Introduction to Algebra

Sets of Numbers

Identifying Sets of Real Numbers

Real Number Basics

 

Integer Operations

Adding Integers

Subtracting Integers

Multiply and Divide Integers

 

Exponents

Exponential Notation

Properties of Exponents 

A Discussion:  Zero to the Power of Zero - 0^0

The Zero Exponent

Ex:  Write Repeated Multiplication Using Exponents

Ex:  Expanding and Evaluating Exponential Notation

Ex:  Simplify Exponential Expressions - Product and Power Rule

Ex:  Simplify Exponential Expressions - Quotient Rule

Ex 1:  Simplify Exponential Expressions - Positive Exponents Only

Ex 2:  Simplify Exponential Expressions - Positive Exponents Only

Ex 3:  Simplify Exponential Expressions - Positive Exponents Only

Ex: Raising Fractions to Powers

Ex: Quotient Rule of Exponents (Positive and Negative)

Ex: Simplify Quotients with Different Bases and Negative Exponents


Order of Operations and Expressions

Order of Operations – The Basics

Order of Operations

Introduction to the Distributive Property

Using the Distributive Property to Multiply

Simplifying Algebraic Expressions

Evaluating Algebraic Expressions

Ex:  Evaluate Exponential Expressions

Ex:  Evaluate Exponential Expression

Ex 1:  Evaluate An Expression Using The Order of Operations

Ex 2:  Evaluate An Expression Using The Order of Operation

Ex 3:  Evaluate An Expression Using The Order of Operation

Ex:  Write Repeated Multiplication Using Exponents

Ex:  Expanding and Evaluating Exponential Notation

Ex:  Simplify Exponential Expressions - Product and Power Rule

Ex:  Simplify Exponential Expressions - Quotient Rule

Ex 1:  Simplify Exponential Expressions - Positive Exponents Only

Ex 2:  Simplify Exponential Expressions - Positive Exponents Only

Ex 3:  Simplify Exponential Expressions - Positive Exponents Only

Introduction to Variables and Variable Expressions

Ex 1:  Writing Variable Expressions

Ex 2:  Write Algebraic Expressions

Ex 1:  Writing Basic Algebraic Expressions

Ex 2:  Writing Basic Algebraic Expressions

 

The Distributive Property and Combine Like Terms

Introduction to the Distributive Property

Ex 1:  The Distributive Property

Ex 2:  The Distributive Property

Using the Distributive Property to Multiply

Combining Like Terms

Ex 1:  Combining Like Terms

Ex 2:  Combining Like Terms

Ex 3:  Combining Like Terms Requiring Distribution

Simplifying Algebraic Expressions

Ex:  Simplify Variable Expressions by Multiplying

Evaluating Algebraic Expressions

 

Linear Equations in One Variable

Types of Linear Equations

Types of Linear Equations: Conditional, Identity, and Contradiction

The Difference Between an Expression and an Equation

 

Solving One-Step Equations with Integers

Solving One Step Equations:  The Basics

Ex:  Solve One Step Equations By Adding and Subtracting Whole Numbers (Var. on Left)

Ex:  Solve One Step Equations By Multiplying and Dividing Whole Numbers (Var. on Left)

Ex:  Solve One Step Equations By Adding and Subtracting Whole Numbers (Var on Right)

Ex:  Solve One Step Equations By Multiplying and Dividing Whole Numbers(Var on Right)

Ex:  Solving One Step Equation by Add/Subtracting Integers (Var on Left)

Ex:  Solving One Step Equation by Add/Subtracting Integers (Var on Right)

Ex:  Solving One Step Equation by Mult/Div.  Integers (Var on Left)

Ex:  Solving One Step Equation by Mult/Div.  Integers (Var on Right)

Ex:  Solving One Step Equation in the Form:  -x = a

Ex:  Solve One Step Equation by Add/Subtract (Simplify 1st)

Ex:  Solve One Step Equation by Mult/Div (Simplify 1st)

Ex: Solve a Linear Equation in One Variable that Requires Simplifying   


Solving One-Step Equations with Fractions and Decimals

Solving One Step Equations Involving Fractions

Ex:  Solve One Step Equations With Fraction by Adding or Subtracting

Ex:  Solve One Step Equations With Fraction by Multiplying

Solving One Step Equations Involving Decimals

Ex:  Solve a One Step Equation With Decimals by Adding and Subtracting

Ex:  Solve a One Step Equation With Decimals by Multiplying

Ex:  Solve a One Step Equation With Decimals by Dividing

Solving One Step Equations:  Summary

 

Solving Two-Step Equations

Solving Two Step Equations:  The Basics

Ex 1:  Solving Two-Step Equations Using Integers

Ex 2:  Solving Two-Step Equations Using Integers

Solving Two Step Equations Involving Fractions

Ex:  Solve a Two-Step Equation with a Fraction

Ex:  Solve an Equation with Fractions

Ex 1: Solve Equations with Fractions (Alternative Method)

Ex 2: Solve Equations with Fractions (Alternative Method)

