INSTRUCTORS  Carleen Eaton Grant Fraser
Home » Mathematics » Algebra 2
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• Level Intermediate
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• Audio: English

Dr. Grant Fraser leads Educator's Algebra II lecture series directly following Algebra I. Our most comprehensive mathematics syllabus covers everything from Matrices, Quadratic/Polynomial Equations, to Exponential/Logarithmic Relations, Conic Sections, and Sequences/Series. In addition to his 27 years of teaching experience, UCLA educated (Ph.D and B.S.) Professor Fraser has also directed summer institutes for 10 years which honed high-school math teachers' instructional skills. Applying his vast experience teaching both students and fellow educators, Dr. Fraser guides you through this course with clear explanations, plenty of worked-out examples, and detailed notes to make sure you effectively learned all concepts.

## Section 1: Equations and Inequalities

Expressions and Formulas 28:56
Intro 0:00
Order of Operations 0:51
Variables and Algebraic Expressions 0:57
Order of Operations 3:05
Monomials 5:25
Examples 5:37
Constant, Coefficient, Degree, Power 6:27
Polynomials 8:29
Examples 8:42
Terms, Like Terms, Binomial, Trinomial 8:59
Formulas 12:35
Examples: Area, Volume, Surface Area 12:50
Lecture Example 1 15:50
Lecture Example 2 21:31
Properties of Real Numbers 23:45
Intro 0:00
Real Numbers 0:15
Rational Numbers 0:40
Irrational Numbers 1:38
Venn Diagram of the Real Numbers 2:55
Properties of Real Numbers 6:49
Commutative Property 7:06
Associative Property 7:27
Identity Property 8:01
Inverse Property 8:42
Distributive Property 10:05
Lecture Example 1 10:43
Lecture Example 2 13:08
Solving Equations 24:41
Intro 0:00
Translations 0:11
Example: Verbal to Algebraic Expressions 0:44
Properties of Equality 2:51
Reflexive, Symmetric, Transitive Properties 2:58
Solving Equations 6:09
Example 6:23
Solving for a Variable 8:49
Example: Surface Area of a Cone 8:58
Lecture Example 1 11:06
Lecture Example 2 12:39
Solving Absolute Value Equations 17:36
Intro 0:00
Absolute Value Expressions 0:10
Example: Positive Distance 0:15
Absolute Value Equations 1:07
Examples 1:18
No Solutions 2:54
Example: Empty Set 2:58
Number of Solutions 3:56
Examples 4:42
Lecture Example 1 6:42
Lecture Example 2 8:54
Solving Inequalities 19:27
Intro 0:00
Properties of Inequality 0:07
Subtraction Property 0:48
Example 1:02
Multiplication Properties 1:44
Multiplying by a Positive Number 1:48
Example: Positive 2:17
Multiplying by a Negative Number 2:25
Example: Negative 2:35
Division Properties 3:23
Example: Positive 3:32
Example: Negative 4:04
Describing the Solution Set 6:00
Set Builder Notation 6:15
Graphing 7:15
Lecture Example 1 8:04
Lecture Example 2 9:09
Solving Compound and Absolute Value Inequalities 24:08
Intro 0:00
Compound Inequalities 0:11
Example 0:33
'And' Inequality 3:41
Example: Set Intersection 4:00
'Or' Inequality 6:01
Example: Set Union 6:15
Absolute Value Inequalities 8:19
Examples 8:37
Lecture Example 1 11:43
Lecture Example 2 14:47

