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In this short introduction to the course, I share a bit about myself and my approach to teaching Algebra. I explain why I consider this to be an extremely important course to take and master.

NO HOMEWORK FOR THIS LESSON

This lesson introduces the concept of positive and negative numbers and shows one method for adding them together.

Homework Video for Lesson 1.3

This lesson shows a more sophisticated method for combining positive and negative integers.

Homework Video for Lesson 1.4

This lessons discusses the unique rules regarding multiplying and dividing positive and negative numbers.

Homework Video for Lesson 1.5

This lesson illustrates how to evaluate an algebraic expression with variables when those variables are given specific values.

Homework Video for Lesson 1.6

This lesson explains Order of Operation. This rule is used for simplifying expressions and is a foundational principle that all Mathematicians must follow.

Homework Video for Lesson 1.7

This lesson focuses on the most common algebraic properties you will see and use in Algebra.

Homework Video for Lesson 1.8

This lesson explains the basics of solving very simple equations. These techniques will be applied in future lessons to more complicated equations.

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This lesson continues with an explanation of solving slightly more difficult equations which require 2 steps to solve.

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This lesson adds a bit more complexity, showing you how to solve equations that require multiple steps.

Homework Video for Lesson 2.3

Sometimes an equation will have no solution or an infinite number of solutions. This lesson explores this concept.

Homework Video for Lesson 2.4

Fractions have often been challenging for students. This lesson shows a very powerful yet simple method for eliminating all fractions so that it can be solved effortlessly.

Homework Video for Lesson 2.5

This lesson continues the discussion of removing fractions from your equation. It is a brilliant method!

Homework Video for Lesson 2.6

Proportions are a unique type of equation with Fractions. This lesson explains how to solve these equations easily and effortlessly.

Homework Video for Lesson 2.7

This lesson discusses the different ways in which you can easily solve equations with decimals.

Homework Video for Lesson 2.8

This lesson illustrates how to solve equations that have absolute value expressions within an equation.

Homework Video for Lesson 2.9

Sometimes equations have several different variables. This lesson discusses how to solve an equation for any given variable.

Homework Video for Lesson 2.10

This lesson discusses how to work with percents mathematically.

Homework Video for Lesson 2.11

This lesson discusses the concept of Percent Change and shows how to find the percent increase or decrease of data that has changed over time.

Homework Video for Lesson 2.12

This lesson is an introduction to words and phrases commonly used in the English language that translate directly into mathematical expressions and equations.

Homework Video for Lesson 3.1

This lesson shares one approach to solving number word problems.

Homework Video for Lesson 3.2

This lesson describes an approach for solving consecutive integer word problems.

Homework Video for Lesson 3.3

In this video I explain how to solve consecutive integer word problems where you have consecutive even or consecutive odd numbers.

Homework Video for Lesson 3.4

This video shares ways of solving a variety of geometry word problems.

Homework Video for Lesson 3.5

This lesson shows an approach that I use to organize data in a way that allows you to solve the problem easily and effortlessly.

Homework Video for Lesson 3.6

Ratios are an important and useful concept in math. This video shows how to solve ratio word problems.

Homework Video for Lesson 3.7

This lesson explains how to solve word problems that utilize percents.

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This lesson discusses what Simple Interest is and how to solve word problems that relate to simple interest.

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This is the first of 3 lessons on solving distance or motion word problems.

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This is the second of 3 lessons on solving distance or motion word problems.

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This is the third of 3 lessons on solving distance or motion word problems.

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This lesson explains how to graph a single variable inequality. It also shows how to write an inequality to describe a graph.

Homework Video for Lesson 4.1

Sometimes an inequality needs to be simplified before it can be graphed. This lesson shows how to do this.

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This lesson begins with a practice session on solving inequalities. It concludes with a discussion on inequalities that may have no solution or an infinite number of solutions.

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Compound inequalities are made up of two inequalities. This lesson discusses what it means to join the two inequalities with the word "AND".

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Compound inequalities are made up of two inequalities. This lesson discusses what it means to join the two inequalities with the word "OR".

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Absolute Value Inequalities are examples of Compound Inequalities. This lesson discusses what needs to be done to solve absolute value inequalities.

Homework Video for Lesson 4.6

This lesson is an introduction of the unique features of equations with 2 variables. Much of Algebra utilizes these types of equations.

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This lesson discusses an important distinction between Relations and Functions. Most of what we will be discussing in this course will involve Functions.

