponential)

Determining Inverse Functions

Inverse Functions
Determine if a Relation Given as a Table is a One-to-One Function
Ex 1:  Determine if the Graph of a Relation is a One-to-One Function
Ex 2:  Determine if the Graph of a Relation is a One-to-One Function
Ex 1: Determine if Two Functions Are InversesEx 2: Determine if Two Functions Are Inverses
Ex:  Find an Inverse Function From a Table
Ex:  Function and Inverse Function Values Using a Table
Ex:  Function and Inverse Function Values Using a Graph
Ex:  Restrict the Domain to Make a Function 1 to 1, Then Find the Inverse
Ex:  Find Inverse Function Values Without Finding the Inverse Function
Ex:  Function and Inverse Function Values
Ex:  Find the Inverse of a Square Root Function with Domain and Range
Ex:  Find the Inverse of a Rational Function
Ex:  Find the Inverse of a Rational Function and an Inverse Function Value
Ex 1:  Determine If Two Functions Are Inverses
Ex 2:  Determine  If Two Functions Are Inverses
Ex 1:  Find the Inverse of a Function
Ex 2:  Find the Inverse of a Function
Ex:  Find the Inverse Function of an Exponential Function

Using the Definition of a Logarithm

Introduction to Logarithms
Ex:  Write Exponential Equations as Logarithmic Equations
Ex:  Write Logarithmic Equations as Exponential Equations
Ex:  Write Exponential Equations as Logarithmic Equations - Variables
Ex:  Write Logarithmic Equations As Exponential Equations - Variables
Ex:  Write Exponential Equations with base 10 as Common Logarithmic Equations
Ex:  Write Exponential Equations as Logarithmic Equations - Natural Logarithms
Use the Definition of a Logarithm to Show the Zero Exponent and Identity Property
Ex 1:  Evaluate Logarithms Without a Calculator - Whole Numbers
Ex: Evaluate Logarithmic Expressions without a Calculator - Different Bases
Ex: Evaluate Logarithmic Expressions without a Calculator - Common Log
Ex: Solve a Basic Exponential Equation with Base Ten Using Logarithm Definition
Ex: Solve a  Exponential Equation with Base Ten Using Logarithm Definition (Multiple Steps)
Ex: Solve a Basic Exponential Equation with Base e Using Logarithm Defintion
Ex: Solve a  Exponential Equation with Base e Using Logarithm Definition (Multiple Steps)
Ex 2:  Evaluate Logarithms Without a Calculator - Fractions
Ex:  Evaluate Common Logarithms on a Calculator
Ex:  Evaluate Common Logarithms Without a Calculator
Ex:  Evaluate Common Logarithms on the Calculator          
Ex:  Evaluate Natural Logarithms on the Calculator
Ex: Determine the Value of a Number on a Logarithmic Scale (Log Form)
Ex: Determine the Value of a Number on a Logarithmic Scale (Exponential Form)
Ex:  Plot Numbers on a Logarithmic Scale
Ex:  Determine the Difference in Order of Magnitude to Two Quantities
Ex:  Determine the Difference in Order of Magnitude to Two Quantities (Application)

Graphing Logarithmic Functions

Ex:  Graph an Exponential Function and Logarithmic Function
Ex: Properties and Characteristics of a Logarithmic Function
Ex 1:  Match Graphs with Exponential and Logarithmic Functions
Ex 2:  Match Graphs with Exponential and Logarithmic Functions - Base 10 and e
Ex:  Vertical Asymptotes and Domain of Logarithmic Functions
Ex:  Find the Domain of Logarithmic Functions

Using the Properties Logarithms

Properties of Logarithms
Expand Logarithms Using the Product Rule for Logs
Expand Logarithms Using Properties of Logarithms Rule and Factoring
Expand Logarithms Using Properties of Logarithms (Expressions)
Ex 1:  Expand Logarithmic Expressions
Ex 2:  Expand Logarithmic Expressions
Ex: Expand a Logarithm Containing a Radical
Using the Power Property of Logarithms
Combine Logarithms Using Properties of Logarithms
Ex:  Combine a Sum and Difference of Two Logarithms
Ex 1:  Combine a Logarithmic Expression Into One Logarithm
Ex 2:  Combine a Logarithmic Expression Into One Logarithm
Ex 1: Evaluate a Natural Logarithmic Expressing Using the Properties of Logarithms
Ex 2: Evaluate a Natural Logarithmic Expressing Using the Properties of Logarithms
Ex 3: Evaluate a Natural Logarithmic Expressing Using the Properties of Logarithms
Ex 4: Evaluate a Natural Logarithmic Expressing Using the Properties of Logarithms
Ex 5: Evaluate a Natural Logarithmic Expressing Using the Properties of Logarithms
Using the Inverse Property of Logarithms and Exponentials to Evaluate Expressions

