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INSTRUCTORSCarleen EatonGrant Fraser

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.

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I. 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 
   Additional Example 3 1:17 
   Additional Example 4 2:38 
  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 
   Additional Example 3 1:47 
   Additional Example 4 5:22 
  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 
    Addition, Subtraction, Multiplication, Division 3:32 
   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 
   Additional Example 3 4:36 
   Additional Example 4 2:09 
  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 
   Additional Example 3 1:55 
   Additional Example 4 5:32 
  Solving Inequalities 19:27
   Intro 0:00 
   Properties of Inequality 0:07 
    Addition Property 0:21 
    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 
   Additional Example 3 3:06 
   Additional Example 4 5:32 
  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 
   Additional Example 3 2:33 
   Additional Example 4 4:49 

II. Linear Relations and Functions

  Relations and Functions 38:15
   Intro 0:00 
   Coordinate Plane 0:38 
    Example: Origin and Quadrants 0:44 
   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 
   Additional Example 3 3:47 
   Additional Example 4 2:03 
  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 
   Additional Example 3 2:06 
   Additional Example 4 2:09 
  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 
   Additional Example 3 2:39 
   Additional Example 4 4:14 
  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 
   Additional Example 3 4:35 
   Additional Example 4 7:05 
  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 
   Additional Example 3 3:10 
   Additional Example 4 4:25 
  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 
   Additional Example 3 4:13 
   Additional Example 4 7:06 

III. 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 
   Additional Example 3 3:29 
   Additional Example 4 3:33 
  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 
   Additional Example 3 6:21 
   Additional Example 4 3:50 
  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 
   Additional Example 3 4:57 
   Additional Example 4 3:31 
  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 
   Additional Example 3 6:53 
   Additional Example 4 3:17 

IV. 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 
   Additional Example 3 0:18 
   Additional Example 4 1:31 
  Matrix Operations 16:40
   Intro 0:00 
   Matrix Addition 0:10 
    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 
   Additional Example 3 1:07 
   Additional Example 4 6:04 
  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 
   Additional Example 3 3:49 
   Additional Example 4 4:31 
  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 
   Additional Example 3 2:32 
   Additional Example 4 3:15 
  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 
   Additional Example 3 5:44 
   Additional Example 4 6:23 
  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 
   Additional Example 3 3:45 
   Additional Example 4 3:37 
  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 
   Additional Example 3 4:31 
   Additional Example 4 4:18 

V. Quadratic Functions and Inequalities

  Graphing Quadratic Equations 26:36
   Intro 0:00 
   Quadratic Functions 0:10 
    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 
   Additional Example 3 4:42 
   Additional Example 4 5:10 
  Solving Quadratic Equations by Graphing 19:26
   Intro 0:00 
   Quadratic Equations 0:18 
    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 
   Additional Example 3 4:21 
   Additional Example 4 4:37 
  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 
   Additional Example 3 2:20 
   Additional Example 4 5:11 
  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 
   Addition and Subtraction 9:43 
    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 
   Additional Example 3 2:10 
   Additional Example 4 6:57 
  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 
   Additional Example 3 1:27 
   Additional Example 4 2:09 
  Quadratic Formula and the Discriminant 17:44
   Intro 0:00 
   Quadratic Formula 0:37 
    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 
   Additional Example 3 2:11 
   Additional Example 4 2:27 
  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 
   Additional Example 3 3:38 
   Additional Example 4 4:40 
  Graphing and Solving Quadratic Inequalities 34:38
   Intro 0:00 
   Graphing Quadratic Inequalities 1:14 
    Example: Linear Inequality 1:29 
    Example: Quadratic Inequality 3:11 
   Solving Quadratic Inequalities 6:32 
    Example 6:38 
   Lecture Example 1 11:50 
   Lecture Example 2 15:09 
   Additional Example 3 5:37 
   Additional Example 4 8:07 