## Section 2: Linear Relations and Functions

Relations and Functions 38:15
Intro 0:00
Coordinate Plane 0:38
Relations 4:08
Example: Ordered Pairs 4:14
Domain and Range 5:05
Functions 5:57
Example: Mapping 6:11
One-to-One Functions 9:58
Example 10:05
Graphs of Relations 13:42
Example: Discrete and Continuous 13:55
Vertical Line Test 16:26
Examples 16:38
Equations, Relations, Functions 19:38
Example: Independent and Dependent Variables 19:45
Function Notation 21:51
Examples 22:27
Lecture Example 1 24:39
Lecture Example 2 28:29
Linear Equations 12:50
Intro 0:00
Linear Equations and Functions 0:12
Example: Linear Equation 0:21
Example: Linear Function 1:16
Standard Form 2:13
Examples 2:43
Graphing with Intercepts 3:26
Example: Intercepts 3:51
Lecture Example 1 6:25
Lecture Example 2 7:53
Slope 20:07
Intro 0:00
Definition of Slope 0:23
Interpretation of Slope 2:19
Example: 0 Slope and Undefined Slope 2:25
Example: Positive Slope 4:04
Example: Negative Slope 4:43
Parallel Lines 6:16
Perpendicular Lines 7:15
Lecture Example 1 8:20
Lecture Example 2 10:45
Writing Linear Functions 27:36
Intro 0:00
Slope Intercept Form 0:08
Origin of Form 0:21
Example 2:08
Point Slope Form 3:47
Origin of Form 4:01
Parallel and Perpendicular Lines 5:36
Example: Find Parallel Line 5:58
Lecture Example 1 8:27
Lecture Example 2 12:08
Special Functions 24:28
Intro 0:00
Step Functions 0:13
Graph 0:21
Example: Birthday Function 2:32
Absolute Value Functions 5:21
Graph 5:27
Piecewise Functions 7:34
Example 7:38
Lecture Example 1 10:20
Lecture Example 2 14:38
Graphing Inequalities 30:37
Intro 0:00
Graphing Linear Inequalities 0:11
Example: Linear Inequalities 0:20
Half Plane 2:04
Test Point 2:53
Graphing Absolute Value Inequalities 5:38
Example: Linear Inequalities 5:49
Example: Absolute Value 8:23
Lecture Example 1 11:39
Lecture Example 2 14:50

## Section 3: Systems of Equations and Inequalities

Solving Systems of Equations by Graphing 21:27
Intro 0:00
Systems of Equations 0:14
Solving by Graphing 0:34
Types of Systems 1:07
Independent (One Solution) 2:02
Dependent (Infinite Solutions) 2:30
Inconsistent (No Solutions, Parallel) 3:37
Lecture Example 1 4:52
Lecture Example 2 8:42
Solving Systems of Equations Algebraically 31:26
Intro 0:00
Solving by Substitution 0:15
Examples 0:50
Solving by Elimination 4:19
Examples 4:27
Solving by Multiplication 7:24
Examples 7:37
Inconsistent and Dependent Systems 11:42
Example: Spotting Differences 12:07
Lecture Example 1 15:00
Lecture Example 2 17:35
Solving Systems of Inequalities by Graphing 20:43
Intro 0:00
Solving by Graphing 0:10
Example: Single Inequality 0:14
No Solution 4:16
Example: No Solution 4:25
Lecture Example 1 6:25
Lecture Example 2 8:23
Solving Systems of Equations in 3 Variables 21:27
Intro 0:00
Solving Systems in Three Variables 0:15
Ordered Triple 0:36
Number of Solutions 1:32
Lecture Example 1 2:19
Lecture Example 2 6:14

