INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith
Home » Mathematics » Algebra 1
No. of
Lectures
Duration
(hrs:min)
61
18:58

# Algebra 1 Online CourseProf. Eric Smith Facebook Twitter More

• Level Intermediate
• 61 Lessons (18hr : 58min)
• 170 already enrolled!
• Audio: English
• English

Professor Eric Smith's comprehensive online course on Algebra 1 will help you become an expert in no time, with clear explanations of common terminology and methods pertinent to the lesson. He illustrates concepts with colorful examples, and reinforces them with plenty of sample problems and step-by-step solutions.

## Section 1: Properties of Real Numbers

Basic Types of Numbers 30:41
Intro 0:00
Objectives 0:07
Basic Types of Numbers 0:36
Natural Numbers 1:02
Whole Numbers 1:29
Integers 2:04
Rational Numbers 2:38
Irrational Numbers 5:06
Imaginary Numbers 6:48
Basic Types of Numbers Cont. 8:09
The Big Picture 8:10
Real vs. Imaginary Numbers 8:30
Rational vs. Irrational Numbers 8:48
Basic Types of Numbers Cont. 10:55
Number Line 11:06
Absolute Value 11:44
Inequalities 12:39
Example 1 13:16
Example 2 17:30
Example 3 21:56
Example 4 24:27
Example 5 27:48
Operations on Numbers 19:26
Intro 0:00
Objectives 0:06
Operations on Numbers 0:25
Subtraction 1:33
Multiplication & Division 2:19
Exponents 3:24
Bases 4:04
Square Roots 4:59
Principle Square Roots 5:09
Perfect Squares 6:32
Simplifying and Combining Roots 6:52
Example 1 8:16
Example 2 12:30
Example 3 14:02
Example 4 16:27
Order of Operations 12:06
Intro 0:00
Objectives 0:06
The Order of Operations 0:25
Work Inside Parentheses 0:42
Simplify Exponents 0:52
Multiplication & Division from Left to Right 0:57
Addition & Subtraction from Left to Right 1:11
Remember PEMDAS 1:21
The Order of Operations Cont. 2:27
Example 2:43
Example 1 3:55
Example 2 5:36
Example 3 7:35
Example 4 8:56
Properties of Real Numbers 18:52
Intro 0:00
Objectives 0:07
The Properties of Real Numbers 0:23
Commutative Property of Addition and Multiplication 0:44
Associative Property of Addition and Multiplication 1:50
Distributive Property of Multiplication Over Addition 3:20
Division Property of Zero 4:46
Division Property of One 5:23
Multiplication Property of Zero 5:56
Multiplication Property of One 6:17
Addition Property of Zero 6:29
Why Are These Properties Important? 6:53
Example 1 9:16
Example 2 13:04
Example 3 14:30
Example 4 16:57

## Section 2: Linear Equations

The Vocabulary of Linear Equations 12:22
Intro 0:00
Objectives 0:09
The Vocabulary of Linear Equations 0:44
Variables 0:52
Terms 1:09
Coefficients 1:40
Like Terms 2:18
Examples of Like Terms 2:37
Expressions 4:01
Equations 4:26
Linear Equations 5:04
Solutions 5:55
Example 1 6:16
Example 2 7:16
Example 3 8:45
Example 4 10:20
Solving Linear Equations in One Variable 28:52
Intro 0:00
Objectives 0:08
Solving Linear Equations in One Variable 0:34
Conditional Cases 0:51
Identity Cases 1:09
Solving Linear Equations in One Variable Cont. 2:00
Addition Property of Equality 2:10
Multiplication Property of Equality 2:43
Steps to Solve Linear Equations 3:14
Example 1 4:22
Example 2 8:21
Example 3 12:32
Example 4 14:19
Example 5 17:25
Example 6 22:17
Solving Formulas 12:02
Intro 0:00
Objectives 0:06
Solving Formulas 0:18
Formulas 0:26
Use the Same Properties as Solving Linear Equations 1:36
Addition Property of Equality 1:55
Multiplication Property of Equality 1:58
Steps to Solve Formulas 2:43
Example 1 3:56
Example 2 6:09
Example 3 8:39
Applications of Linear Equations 28:41
Intro 0:00
Objectives 0:10
Applications of Linear Equations 0:43
The Six-Step Method to Solving Word Problems 0:55
Common Terms 3:12
Example 1 5:03
Example 2 9:40
Example 3 13:48
Example 4 17:58
Example 5 23:28
Applications of Linear Equations, Motion & Mixtures 24:26
Intro 0:00
Objectives 0:21
Motion and Mixtures 0:46
Motion Problems: Distance, Rate, and Time 1:06
Mixture Problems: Amount, Percent, and Total 1:27
The Table Method 1:58
The Beaker Method 3:38
Example 1 5:05
Example 2 9:44
Example 3 14:20
Example 4 19:13