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This lesson shows how to graph functions on a Cartesian Plane using T-charts.

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This lesson shows a shortcut on how to easily and quickly graph an equation that is written in Slope-Intercept Form.

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This lesson shows a shortcut on how to easily and quickly graph an equation that is written in Point-Slope Form.

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This lesson shows a shortcut on how to easily and quickly graph an equation that is written in Standard Form.

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It is always good to take extra time to practice graphing so that you can do it effortlessly. This lesson gives you the opportunity to practice the three methods discussed in the last 3 lessons.

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This lesson discusses the Slope Formula and how to use it to find the slope of a line passing through two points.

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Sometimes you need to write equations of lines that have certain data points. This lesson discusses how to do this.

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This lesson shows you how to easily convert equations from one form to another.

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This lesson illustrates how to write equations of lines that are parallel or perpendicular to another line.

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This lesson explains how to take data and identify trends, if any, of the data. It shows how to graph the data and create trend lines when trends exist.

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This lesson discusses the unique qualities of an equation that represents Direct Variation.

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This lesson illustrates how to graph absolute value functions.

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This lesson demonstrates how to graph one-variable inequalities on a Cartesian Plane.

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This lesson demonstrates how to graph two-variable inequalities on a Cartesian Plane.

Homework Video for Lesson 5.16

Solving Systems of Equations by Graphing

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This is the first of two lessons explaining how to "solve" linear systems algebraicly using a substitution method.

Homework Video for Lesson 6.2

This is the last of two lessons explaining how to "solve" linear systems algebraicly using a substitution method.

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This is the first of four lessons explaining how to "solve" linear systems algebraicly using a method called "Elimination".

Homework Video for Lesson 6.4

This is the second of four lessons explaining how to "solve" linear systems algebraicly using a method called "Elimination".

Homework Video for Lesson 6.5

This is the third of four lessons explaining how to "solve" linear systems algebraicly using a method called "Elimination".

Homework Video for Lesson 6.6

This is the last of four lessons explaining how to "solve" linear systems algebraicly using a method called "Elimination".

Homework Video for Lesson 6.7

Some linear systems have no solutions or an infinite number of solutions. This lesson explores these situations.

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This is the first of 5 types of word problems in which systems of equations are used in finding the solution.

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This is the second of 5 types of word problems in which systems of equations are used in finding the solution.

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This is the third of 5 types of word problems in which systems of equations are used in finding the solution.

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This is the fourth of 5 types of word problems in which systems of equations are used in finding the solution.

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This is the last of 5 types of word problems in which systems of equations are used in finding the solution.

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You can also solve "systems" of inequalities by graphing. This lesson explains the process.

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When your system involves two inequalities that are parallel to each other, you can have some interesting effects. This lesson explores these cases.

Homework for Lesson 6.15

This lessons illustrates how to solve word problems which include inequalities.

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In this lesson, I introduce exponents and discuss rules relating to zero exponents and negative exponents.

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This lesson explains the rules you need to follow when multiplying same bases with exponents.

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This lesson explains the rules you need to follow when dividing same bases with exponents.

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For some types of problems when dividing same bases with exponents, there is a cool little trick that makes it easy and effortless. This lesson explains this trick.

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Scientific Notation is a practical application of exponents when dealing with numbers that are very large or very small. This lesson illustrates these cases.

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This lesson explores what exponential functions look like on a Cartesian Plane.

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This lesson discusses exponential growth and decay, demonstrating their respective formulas and how to use them in real-life situations.

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This lesson explores compound interest, showing the formula and the powerful results that this type of interest can create.

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In this lesson, I introduce radicals and show how to simplify radicals with numbers.

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In this lesson, I show how to simplify radicals with variables.

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This lesson explains the rules and process regarding adding and subtracting radicals.

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This is the first of two lessons explaining the rules and processes used to multiply radicals.

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This is the last of two lessons explaining the rules and processes used to multiply radicals.

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This lesson demonstrates the rules and processes used when dividing radicals. It also shows how to "rationalize" the denominator and when to use it.

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Since students sometimes struggle with all the different rules regarding radicals, I put together this lesson to allow you to practice these techniques.

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This is the first of two lessons explaining how to solve simple radical equations.

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This is the last of two lessons explaining how to solve simple radical equations.

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In this lesson, I show how to graph radical equations.

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In this lesson, I introduce polynomials and several terms that you will need to know. I also show how to write them in standard form.