## Section 4: Matrices

Basic Matrix Concepts 14:08
Intro 0:00
What is a Matrix? 0:33
Example: Rectangular Array 0:41
Element 1:52
Examples: More Matrices 2:04
Dimensions 3:40
Examples 4:53
Special Matrices 6:31
(m x 1) Matrix 6:36
Square Matrix 7:01
Zero Matrix 7:38
Equal Matrices 8:23
Examples 8:32
Lecture Example 1 10:56
Lecture Example 2 11:28
Matrix Operations 16:40
Intro 0:00
Example 1:07
Matrix Subtraction 2:12
Example 2:31
Scalar Multiplication 3:23
Example 4:05
Properties of Matrix Operations 5:31
Commutative Property 5:48
Associative Property 5:59
Distributive Property 6:34
Lecture Example 1 7:03
Lecture Example 2 8:15
Matrix Multiplication 22:47
Intro 0:00
Dimension Requirement 0:19
Example 0:45
Matrix Multiplication 1:35
Example 2:21
Properties of Matrix Multiplication 6:46
Associative Property 6:59
Distributive Property 7:15
Commutative Property 7:39
Lecture Example 1 8:49
Lecture Example 2 11:43
Determinants 25:47
Intro 0:00
What is a Determinant 0:15
Determinant of a 2x2 Matrix 0:56
Difference from Matrices 1:16
Second Order Determinant 1:38
Example 2:06
Determinant of a 3x3 Matrix 3:20
Third Order Determinants 3:25
Origin of Equation (Minors) 3:38
Expansion by Minors 6:05
Example: 3x3 Matrix 8:55
Diagonal Method for 3x3 Matrix 12:45
Example 12:55
Lecture Example 1 17:03
Lecture Example 2 17:42
Cramer's Rule 25:42
Intro 0:00
System of 2 Equations in 2 Variables 0:27
Example 1:20
System of 3 Equations in 3 Variables 3:10
Example 3:51
Lecture Example 1 6:45
Lecture Example 2 10:22
Identity and Inverse Matrices 27:01
Intro 0:00
Identity Matrix 0:10
Example: 2x2 Matrix 2:18
Matrix Inverses 4:40
Example: Does Not Exist 6:04
Inverse of a 2x2 Matrix 8:17
Example 9:38
Lecture Example 1 13:19
Lecture Example 2 15:57
Solving Systems of Equations with Matrices 28:40
Intro 0:00
Matrix Equations 0:22
Example 0:40
Solving Systems of Equations 4:20
Example 5:58
Lecture Example 1 9:11
Lecture Example 2 15:09

## Section 5: Quadratic Functions and Inequalities

Intro 0:00
Parabola 0:50
Example: Opens Upward 1:03
Example: Opens Downward 1:54
Properties of Parabolas 3:17
Axis of Symmetry 3:26
Vertex 4:05
Example 4:28
Maximum and Minimum Values 7:10
Example: Upwards/Minimum 7:32
Example: Downwards/Maximum 8:19
Lecture Example 1 9:09
Lecture Example 2 13:05
Solving Quadratic Equations by Graphing 19:26
Intro 0:00
Example: Standard Form 0:55
Solving by Graphing 1:39
Roots 1:48
Example: 2 Solutions 1:56
Example: 1 Solution 2:39
Example: 0 Solutions 3:10
Estimating Solutions 3:55
Example 4:07
Lecture Example 1 5:16
Lecture Example 2 7:51
Solving Quadratic Equations by Factoring 17:46
Intro 0:00
Factoring Techniques 0:16
Greatest Common Factor (GCF) 0:29
Difference of Two Squares 1:45
Perfect Square Trinomials 2:07
General Trinomials 3:16
Zero Product Rule 4:50
Example 5:01
Lecture Example 1 6:19
Lecture Example 2 8:13
Imaginary and Complex Numbers 37:41
Intro 0:00
Properties of Square Roots 0:17
Example: Product and Quotient Rules 0:33
Imaginary Numbers 4:04
Powers of Imaginary Numbers 5:06
Example 6:27
Complex Numbers 7:21
Real and Complex Numbers 8:19
Equality 9:04
Example 9:17
Example 9:55
Complex Plane 11:38
Example 11:52
Multiplication 13:34
Example 13:43
Division 16:36
Complex Conjugates 16:45
Example 18:16
Lecture Example 1 23:40
Lecture Example 2 26:34
Completing the Square 16:42
Intro 0:00
Square Root Property 0:22
Examples 0:33
Completing the Square 1:48
Example: Making into Perfect Square 1:50
Solve Equations 3:43
Example 3:53
Equations Where 'a' Not Equal to 1 6:47
Example 6:57
Complex Solutions 10:14
Example 10:22
Lecture Example 1 11:30
Lecture Example 2 12:34
Quadratic Formula and the Discriminant 17:44
Intro 0:00
Example 0:56
One Rational Root 3:10
Why It Works 3:26
Repeated/Double Root 3:49
Complex Solutions 4:31
Example 4:50
Discriminant 7:19
Discriminant Value and Root Type 8:50
Lecture Example 1 12:08
Lecture Example 2 14:15
Analyzing the Graphs of Quadratic Functions 23:00
Intro 0:00
Vertex Form 0:24
Example 1:56
Significance of Coefficient 'a' 3:15
Example 3:39
Writing Quadratic Equations in Vertex Form 4:51
Examples 5:19
Lecture Example 1 8:14
Lecture Example 2 10:22
Graphing and Solving Quadratic Inequalities 34:38
Intro 0:00
Example: Linear Inequality 1:29
Example 6:38
Lecture Example 1 11:50
Lecture Example 2 15:09