Ex 1: Solving a Two Step Equation with Fractions - NOT Clearing the Fractions

Ex 2: Solving a Two Step Equation with Fractions - NOT Clearing the Fractions

Ex 3: Solving a Two Step Equation with Fractions - NOT Clearing the Fractions

Ex 4: Solving a Two Step Equation with Fractions - NOT Clearing the Fractions

Ex 5: Solving a Two Step Equation with Fractions - NOT Clearing the Fractions

Ex 1: Solving a Two Step Equation with Fractions - Clearing the Fractions

Ex 2: Solving a Two Step Equation with Fractions - Clearing the Fractions

Ex 3: Solving a Two Step Equation with Fractions - Clearing the Fractions

Ex 4: Solving a Two Step Equation with Fractions - Clearing the Fractions

Ex 5: Solving a Two Step Equation with Fractions - Clearing the Fractions

Solving Two Step Equations Involving Decimals

Ex:  Solve a Two-Step Equation with Decimals

Solving Two Step Equations:  Summary

 

Solving Multi-Step Equations

Solving Multiple Step Equations

Ex 1:  Solve an Equation with Parentheses

Ex 2:  Solve an Equation with Parentheses

Ex:  Solve an Equation with Variable Terms on Both Sides

Ex 1:  Solve an Equation with Variables and Parentheses on Both Sides

Ex 2:  Solve an Equation with Variables and Parentheses on Both Sides

Ex :  Solving a Multi-Step Linear Equation in One Variable

Ex:  Solving a Multi-Step Linear Equation in One Variable

Ex 1:  Solve an Equation with Fractions with Variable Terms on Both Sides

Ex 2:  Solve an Equation with Fractions with Variable Terms on Both Sides

Solving Multiple Step Equations Involving Decimals

Ex:  Solve a Linear Equation With Decimals and Variables on Both Sides

Ex: Solve an Equation with Decimals and Parentheses

Ex: Solve a Linear Equation in One Variable that Requires Simplifying   

Examples 1:  Solving a Formula for a Variable

Examples 2:  Solving a Formula for a Variable

 

Solving Equations Graphically

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

 

Solving Linear Equation Application Problems

Problem Solving with Equations

Ex: Find the Area of a Rectangle Given the Perimeter

Ex:  Linear Equation Application - Car Repair with Labor and Parts

Ex:  Linear Equation Application - Depth Under Water

Distance = Rate x Time Application Problem

Ex:  Midpoint of a Segment

Ex: Find the Endpoint of a Segment Given the Midpoint and One Endpoint

Ex: Find Grade Category Percentages and Course Grade Percentage Based on Total Points

Ex: Find the Points Needed to Receive an A in a Class Based on Total Points

Ex:  Find a Course Percentage and Grade Using a Weighted Average

Ex: Find a Final Exam Score to Receive a Specific Grade Using Weighted Averages

Ex: Determine How a Final Exam Score Affect a Course Grade using the TI84 (Weighted Averages)

 

Linear Equations in Two Variables

The Coordinate Plane and Plotting Points

Plotting Points on the Coordinate Plane

Identify the Quadrant of a Point on the Coordinate Plane

Ex:  Plotting Points on the Coordinate Plane

Ex:  Identifying the Coordinates of Points on the Coordinate Plane

Ex:  Determine if Points are on a Given Line

Graphing By Plotting Points:  Part 1, Part 2

Ex: Area of a Parallelogram on the Coordinate Plane

Ex: Area of a Trapezoid on the Coordinate Plane


Graphing Linear Equations Using a Table of Values

Ex 1:  Graph a Linear Equation Using a Table of Values

Ex 2:  Graph a Linear Equation Containing Fractions Using a Table of Values

Ex 3:  Graph a Linear Equation in Standard Form Using a Table of Values

Graphing Horizontal and Vertical Lines

Ex:  Graph a Horizontal Line Using a Table of Values

Ex:  Graph a Vertical Line Using a Table of Values

Graphing Linear Equations by Finding Intercepts

Ex:  State the X and Y Intercepts Given the Graph of a Line

Ex 1:  Graph a Linear Equation in Standard Form Using the Intercepts

Ex 2:  Graph a Linear Equation in Standard Form Using the Intercepts

Ex:  Determine the x and y Intercepts of a Linear Equation in Slope Intercept Form

Using Models

 

Determining Rate of Change and Slope

Rate and Slope

Ex:  Determine Which Tables Represent a Linear Function or Linear Relationship

Ex:  Given Linear Function, Find the Rate of Change and Initial Value

Ex 1: Determine the Slope Given the Graph of a Line (positive slope)

Ex 2: Determine the Slope Given the Graph of a Line (negative slope)

Ex: Find the Slope Given Two Points and Describe the Line

Ex: Find the Slope Given Two Points Containing Fractions and Describe the Line

Ex: Determine the Slope Given the Graph of a Horizontal and Vertical Line

Ex 1:  Determine the Slope a Line Given Two Points on a Line

Ex 2:  Determine the Slope a Line Given Two Points on a Line

Ex:  Determine the Slope a Line Given Two Points on a Horizontal and Vertical Line

Ex:  Find the Average Rate of Change From a Table - Temperatures

Ex: Find the Average Rate of Change - Miles Per Hour

Ex:  Find the Average Rate of Change from a Graph

Ex:  Find the Average Rate of Change Given a Function Rule

Ex:  Average Rate of Change Application - Hot Air Balloon Function

Ex:  Find the Average Rate of Change Given a Function on [2,t]

Ex:  Find the Average Rate of Change Given a Function on [3, 3+h]

Ex:  Slope Application Involving Population Growth

Ex:  Slope Application Involving Production Costs

 

Graphing a Linear Equations in Slope-intercept form: y=mx+b

Graphing a Line in Slope-Intercept Form (new)