Evaluating Logarithmic Expressions

Ex 1:  Evaluate a Logarithmic Expression Using the Properties of Logarithms
Ex 2:  Evaluate a Logarithmic Expression Using the Properties of Logarithms
Ex:  Simplify Log Expression with the Base and Base of the Number are the Same
Ex:  Evaluate Exponential Expressions with Logarithmic Exponents
Logarithm Review
Logarithms: Change of Base Formula
Ex:  Change of Base Formula to Evaluate Logarithmic Expressions
Ex:  Change of Base Formula to Solve Basic Exponential Equations
Ex: Evaluate Logarithmic Functions Using the Change of Base Formula

Solving Logarithmic Equations

Solving Logarithmic Equations
Solve a Log Equation with Two Logs Equal to Each Other
Ex: Solve a Logarithmic Equations - One Step by Dividing with Rational Solution
Ex: Solve a Logarithmic Equations - One Step by Dividing with Irrational Solution
Ex: Solve a Logarithmic Equations - One Step by Dividing with Log of a Quantity
Ex: Solving a Variety of Logarithmic Equations
Ex: Solve a Basic Logarithmic Equation - Linear and Quadratic
Ex:  Solve Basic Logarithmic Equation - Radicals
Ex:  Solve Logarithmic Equations Containing Only Logarithms
Ex:  Solve a Logarithmic Equation With a Difference - Linear
Ex:  Solve a Logarithmic Equation With a Sum - Quadratic Formula
Ex:  Solve a Logarithmic Equation With a Difference - Quadratic Formula
Ex: Solve a Logarithmic Equation Requiring the Quadratic Formula
Ex 1:  Solve Basic Logarithmic Equations
Ex 2:  Solve Logarithmic Equations
Ex 3:  Solve Logarithmic Equations - Base and Number are the Same
Ex 1:  Solve Logarithmic Equations
Ex 2:  Solve Logarithmic Equations
Ex 3:  Solve Logarithmic Equations
Ex:  Solve a Logarithmic Equation - Composite Log Expression
Ex:  Solve a Logarithmic Equation in Terms of Other Variables
Ex: Solve a Logarithmic Equation with a Fractional Exponent

 

Solving Applications Using Logarithmic Equations

Logarithm Application: Magnitude of an Earthquake
Logarithm Application:  Intensity of Two Sounds (Decibels)
Ex:  Logarithmic Function Application - Test Scores
Ex:  Logarithm Application - pH
Ex:  Exponential Function Application with Logarithms
Ex:  Logarithmic Function Application - pH (Outputs and Inputs)
Ex:  Logarithmic Function Application - Preston Curve (Outputs and Inputs)

Solving Exponential Equations Without Logarithms

Solving Exponential Equations by Obtaining a Common Base
Ex 1:  Solve Exponential Equations Using Like Bases - No Logarithms
Ex 2:  Solve Exponential Equations Using Like Bases - No Logarithms
Ex 3:  Solve Exponential Equations Using Like Bases - No Logarithms
Ex 4:  Solve Exponential Equations Using Like Bases - No Logarithms
Ex 5:  Solve Exponential Equations Using Like Bases - No Logarithms
Ex 6:  Solve Exponential Equations Using Like Bases - No Logarithms

Solving Exponential Equations With Logarithms

Ex:  Solve an Exponential Equation Graphically on the TI84
Solving Exponential Equations Using Logarithms
Ex 1: Solve a Basic Exponential Equation Using the Definition of a Logarithm
Ex 2: Solve a Basic Exponential Equation Using the Definition of a Logarithm
Ex 1:  Solve Exponential Equations Using Logarithms
Ex 2:  Solve Exponential Equations Using Logarithms
Ex 3:  Solve Exponential Equations Using Logarithms
Ex 4:  Solve Exponential Equations Using Logarithms
Ex 5:  Solve Exponential Equations with Two Exponential Parts Using Logarithms
Ex 6: Solve an Exponential Equation Using Common Log
Ex 7: Solve an Exponential Equation Using Natural Log (Factoring)
Ex: Solve an Exponential Equation Using Logarithms
Ex:  Solve an Exponential Equation with Logarithms - Variable on Both Sides
Ex:  Rewrite Exponential Functions:  y = ab^t to y = ae^(kt)
Ex:  Rewrite Exponential Functions: y = ae^(kt) to y = ab^t

