×
Home » Mathematics » Algebra 1
No. of
Lectures
Duration
(hrs:min)

4.5
651 ratings • 71 reviews
• Level Intermediate
• Lessons (min)
• Audio: English

In Educator's Algebra I course, instructor Dr. Grant Fraser walks you through the building blocks of mathematics, starting from Functions, Graphs, and Inequalities, to Factoring, Polynomials, and Rational Expressions. Utilizing his 27 years of teaching experience, UCLA educated (Ph.D and B.S.) Professor Fraser carefully explains each concept from multiple angles to ensure learners of any math ability can master Algebra. Dr. Fraser finishes off every idea with a reinforcing example in addition to the four worked-out video examples and things to remember at the end of each lecture.

## Section 1: Basic Concepts

Variables and Expressions 24:05
Intro 0:00
Definitions 0:20
Variable 0:27
Algebraic Expression 2:21
Arithmetic Operations 2:27
Lecture Example 1 7:16
Lecture Example 2 8:27
Order of Operations 22:16
Intro 0:00
Why We Need It 0:15
Example: Order of Operations 1:25
Procedure To Evaluate 3:22
Lecture Example 1 6:45
Lecture Example 2 10:55
The Distributive Property 16:27
Intro 0:00
The Distributive Property 0:20
Extension to Several Numbers 2:05
Lecture Example 1 2:50
Lecture Example 2 5:15
The Real Number System 22:35
Intro 0:00
The Real Number System 0:21
Natural Numbers 0:22
Whole Numbers 0:37
Integers 1:06
Rational Numbers 1:35
Example: Decimals 2:07
The Real Number System, Cont. 5:00
Square Roots 5:10
Principle Square Root 6:04
Irrational Numbers 6:35
The Real Number System, Cont. 9:11
Picture Representation 9:25
Lecture Example 1 11:54
Lecture Example 2 14:10
Functions and Graphs 27:49
Intro 0:00
Functions 0:30
Definition 0:30
Example: Square Roots 1:18
Example: Gas Prices 3:20
Graphs 4:03
Definition 4:03
Example: Square Roots 4:48
Domain and Range 9:30
Definition 9:30
Example: Square Roots 10:01
Lecture Example 1 11:22
Lecture Example 2 13:58

## Section 2: Solving Linear Equations

From Sentences to Equations 22:13
Intro 0:00
Strategy 1:40
Using Variables 1:55
Translating Phrases 2:18
Equality 3:00
Lecture Example 1 3:52
Lecture Example 2 8:36
Intro 0:00
Techniques 0:22
Example 0:47
Subtracting the Same Number 1:50
Example 1:54
Strategy 2:36
Isolate the Variable 2:46
Lecture Example 1 3:48
Lecture Example 2 5:41
Multiplication and Division Techniques 19:19
Intro 0:00
Techniques 0:16
Multiplied by the Same Number 0:18
Example 0:26
Divided by the Same Number 1:23
Non-zero Exception 1:28
Dividing by Zero 2:17
Example 3:01
Strategy 3:51
Isolate the Variable 3:55
Lecture Example 1 4:55
Lecture Example 2 6:40
Techniques for Multi-Step Equations 19:13
Intro 0:00
What are Multi-step Equations? 0:08
Strategy 0:30
Opposite Operations 0:50
Last Operation 1:18
Lecture Example 1 1:54
Lecture Example 2 4:16
When the Variable is on Both Sides of the Equation 24:16
Intro 0:00
Solving More Complicated Equations 0:17
Distributive Property and Grouping Symbols 0:36
Combining 0:51
Moving Variables to One Side 1:06
Possible Outcomes 1:50
Exactly One Solution 2:02
No Solution 2:35
Example 2:51
Identities-True for All Real Numbers 4:26
Example 4:45
Lecture Example 1 6:17
Lecture Example 2 9:39
Ratios and Proportions 22:39
Intro 0:00
Definitions 0:16
Ratio 0:21
Proportion 0:56
Example 1:13
Cross Products 3:00
Example: Original Proportion 3:12
Example 2 5:24
Rates 6:55
Example: Gas 7:22
Example 2: Apples 7:43
Example 3: Speed 8:16
Lecture Example 1 9:17
Lecture Example 2 11:53
Applications of Percents 20:38
Intro 0:00
Definitions 0:22
Percent of Change 0:23
Percent of Increase 0:42
Percent of Decrease 0:55
Examples of Percent of Change 1:14
Sales Tax 1:21
Discount 1:57
Lecture Example 1 2:51
Lecture Example 2 4:46
More Than One Variable 22:34
Intro 0:00
More Than One Variable 0:21
Strategy 1:02
Typical Application 1:33
Example: Circumference 1:48
Example: Perimeter 2:21
Lecture Example 1 2:53
Lecture Example 2 5:43