Using Slope Intercept Form of a Line

Animation:  y = mx + b

Ex: Matching Linear Equations to Graphs of Lines

Graphing Lines in the form y = mx + b – Slope Intercept Form

Slope-Intercept form of a Line

Ex 1:  Graph a Linear Equation in Slope-Intercept Form

Ex 2:  Graph a Linear Equation in Slope-Intercept Form

Ex 3:  Graph a Linear Equation in Slope-Intercept Form

Ex 4:  Graph a Linear Equation in Slope-Intercept Form

Ex 1:  Graph a Linear Equation in Standard From by Writing in Slope-Intercept Form

Ex 2:  Graph a Linear Equation in Standard From by Writing in Slope-Intercept Form

Ex 3:  Graph a Linear Equation in Standard From by Writing in Slope-Intercept Form

Ex: Given Linear Equations, Find the Slope and Intercepts

Graphing Lines on the Graphing Calculator

 

Determining Linear Equations of Lines in Slope-intercept Form:
y=mx+b

Determine the Equation of a Line in Slope-Intercept Form

Ex 1:  Find the Equation of a Line in Slope Intercept Form Given the Graph of a Line

Ex 2:  Find the Equation of a Line in Slope Intercept Form Given the Graph of a Line

Ex:  Find the Equation of a Line in Slope Intercept Form Given the Slope and a Point

Ex 2:  Find the Equation of a Line in Slope Intercept Form Given the Graph of a Line

Ex:  Find the Equation of a Horizontal and Vertical Line Given the Graph

Ex 1:  Find the Equation of a Line in Slope Intercept Form Given Two Points

Ex 2:  Find the Equation of a Line in Slope Intercept Form Given Two Points

Ex:  Find the Linear Function Given Two Function Value in Function Notation

Ex:  Find the Equation of a Line in Slope Intercept Form Given the X and Y Intercepts

Ex:  Find the Equation of a Horizontal Line Given Two Points on the Line

Ex:  Find the Equation of a Vertical Line Given Two Points on the Line

Ex:  Linear Equation Application (Write a Cost Equation)

Ex:  Linear Equation Application (Write a Profit Equation)

Ex: Function Inputs and Outputs of a Cost Function (Linear)

Ex:  Determine Total Cost and Marginal Cost (No Derivative)

Ex: Find an Output, Input, and Intercept of a Demand Function

Ex: Find Total Revenue, Total Cost, and Total Profit Functions


Graphing and Determining Linear Equations in  Standard Form: 
Ax + By = C

Standard Form of a Line

Graphing Lines by Finding Intercepts

Ex:  Graph a Linear Equation in Standard Form Using a Table of Values

Ex:  Graph a Linear Equation in Standard Form Using the Intercepts

Ex 1:  Given Linear Equation in Standard Form, Write in Slope-Intercept Form to Graph

Ex 2:  Given Linear Equation in Standard Form, Write in Slope-Intercept Form to Graph

Ex:  Match the Graph of a Line to the Correct Equation in Standard Form

Ex 1: Find the Equation of a Line in Standard Form Given Two Points

Ex 2: Find the Equation of a Line in Standard Form Given Two Points

 

Graphing and Determining Linear Equations in  Point-slope Form: 
y-y1=m(x-x1)

Point Slope Form of  a Line

Ex:  Graph a Linear Equation in Point-Slope Form

Ex:  Find the Equation of a Line in Point Slope and Slope Intercept Form Given a Graphed Line

Ex:  Find the Equation of a Line in Point Slope and Slope Intercept Form Given the Slope and a Point

Ex:  The Equation of the Line in Point-Slope and Slope Intercept Form Given Two Points

Finding Linear Equations

 

Determining Linear Equations of Parallel and Perpendicular Lines

Parallel and Perpendicular Lines:  Part 1, Part 2

Parallel and Perpendicular Lines (old)

Ex 1:  Find the Equation of a Line Parallel to a Given Line Passing Through a Given Point

Ex 2:  Find the Equation of a Line Parallel to a Given Line Passing Through a Given Point

Ex 1:  Find the Equation of a Line Perpendicular to a Given Line Passing Through a Given Point

Ex 2:  Find the Equation of a Line Perpendicular to a Given Line Passing Through a Given Point

Ex: Find the Equation of a Perpendicular and Horizontal Line to a Horizontal Line

Ex: Find the Equation of a Perpendicular and Horizontal Line to a Vertical Line


Solving Linear Equation Applications

Ex:  Percent Equation to Determine a Sale Price

Ex 1:  Number Problem:  Find a Number given a Relationship

Ex 2:  Number Problem:  Find a Number given a Relationship

Ex: Find the Length of Two Pieces Cut From a Large Piece Given a Relationship

Ex:  Find the Dimensions and Area of a Field Given the Perimeter

Ex:  Find the Dimensions of a Bookcase Using  a Linear Equation

Ex:  Find a Monthly Salary given Annual Salary Including a Bonus

Ex:  Find the Number of Coins in a Bag Given the Total Value

Ex:  Given the Interest, Find the Amount of Money in Two Accounts Earning Different Interest

Ex:  Find the Rate of Two Cyclist Traveling Toward Each Other

Ex:  Find the Distance Between To Cities Using d = rt formula

Ex:  Find When Two People Leaving the Same Place At Different Rates and Time Will Meet

Linear Business Application

Ex:  Linear Equation Application (Cost of a Rental Car)

Ex:  Linear Equation Application (Write a Cost Equation)