Solving Applications of Exponential Growth and Decay

Introduction to Exponential Functions in the Form f(x)=ab^x - Part 1
Introduction to Exponential Functions in the Form f(x)=ab^x - Part 2
Introduction to Exponential Functions in the Form f(x)=ae^(kx) - Part 1
Introduction to Exponential Functions in the Form f(x)=ae^(kx) - Part 2
Determine a Continuous Exponential Decay Function and Make a Prediction
Exponential Growth:  Part 1, Part 2
Ex: Write Linear and Exponential Functions Based Upon Given Information
Write an Exponential Function for Growth over Different Time Intervals
Ex: Find a Linear and Exponential Model for Population Growth
Ex:  Use a Given Exponential Growth Function
Ex:  Exponential Growth of Bacteria (Intro Question)
Ex: Solve an Exponential Growth Equation Graphically Using the TI84 (Application)
Ex: Compare Simple Interest and Annual Compounded Interest
Ex: Solve an Exponential Growth Equation Graphically Using the Desmos (Application)
Ex: Solve an Exponential Decay Equation Graphically Using the TI84 (Application)
Ex: Solve an Exponential Decay Equation Graphically Using the Desmos (Application)
Ex: Determine the Doubling Time of an Investment Account Graphically (TI84)
Exponential Growth App (y=ab^t) - Given Doubling Time  
Ex: Determine the Half-Life of a Fish Population Graphically (TI84)
Ex: Exponential Function Applications - Increasing Investment Value (Change of Base Used)
Ex: Exponential Function Applications - Decreasing Water Level (Change of Base Used)
Ex:  Exponential Growth Function - Population
Ex:  Exponential Function Application Using Logs - Export Values
Ex:  Exponential Growth Function - Bacterial Growth
Exponential Decay:  Part 1, Part 2
Ex:  Exponential Decay Function with Logarithms
Ex: Exponential Growth Application - Predicting World Population
Ex: Basic Example of Exponential Decay Model
Ex:  Exponential Decay Function - Half Life
Ex: Find the Initial Value and Exponential Growth or Decay Rate Given an Exponential Function
Ex: Exponential Functions: Growth Rate and Growth Factor
Ex: Exponential Functions: Decay Rate and Decay Factor
Ex: Determine Growth Exponential Functions Given Growth Rate and Initial Value (y=ab^x)
Ex: Determine Exponential Decay Functions Given Decay Rate and Initial Value (y=ab^x)
Exponential Decay App  (y=ab^x) - Given Half Life
Exponential Decay App  (y=ae^(kt)) - Given Half Life
Exponential Decay App (y=ab^t) - Find Initial Amount Given Half Life
Exponential Decay App with Logs  (y=ae^(kt)) - Find Half Life
Ex: Exponential Model - Determine Age Using Carbon-14 Given Half Life
Exponential Growth App (y=ab^t) - Given Doubling Time
Exponential Growth App (y=ab^t) - Find Initial Amount Given Doubling Time
Ex: Practice Writing Exponential Equations - Doubling Equation and Halving Equation
Exponential Growth App with Logs (y=ae^(kt)) - Find Initial Amount Given Doubling Time
Ex:  Find an Exponential Growth Function Given Two Points - Initial Value Given
Ex:  Find an Exponential Decay Function Given Two Points - Initial Value Given
Ex:  Find an Exponential Function Given Two Points - Initial Value Not Given
Exponential Function Application (y=ab^x) - Population Growth of India
Exponential Function Application (y=ab^x) - Population Decline of Chicago
Exponential Function Application (y=ab^x) - Depreciation of a Car
Exponential Function Application (y=ab^x) - Declining Computer Value
Exponential Function Application (y=ab^x) - Home Values
Exponential Function Application (y=ae^(kt)) - Bacteria Growth
Ex: Application - Cyclical Around Linear Growth
Ex: Application - Cyclical Around Exponential Growth
Ex: Find Annual Interest Rate Given f(t)=ae^(kt)
Ex: Find Annual Depreciation Rate Given f(t)=ae^(kt)
Ex: Find Continuous Interest Rate Given f(t)=ab^t
Ex: Find Continuous Depreciation Rate Given f(t)=ab^t
Comparing Forms of Exponential Functions:  y = ab^x and y = ae^(kx)
Ex: Find Annual Interest Rate Given f(t)=ae^(kt)
Ex: Find Annual Depreciation Rate Given f(t)=ae^(kt)
Ex: Find Continuous Interest Rate Given f(t)=ab^t
Ex: Find Continuous Depreciation Rate Given f(t)=ab^t

Solving Applications Using Exponential Equations / Compounded and Continuous Interest / Exponential Regression

Compounded Interest
Continuous Interest Formula
Ex 1:  Compounded Interest – Quarterly
Ex 2:  Compounded Interest with Logarithms
Ex: Find Exponential Growth Rate and Make Prediction of a Future Home Value
Continuous Interest Formula - Derivation
Effective Yield for Compounded Interest
Effective Yield for Continuous Interest
Effective Interest Rate (Effective Yield)
Ex 1:  Continuous Interest
Ex 2:  Continuous Interest with Logarithms
Ex 3:  Continuous Interest with Logarithms and Doubling Time
Continuous Interest - Find the Initial Investment Needed
Ex:  Perform Exponential Regression on a Graphing Calculator
Ex: Exponential Regression Application on the TI84 (Decreasing Polio Case)
Ex: Exponential Decay Regression Model (Declining Population)
Ex: Exponential Growth Regression Model (Investment Account)
Ex:  Comparing Linear and Exponential Regression
Ex:  Find an Exponential Function for a Semi-Log Graph
Ex:  Newton's Law of Cooling - Exponential Function App
Exponential Function App. With Logs (y=ae^(kt))- Radioactive Dye
Ex:  Compounded Interest with Different Compounding