## Section 6: Polynomial Functions

Properties of Exponents 20:28
Intro 0:00
Simplifying Exponential Expressions 0:32
Negative Exponents 0:54
Example: Base 0 1:16
Examples 1:30
Properties of Exponents 2:22
Base and Exponent 2:52
Lecture Example 1 8:29
Lecture Example 2 10:58
Operations on Polynomials 16:13
Intro 0:00
Example: Signs 0:34
Multiplying Polynomials 3:04
Example 3:12
Lecture Example 1 6:40
Lecture Example 2 7:21
Dividing Polynomials 29:26
Intro 0:00
Dividing by a Monomial 0:16
Example 0:28
Long Division 3:24
Example: Missing Terms, Remainder 3:49
Example: Long Division 6:51
Synthetic Division 10:13
Example 10:44
Divisor in Synthetic Division 13:18
Example: Coefficient Not 1 13:30
Lecture Example 1 16:41
Lecture Example 2 18:22
Polynomial Functions 29:34
Intro 0:00
Polynomial in One Variable 0:17
Degree n 0:30
Descending Order 0:43
Function Values 3:31
Example 3:42
Zeros of Polynomial Functions 5:45
Example: Zeros 6:04
End Behavior 9:51
Example: 4 Situations 10:51
Lecture Example 1 17:30
Lecture Example 2 19:11
Analyzing Graphs of Polynomials 34:36
Intro 0:00
Graphing Polynomial Functions 0:09
End Behavior 0:19
Examples: Degree and Sign of Polynomials 1:13
Location Principle 4:50
Example 6:19
Maximum and Minimum Points 7:34
Example: Relative Maximum and Relative Minimum 7:44
Lecture Example 1 10:17
Lecture Example 2 15:13
Solving Polynomial Equations 19:23
Intro 0:00
Factoring Polynomials 0:08
Example: Greatest Common Factor (GCF) 0:40
Example: Perfect Square Trinomials 1:30
Example: General Trinomials 2:48
Sum and Difference of Two Cubes 3:25
Example 4:18
Lecture Example 1 7:30
Lecture Example 2 10:43
Remainder and Factor Theorems 27:52
Intro 0:00
Remainder Theorem 0:04
Quotient and Remainder 0:30
Examples 1:34
Synthetic Substitution 5:04
Example 5:28
Factor Theorem 10:00
Factoring Polynomials 11:21
Example 11:51
Lecture Example 1 16:38
Lecture Example 2 18:41
Roots and Zeros 31:04
Intro 0:00
Numbers of Roots 0:10
Example: Real and Complex Roots 0:23
Descartes' Rule of Signs 3:43
Example: Positive Real Roots 4:58
Example: Negative Real Roots 8:00
Finding the Roots 12:11
Conjugate Roots 13:24
Lecture Example 1 15:41
Lecture Example 2 19:41
Rational Zero Theorem 29:27
Intro 0:00
Equation 0:14
Leading Coefficient and Constant Term 0:30
Example 2:15
Leading Coefficient Equal to 1 8:08
Example 9:20
Finding Rational Zeros 11:48
Lecture Example 1 12:10
Lecture Example 2 15:59