## Section 3: Graphing

Rectangular Coordinate System 22:55
Intro 0:00
Objectives 0:11
The Rectangular Coordinate System 0:39
The Cartesian Coordinate System 0:40
X-Axis 0:54
Y-Axis 1:04
Origin 1:11
Ordered Pairs 2:10
Example 1 2:55
The Rectangular Coordinate System Cont. 6:09
X-Intercept 6:45
Y-Intercept 6:55
Relation of X-Values and Y-Values 7:30
Example 2 11:03
Example 3 12:13
Example 4 14:10
Example 5 18:38
Slope & Graphing 27:58
Intro 0:00
Objectives 0:11
Slope and Graphing 0:48
Standard Form 1:14
Example 1 2:24
Slope and Graphing Cont. 4:58
Slope, m 5:07
Slope is Rise over Run 6:11
Don't Mix Up the Coordinates 8:20
Example 2 9:39
Slope and Graphing Cont. 14:26
Slope-Intercept Form 14:34
Example 3 16:55
Example 4 18:00
Slope and Graphing Cont. 19:00
Rewriting an Equation in Slope-Intercept Form 19:39
Rewriting an Equation in Standard Form 20:09
Slopes of Vertical & Horizontal Lines 20:56
Example 5 22:49
Example 6 24:09
Example 7 25:59
Example 8 26:57
Linear Equations in Two Variables 20:36
Intro 0:00
Objectives 0:13
Linear Equations in Two Variables 0:36
Point-Slope Form 1:07
Substitute in the Point and the Slope 2:21
Parallel Lines: Two Lines with the Same Slope 4:05
Perpendicular Lines: Slopes are Negative Reciprocals of Each Other 4:39
Perpendicular Lines: Product of Slopes is -1 5:24
Example 1 6:02
Example 2 7:50
Example 3 10:49
Example 4 13:26
Example 5 15:30
Example 6 17:43

## Section 4: Functions

Introduction to Functions 21:24
Intro 0:00
Objectives 0:07
Introduction to Functions 0:58
Relations 1:03
Functions 1:37
Independent Variables 2:00
Dependent Variables 2:11
Function Notation 2:21
Function 3:43
Input and Output 3:53
Introduction to Functions Cont. 4:45
Domain 4:46
Range 4:55
Functions Represented by a Diagram 6:41
Natural Domain 9:11
Evaluating Functions 12:02
Example 1 13:13
Example 2 15:03
Example 3 16:18
Example 4 19:54
Graphing Functions 16:12
Intro 0:00
Objectives 0:09
Graphing Functions 0:54
Using Slope-Intercept Form 1:56
Vertical Line Test 2:58
Determining the Domain 4:20
Determining the Range 5:43
Example 1 6:06
Example 2 7:18
Example 3 8:31
Example 4 11:04

## Section 5: Systems of Linear Equations

Systems of Linear Equations 25:54
Intro 0:00
Objectives 0:13
Systems of Linear Equations 0:46
System of Equations 0:51
System of Linear Equations 1:15
Solutions 1:35
Points as Solutions 1:53
Finding Solutions Graphically 5:13
Example 1 6:37
Example 2 12:07
Systems of Linear Equations Cont. 17:01
One Solution, No Solution, or Infinite Solutions 17:10
Example 3 18:31
Example 4 22:37
Solving a System Using Substitution 20:01
Intro 0:00
Objectives 0:09
Solving a System Using Substitution 0:32
Substitution Method 1:24
Substitution Example 2:35
One Solution, No Solution, or Infinite Solutions 7:50
Example 1 9:45
Example 2 12:48
Example 3 15:01
Example 4 17:30
Solving a System Using Elimination 19:40
Intro 0:00
Objectives 0:09
Solving a System Using Elimination 0:27
Elimination Method 0:42
Elimination Example 2:01
One Solution, No Solution, or Infinite Solutions 7:05
Example 1 8:53
Example 2 11:46
Example 3 15:37
Example 4 17:45
Applications of Systems of Equations 24:34
Intro 0:00
Objectives 0:12
Applications of Systems of Equations 0:30
Word Problems 1:31
Example 1 2:17
Example 2 7:55
Example 3 13:07
Example 4 17:15