Using the Properties of Hyperbolic Functions

Introduction to Hyperbolic Functions
Prove a Property of Hyperbolic Functions: (sinh(x))^2 - (cosh(x))^2 = 1
Prove a Property of Hyperbolic Functions: (tanh(x))^2 + (sech(x))^2 = 1
Prove a Property of Hyperbolic Functions: sinh(x+y)=sinh(x)cosh(y)+cosh(x)sinh(y)
Prove a Property of Hyperbolic Functions: (sinh(x))^2=(-1+cosh(2x))/2

Function Transformations
Determining Transformations of Functions

Horizontal and Vertical Stretches and Compressions
Vertical and Horizontal Translations or Shifts
Ex: Reflect a Point about the x-axis, y-axis, and the Origin
Reflections across the x-axis and y-axis
Summary of Function Transformations
Ex 1: Translate a Point Given Function Notation
Ex 2: Translate a Point Given Function Notation
Ex: Identify Function Translations using Function Notation
Ex: Identify Horizontal and Vertical Stretches and Compressions – Function Notation
Ex: Function Notation for Horizontal and Vertical Stretches and Compressions
Ex:  Equations of a Transformed Exponential Function
Ex: Translate a Quadratic Function on the Coordinate Plane
Ex 1:  Write a Function Rule in Terms of f(x) for a Transformed Function
Ex 2:  Write a Function Rule in Terms of f(x) for a Transformed Function
Ex 1: Find the Equation of a Translated Square Root Function Given a Translation
Ex 2:  Find the Equation of a Translated Quadratic Function Given a Tranlsation
Graphing Multiple Function Transformations Part 1 of 2
Graphing Multiple Function Transformations Part 2 of 2
Determine a Vertical Stretch or Vertical Compression
Determine a Horizontal Stretch or Horizontal Compression
Ex: Determine a Function Rule for a Translations from a Table of Values
Ex: Matching Transformations of the Basic Rational Function
Graphing Transformations of the Cube Root Function
Ex: Determine the Equation of a Transformation of y=2^x

 

Graphing and Finding Equations of Transformed Absolute Value Functions

Ex 1: Graph a Transformation of an Absolute Value Function Using a Table
Ex 2: Graph a Transformation of an Absolute Value Function Using a Table
Ex:  Graph an Absolute Value Function Using a Table of Values
Ex 1: Find the Equation of a Transformed Absolute Value Function From a Graph
Ex 2: Find the Equation of a Transformed Absolute Value Function From a Graph
Ex 3: Find the Equation of a Transformed Absolute Value Function From a Graph
Ex 4: Find the Equation of a Transformed Absolute Value Function From a Graph

Graphing and Finding Equations of Transformed Square Root Functions

Reflections of the Square Root Function
Horizontal and Vertical Shifts of the Square Root Function
Horizontal and Vertical Stretches and Compressions of the Square Root Function
Ex 1:  Find the Equation of a Transformed Square Root Function
Ex 2:  Find the Equation of a Transformed Square Root Function
Ex 1:  Graphing a Transformation of the Square Root Function
Ex 2:  Graphing a Transformation of the Square Root Function
Ex: Find the Equation of a Transformed Square Root Function From a Graph
Function Transformation Summary - The Square Root Function

Graphing and Finding Equations of Transformed Quadratic and Exponential Functions

Ex 1: Find the Equation of a Transformed Quadratic Function From a Graph
Ex 2: Find the Equation of a Transformed Quadratic Function From a Graph
Ex: Match the Graphs of Translated Exponential Function to Equations
Ex: Match the Graphs of Reflected Exponential Functions to Equations

Sequences and Series
Sequences

Introduction to Sequences
Arithmetic Sequences
Geometric Sequences
Ex 1:  Finding Terms in a Sequence Given the Sequence Formula
Ex 2:  Finding Terms in a Sequence Given the Sequence Formula in Fraction Form
Ex 3: Finding Terms in a Sequence Given the Sequence Formula in Fraction Form
Ex: Finding Terms in a Sequence Given the Recursive Formula
Define an Arithmetic and Geometric Sequence
Ex: Determine the Type of Sequence Given a Sequence Formula
Ex: Determine if a Sequence is Arithmetic or Geometric (arithmetic)
Ex: Determine if a Sequence is Arithmetic or Geometric (geometric)
Ex 1:  Find the Formula for an Arithmetic or Geometric Sequence
Ex 2:  Find the Formula for an Arithmetic or Geometric Sequence
Ex: Find the Formula for a Geometric Sequence Given Terms
Ex: Find the Formula and Terms of a Arithmetic Sequence
Ex: Find the Formula and Terms of a Geometric Sequence
Sequences and Series on the TI84

Series

Arithmetic Series
Sequences on the TI84 Graphing Calculator
Geometric Series
Ex 1: Find a Sum Written in Summation / Sigma Notation
Ex 2: Find a Sum Written in Summation / Sigma Notation
Ex: Write a Sum Using Summation / Sigma Notation
Ex 1: Find the Partial Sum of an Arithmetic Series
Ex 2: Find the Sum of an Arithmetic Series
Ex 1: Find the Partial Sum of an Geometric Series
Ex 2: Find the Sum of an Geometric Series
Ex: Sigma Notation  - Summation Involving a Quadratic
Ex: Sigma Notation  - Summation Involving Sine
Sequences and Series on the TI84