## Section 3: Functions

Relations 24:39
Intro 0:00
Definition 0:17
List, Table, Graph 0:42
Example: List 0:56
Example: Table 2:00
Example: Graph 2:47
Domain and Range 4:10
Inverse of a Relation 5:01
Example 5:21
Lecture Example 1 7:26
Lecture Example 2 10:39
Functions 19:03
Intro 0:00
Definition 0:21
Function 0:24
Example: Relation 0:50
Vertical Line Test 1:48
Example: Pass 2:02
Example 2: Fail 3:32
Example 3: Fail 4:18
Function Notation 5:33
Proper Notation 5:43
Example 6:29
Domain and Range 7:32
Lecture Example 1 8:06
Lecture Example 2 9:39
Linear Functions 20:03
Intro 0:00
Definition 0:12
Linear Equation 0:15
Example: A and B not zero 0:27
Example: B is zero 0:58
Example: A is zero 1:13
Graph and Intercepts 1:43
Straight Line 1:52
x-intercepts, y-intercepts 2:19
Example: Intercepts 2:27
Graphing Linear Equations 4:19
Example 4:40
Linear Functions 7:23
Example 8:00
Lecture Example 1 10:11
Lecture Example 2 12:42

## Section 4: Linear Functions and their Graphs

Slope and Rate of Change 23:58
Intro 0:00
Rate of Change 0:27
Independent Variable 0:37
Dependent Variable 0:51
Slope 2:02
Example 2:19
Steepness of the Line 4:56
Possible Slopes 5:58
Positive 6:13
Negative 6:34
Zero 6:50
Undefined 7:11
Lecture Example 1 8:03
Lecture Example 2 10:34
Direct Variation 13:18
Intro 0:00
Definitions 0:13
Direct Variation 0:14
Constant of Variation 0:26
Graph 1:02
Example: Positive and Negative k 1:18
Applications 1:49
Lecture Example 1 2:16
Lecture Example 2 4:39
Slope Intercept Form of an Equation 17:11
Intro 0:00
Slope Intercept Form 0:16
Example 0:37
Lecture Example 1 2:24
Lecture Example 2 5:43
Point Slope Form of an Equation 10:32
Intro 0:00
Point Slope Form 0:11
Example 0:50
Lecture Example 1 2:03
Lecture Example 2 3:03
Parallel and Perpendicular Lines 18:15
Intro 0:00
Parallel Lines 0:12
Example: Non-vertical Lines 0:32
Perpendicular lines 1:57
Example: Slope Product is -1 2:15
Negative Reciprocal 3:08
Lecture Example 1 3:58
Lecture Example 2 7:12

## Section 5: Systems of Equations

Graphing Systems of Equations 20:01
Intro 0:00
System of Equations 0:09
Definition 0:15
Solution 0:59
Solving by Graphing 1:27
Example 2:33
Number of Solutions 3:37
Independent 3:58
Dependent 4:03
Inconsistent 4:08
Example: 1 Solution 4:15
Example: No Solution 4:34
Example: Infinite Solution 4:51
Lecture Example 1 5:39
Lecture Example 2 8:51
Solving by Substitution 24:12
Intro 0:00
Substitution 0:17
Example 0:51
Number of Solutions 1:43
Infinite Solutions 2:14
No Solutions 2:50
Lecture Example 1 3:40
Lecture Example 2 6:56
Solving by Addition and Subtraction 12:18
Intro 0:00
Fundamental Principle 0:18
Lecture Example 1 1:23
Lecture Example 2 4:03
Solving by Multiplication 19:11
Intro 0:00
Fundamental Principle 0:24
Multiplication 0:28
Lecture Example 1 1:40
Lecture Example 2 6:36
Applications: Systems of Equations 18:24
Intro 0:00
Solving Systems of Equations 0:08
Graphing 0:32
Subtraction 1:04
Multiplication 1:13
Substitution 1:30
Lecture Example 1 3:20
Lecture Example 2 4:27