## Section 6: Inequalities

Solving Linear Inequalities in One Variable 17:13
Intro 0:00
Objectives 0:08
Solving Linear Inequalities in One Variable 0:37
Inequality Expressions 0:46
Linear Inequality Solution Notations 3:40
Inequalities 3:51
Interval Notation 4:04
Number Lines 4:43
Set Builder Notation 5:24
Use Same Techniques as Solving Equations 6:59
'Flip' the Sign when Multiplying or Dividing by a Negative Number 7:12
'Flip' Example 7:50
Example 1 8:54
Example 2 11:40
Example 3 14:01
Compound Inequalities 16:13
Intro 0:00
Objectives 0:07
Compound Inequalities 0:37
'And' vs. 'Or' 0:44
'And' 3:24
'Or' 3:35
'And' Symbol, or Intersection 3:51
'Or' Symbol, or Union 4:13
Inequalities 4:41
Example 1 6:22
Example 2 9:30
Example 3 11:27
Example 4 13:49
Solving Equations with Absolute Values 14:12
Intro 0:00
Objectives 0:08
Solve Equations with Absolute Values 0:18
Solve Equations with Absolute Values Cont. 1:11
Steps to Solving Equations with Absolute Values 2:21
Example 1 3:23
Example 2 6:34
Example 3 10:12
Inequalities with Absolute Values 17:07
Intro 0:00
Objectives 0:07
Inequalities with Absolute Values 0:23
Recall… 2:08
Example 1 3:39
Example 2 6:06
Example 3 8:14
Example 4 10:29
Example 5 13:29
Graphing Inequalities in Two Variables 15:33
Intro 0:00
Objectives 0:07
Graphing Inequalities in Two Variables 0:32
Split Graph into Two Regions 1:53
Graphing Inequalities 5:44
Test Points 6:20
Example 1 7:11
Example 2 10:17
Example 3 13:06
Systems of Inequalities 21:13
Intro 0:00
Objectives 0:08
Systems of Inequalities 0:24
Test Points 1:10
Steps to Solve Systems of Inequalities 1:25
Example 1 2:23
Example 2 7:28
Example 3 12:51

## Section 7: Polynomials

Integer Exponents 44:51
Intro 0:00
Objectives 0:09
Integer Exponents 0:42
Exponents 'Package' Multiplication 1:25
Example 1 2:00
Example 2 3:13
Integer Exponents Cont. 4:50
Product Rule for Exponents 4:51
Example 3 7:16
Example 4 10:15
Integer Exponents Cont. 13:13
Power Rule for Exponents 13:14
Power Rule with Multiplication and Division 15:33
Example 5 16:18
Integer Exponents Cont. 20:04
Example 6 20:41
Integer Exponents Cont. 25:52
Zero Exponent Rule 25:53
Quotient Rule 28:24
Negative Exponents 30:14
Negative Exponent Rule 32:27
Example 7 34:05
Example 8 36:15
Example 9 39:33
Example 10 43:16
Adding & Subtracting Polynomials 18:33
Intro 0:00
Objectives 0:07
Adding and Subtracting Polynomials 0:25
Terms 0:33
Coefficients 0:51
Like Terms 1:29
Polynomials 2:21
Monomials, Binomials, Trinomials, and Polynomials 5:41
Degrees 7:00
Evaluating Polynomials 8:12
Adding and Subtracting Polynomials Cont. 9:25
Example 1 11:48
Example 2 13:00
Example 3 14:41
Example 4 16:15
Multiplying Polynomials 25:07
Intro 0:00
Objectives 0:06
Multiplying Polynomials 0:41
Distributive Property 1:00
Example 1 2:49
Multiplying Polynomials Cont. 8:22
Organize Terms with a Table 8:23
Example 2 13:40
Multiplying Polynomials Cont. 16:33
Multiplying Binomials with FOIL 16:48
Example 3 18:49
Example 4 20:04
Example 5 21:42
Dividing Polynomials 44:56
Intro 0:00
Objectives 0:07
Dividing Polynomials 0:29
Dividing Polynomials by Monomials 2:10
Dividing Polynomials by Polynomials 2:59
Dividing Numbers 4:09
Dividing Polynomials Example 8:39
Example 1 12:35
Example 2 14:40
Example 3 16:45
Example 4 21:13
Example 5 24:33
Example 6 29:02
Dividing Polynomials with Synthetic Division Method 33:36
Example 7 38:43
Example 8 42:24