Infinite Series

Infinite Geometric Series
Ex 1: Find the Sum of an Infinite Geometric Series
Ex 2: Find the Sum of an Infinite Geometric Series
Ex: Arithmetic Series Application - Number of Auditorium Seats
Ex: Geometric Series Application - Total Income with Doubling Pay

 

Mathematical Induction

Mathematical Induction

Using the Binomial Theorem / Combinations

Ex 1 :Simplify Expressions with Factorials
Ex 2: Simplify Expressions with Factorials Containing Variables
Ex: Evaluate Combinations
Ex 1: The Binomial Theorem Using Combinations
Ex 2: The Binomial Theorem Using Combinations
Ex 3: The Binomial Theorem Using Combinations
Ex: Find a Single Term in a Binomial Expansion
Ex 1: The Binomial Theorem Using Pascal's Triangle
Ex 2: The Binomial Theorem Using Pascal's Triangle
Ex 3: The Binomial Theorem Using Pascal's Triangle
The Binomial Theorem Using Pascal’s Triangle

Matrices
Introduction to Matrices
Dimensions of a Matrix

Using Augmented Matrices

Introduction to Augmented Matrices
Augmented Matrices:  Row Echelon Form
Perform Matrix Row Operations Using the TI84 Matrix Menu
Perform Matrix Row Operations Using the TI84 Home Screen
Ex 1: Solve a System of Two Equations with Using an Augmented Matrix (Row Echelon Form)
Ex 2: Solve a System of Two Equations with Using an Augmented Matrix (Row Echelon Form)
Ex 3: Solve a System of Two Equations with Using an Augmented Matrix (Row Echelon Form)
Ex 1: Solve a System of Three Equations with Using an Augmented Matrix (Row Echelon Form)
Ex 2: Solve a System of Three Equations with Using an Augmented Matrix (Row Echelon Form)
Ex 3: Solve a System of Three Equations with Using an Augmented Matrix (Row Echelon Form)
Augmented Matrices: Reduced Row Echelon Form (update)
Augmented Matrices:  Reduced Row Echelon Form
Ex 1: Solve a System of Two Equations Using an Augmented Matrix (Reduced Row Echelon Form)
Ex 2: Solve a System of Two Equations Using an Augmented Matrix (Reduced Row Echelon Form)
Ex 3: Solve a System of Two Equations Using an Augmented Matrix (Reduced Row Echelon Form)
Ex: Solve a System of Three Equations Using an Augmented Matrix (Reduced Row Echelon Form)
Augmented Matrices on the Graphing Calculator

Performing Matrix Operations

Matrix Addition, Subtraction and Scalar Multiplication
Ex: Matrix Addition and Subtraction
Ex: Matrix Scalar Multiplication
Ex: Matrix Operations - Scalar Multiplication, Addition, and Subtraction
Ex: Matrix Addition Application - Translation
Ex: Matrix Scalar Multiplication Application - Dilation
Matrix Multiplication
Ex 1: Matrix Multiplication (Basic)
Ex 2: Matrix Multiplication (2x3)*(3x2)
Ex 3: Matrix Multiplication (3x2)*(2x3)
Ex Applicaton of Matrix Multiplication - Transformation
Matrix Multiplication on the Graphing Calculator
Animation:  Matrix Multiplication

Determining Inverse Matrices

The Identity Matrix
2 x 2 Inverse Matrix Formula
Inverse Matrices Using Augmented Matrices
Inverse Matrices on the Graphing Calculator
Ex: Find the Inverse of a 2x2 Matrix Using a Formula
Ex: Inverse of a 2x2 Matrix Using an Augmented Matrix
Ex 1: Inverse of a 3x3 Matrix Using an Augmented Matrix
Ex 2: Inverse of a 3x3 Matrix Using an Augmented Matrix

Using The Matrix Equation

Matrix Equations
Ex 1: Solve a System of Two Equations Using a Matrix Equation
Ex 2: Solve a System of Two Equations Using a Matrix Equation
Ex: Solve a System of Three Equations Using a Matrix Equation

Finding and Using Determinants

Determinants
Ex: Determinant of a 2x2 Matrix
Ex 1: Determinant of 3x3 Matrix - Diagonal Method
Ex 2: Determinant of 3x3 Matrix - Diagonal Method
Ex 1: Determinant of 3x3 Matrix - Cofactor Method
Ex 2: Determinant of 3x3 Matrix - Cofactor Method
Determinants on the Graphing Calculator
Cramer’s Rule
Ex: Solve a System of Two Equations Using Cramer's Rule
Ex: Solve a System of Three Equations Using Cramer's Rule
Area Using Determinants

Linear Programming

Introduction to Linear Programming
Ex: Find the Maximum and Minimum of an Objective Function Given the Feasible Region Using Linear Programming
Ex: Find the Minimum of an Objective Function Given Constraints Using Linear Programming (unbounded)
Ex: Find the Maximum of an Objective Function Given Constraints Using Linear Programming (bounded)
Ex: Use Linear Programming to Maximize Profit from Two Crops
Ex: Use Linear Programming to Maximize Income from Two Desserts
Ex: Use Linear Programming to Maximize Profit from Two DVD Players