## Section 7: Rational Equations and Inequalities

Operations on Functions 35:12
Intro 0:00
Arithmetic Operations 0:12
Example: Domain 0:25
Composition of Functions 7:35
Example 7:55
Composition is Not Commutative 17:13
Example 18:18
Lecture Example 1 21:51
Lecture Example 2 24:25
Inverse Functions and Relations 18:12
Intro 0:00
Inverse of a Relation 0:24
Example: Ordered Pairs 0:33
Inverse of a Function 2:15
Procedure to Construct an Inverse Function 4:28
Example: Inverse Function 4:58
Example: Inverse Function 2 7:31
Inverses and Compositions 8:41
Lecture Example 1 9:59
Lecture Example 2 10:45
Square Root Functions and Inequalities 26:24
Intro 0:00
Square Root Functions 0:06
Example: Not Square Root Function 0:23
Example: Square Root Function 1:17
Graphing Square Root Functions 3:11
Square Root Inequalities 6:51
Example 7:13
Lecture Example 1 11:27
Lecture Example 2 14:05
nth Roots 24:06
Intro 0:00
Definition of the nth Root 0:13
Example 0:36
Principal nth Root 2:18
Index 3:04
Examples 3:20
Using Absolute Values 6:25
Examples 6:52
Lecture Example 1 11:26
Lecture Example 2 13:17
Intro 0:00
Example 1:37
Examples 3:24
Rationalizing Denominators 4:08
Examples 4:18
Example 8:09
Examples 11:44
Examples 13:03
Lecture Example 1 16:53
Lecture Example 2 20:11
Rational Exponents 24:36
Intro 0:00
Definition 1 0:24
nth Root 0:44
Example: Even 1:29
Definition 2 2:55
Simplifying Expressions 3:20
Examples 3:40
Simplified Form 7:07
Example 7:32
Lecture Example 1 8:18
Lecture Example 2 10:20
Solving Radical Equations and Inequalities 38:46
Intro 0:00
Examples 0:34
Extraneous Roots 12:29
Eliminating nth Roots 14:28
Examples 14:54
Example 17:18
Lecture Example 1 20:28
Lecture Example 2 22:57

## Section 8: Radical Expressions and Equations

Multiplying and Dividing Rational Expressions 30:11
Intro 0:00
Simplifying Rational Expressions 0:12
Examples: Rational Expressions 0:31
Factoring -1 3:26
Example 3:33
Multiplying and Dividing Rational Expressions 4:50
Multiplying 5:08
Dividing 5:16
Example 6:10
Factoring 9:13
Example 9:33
Complex Fractions 13:15
Example 13:27
Lecture Example 1 15:36
Lecture Example 2 18:25
Adding and Subtracting Rational Exprsesions 51:53
Intro 0:00
Example: Fractions 0:22
Least Common Multiple (LCM) 1:36
Example 2:07
Least Common Denominator (LCD) 8:01
Example: Fractions 8:14
Example: Rational Expression 10:23
Equivalent Fractions 13:45
Example 14:20
Simplifying Complex Fractions 20:03
Example 20:28
Lecture Example 1 26:34
Lecture Example 2 31:06
Graphing Rational Functions 45:13
Intro 0:00
Rational Functions 0:35
Example 0:57
Breaks in Continuity 2:48
Discontinuities 3:19
Example: Excluded Values 3:52
Graphs and Discontinuities 4:36
Example: Hole Discontinuity 6:07
Example: Asymptote 8:53
Horizontal Asymptotes 13:34
Example 13:54
Lecture Example 1 17:58
Lecture Example 2 20:29
Direct, Joint, and Inverse Variation 21:49
Intro 0:00
Direct Variation 0:16
Constant of Variation 0:44
Graph of Direct Variation 1:28
Example: Straight Line 1:36
Joint Variation 2:55
Inverse Variation 4:17
Example 4:50
Graph of Inverse Variation 5:35
Example 6:00
Proportions 8:00
Example 9:28
Lecture Example 1 12:32
Lecture Example 2 14:26
Solving Rational Equations and Inequalities 53:21
Intro 0:00
Rational Equations 0:15
Example: Not Rational Equation 0:26
Example: X in Denominator 0:38
Example: LCD 1:08
Example: Rational Equations 5:19
Extraneous Solutions 12:08
Example 12:42
Rational Inequalities 15:31
Example 15:45
Example: Rational Inequalities 12:05
Lecture Example 1 32:06
Lecture Example 2 35:18