Ex:  Linear Equation Application:  Write a Profit Equation

Ex:  Linear Equation Model for Submarine Depth

Ex:  Linear Application:  Oil Reserves

Ex: Find a Final Exam Score to Receive a Specific Grade Using Weighted Averages

Ex: Determine How a Final Exam Score Affect a Course Grade using the TI84 (Weighted Averages)

Ex:  Find a Course Percentage and Grade Using a Weighted Average

Ex: Find Grade Category Percentages and Course Grade Percentage Based on Total Points

Ex: Find the Points Needed to Receive an A in a Class Based on Total Points

Ex:  Given a Linear Model, Interpret the Meaning of the Slope and Make Predictions

Ex:  Determining Linear Model for Population Growth

Ex: Find a Linear Equation Application - Cell Phone Plan


Direct Variation

Direct Variation

Ex 1:  Graph a Direct Variation Equation (positive slope)

Ex 2:  Graph a Direct Variation Equation (negative slope)

Ex:  Direct Variation Equation

Ex: Direct Variation (Distance = Rate x Time)

Hooke's Law - Direction Variation Application 


Performing Linear Regression

Introduction to Regression Analysis

Linear Regression

Ex: Make a Prediction Given the Results of Performing Linear Regression

Ex: Graphical Interpretation of a Scatter Plot and Line of Best Fit

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

Linear Regression on the TI84 Graphing Calculator

 

Introduction to Functions

Function Basics

Introduction to a Function:  Part 1, Part 2

Ex: Determine if Statements Represent Functions

Function Notation Application

Linear Functions

Ex: Interpret the y-intercept and Slope of a Linear Model

Ex:  Determine if a Linear Function is Increasing or Decreasing

Ex: Determine a Linear Function Model - Price and Quantity

Ex: Function Notation Application Problem

Ex:  Write a Cost Function and Complete a Table of Values

Ex:  Complete a Table of Values Given a Function Rule

Ex 1:  Write a Function Rule Given a Table of Values

Ex 2:  Write a Function Rule Given a Table of Values

Ex 3:  Write a Function Rule Given a Table of Values

Ex:  Graph a Linear Function Using a Table of Values

Write Basic Functions from Applications - One Step

Ex: Writing Function Rules - Two Operations

Ex: Writing Function Rules - Three Operations

Ex: Determine a Linear Demand Function


Determining Function Values

Function Notation

Finding Values of Functions

Ex: Find an Output of a Demand Function

Ex 1:  Determine Function Values Given a Quadratic Function

Ex 2:  Determine Function Values Given a Square Root Function

Ex 3:  Determine Function Values Given a Rational Function

Ex 1:  Determine a Function Value From a Graph

Ex 2:  Determine a Function Value From a Graph

Ex 3:  Determine a Function Value From a Piecewise Defined Graph

Ex:  Evaluate and Solve for Functions Given as a Table

Ex1:  Evaluate a Function and Solve for a Function Value Given a Graph

Ex2:  Evaluate a Function and Solve for a Function Value Given a Graph

Ex: Linear Function Application - Output/Input

Ex:  The Sum of Two Function Values With the Same Input

Ex:  The Difference of Two Function Values With the Same Input

Ex:  The Sum and Difference of Two Function Values With Different Inputs

Ex:  Given a Graph and a Function Value, Determine the Input or X-Value

Ex 1:  The Difference Quotient (Linear Function)

Ex 2:  The Difference Quotient (Quadratic Function)

Ex 3:  The Difference Quotient (Quadratic Function)

Determine Function Values Using Function Notation on the TI84

 

 

The Properties of Functions

The Algebra of Functions

Ex:  Function Arithmetic - Determine Function Values from a Table

Ex:  Function Arithmetic - Determine Function Values from a Graph

Ex: Function Values Using Function Arithmetic

Ex 1: Function Arithmetic - Addition and Subtraction

Ex 2: Function Arithmetic - Addition and Subtraction with Fractional Inputs

Ex 1: Function Arithmetic - Add, Subtract, Multiply, and Divide

Ex 2: Function Arithmetic - Add, Subtract, Multiply, and Divide with Fractional Inputs

Ex: Function Arithmetic - Function Division (Dividing by a Monomial)

Ex 1: Find Sum, Difference, Product, and Quotient of Function (Function Arithmetic)

Ex 2: Find Sum, Difference, Product, and Quotient of Function (Function Arithmetic)

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

Symmetry Introduction:  x-axis, y-axis, the origin

Introduction to Symmetry about the x-axis, y-axis, and the origin Using Points

Determine Points that are Symmetrical Across the x-axis, y-axis, and the Origin

Ex:  Symmetry:  x-axis, y-axis, the origin


Graphing Functions

Graphing 9 Basic Functions

The Domain and Range of 9 Basic Functions

Symmetry Introduction:  x-axis, y-axis, the origin

Ex:  Symmetry:  x-axis, y-axis, the origin

Ex:  Graph an Absolute Value Function Using a Table of Values

Ex:  Graph a Square Root Function Using a Table of Values

Ex:  Graph a Quadratic Function Using a Table of Values

Graphing Cubic Functions

Ex:  Graph a Cubic Function Using a Table of Values

Graphing Nonlinear Functions

Graphing the Basic Square Root Function

Graphing Rational Functions

Interpreting and Graphing Piecewise Functions

Graphing Piecewise Defined Function by Hand and on the Calculator

Ex:  Determine Function Values for a Piecewise Defined Function

Ex 1:  Graph a Piecewise Defined Function

Ex 2:  Graph a Piecewise Defined Function

Ex 3:  Graph a Piecewise Defined Function

Ex 1:  Determine the Function From the Graph of a Piecewise Defined Function

Ex 2:  Determine the Function From the Graph of a Piecewise Defined Function

Ex 1:  Solve Equations and Inequalities Expressed Using Function Notation Graphically