The Simplex Method

Perform Matrix Row Operations Using the TI84 Matrix Menu
Perform Matrix Row Operations Using the TI84 Home Screen
Introduction to the Simplex Method: Standard Maximization (2 variables)
Using Simplex Method an a Standard Maximization Problem (3 variables)
Ex: Simplex Method - Set Up Initial Tableau From a Word Problem (Standard Max)
Ex: Simplex Method - Set Up Initial Tableau Given Objective Function and Constraints (Standard Max)
Ex: Simplex Method - Interpret the Final Tableau
Ex: Simplex Method - Given a Tableau, Determine the Pivot Column and Pivot Row
Ex: Simplex Method - Determine the Active Variables and the Basic Solution
Ex:  Simplex Method - Perform the Pivot Operation Given a Tableau
Solving a Standard Minimization Problem Using The Simplex Method (Duality)
Ex 1:  Determine a Dual Problem Given a Standard Minimization Problem
Ex 2:  Determine a Dual Problem Given a Standard Minimization Problem
Ex 1:  Interpret the Final Tableau of a Dual Problem
Ex 2:  Interpret the Final Tableau of a Dual Problem

Counting and Probability
Counting Principle

The Counting Principle
Ex: Determine the Number of Possible Outfits - Counting Principle
Ex: Determine the Number of Three Letter Codes - Counting Principle
Ex: Determine the Outcomes Rolling Colored Dice - Counting Principle
Ex:  Determine the Number of Possible License Plates - Counting Principle
Ex: Determine the Number of Ways to Complete a True/False Test - Counting Principle

Permutations and Combinations

Permutations
Ex: Evaluate a Combination and a Permutation - (n,r)
Ex: Evaluate a Combination and a Permutation - (n,1)
Ex: Determine the Number of Ways Six Runners Can Finish - Counting/Permutation
Ex: Determine the Possible Number of 4 Color Striped Flags (Permutation)
Ex: Determine the Possible Number of of Ways 255 Contestants can Win 3 Prizes (Permutation)
Ex1: Determine the Number of Permutations With Repeated Items
Ex2: Determine the Number of Permutations With Repeated Items
Combinations
Ex: Determine the Number of Ways 6 Books can be Selected from 9 Books (Combination)
Ex: Determine the Number of Ways 3 Varieties can be Selected from 12 (Combination)
Ex: Determine the Number of 4 Topping Pizzas from 14 Toppings (Combination)
Ex: Determine the Number of 4 Card Hands from 52 Cards
Solving Counting Problems

Probability

Introduction to Probability
Ex: Find the Probability of Landing On a Single Number Using  a Spinner
Ex: Find the Probability of Landing On Two Numbers Using  a Spinner
Ex: Find the Probability of Landing On a Multiple of 3 Using  a Spinner
Ex: Find the Probability of Landing On an Odd Number Using  a Spinner
Ex: Find the Probability of Landing On an Number Greater Than 5 Using  a Spinner
Ex: Find the Probability of Landing On an Number Less Than Than 6 Using  a Spinner
Ex: Find the Probability of a Sum of 7 Using Two Dice
Ex:  Find the Probability of Selecting the Same Cookie Twice (Dependent)
Determining Probability
Ex:  Determine Odds In Favor and Odds Against from a Given Probability
Probability of a Union of Events
Conditional Probability
Ex 1: Determine a Conditional Probability Using a Venn Diagram  - P(B|A)
Ex 2: Determine a Conditional Probability Using a Venn Diagram  - P(B|not A)
Ex 3: Determine a Conditional Probability Using a Venn Diagram - P(not B|A)
Ex:  The Probability of the Complement of an Event
Ex: Find a Probability Using the Complement of an Event (At Least One)
Ex: The Counting Principle and Probability Using the Counting Principle
Ex: Probability of Events that are Mutually Exclusive Events
Ex: Probability of Events that are NOT Mutually Exclusive Events
Ex: Probability using Permutations (Ordering)
Ex:  Determine a Probability Using a Permutation - Match Phone Digits
Ex:  Determine a Probability Using a Combination - Select Oldest Group
Ex 1:  Probability Using Combinations (Lottery)
Ex 2:  Probability Using Combinations (Groups)
Ex: Determine Odds Using Probability
Ex: Determine Odds from Given Information (Basic)
Ex: Determine Probability Given Odds

The Binomial Theorem

The Binomial Theorem using Combinations
Ex 1: The Binomial Theorem Using Combinations
Ex 2: The Binomial Theorem Using Combinations
Ex 3: The Binomial Theorem Using Combinations