## Section 9: Exponential and Logarithmic Relations

Exponential Functions 28:22
Intro 0:00
What is an Exponential Function? 0:11
Exponent and Base 0:38
Graphing Exponential Functions 1:31
Example 1:34
Properties 4:05
Growth and Decay 9:38
Equations 10:32
Example 11:05
Inequalities 13:00
Example 14:29
Lecture Example 1 16:48
Lecture Example 2 18:50
Logarithms and Logarithmic Functions 36:31
Intro 0:00
What are Logarithms? 0:17
Examples 1:30
Logarithmic Functions 4:09
Graph of the Logarithmic Function 4:52
Properties 9:08
Inverse Property 10:47
Equations 11:44
Example 12:11
Inequalities 14:45
Equations with Logarithms on Both Sides 17:00
Example 17:18
Inequalities with Logarithms on Both Sides 19:17
Example 19:32
Lecture Example 1 20:31
Lecture Example 2 22:38
Properties of Logarithms 29:50
Intro 0:00
Product Property 0:08
Example 0:26
Quotient Property 1:06
Example 1:12
Power Rule 3:29
Example 3:33
Equations 5:43
Example 6:19
Lecture Example 1 12:19
Lecture Example 2 16:13
Common Logarithms 27:10
Intro 0:00
What are Common Logarithms? 0:54
Base 10 0:58
Equations 2:00
Examples 2:22
Inequalities 5:35
Example 5:42
Change of Base 9:23
Example 10:09
Lecture Example 1 12:04
Lecture Example 2 15:16
Base 'e' and Natural Logarithms 19:52
Intro 0:00
The Number 'e' 0:32
Natural Base 0:44
Euler 1:12
Natural Exponential Function 1:38
Natural Log Function 2:44
Growth and Decay 2:55
Natural Logarithms 3:16
Graph (Inverse) 3:34
Equations and Inequalities 4:49
Lecture Example 1 7:21
Lecture Example 2 9:10
Exponential Growth and Decay 28:10
Intro 0:00
Decay 0:15
Fixed Percentage 0:24
Rate of Decay 2:35
Scientific Model of Decay (Exponential Decay) 4:17
Graph 5:19
Growth 6:19
Rate of Growth 6:36
Scientific Model of Growth (Exponential Growth) 6:41
Graph 6:48
Lecture Example 1 7:48
Lecture Example 2