## Section 8: Factoring Polynomials

Greatest Common Factor & Factor by Grouping 28:27
Intro 0:00
Objectives 0:09
Greatest Common Factor 0:31
Factoring 0:40
Greatest Common Factor (GCF) 1:48
GCF for Polynomials 3:28
Factoring Polynomials 6:45
Prime 8:21
Example 1 9:14
Factor by Grouping 14:30
Steps to Factor by Grouping 17:03
Example 2 17:43
Example 3 19:20
Example 4 20:41
Example 5 22:29
Example 6 26:11
Factoring Trinomials 21:44
Intro 0:00
Objectives 0:06
Factoring Trinomials 0:25
Recall FOIL 0:26
Factor a Trinomial by Reversing FOIL 1:52
Tips when Using Reverse FOIL 5:31
Example 1 7:04
Example 2 9:09
Example 3 11:15
Example 4 13:41
Factoring Trinomials Cont. 15:50
Example 5 18:42
Factoring Trinomials Using the AC Method 30:09
Intro 0:00
Objectives 0:08
Factoring Trinomials Using the AC Method 0:27
Factoring when Leading Term has Coefficient Other Than 1 1:07
Reversing FOIL 1:18
Example 1 1:46
Example 2 4:28
Factoring Trinomials Using the AC Method Cont. 7:45
The AC Method 8:03
Steps to Using the AC Method 8:19
Tips on Using the AC Method 9:29
Example 3 10:45
Example 4 16:50
Example 5 21:08
Example 6 24:58
Special Factoring Techniques 30:14
Intro 0:00
Objectives 0:07
Special Factoring Techniques 0:26
Difference of Squares 1:46
Perfect Square Trinomials 2:38
No Sum of Squares 3:32
Special Factoring Techniques Cont. 4:03
Difference of Squares Example 4:04
Perfect Square Trinomials Example 5:29
Example 1 7:31
Example 2 9:59
Example 3 11:47
Example 4 15:09
Special Factoring Techniques Cont. 19:07
Sum of Cubes and Difference of Cubes 19:08
Example 5 23:13
Example 6 26:12

## Section 9: Quadratic Equations

Solving Quadratic Equations by Factoring 23:38
Intro 0:00
Objectives 0:08
Solving Quadratic Equations by Factoring 0:19
Zero Factor Property 1:39
Zero Factor Property Example 2:34
Example 1 4:00
Solving Quadratic Equations by Factoring Cont. 5:54
Example 2 7:28
Example 3 11:09
Example 4 14:22
Solving Quadratic Equations by Factoring Cont. 18:17
Higher Degree Polynomial Equations 18:18
Example 5 20:22
Solving Quadratic Equations 29:27
Intro 0:00
Objectives 0:12
Solving Quadratic Equations 0:29
Linear Factors 0:38
Not All Quadratics Factor Easily 1:22
Principle of Square Roots 3:36
Completing the Square 4:50
Steps for Using Completing the Square 5:15
Completing the Square Works on All Quadratic Equations 6:41
The Quadratic Formula 7:28
Discriminants 8:25
Solving Quadratic Equations - Summary 10:11
Example 1 11:54
Example 2 13:03
Example 3 16:30
Example 4 21:29
Example 5 25:07
Equations in Quadratic Form 16:47
Intro 0:00
Objectives 0:08
Equations in Quadratic Form 0:24
Using a Substitution 0:53
U-Substitution 1:26
Example 1 2:07
Example 2 5:36
Example 3 8:31
Example 4 11:14
Quadratic Formulas & Applications 29:04
Intro 0:00
Objectives 0:09
Quadratic Formulas and Applications 0:35
Squared Variable 0:40
Principle of Square Roots 0:51
Example 1 1:09
Example 2 2:04
Quadratic Formulas and Applications Cont. 3:34
Example 3 4:42
Example 4 13:33
Example 5 20:50
Graphs of Quadratics 26:53
Intro 0:00
Objectives 0:06
Graphs of Quadratics 0:39
Axis of Symmetry 1:46
Vertex 2:12
Transformations 2:57
Graphing in Quadratic Standard Form 3:23
Example 1 5:06
Example 2 6:02
Example 3 9:07
Graphs of Quadratics Cont. 11:26
Completing the Square 12:02
Vertex Shortcut 12:16
Example 4 13:49
Example 5 17:25
Example 6 20:07
Example 7 23:43
Polynomial Inequalities 21:42
Intro 0:00
Objectives 0:07
Polynomial Inequalities 0:30
Solving Polynomial Inequalities 1:20
Example 1 2:45
Polynomial Inequalities Cont. 5:12
Larger Polynomials 5:13
Positive or Negative Intervals 7:16
Example 2 9:01
Example 3 13:53