Conic Sections

Introduction to Conic Section

Introduction to Conic Sections

Graphing and Writing Equations of Circles

Conic Sections:  The Circle
Ex:  Write the Standard Form of a Circle From a Graph
Ex: Graph a Circle in Standard Form
Ex 1: Write the General Equation of a Circle in Standard Form
Ex 2: Write the General Equation of a Circle in Standard Form (Fractions)
Ex 3: Write General Equation of a Circle in Standard Form  (Coefficent Not 1)
Ex 4: Write General Equation of a Circle in Standard Form  (Coefficent Not 1 and Fractions)
Ex: Find Standard Equation of a Circle Given Center and Point on the Circle
Ex 1: Find Standard Equation of a Circle Given the Endpoints of a Diameter
Ex 2: Find Standard Equation of a Circle Given the Endpoints of a Diameter
Ex : Find the Intercepts of a Circle
Ex:  Intersection of a Line and a Circle - Applications
Ex: Find a Point on the Unit Circle Given One Coordinate
Ex 1: Find a Point of Intersection of a Line and a Circle
Ex 2: Find a Point of Intersection of a Line and a Circle

Graphing and Writing Equations of Ellipses

Conic Sections:  The Ellipse part 1 of 2
Conic Sections:  The Ellipse part 2 of 2
Ex: Match Graphs of Ellipses to Equations
Ex: Application of the Reflective Property of an Ellipse
Ex 1: Graph an Ellipse with Center at the Origin and Horizontal Major Axis
Ex 2: Graph an Ellipse with Center at the Origin and Vertical Major Axis
Ex 1: Graph an Ellipse with Center NOT at the Origin and Horizontal Major Axis
Ex 2: Graph an Ellipse with Center NOT at the Origin and Vertical Major Axis
Ex: Write the General Equation of an Ellipse in Standard Form and Graph (Horizontal)
Ex: Write the General Equation of an Ellipse in Standard Form and Graph (Vertical)
Ex: Find the Equation of an Ellipse Given Foci and Length of Minor Axis
Ex: Find the Equation of an Ellipse Given the Center, Focus, and Vertex (Horizontal)
Ex: Find the Equation of an Ellipse Given the Center, Focus, and Vertex (Vertical)
Ex: Find the Equation of an Ellipse Given the Center, Vertex, and Eccentricity (Vertical)
Ex: Find the Equation of an Ellipse Given the Foci and the Distance Sum
Ex: Find Standard Form of an Equation of an Ellipse from a Graph (Horizontal Major Axis)
Ex: Find Standard Form of an Equation of an Ellipse from a Graph (Vertical Major Axis)
Ex: Write the General Equation of an Ellipse in Standard Form and Graph (Horizontal)

Graphing and Writing Equations of Parabolas

Conic Sections:  The Parabola part 1 of 2
Conic Sections:  The Parabola part 2 of 2
Ex 1: Conic Section: Parabola with Vertical Axis and Vertex at the Origin (Up)
Ex 2: Conic Section: Parabola with Vertical Axis and Vertex at the Origin (Down)
Ex 3: Conic Section: Parabola with Horizontal Axis and Vertex at the Origin (Right)
Ex 4: Conic Section: Parabola with Horizontal Axis and Vertex at the Origin (Left)
Ex 1: Conic Section: Parabola with Vertical Axis and Vertex NOT at the Origin (Up)
Ex 2: Conic Section: Parabola with Vertical Axis and Vertex NOT at the Origin (Down)
Ex 3: Conic Section: Parabola with Vertical Axis and Vertex NOT at the Origin (Up)
Ex 4: Conic Section: Parabola with Vertical Axis and Requires Completing the Square (Up)
Ex 5: Conic Section: Parabola with Vertical Axis and Requires Completing the Square (Down)
Ex 6: Conic Section: Parabola with Horizontal Axis and Vertex NOT at the Origin (Right)
Ex 7: Conic Section: Parabola with Horizontal Axis and Vertex NOT at the Origin (Left)
Ex 8: Conic Section: Parabola with Horizontal Axis and Vertex NOT at the Origin (Right)
Ex 9: Conic Section: Parabola with Horizontal Axis and Requires Completing the Square (Right)
Ex 10: Conic Section: Parabola with Horizontal Axis and Requires Completing the Square (Left)
Ex 1: Find the Equation of a Parabola Given the Focus and Vertex.  (Positive a)
Ex 2: Find the Equation of a Parabola Given the Focus and Vertex.  (Negative a)

Graphing and Writing Equations of Hyperbolas

Conic Sections:  The Hyperbola part 1 of 2
Conic Sections:  The Hyperbola part 2 of 2
Ex 1: Conic Section - Graph a Hyperbola with Center at the Origin (Horizontal)
Ex 2: Conic Section - Graph a Hyperbola with Center at the Origin (Vertical)
Ex 3: Conic Section - Graph a Hyperbola with Center NOT at the Origin (Horizontal)
Ex 4: Conic Section - Graph a Hyperbola with Center NOT at the Origin (Vertical)
Ex: Find the Equation of a Hyperbola Given the Center, Focus, and Vertex
Determining the Type of Conic Section from General Form

Set Theory

Introduction to Set Theory
Introduction to Subsets
Set Operations and Venn Diagrams - Part 1 of 2
Set Operations and Venn Diagrams - Part 2 of 2
Solving Problems Using Venn Diagrams