Ex 2:  Solve Equations and Inequalities Expressed Using Function Notation Graphically

 

Determining if a Relations is a Function

Determine if a relation is Function

The Vertical Line Test

Ex:  Determine if a  Table Values Represents a Function

Ex 1: Use the Vertical Line Test to Determine if a Graph Represents a Function

Ex 2: Use the Vertical Line Test to Determine if a Graph Represents a Function

 

Determining the Domain and Range of a Function

Find the domain and range

Ex 1:  Determine the Domain and Range of the Graph of a Function

Ex 2:  Determine the Domain and Range of the Graph of a Function

Ex:  Determine the Domain of a Square Root Function

Ex:  Determine the Domain of an Absolute Value Function

Ex:  Determine the Domain of a Rational Function

Ex: The Domain of a Function Containing a Square Root and a Denominator

 

Determining Odd and Even Functions

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

Symmetry Introduction:  x-axis, y-axis, the origin

Introduction to Symmetry about the x-axis, y-axis, and the origin Using Points

Determine Points that are Symmetrical Across the x-axis, y-axis, and the Origin

Ex:  Symmetry:  x-axis, y-axis, the origin

 


Linear Inequalities in One Variable

Solving Linear Inequalities

Solving One-Step Linear Inequalities in One Variable

Ex: Graphing Basic Inequalities and Expressing Using Interval Notation

Ex:  Solving One Step Inequalities by Adding and Subtracting (Variable Left Side)

Ex:  Solving One Step Inequalities by Adding and Subtracting (Variable Right Side)

Ex:  Solve One Step Linear Inequality by Dividing (Variable Left)

Ex:  Solve One Step Linear Inequality by Dividing (Variable Right)

Ex:  Solving a One Step Linear Inequality by Multiplying

Solving Two-Step Linear Inequalities in One Variable

Ex:  Solve a Two Step Linear Inequality  (Variable Left)

Ex:  Solve a Two Step Linear Inequality  (Variable Right)

Solving Linear Inequalities in One Variable 

Ex:  Solve a Linear Inequality Requiring Multiple Steps (Parentheses)

Ex:  Solve a Multiple Step Linear Inequality  (Variable Both Sides)

Problem Solving with Inequalities

 

Using Interval Notation

Interval Notation

Set-Builder Notation

Intervals: Given an Inequality, Graph the Interval and State Using Interval Notation

Intervals: Given the Graph of an Interval, State as an Inequality and Using Interval Notation

Intervals: Given Interval Notation, Graph the Interval and State as an Inequality

 

Solving and Graphing Compound Inequalities

Compound Inequalities

Ex:  Graph Basic Compound Inequalities

Ex 1:  Solve a Compound Inequality Involving AND (Intersection)

Ex 2:  Solve a Compound Inequality Involving AND (Intersection)

Ex 3:  Solve a Compound Inequality Involving AND (Intersection)

Ex:  Solve a Compound Inequality Involving OR (Union)

Ex:  Solve a Multiple Step Compound Inequality (OR / Union)

Ex:  Solve a Compound Inequality (No Solution)

Ex:  Solve a Compound Inequality (All Real Numbers Solution)

 

Absolute Value Equations and Absolute Value Inequalities

Solving Absolute Value Equations

Absolute Value Equations

Ex 1:  Solving Absolute Value Equations

Ex 2:  Solving Absolute Value Equations

Ex 3:  Solving Absolute Value Equations (Requires Isolating Abs. Value)

Ex 4:  Solving Absolute Value Equations (Requires Isolating Abs. Value)

Ex 5:  Solving Absolute Value Equations (Requires Isolating Abs. Value)

Ex: Solving Absolute Value Equations on the Graphing Calculator

 

Solving Absolute Value Inequalities

Absolute Value Inequalities

Ex 1:  Solve and Graph Basic Absolute Value inequalities

Ex 2:  Solve and Graph Absolute Value inequalities

Ex 3:  Solve and Graph Absolute Value inequalities

Ex 4:  Solve and Graph Absolute Value inequalities  (Requires Isolating Abs. Value)

Ex 5:  Solve and Graph Absolute Value inequalities Involving Fractions

Ex 6:  Solve and Graph Absolute Value inequalities  (Requires Isolating Abs. Value)

Ex: Solve Absolute Value Inequalities on the  Graphing Calculator

 

Linear Inequalities in Two Variables

Solving Linear Inequalities in Two Variables

Linear Inequalities in Two Variables

Ex:  Determine if Ordered Pairs Satisfy a Linear Inequality

Ex 1:  Graphing Linear Inequalities in Two Variables (Slope Intercept Form)

Ex 2:  Graphing Linear Inequalities in Two Variables (Standard Form)

Ex:  Graphing a Linear Inequality in One Variable on the Coordinate Plane (Horizontal Line)

Ex:  Graphing a Linear Inequality in One Variable on the Coordinate Plane (Vertical Line)

Ex:  Linear Inequality in Two Variables Application Problem  (Phone Cost:  Day and Night Minutes)

 