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This lesson illustrates how to add and subtract polynomials and identifies key issues that are sometimes overlooked by students.

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This lesson introduces rules needed in order to multiply polynomials.

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This lesson shows a slightly different approach often used to multiply binomials together. The process is usually called "FOIL".

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This lesson focuses on special products that sometimes result from multiplying binomials together. It is useful to be aware to look for these scenarios.

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This lesson focuses on techniques for factoring polynomials. In particular I demonstrate tree factorization and the "upside-down birthday cake" method.

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Factoring out the Greatest Common Factor (GCF) is a key concept in Algebra. This lesson shows how to do this with polynomials.

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Sometimes the Greatest Common Factor in two terms a binomial. This "blob" can be factored out of both terms easily. This lesson shows how.

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This lesson focuses on a particular type of factoring in which there are four terms. It consists of grouping terms into pairs and factoring each pair individually.

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This lesson identifies an extremely important approach for factoring quadratic trinomials.

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This lesson shows how to factor quadratic trinomials in which the leading coefficient is a number other than "one".

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This lesson demonstrates and extremely helpful trick in factoring quadratic trinomials where the leading coefficient is not "one".

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This lesson shows how to factor expressions where there is a difference (subtraction) of two perfect squares.

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Students always need extra practice in factoring expressions. This lesson gives you the opportunity to do just that!

Homework Video for Lesson 9.14

Now it is time to learn the true power of the skills you learned in the last chapter. This lesson focuses on solving quadratic equations.

Homework Video for Lesson 10.1

This lesson continues the conversation on solving quadratic equations.

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This lesson shows another approach that can sometimes be utilized when solving quadratic equations.

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This lesson looks at the Vertical Motion Model and shows its power in solving real-life word problems.

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Sometimes a quadratic equation cannot be factored. In this case, there is a powerful approach that can be used called Completing the Square. This lesson shows how.

Homework Video for Lesson 10.5

NO HOMEWORK FOR THIS LESSON.
In this lesson, I show how the famous Quadratic Formula was created.

In this lesson, I show how to use the Quadratic Formula to find where a parabola crosses the x-axis. It is important to master using this formula!

Homework Video for Lesson 10.7

In this lesson, we explore a part of the Quadratic Formula called the Discriminant, and we discuss what exactly this can tell you immediately about a given equation.

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In this lesson, we dive into word problems to see the power of factoring and solving quadratics.

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This lesson explores how to find the vertex of any parabola by first locating the Axis of Symmetry.

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This lesson continues our exploration of quadratic word problems.

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In this lesson, I break the quadratic equation down into its parts and explain how each part affects the graph of a parabola.

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In this video, I demonstrate a very simple approach to graphing most quadratic equations.

Homework Video for Lesson 10.13

NO HOMEWORK FOR THIS LESSON. This lesson takes a detour from the chapter and does a quick review of all the different types of graphs we have seen so far in this course.

This lesson explores the idea of functions and how to write the domain and range in set notation.

Homework Video for Lesson 10.15

In this Video, I explain what a rational expression is and how you can identify values for x that are excluded, hence illegal, according to rules of mathematics.

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This lesson explains how to simplify Rational Expressions.

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This lesson identifies an important trick that can be used in cases where you have "opposite binomials" in the numerator or denominator.

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This lesson demonstrates the steps necessary in order to easily multiply and divide Rational Expressions. By following these rules, your final fraction will be written in lowest terms.

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In this lesson, I show how to add and subtract rational expressions that already have common denominators.

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In this lesson, I show how to add and subtract rational expressions and how to find and create common denominators.

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This lesson demonstrates how to divide polynomials using long division. This is one way to find factors of a polynomial.

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A proportion is one example of a simple rational equation. This lesson shows how to solve rational proportions and identify any excluded values.

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Most Rational Equations are not proportions and therefore need a different approach for solving them. This lesson discusses this important approach.

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Sometimes you will solve a rational equation and get more than one answer. This lesson identifies how to know if both answers are valid and "legal". Illegal or invalid answers are called Extraneous solutions.

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Inverse variation is an example of a rational equation. This lesson shows how to graph inverse variation equations.

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In this video, we explore the differences between direct variation and inverse variation.

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This lesson illustrates how to graph rational functions using asymptotes and T-charts.

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In this lesson, we dive into solving work word problems which involve creating and solving rational equations.