Regression

Introduction to Regression Analysis
Linear Regression – Example 1, Example 2
Quadratic Regression – Example 1, Example 2
Ex 1: Cubic Regression on the TI84 – Natural Gas Consumption
Ex 2: Cubic Regression on the TI84 - Total Sales
Exponential Regression – Example 1, Example 2
Ex: Exponential Decay Regression Model (Declining Population)
Ex: Exponential Growth Regression Model (Investment Account)
Logarithmic Regression
Logistic Regression

Financial Mathematics

 Simple Interest Formula
Compounded and Continuous Interest
Effective Yield
Effective Yield on the TI84
Derive the Value of an Annuity Formula (Compounded Interest)
Determining the Value of an Annuity
Determining the Value of an Annuity Using the TI84
Determining the Monthly Saving Required to Reach a Financial Goal
Determining the Monthly Saving Required to Reach a Financial Goal on the TI84
Ex 1: Find a Monthly Mortgage Payment with a Down Payment
Ex 2: Find a Monthly Mortgage Payment with a Down Payment and Points
Ex: Comparing Two Installments Loans  (Car Loans)
Ex: Simple Interest Discounted Loan
Determining the Monthly Payments for a Loan
Determining the Monthly Payments for a Loan on the TI84

Graphing Calculator
Basics:  Evaluating Expressions and Determining Function Values

Graphing Calculator Basics
The Table Feature of the Graphing Calculator
Evaluating Radical Expressions on the TI83/84
Determine Function Values Using Function Notation on the TI84

Graphing Functions and Determining Key Components of Functions

Graphing Lines on the Graphing Calculator
Determining the Intersection of Two Graph on the TI83/84
Determining Relative Extrema on the Graphing Calculator
Determine Function Values Using Function Notation on the TI84
Determine the value of the derivative function on the graphing calculator
Determining the value of a definite integral on the graphing calculator
Determining the Intersection of Two Graph on the TI83/84
Determining the Zeros or Roots of a Polynomial Function on the TI83/84
Determining When a Polynomial Function is Increasing and Decreasing
Determining the Zeros or Roots of a Polynomial Function on the TI83/84
Ex:  Quadratic Function Application Using a Graphing Calculator - Rocket Launch
Ex 1:  The Zero Feature of the TI84 to Find Rational Zeros of a Polynomial
Ex 2:  The Zero Feature of the TI84 to Find Rational Zeros of a Polynomial
Ex 1:  The Intersection Feature of the TI84 to Find Rational Zeros of a Polynomial
Ex 2:  The Intersection Feature of the TI84 to Find Rational Zeros of a Polynomial

Solving Equations on the Graphing Calculator

Solving Linear Equations Graphically
Ex: Solve a Linear Equation in One Variable Graphically using the TI84
Ex: Solve a Linear Inequality in One Variable Graphically using the TI84
Ex: Solving Absolute Value Equations on the Graphing Calculator
Ex 1:  Solve a Quadratic Equation Graphically on Calculator
Ex 2:  Solve a Quadratic Equation Graphically on Calculator
Ex: Determine How a Final Exam Score Affect a Course Grade using the TI84 (Weighted Averages)
Solving Polynomial Equations Graphically

Logarithms on the Graphing Calculator

Ex:  Evaluate Common Logarithms on a Calculator
Ex:  Evaluate Common Logarithms on the Calculator   
Ex:  Evaluate Natural Logarithms on the Calculator
Ex:  Change of Base Formula to Evaluate Logarithmic Expressions
Ex:  Change of Base Formula to Solve Basic Exponential Equations
Ex: Evaluate Logarithmic Functions Using the Change of Base Formula
Ex:  Solve an Exponential Equation Graphically on the TI84
Ex:  Perform Exponential Regression on a Graphing Calculator
Ex:  Comparing Linear and Exponential Regression
Sequences and Series on the TI84
Sequences and Series on the TI84

Matrices on the Graphing Calculator

Augmented Matrices on the Graphing Calculator
Matrix Multiplication on the Graphing Calculator
Inverse Matrices on the Graphing Calculator
Ex 1: Solve a System of Two Equations Using a Matrix Equation
Ex 2: Solve a System of Two Equations Using a Matrix Equation
Ex: Solve a System of Three Equations Using a Matrix Equation
Determinants on the Graphing Calculator
Ex: Solve a System of Three Equations Using Cramer's Rule

Regression on the Graphing Calculator

Ex 1:  Create a Scatter Plot and then Perform Linear Regression on the Calculator
Ex 2:  Creating a Scatter Plot and Performing Linear Regression on the Calculator
Linear Regression – Example 1, Example 2
Ex: Matching Correlation Coefficients to Scatter Plots
Quadratic Regression – Example 1, Example 2
Ex:  Quadratic Regression on the TI84 - Stopping Distance
Exponential Regression – Example 1, Example 2
Logarithmic Regression
Logistic Regression
Regression and Systems of Equations:  Application

Financial Mathematics on the Graphing Calculator

Loan Information on the TI83/84
Effective Yield on the TI84
Determining the Value of an Annuity Using the TI84
Determining the Monthly Payments for a Loan on the TI84
Determining the Monthly Saving Required to Reach a Financial Goal on the TI84

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