System of Equations and Inequalities

Solving Systems of Equations by Graphing

Solving Systems of Equations by Graphing

Determining the Intersection of Two Graph on the TI83/84

Ex:  Identify the Solution to a System of Equation Given a Graph, Then Verify

Ex 1:  Solve a System of Equations by Graphing

Ex 2:  Solve a System of Equations by Graphing

Ex: Solve a System of Equations by Graphing (Infinite Solutions)

Ex: Solve a System of Equations by Graphing (No Solution)

Ex 1:  Find the Intersection of Two Linear Functions

Ex 2:  Find the Intersection of Two Linear Functions

Ex:  Find the Area of a Triangle Bounded by a Line, a Perpendicular Line, and the Y-Axis

Regression and Systems of Equations:  Application

 

Solving Systems of Equations Using Substitution

Solving Systems of Equations by Substitution

Ex 1:  Solve a System of Equations Using Substitution

Ex 2:  Solve a System of Equations Using Substitution

Ex 3:  Solve a System of Equations Using Substitution

Ex 4:  Solve a System of Equations Using Substitution

Ex:  Solve a System of Equations Using Substitution - Infinite Solutions

Ex:  Solve a System of Equations Using Substitution - No Solution

Ex:  Intersection of a Line and a Circle - Applications


Solving Systems of Equations Using Elimination

Solving Systems of Equations by Elimination

Ex 1:  Solve a System of Equations Using the Elimination Method

Ex 2:  Solve a System of Equations Using the Elimination Method

Ex 3:  Solve a System of Equations Using the Elimination Method

Ex:  System of Equations Using Elimination (Infinite Solutions)

Ex:  System of Equations Using Elimination (No Solution)

 

Solving Applications Using Systems of Equations

Applications Involving Systems of Equations

More Applications Involving Systems of Equations

Ex:  System of Equations Application - Number Problem Using Substitution

Ex:  System of Equations Application - Number Problem Using Elimination

Ex:  System of Equations Application - Compare Phone Plans

Ex:  System of Equations Application - Entrance Fees

Ex:  System of Equations Application - Coin Problem

Ex:  System of Equations Application - Plane and Wind Problem

Ex:  System of Equations Application - Commission and Salary

Ex:  System of Equations Application - Investment Accounts

Ex:  System of Equations Application  (Corral Perimeter)

Ex:  System of Equations Application - Mixture Problem

Ex: System of Linear Function Application - Median Home Prices

Ex: System of Equations Application - Supply and Demand

Ex:  Intersection of a Line and a Circle - Applications


Solving Systems of Linear Inequalities

Systems of Linear Inequalities

Ex 1:  Graph a System of Linear Inequalities

Ex 2:  Graph a System of Linear Inequalities

Ex 3:  Graph the feasible Region of a System of Linear Inequalities

 

Solving Systems of Three Equations with Three Unknowns

System of Equations in Three Variables:  Part 1Part 2

Ex 1: System of Three Equations with Three Unknowns Using Elimination

Ex 2: System of Three Equations with Three Unknowns Using Elimination

Ex 3: System of Three Equations with Three Unknowns Using Elimination (Fractions)

Ex 4: System of Three Equations with Three Unknowns Using Elimination (No Solution)

Ex 5: System of Three Equations with Three Unknowns Using Elimination (Infinite Solutions)

System of 3 Equations with 3 Unknowns Application - Interest Problem

System of 3 Equations with 3 Unknowns Application - Concentration Problem

System of 3 Equations with 3 Unknowns Application - Ticket Sales

Solving Systems of Non-Linear Equations

Ex 1: Solve a System of Nonlinear Equations (Substitution)

Ex 2: Solve a System of Nonlinear Equations (Substitution)

Ex 3: Solve a System of Nonlinear Equations (Elimination)

 

Exponents and Polynomials

Exponents and Simplifying Expressions with Exponents

Exponential Notation

Properties of Exponents 

Ex:  Write Repeated Multiplication Using Exponents

Ex:  Expanding and Evaluating Exponential Notation

Ex:  Simplify Exponential Expressions - Product and Power Rule

Ex:  Simplify Exponential Expressions - Quotient Rule

Ex 1:  Simplify Exponential Expressions - Positive Exponents Only

Ex 2:  Simplify Exponential Expressions - Positive Exponents Only

Ex 3:  Simplify Exponential Expressions - Positive Exponents Only

Ex 1:  Simplify Exponential Expressions With Negative Exponents – Basic

Ex 2:  Simplify Exponential Expressions With Negative Exponents – Basic

Negative Exponents

Scientific Notation

Ex 1:  Simplify an Exponential Expression with Negative Exponents

Ex 2:  Simplify an Exponential Expression with Negative Exponents

Ex 3:  Simplify an Exponential Expression with Negative Exponents

Ex 4:  Simplify Expressions with Negative Exponents

Ex 5:  Simplify Expressions with Negative Exponents

Ex 6:  Simplify Expressions with Negative Exponents

Ex 1: Exponent Review

Ex 2: Exponent Review


Introduction to Polynomials

Introduction to Polynomials

Ex:  Intro to Polynomials in One Variable

Ex:  Intro to Polynomials in Two Variables

Combine Like Terms

Evaluating Algebraic Expressions

Evaluating Polynomial Expressions and Functions

Evaluate a Quadratic Equation - Death Application

Evaluate a Polynomial Equation - Flu Virus Application

Ex: Quadratic Equation Application - Evaluate and Factor


Adding and Subtracting Polynomials

Add and Subtract Polynomials

Ex:  Adding Polynomials

Ex:  Subtracting Polynomials

Ex:  Adding and Subtracting Polynomials

Ex: Simplify Polynomial Expressions - Add/Subtract/Multiply

 