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This lesson focuses on more types of rational word problems, how to set them up and how to solve them.

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This lesson is the first of four review lessons in which I cover a large percentage of the material we covered in this course.

Homework Video for Lesson 12.1

This lesson is the second of four review lessons in which I cover a large percentage of the material we covered in this course.

Homework Video for Lesson 12.2

This lesson is the third of four review lessons in which I cover a large percentage of the material we covered in this course.

Homework Video for Lesson 12.3 (Part 1)

Homework Video for Lesson 12.3 (Part 2)

This lesson is the last of four review lessons in which I cover a large percentage of the material we covered in this course.

Homework Video for Lesson 12.4

In this video I present a short introduction and explanation of the FINAL EXAM. (This exam is optional, but recommended)

Final Exam Solutions Video (Problems 1-15)

Final Exam Solutions Video (Problems 16-24)

**Algebra 1 Course Description**

In this course, I strive to provide all students with a dynamic mathematics education that balances a solid foundation of basic algebraic skills with a constructed understanding of concepts that challenges, supports, and instills an excitement for math. My goal is to help students develop as curious and flexible thinkers who are confident in their individual mathematical abilities, allowing them to feel prepared to meet the challenges of higher mathematics. Topics mastered include number sense, graphing and solving linear and quadratic equations, solving systems of equations and inequalities, exponent rules, radical and rational expressions and equations, parabolas and real-life applications through word problems. It is a rich curriculm which is designed to challenge each student while at the same time help him/her begin to enjoy the world of mathematics. Homework pdfs are included, as well as short videos to review the homework solutions. Each homework has a few problems from previous lessons so that students practice recalling and implementing previously learned skills.

**This course includes:**

- 12 Chapters
- 132 Homework Worksheets
- 272 Videos Total
- 138 Lesson Videos
- 134 Homework Solutions Videos (I work out on the board the solutions to each problem step by step)

- 4 Final Exam Review Lessons
- 1 FINAL EXAM
- Over 75 Hours of Video Instruction!

**COURSE TOPICS**

**Chapter 1: Foundations of Algebra**

**Lessons:**

Introduction to Course

Classification of Real Numbers

Adding & Subtracting Positive and Negative Numbers (Part 1)

Adding & Subtracting Positive and Negative Numbers (Part 2)

Multiplying & Dividing Positive and Negative Numbers

Evaluating Algebraic Expressions

Order of Operations

Some Key Properties in Algebra

**Chapter 2: Linear Equations**

**Lessons:**

Solving One-Step Equations

Solving Two-Step Equations

Solving Multi-Step Equations

Equations with Infinite and Zero Solutions

Solving Equations with Fractions (Same Denominators)

Solving Equations with Fractions (Different Denominators)

Solving Proportions

Solving Equations with Decimals

Solving Absolute Value Equations

Solving Literal Equations

Solving Percent Equations

Percent Increase or Decrease

**Chapter 3: Introduction to Word Problems**

**Lessons:**

Translating English into Math

Number Word Problems

Consecutive Integer Word Problems (Part 1)

Consecutive Integer Word Problems (Part 2)

Geometry Word Problems

Age Word Problems

Ratio Word Problems

Percent Word Problems

Simple Interest Word Problems

Distance / Motion Word Problems (Parts 1,2 &3)

**Chapter 4: Linear Inequalities**

**Lessons:**

Graphing and Writing Single-Variable Inequalities

Solving Single-Variable Inequalities

More Practice solving Inequalites; Examples of Zero and Infinite Solutions

Solving and Graphing Compound Inequalities with “AND” Statements

Solving and Graphing Compound Inequalities with “OR” Statements

Absolute Value Inequalities

**Chapter 5: Graphing and Writing Functions**

**Lessons:**

Introduction to Equations with Two Variables

Relations vs. Functions

Graphing on a Cartesian Plane with T-charts

Graphing Equations in Slope Intercept Form (Using Shortcut)

Graphing Equations in Point-Slope Form

Graphing Equations in Standard Form

Graphing Practice

Finding the Slope Using The Slope Formula

Writing Equations With Given Data

Converting Equations From One Form to Another

Parallel and Perpendicular Lines

Scatter Plots and Trend Lines

Direct Variation

Graphing Absolute Value Functions

Graphing One-Variable Inequalities on Cartesian Plane

Graphing Two-Variable Inequalities on Cartesian Plane

**Chapter 6: Systems of Equations and Inequalities**

**Lessons:**

Solving Systems of Equations by Graphing

Solving Systems of Equations by Substitution (Parts 1-2)