## Section 10: Rational Equations

Multiply & Divide Rational Expressions 26:41
Intro 0:00
Objectives 0:09
Multiply and Divide Rational Expressions 0:44
Rational Numbers 0:55
Dividing by Zero 1:45
Canceling Extra Factors 2:43
Negative Signs in Fractions 4:52
Multiplying Fractions 6:26
Dividing Fractions 7:17
Example 1 8:04
Example 2 14:01
Example 3 16:23
Example 4 18:56
Example 5 22:43
Adding & Subtracting Rational Expressions 20:24
Intro 0:00
Objectives 0:07
Adding and Subtracting Rational Expressions 0:41
Common Denominators 0:52
Common Denominator Examples 1:14
Steps to Adding and Subtracting Rational Expressions 2:39
Example 1 3:34
Example 2 5:27
Adding and Subtracting Rational Expressions Cont. 6:57
Least Common Denominators 6:58
Transitioning from Fractions to Rational Expressions 9:08
Identifying Least Common Denominators for Rational Expressions 9:56
Subtracting vs. Adding 10:41
Example 3 11:19
Example 4 12:36
Example 5 15:08
Example 6 16:46
Complex Fractions 18:23
Intro 0:00
Objectives 0:09
Complex Fractions 00:37
Dividing to Simplify Complex Fractions 1:10
Example 1 2:03
Example 2 3:58
Complex Fractions Cont. 9:15
Using the Least Common Denominator to Simplify Complex Fractions 9:16
Both Methods Lead to the Same Answer 10:07
Example 3 10:42
Example 4 14:28
Solving Rational Equations 16:24
Intro 0:00
Objectives 0:07
Solving Rational Equations 0:23
Isolate the Specified Variable 1:23
Example 1 1:58
Example 2 5:00
Example 3 8:23
Example 4 13:25
Rational Inequalities 18:54
Intro 0:00
Objectives 0:06
Rational Inequalities 0:18
Testing Intervals for Rational Inequalities 0:38
Steps to Solving Rational Inequalities 1:05
Tips to Solving Rational Inequalities 2:27
Example 1 3:33
Example 2 12:21
Applications of Rational Expressions 20:20
Intro 0:00
Objectives 0:07
Applications of Rational Expressions 0:27
Work Problems 1:05
Example 1 2:58
Example 2 6:45
Example 3 13:17
Example 4 16:37
Variation & Proportion 27:04
Intro 0:00
Objectives 0:10
Variation and Proportion 0:34
Variation 0:35
Inverse Variation 1:01
Direct Variation 1:10
Setting Up Proportions 1:31
Example 1 2:27
Example 2 5:36
Variation and Proportion Cont. 8:29
Inverse Variation 8:30
Example 3 9:20
Variation and Proportion Cont. 12:41
Constant of Proportionality 12:42
Example 4 13:59
Variation and Proportion Cont. 16:17
Varies Directly as the nth Power 16:30
Varies Inversely as the nth Power 16:53
Varies Jointly 17:09
Combining Variation Models 17:36
Example 5 19:09
Example 6 22:10