## Section 6: Inequalities

Inequalities: Addition and Subtraction Techniques 10:08
Intro 0:00
Fundamental Principle 0:11
Solutions of Inequalities 0:55
Inequality 1:02
Set Builder Notation 1:13
Example 1:15
Graph on a Number Line 2:13
Lecture Example 1 3:29
Lecture Example 2 5:14
Inequalities: Multiplication and Division Techniques 10:59
Intro 0:00
Fundamental Principle 0:11
Example: Positive Number 0:51
Fundamental Principle 1:35
Example: Negative Number 1:50
Lecture Example 1 4:05
Lecture Example 2 5:12
Techniques for Multi-Step Inequalities 16:21
Intro 0:00
Similarity to Multi-step Equations 0:15
Inequalities Containing Grouping Symbols 1:03
Special Cases 1:26
Solution: All Real Numbers 1:40
Solution: Empty Set 2:16
Lecture Example 1 2:54
Lecture Example 2 4:37
Compound Inequalities 23:00
Intro 0:00
Inequalities Combined by 'And' 0:12
Three Ways to Write Solution Set 1:41
Set Notation 2:01
Inequalities 2:12
Graph 2:29
Examples 2:31
Inequalities Combined by 'Or' 4:45
Example 5:59
Lecture Example 1 7:40
Lecture Example 2 10:55
Equations with Absolute Values 23:13
Intro 0:00
Absolute Value 0:15
Example: Distance 1:00
Absolute Value Function 2:34
Example 3:05
Lecture Example 1 4:57
Lecture Example 2 8:28
Inequalities with Absolute Values 17:34
Intro 0:00
Inequalities of the Form |x|< n 0:22
Inequalities of the Form |x|> n 3:30
Lecture Example 1 5:33
Lecture Example 2 8:50
Graphing Inequalities with Two Variables 30:50
Intro 0:00
Graph 0:22
Half-Plane 0:28
Boundary 1:37
Technique for Graphing 3:14
Example 4:01
Dashed Line 5:13
Solid Line 6:30
Technique for Graphing, cont. 8:58
Example 9:09
Lecture Example 1 12:19
Lecture Example 2 15:48
Graphing Systems of Inequalities 27:38
Intro 0:00
System of Inequalities 0:26
Example 0:43
Solving a System of Inequalities 1:17
Example 1:41
Lecture Example 1 2:58
Lecture Example 2 7:22

## Section 7: Polynomials

Multiplying Monomials 19:55
Intro 0:00
What is a Monomial? 0:43
Constant 1:11
Power 1:48
Exponent and Base 2:39
Properties of Exponents 3:02
Simplified Form 5:52
Each Base Appears Exactly Once 6:02
No Powers of Powers 6:18
All Fractions Simplified 6:33
Lecture Example 1 6:43
Lecture Example 2 8:12
Dividing Monomials 23:09
Intro 0:00
Properties of Exponents 0:26
Example 1:07
Properties of Exponents, cont 2:18
Example 3:18
Properties of Exponents, cont 4:55
Example 5:32
Properties of Exponents, cont 8:49
Lecture Example 1 11:43
Lecture Example 2 13:13
Polynomials 16:35
Intro 0:00
What is a Polynomial 0:45
Monomial 0:47
Example: Trinomial 1:46
Trinomial 2:10
Example: Binomial 2:21
Binomial 2:30
Degree of a Polynomial 4:28
Example 4:40
Ordering Polynomials 6:45
Example 7:27
Lecture Example 1 9:27
Lecture Example 2 10:31
Intro 0:00
Like Polynomials 0:48
Example 1:04
Subtracting Polynomials 3:55
Example 4:01
Lecture Example 1 5:30
Lecture Example 2 8:04
Multiplying Polynomials by Monomials 24:08
Intro 0:00
Distributive Property 0:22
Basic Principle 0:42
Example 1:04
Solving Equations 3:25
Lecture Example 1 4:26
Lecture Example 2 7:51
Multiplying Polynomials 26:37
Intro 0:00
Distributive Property 0:23
Example 0:34
Example 1:55
Foil Method 5:17
Lecture Example 1 7:44
Lecture Example 2 10:15
Special Products 19:40
Intro 0:00
Square of a Sum 0:12
Perfect Square Trinomial 1:43
Example 2:13
FOIL Technique 3:09
Square of a Difference 3:38
Example 5:27
Difference of Two Squares 6:12
Example 7:43
Lecture Example 1 8:51
Lecture Example 2 11:06