Multiplying Polynomials

Multiplying Polynomials

Ex:  Multiplying Polynomials

Special Products of Polynomial

Ex:  Multiplying Monomials

Ex:  Multiplying Using the Distributive Property

Ex:  Multiplying Binomials

Ex:  Squaring Binomials

Ex: Multiplying Binomial Conjugates - Special Binomial Products

Ex:  Polynomial Multiplication Involving Binomials and Trinomials

Ex:  Simplify an Expression Involving Squares of Two Binomials

Ex:  Find the Area of a Rectangle Using a Polynomial

Ex:  Determine the Area of a Shaded Region Using a Polynomial

 

Dividing Polynomials

Dividing Polynomials by a Monomial

Dividing Polynomials – Long Division

Ex 1:  Divide a Trinomial by a Binomial Using Long Division

Ex 2:  Divide a Trinomial by a Binomial Using Long Division

Ex 3:  Divide a Polynomial by a Binomial Using Long Division

Ex 4:  Divide a Polynomial by a Binomial Using Long Division

Ex 5:  Divide a Polynomial by a Binomial Using Long Division

Dividing Polynomials – Synthetic Division

Ex: Divide a Polynomial by a Monomial

Ex 6:  Divide a Polynomial by a Degree Two Binomial Using Long Division

Ex 1:  Divide a Trinomial by a Binomial Using Synthetic Division

Ex 2:  Divide a Polynomial by a Binomial Using Synthetic Division

Ex 3:  Divide a Polynomial by a Binomial Using Synthetic Division

Ex 4:  Divide a Polynomial by a Binomial Using Synthetic Division

 

Factoring

Determining the Greatest Common Factor and Factoring by Grouping

Factoring:  Greatest Common Factor

Ex:  Factor a Binomial - Greatest Common Factor

Ex 1:  Identify GCF and Factor a Binomial

Ex 2:  Identify GCF and Factor a Trinomial

Factoring:  Grouping Technique

Ex:  Factor a Polynomial Using the Grouping Technique

 

Factoring Trinomials with a Leading Coefficient of 1

Factoring a Trinomial With Leading Coefficient equal to 1 – The Basics

Factoring:  Basic Trinomials with a = 1

Ex: Factor Trinomials When A equals 1

Ex:  Factoring Polynomials with Common Factors

 

Factoring Trinomials with a Leading Coefficient Not 1

Factoring:  Trinomials using Trial and Error and Grouping

Ex:  Factor Trinomials When A is NOT Equal to 1 - Trial and Error Method

Ex:  Factor Trinomials When A is NOT Equal to 1 - Grouping Method

Factoring:  Trinomials using Bottoms-Up

Proof:  Bottoms Up Factoring Method

Ex:  Factor Trinomials When A is NOT Equal to 1 - Bottoms Up Method

 

Factoring a Difference of Squares

Factoring:  Difference of Squares

Ex:  Factor a Difference of Squares

Ex:  Factor a Difference of Squares with a Common Factor

Ex:  Factor a Difference of Squares in the Form a^2 - x^2

 

Factoring Perfect Square Trinomials

Factoring:  Perfect Square Trinomials

Ex:  Factor Perfect Square Trinomials

 

Factoring a Sum or Difference of Cubes

Factoring:  Sum and Difference of Cubes

Ex 1:  Factor a Sum or Difference of Cubes

Ex 2:  Factor a Sum or Difference of Cubes

Ex 3:  Factor a Sum or Difference of Cubes

 

Solving Polynomial Equations / Increasing and Decreasing Polynomials

Solving Polynomial Equations Graphically

Determining When a Polynomial Function is Increasing and Decreasing

Determining the Zeros or Roots of a Polynomial Function on the TI83/84


Quadratic Functions and Equations

Solving Quadratic Equations by Factoring

The Zero-Product Property

Solving Quadratic Equations by Factoring

Ex: Solve an Equation in Factored Form

Ex:  Factor and Solve Quadratic Equation - Greatest Common Factor Only

Ex 1:  Factor and Solve a Quadratic Equation - GCF

Ex 2:  Factor and Solve a Quadratic Equation - GCF

Ex 1:  Factor and Solve a Quadratic Equation - Factor by Grouping

Ex 2:  Factor and Solve a Quadratic Equation - Factor by Grouping

Ex: Factor and Solve Quadratic Equations When A equals 1

Ex 1: Factor and Solve Quadratic Equation - Trinomial a = 1

Ex 2: Factor and Solve Quadratic Equation - Trinomial a = 1

Ex: Factor and Solve Quadratic Equation - Trinomial a = -1

Ex:  Factor and Solve Quadratic Equation - Difference of Squares

Ex 1:  Factor and Solve a Quadratic Equation Using Difference of Squares

Ex 2:  Factor and Solve a Quadratic Equation Using Difference of Squares

Ex: Factor and Solve a Quadratic Equation - Perfect Square Trinomials

Ex: Factor and Solve Quadratic Equation - Perfect Square Trinomials

Ex:  Factor and Solve Quadratic Equation - Greatest Common Factor +

Ex 1:  Factor and Solve a Quadratic Equation - a not 1

Ex 2:  Factor and Solve a Quadratic Equation - a not 1

Ex 1:  Solve Quadratic Equations by Factoring Completely

Ex 2:  Solve Quadratic Equations by Factoring Completely

Ex: Factor and Solve a Polynomial Equation

Ex:  Factor and Solve a Polynomial Equation

 