## Section 10: Conic Sections

Midpoint and Distance Formulas 29:35
Intro 0:00
Midpoint Formula 0:35
Distance Formula 1:42
Example 2:52
Lecture Example 1 3:40
Lecture Example 2 6:37
Parabolas 26:11
Intro 0:00
What is a Parabola? 0:21
Focus and Directrix 0:33
Axis of Symmetry 1:41
Vertex 2:03
Example 2:15
Standard Form 3:11
Upward and Downward 4:07
Graphing Parabolas 5:24
Example 6:32
Latus Rectum 7:37
Horizontal Parabolas 9:10
Focus and Direction 12:31
Lecture Example 1 13:11
Lecture Example 2 16:46
Circles 17:33
Intro 0:00
What are Circles 0:17
Equation (Standard Form) 0:46
Graphing 1:21
Center Not at Origin 1:53
Example 2:06
Lecture Example 1 4:16
Lecture Example 2 8:22
Ellipses 38:57
Intro 0:00
What are Ellipses? 0:59
Foci 1:04
Properties 3:47
Major Axis, Minor Axis 4:03
Standard Form 7:22
Example 8:05
Vertical Major Axis 10:12
Example 10:40
Graphing Ellipses 13:33
Example: Completing the Square 14:04
Equation with Center at (h,k) 17:25
Example 17:53
Lecture Example 1 19:36
Lecture Example 2 23:52
Hyperbolas 37:59
Intro 0:00
What are Hyperbolas? 1:09
Properties 2:35
Transverse Axis, Conjugate Axis 2:57
Center, Vertices 3:54
Standard Form 4:33
Vertical Transverse Axis 6:35
Asymptotes 10:17
Graphing Hyperbolas 13:44
Example 17:23
Equation with Center at (h,k) 18:20
Lecture Example 1 20:19
Lecture Example 2 23:25
Conic Sections 23:10
Intro 0:00
What are Conic Sections? 2:16
Standard Form 2:58
Example 5:29
Identifying Conic Sections 6:14
Example 6:55
Lecture Example 1 8:55
Lecture Example 2 11:18
Intro 0:00
Example 0:28
Solutions 3:13
Example: Elimination 3:45
Solutions 7:34
Example 8:07
Lecture Example 1 11:10
Lecture Example 2 16:12

## Section 11: Sequences and Series

Arithmetic Sequences 27:44
Intro 0:00
Sequences 0:27
Example: Term 0:36
Arithmetic Sequence 2:13
Common Difference 2:22
Example 2:35
Formula for nth Term 3:39
Example 4:29
Equation for nth Term 5:58
Example 6:10
Arithmetic Means 7:40
Example 8:13
Lecture Example 1 14:08
Lecture Example 2 15:35
Arithmetic Series 29:12
Intro 0:00
What are Arithmetic Series? 0:22
Example: Sequence 0:29
Example: Common Difference (d) 0:35
Sum of Arithmetic Series 2:52
Example 3:44
Sigma Notation 6:10
Example 6:48
Lecture Example 1 8:32
Lecture Example 2 12:39
Geometric Sequences 24:52
Intro 0:00
What are Geometric Sequences? 0:20
Common Ratio 1:03
Example 1:20
nth Term of a Geometric Sequence 3:39
Geometric Means 4:16
Example: Missing Term 5:06
Lecture Example 1 8:09
Lecture Example 2 11:42
Geometric Series 27:02
Intro 0:00
What are Geometric Series? 0:20
Example: Common Ratio 1:00
Sum of Geometric Series 2:27
Example 4:01
Sigma Notation 4:56
Example: Index 5:24
Example 6:20
Another Sum Formula 7:51
Specific Terms 9:19
Lecture Example 1 11:15
Lecture Example 2 14:30
Infinite Geometric Series 24:01
Intro 0:00
What are Infinite Geometric Series? 0:35
Partial Sums of the Infinite Series 1:17
Example 1:24
Sum of an Infinite Geometric Series 3:16
Convergent Series 3:25
Example 4:17
Sigma Notation 5:31
Example 5:43
Repeating Decimals 6:38
Example 6:48
Lecture Example 1 9:33
Lecture Example 2 11:20
Recursion and Special Sequences 17:11
Intro 0:00
Fibonacci Sequence 0:17
Example: Fibonacci Sequence 0:36
Example: Recursive Formula 2:38
Iteration 3:40
Example 4:57
Lecture Example 1 7:10
Lecture Example 2 9:03
Binomial Theorem 38:25
Intro 0:00
Pascal's Triangle 0:11
General Form 2:43
Properties 7:01
Binomial Theorem 9:20
Example 11:47
Finding a Specific Term 16:24
Example 16:32
Lecture Example 1 20:35
Lecture Example 2 23:30
Proof and Mathematical Induction 19:53
Intro 0:00
Math Induction Principle 0:19
Example 0:29
Counter Examples 5:00
Example 5:14
Lecture Example 1 7:16
Lecture Example 2 10:53

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