## Section 8: Factoring

Factoring Monomials 27:25
Intro 0:00
Prime and Composite Numbers 1:01
Prime Number 1:23
Composite Number 3:03
Factored Forms 4:07
Prime Factored Form 4:19
Factored Form 5:40
Greatest Common Factor (GCF) 7:41
Example 8:00
GCF of Monomials 10:07
Example 10:18
Lecture Example 1 12:52
Lecture Example 2 17:08
Factoring Using Greatest Common Factor (GCF) 26:03
Intro 0:00
Distributive Property 0:19
Factor Out an Expression 1:21
Example 2:52
Factoring by Grouping 4:40
Example 6:00
Zero Product Property 8:24
Example 9:03
Lecture Example 1 11:19
Lecture Example 2 14:19
Factoring Trinomials with Leading Coefficient 1 27:37
Intro 0:00
Factoring Trinomials 0:23
Example 2:06
Rules for Signs 6:27
Both Positive 6:41
Both Negative 7:00
Opposite Signs 7:33
Solving Equations 8:26
Example 8:59
Lecture Example 1 11:14
Lecture Example 2 14:01
Factoring General Trinomials 34:11
Intro 0:00
Factoring Trinomials 0:40
Example: List 1:38
Grouping 5:46
Example 5:55
Rules for Signs 9:04
Example 9:22
Greatest Common Factor (GCF) 10:29
Prime Polynomials 11:03
Example 11:32
Solving Equations 12:32
Lecture Example 1 13:11
Lecture Example 2 18:37
Factoring the Difference of Two Squares 20:22
Intro 0:00
Difference of Two Squares 0:40
Example 1:56
Factoring Using Several Techniques 3:33
Solving Equations 4:11
Lecture Example 1 4:55
Lecture Example 2 6:05
Factoring Perfect Squares 18:07
Intro 0:00
Perfect Squares 0:10
Perfect Square Trinomials 1:17
Solving Equations 2:53
Square Root Property 2:58
Example 3:06
Lecture Example 1 4:23
Lecture Example 2 6:56

Intro 0:00
Parabolas 0:09
Parabolas That Open Upward 3:58
Minimum 4:26
Parabolas That Open Downward 4:54
Maximum 5:09
Vertex 7:28
Example 8:01
Axis of Symmetry 11:03
Lecture Example 1 13:27
Lecture Example 2 17:17
Solving Equations by Graphing 28:18
Intro 0:00
Example 0:50
Two Distinct Solutions/Roots 5:08
One Double Root 5:58
No Real Roots 7:14
Estimating Solutions 8:00
Example 8:16
Example 8:31
Lecture Example 1 9:43
Lecture Example 2 14:10
Solving Equations by Completing the Square 25:07
Intro 0:00
Perfect Square Trinomials 0:22
Example 1:12
Completing the Square 3:17
Example 3:25
Solving Equations 6:12
Example 6:27
Lecture Example 1 10:23
Lecture Example 2 14:17
Solving Equations Using the Quadratic Formula 24:15
Intro 0:00
Example 2:23
Discriminant 4:28
Two Distinct Real Roots 5:07
One Double Real Root 5:23
No Real Root 5:42
Why Does It Work? 6:05
Lecture Example 1 7:53
Lecture Example 2 11:50

## Section 10: Radical Expressions and Equations

Intro 0:00
Example 0:32
Simplest Form 1:07
Example 1:35
Product Property 2:34
Verifications 2:47
Square Roots of Variables with Even Powers 4:27
Quotient Rule 6:45
Example 6:55
Rationalizing Denominators 7:32
Example 7:41
Conjugates 10:44
Examples 10:59
Example 15:39
Lecture Example 1 17:34
Lecture Example 2 19:38
Intro 0:00
Example 0:19
Example 2:07
Lecture Example 1 5:29
Lecture Example 2 6:36
Intro 0:00
Example 0:33
Example 2:16
Extraneous Solutions 3:14
Example 4:31
Lecture Example 1 7:33
Lecture Example 2 9:45
Pythagorean Theorem 19:08
Intro 0:00
Right Triangles 0:51
Right Angle 1:03
Vertex 1:11
Symbol 1:16
Hypotenuse and Legs 1:42
Pythagorean Theorem 2:27
Example 2:47
Example 3:12
Pythagorean Triples 4:03
Converse of the Pythagorean Theorem 6:39
Example 7:41
Lecture Example 1 8:57
Lecture Example 2 10:05
Distance Formula 18:27
Intro 0:00
Distance Formula 0:17
Missing Coordinates 1:46
Example 1:55
Lecture Example 1 4:10
Lecture Example 2 5:57