## Section 11: Radical Equations

Rational Exponents 14:32
Intro 0:00
Objectives 0:07
Rational Exponents 0:32
Power on Top, Root on Bottom 1:05
Example 1 1:37
Rational Exponents Cont. 4:04
Using Rules from Exponents for Radicals as Exponents 4:05
Combining Terms Under a Single Root 4:50
Example 2 5:21
Example 3 7:39
Example 4 11:23
Example 5 13:14
Simplify Rational Exponents 15:12
Intro 0:00
Objectives 0:07
Simplify Rational Exponents 0:25
Product Rule for Radicals 0:26
Product Rule to Simplify Square Roots 1:11
Quotient Rule for Radicals 1:42
Applications of Product and Quotient Rules 2:17
Higher Roots 2:48
Example 1 3:39
Example 2 6:35
Example 3 8:41
Example 4 11:09
Intro 0:00
Objectives 0:07
Like Terms 1:29
Bases and Exponents May be Different 2:02
Bases and Powers Must be Same when Adding and Subtracting 2:42
Example 1 4:47
Example 2 6:00
Simplify the Bases to Look the Same 7:25
Example 3 8:23
Example 4 11:45
Example 5 15:10
Multiply & Divide Radicals 19:24
Intro 0:00
Objectives 0:08
Multiply and Divide Radicals 0:25
Rules for Working With Radicals 0:26
Using FOIL for Radicals 1:11
Don’t Distribute Powers 2:54
Dividing Radical Expressions 4:25
Rationalizing Denominators 6:40
Example 1 7:22
Example 2 8:32
Multiply and Divide Radicals Cont. 9:23
Rationalizing Denominators with Higher Roots 9:25
Example 3 10:51
Example 4 11:53
Multiply and Divide Radicals Cont. 13:13
Rationalizing Denominators with Conjugates 13:14
Example 5 15:52
Example 6 17:25
Solving Radical Equations 15:05
Intro 0:00
Objectives 0:07
Solving Radical Equations 0:17
Isolate the Roots and Raise to Power 0:34
Example 1 1:13
Example 2 3:09
Solving Radical Equations Cont. 7:04
Solving Radical Equations with More than One Radical 7:05
Example 3 7:54
Example 4 13:07
Complex Numbers 29:16
Intro 0:00
Objectives 0:06
Complex Numbers 1:05
Imaginary Numbers 1:08
Complex Numbers 2:27
Real Parts 2:48
Imaginary Parts 2:51
Commutative, Associative, and Distributive Properties 3:35
Adding and Subtracting Complex Numbers 4:04
Multiplying Complex Numbers 6:16
Dividing Complex Numbers 8:59
Complex Conjugate 9:07
Simplifying Powers of i 14:34
Shortcut for Simplifying Powers of i 18:33
Example 1 21:14
Example 2 22:15
Example 3 23:38
Example 4 26:33

Duration: 18 hours, 58 minutes

Number of Lessons: 61

This fun & straightforward course in Algebra 1 is perfect for students learning Algebra for the first time or just someone brushing up on their math skills.

• Free Sample Lessons
• Closed Captioning (CC)
• Practice Questions
• Study Guides

Topics Include:

• Properties of Real Numbers
• Linear Equations in One Variable
• Slope & Graphing
• Systems of Equations
• Compound Inequalities
• Polynomials
• Factoring Trinomials
• Complex Fractions

Professor Eric Smith has been teaching math at the high school and college level for 10+ years.

### Student Testimonials:

“Nice Lecture Sir! It helped me study for my test! AND I GOT 100!!! Thank you so much!” — Arvind G.

“Thank you so much!! That was incredibly helpful. Love your lessons they are explained to perfection. Great job!” — Denise B.

"I must say that you teach this area of algebra extremely well. I bought the book Practical Algebra a few weeks ago and it ruined and confused my confidence in Math. You have restored my faith in this subject." — Jeremy C.

"Thanks Professor, I really like your teaching style. You explain everything well and why it works. I hope you do an Algebra 2 course. I appreciate your work!" — Rana L.

"You are an outstanding teacher. Thanks for all your help!" — Jonathan T.

Visit Prof. Smith’s page

OR

### Start Learning Now

Our free lessons will get you started (Adobe Flash® required).
Get immediate access to our entire library.