Solving Quadratic Equations Graphically

Ex 1:  Solve a Quadratic Equation Graphically on Calculator

Ex 2:  Solve a Quadratic Equation Graphically on Calculator

Ex 1:  Solving Quadratic Equations Graphically Using x-Intercepts

Ex 2:  Solving Quadratic Equations Graphically Using the Intersection Method

 

Solving Quadratic Equations Using the Square Root Property

Solving Quadratic Equations Using Square Roots

Ex 1:  Solving Quadratic Equations Using Square Roots

Ex 2:  Solving Quadratic Equations Using Square Roots

Ex 3:  Solving Quadratic Equations Using Square Roots

Ex 4:  Solving Quadratic Equations Using Square Roots

Ex:  Solve Basic Quadratic Equations Using Square Roots

Ex:  Solve Quadratic Equations Using Square Roots

 

Solving a Quadratic Equation by Completing the Square

Ex:  Creating a Perfect Square Quadratic Trinomial Expression

Ex:  Create an Expression with a Perfect Square Quadratic Trinomial

Completing the Square

Ex 1:  Completing the Square - Real Rational Solutions

Ex 2:  Completing the Square - Real Irrational Solutions

Ex 3:  Completing the Square - Complex Solutions

Ex 4:  Completing the Square - Leading Coefficient Not 1

 Ex 5: Completing the Square - Leading Coefficient Not 1 (Complex)

 

Solving a Quadratic Equation Using the Quadratic Formula

Ex:  Simplify a Radical Expression (Quadratic Formula Practice)

Using the Quadratic Formula

Ex:  The Discriminant

Proof of The Quadratic Formula

Ex:  Quadratic Formula - Two Real Rational Solutions

Ex:  Quadratic Formula - One Real Rational Repeated Solution

Ex1:  Quadratic Formula - Two Real Irrational Solutions

Ex2:  Quadratic Formula - Two Real Irrational Solutions

Ex:  Quadratic Formula - Complex Solutions

Ex : Solve a Quadratic Equation Using the Quadratic Formula - Difference of Squares

Ex :  Solve a Quadratic Equation Using the Quadratic Formula - 2 Real Irrational Solutions

Ex : Solve a Quadratic Equation Not Set Equal to Zero Using the Quadratic Formula

 

Graphing Quadratic Functions

Graphing Quadratic Functions in Standard Form

Graphing Quadratic Functions in General Form

Ex: Find the Intercepts of a Quadratic Function - Requires the Quadratic Formula

Ex: Graph a Quadratic Function in General Form (Online Graphing Tool)

Ex: Graph a Quadratic Function in Standard Form (Online Graphing Tool)

Graphing Quadratic Functions Using Symmetric Points

Ex1:  Graph a Quadratic Function in General Form

Ex2:  Graph a Quadratic Function in General Form

Ex 3:  Graph a Quadratic Function in General Form

Ex 4:  Graph a Quadratic Function in General Form by Finding Key Components

Ex 1:  Graph a Quadratic Function in Standard Form

Ex 2:  Graph a Quadratic Function in Standard Form

Ex1:  Write a Quadratic Function in Standard Form to Graph

Ex2:  Write a Quadratic Function in Standard Form to Graph (a not 1)

Ex:  Quadratic Function Review

Ex 1: Key Characteristics of the Graph of  a Quadratic Function (Opens Up)

Ex 2: Key Characteristics of the Graph of  a Quadratic Function (Opens Down)

 

Determining Equations of Quadratic Functions

Ex:  Find the Equation of a Quadratic Function from the Graph

Ex:  Find a Quadratic Function Given the Intercepts of the Graph

Ex:  Find a Quadratic Function Given the Vertex and the Leading Coefficient.

Ex: Find the Vertex Form of a Quadratic Function Given the Vertex and a Point

Ex 1:  Find a Quadratic Function With Integer Zeros

Ex 2:  Find a Quadratic Function With Fractional Real Zeros

Ex 3:  Find a Quadratic Function With Imaginary Zeros

Ex 4:  Find a Quadratic Function With Complex Zeros

Ex 5:  Find a Quadratic Function With Complex Zeros (Alternative Method)

Ex 1:  Find a Quadratic Function Using Sum and Product of Zeros (Integer and Fraction Zeros)

Ex 2:  Find a Quadratic Function Using Sum and Product of Zeros (Complex)

 

Applications of Quadratic Equations

Ex:  Find the Length of the Diagonal of a Rectangle Given the Area

Ex: Find the Perimeter of an Equilateral Triangle Given the Area without Trigonometry

Ex:  Quadratic Function Application - Blood Pressure

Ex:  Quadratic Function Application Using Formulas - Rocket Launch

Ex:  Quadratic Function Application Using a Graphing Calculator - Rocket Launch

Ex:  Find the Size of Cardboard Needed to Make a Box with a Given Volume

Ex: Quadratic Function Application - Horizontal Distance and Vertical Height

Ex: Quadratic Function Application - Time and Vertical Height

Ex:  Quadratic Model Application - Ticket Price to Maximize Revenue

Ex: Quadratic Function Application - Maximum Area

Ex:  Quadratic Regression on the TI84 - Stopping Distance



Solving Quadratic Inequalities
 
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