## Section 11: Rational Expressions and Equations

Inverse Variation 14:43
Intro 0:00
Inverse Variation 0:23
Constant of Variation 0:37
Graphing Inverse Variation 1:08
Example: Hyperbola 1:15
Product Rule 3:54
Lecture Example 1 5:31
Lecture Example 2 7:43
Rational Expressions 32:43
Intro 0:00
Rational Expression 0:55
Example 1:03
Excluded Values 1:29
Examples 1:40
Simplifying Rational Expressions 5:36
Greatest Common Factor (GCF) 5:46
Example 5:55
Example 7:42
Simplifying and Excluded Values 9:34
Lecture Example 1 9:50
Lecture Example 2 13:55
Multiplying Rational Expressions 27:22
Intro 0:00
Procedure 0:16
Example 0:33
Cancel Before Multiplication 3:44
Example 3:55
Rational Expressions Containing Polynomials 6:19
Example 6:26
Lecture Example 1 11:09
Lecture Example 2 15:39
Dividing Rational Expressions 28:30
Intro 0:00
Procedure 0:21
Example 0:59
Cancel Before Multiplication 4:31
Example 4:39
Rational Expressions Containing Polynomials 8:01
Example 8:08
Lecture Example 1 10:43
Lecture Example 2 13:46
Dividing Polynomials 29:44
Intro 0:00
Dividing a Polynomial by a Monomial 1:07
Example 1:14
Dividing a Polynomial by a Binomial 3:30
Example 3:51
Long Division 5:20
Example 6:25
Missing Terms 11:11
Example 12:25
Lecture Example 1 14:54
Lecture Example 2 16:35
Adding and Subtracting Rational Expressions with Like Denominators 16:50
Intro 0:00
Example 0:41
Subtraction with Like Denominators 2:23
Example 2:30
Denominators That Are Additive Inverses 2:55
Example 3:03
Lecture Example 1 6:41
Lecture Example 2 7:09
Adding and Subtracting Rational Expressions with Unlike Denominators 36:00
Intro 0:00
Least Common Multiple (LCM) of Polynomials 0:34
Example 0:45
Example 1:55
Example 4:45
Lecture Example 1 8:13
Lecture Example 2 10:22
Complex Fractions 18:43
Intro 0:00
Mixed Expression 0:08
Example 0:30
Complex Fraction 2:45
Example 2:57
Example 3:11
Example 3:22
Simplifying Complex Fractions 3:58
Why Does It Work? 4:22
Lecture Example 1 4:48
Lecture Example 2 8:44
Rational Equations 39:10
Intro 0:00
Definition 0:08
Examples 0:17
Solving Rational Expressions 3:02
Example 3:09
Work Problems 6:31
Example 6:48
Extraneous Solutions 13:12
Example 14:13
Lecture Example 1 17:21
Lecture Example 2 19:59

Duration: minutes

Number of Lessons:

#### Student Feedback

4.5

71 Reviews

53%
40%
7%
0%
0%
By Miriam RaveloJuly 17, 2013
Thank you this helped me tremendously!
By Taylor WrightJune 22, 2013
You are a great professor. I really enjoy it when a teacher/prof doesn't have to continually look at notes when working through problems, it really shows that they know the material and aren't just going through the motions.

Thanks!
By Jorge SardinasMay 20, 2012
Okay he made one mistake give him a break.He's done fantastic on the other videos!He is a very good mathematician.
By Jorge SardinasApril 28, 2012
"But on the other side it was very good and interesting I LOVE THE VIDEO!!!!!!!!! Its worth money\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$
By Ronnie NivenApril 20, 2012
Very good and well explained.

OR

### Start Learning Now

Our free lessons will get you started (Adobe Flash® required).