Solving Systems of Equations by Elimination (Parts 1-4)

Systems with No Solutions or Infinite Solutions

Systems of Equations Word Problems (5 Types)

Graphing Systems of Inequalities with Parallel Boundary Lines

Systems of Inequalities Word Problems

**Chapter 7: Exponents and Exponential Functions**

**Lessons:**

Introduction to Exponents; Rules for Zero and Negative Exponents

Multiplication Properties of Exponents

Division Properties of Exponents

Division Property: A Cool Little Trick

Scientific Notation

Exponential Functions and Their Graphs

Exponential Growth and Decay

Compound Interest

**Chapter 8: Radicals and Radical Functions**

**Lessons:**

Introduction to Radicals; Simplifying Radicals with Numbers

Simplifying Radicals with Variables

Adding and Subtracting Radicals

Multiplying Radicals (Parts 1 & 2)

Dividing Radicals and Rationalizing the Denominator

Practicing with Radicals

Solving Radical Equations (Parts 1 & 2)

Graphing Radical Equations

**Chapter 9: Polynomials: Combining, Multiplying and Factoring**

**Lessons:**

Introduction to Polynomials

Adding and Subtracting Polynomials

Multiplying Polynomials

Multiplying Binomials using FOIL

Special Products of Binomials

Factoring Polynomials: Finding Factors, Tree Factorization, Greatest Common Factor

Factoring Out the Greatest Common Factor

Factoring Out the “Blobs” (…or Binomials)

Factoring by Grouping

Factoring Quadratic Trinomials: a = 1

Factoring Quadratic Trinomials: ”a” is Not 1

Gary’s Terrific Trick

Factoring the Difference of Two Squares

Factoring Practice

**Chapter 10: Quadratic Functions and Equations **

**Lessons:**

Understanding and Solving Quadratic Equations (Parts 1 & 2)

Using Square Roots to Solve Quadratic Equations

Vertical Motion Model Word Problems

Completing the Square

Deriving the Quadratic Formula

Using the Quadratic Formula

Understanding the Discriminant

Quadratic Word Problems – Rectangles

Finding the Axis of Symmetry and Vertex

More Quadratic Word Problems

Anatomy of a Quadratic Equation

Graphing Quadratics with “Standard Parabola Guy”

Reviewing Different Types of Graphs

Functions, Set Notation, Domain and Range

**Chapter 11: Rational Expressions and Equations**

**Lessons:**

Rational Expressions: Finding the Excluded Value

Simplifying Rational Expressions

Simplifying Rational Expressions with Opposite Binomials

Multiplying and Dividing Rational Expressions

Adding and Subtracting Rational Expressions (Parts 1 & 2)

Dividing Polynomials Using Long Division

Solving Rational Equations: Proportions

Solving Rational Equations: Multiplying by LCD

Solving Rational Equations: Extraneous Solutions

Understanding and Graphing Inverse Variation

Direct Variation vs. Inverse Variation

Graphing Rational Functions Using Asymptotes & T-charts

Work Word Problems

Inverse Variation Word Problems and Other Rational Word Problems

**Chapter 12: End-of-Course Review**

**Lessons:**

Final Exam Prep #1

Final Exam Prep #2

Final Exam Prep #3

Final Exam Prep #4

FINAL EXAM

- Teacher: Gary
- Areas of expertise: Algebra
- Education: B.A. in Business Administration from Principia College; Tutoring and teaching middle school and High School math for over 20 years.
- Interests: Math, music, sports, sailing, water, quantum physics, healing, woodworking, helping kids grow in their appreciation for their unique talents and skills
- Skills: Teaching math to kids
- Associations: Chair of the Math Department at Santa Fe School for the Arts & Sciences in Santa Fe, NM
- Issues I care about: I care deeply about making this world a kinder place where each person feels safe to be exactly who they are.

I have taught and tutored High School and Middle School math for over twenty years. My passion is to awaken the love of math in my students. It does not have to be a scary subject. I find that if students are allowed to question freely, they begin to enjoy the class, and their brilliance begins to shine. My best classes have been guided by the insightful questions of my students where we can explore and learn together. I have recorded many lectures on Youtube and now have a significant following of students from around the world. I'm inspired by the number of wonderful students who truly wish to learn this material.

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