VI. 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 
   Additional Example 3 5:05 
   Additional Example 4 2:01 
  Operations on Polynomials 16:13
   Intro 0:00 
   Adding and Subtracting Polynomials 0:24 
    Example: Signs 0:34 
   Multiplying Polynomials 3:04 
    Example 3:12 
   Lecture Example 1 6:40 
   Lecture Example 2 7:21 
   Additional Example 3 3:06 
   Additional Example 4 3:50 
  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 
   Additional Example 3 2:08 
   Additional Example 4 6:27 
  Polynomial Functions 29:34
   Intro 0:00 
   Polynomial in One Variable 0:17 
    Degree n 0:30 
    Descending Order 0:43 
    Example: Leading Coefficient 1:04 
   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 
   Additional Example 3 3:43 
   Additional Example 4 4:27 
  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 
   Additional Example 3 6:11 
   Additional Example 4 7:28 
  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 
   Quadratic Form 6:20 
   Lecture Example 1 7:30 
   Lecture Example 2 10:43 
   Additional Example 3 2:27 
   Additional Example 4 4:06 
  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 
   Additional Example 3 1:52 
   Additional Example 4 3:06 
  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 
   Additional Example 3 4:04 
   Additional Example 4 5:04 
  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 
   Additional Example 3 3:15 
   Additional Example 4 5:17 

VII. 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 
   Additional Example 3 3:12 
   Additional Example 4 4:18 
  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 
   Additional Example 3 1:48 
   Additional Example 4 4:32 
  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 
    Example: Radicand 3:21 
   Square Root Inequalities 6:51 
    Example 7:13 
   Lecture Example 1 11:27 
   Lecture Example 2 14:05 
   Additional Example 3 3:07 
   Additional Example 4 4:36 
  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 
   Additional Example 3 3:05 
   Additional Example 4 2:54 
  Operations with Radical Expressions 34:38
   Intro 0:00 
   Properties of Radicals 0:22 
    Example 1:37 
   Simplifying Radical Expressions 2:58 
    Examples 3:24 
   Rationalizing Denominators 4:08 
    Examples 4:18 
   Conjugate Radical Expressions 8:01 
    Example 8:09 
   Adding and Subtracting Radicals 11:23 
    Examples 11:44 
   Multiplying Radicals 12:57 
    Examples 13:03 
   Lecture Example 1 16:53 
   Lecture Example 2 20:11 
   Additional Example 3 4:16 
   Additional Example 4 6:49 
  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 
   Additional Example 3 6:35 
   Additional Example 4 5:57 
  Solving Radical Equations and Inequalities 38:46
   Intro 0:00 
   Radical Equations 0:23 
    Examples 0:34 
   Example: Radical Equation 4:47 
   Extraneous Roots 12:29 
   Eliminating nth Roots 14:28 
    Examples 14:54 
   Radical Inequalities 16:38 
    Example 17:18 
   Lecture Example 1 20:28 
   Lecture Example 2 22:57 
   Additional Example 3 4:27 
   Additional Example 4 7:27 

VIII. 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 
   Additional Example 3 4:30 
   Additional Example 4 5:02 
  Adding and Subtracting Rational Exprsesions 51:53
   Intro 0:00 
    Example: Fractions 0:22 
   Least Common Multiple (LCM) 1:36 
    Example 2:07 
   Adding and Subtracting 7:56 
    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 
   Additional Example 3 7:30 
   Additional Example 4 5:46 
  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 
   Additional Example 3 9:04 
   Additional Example 4 8:38 
  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 
   Additional Example 3 2:46 
   Additional Example 4 2:32 
  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 
   Additional Example 3 6:38 
   Additional Example 4 6:35 

IX. 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 
   Additional Example 3 3:16 
   Additional Example 4 3:48 
  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 
   Additional Example 3 4:03 
   Additional Example 4 7:53 
  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 
   Additional Example 3 4:43 
   Additional Example 4 4:56 
  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 
   Additional Example 3 4:52 
   Additional Example 4 5:49 
  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 
   Additional Example 3 2:05 
   Additional Example 4 3:58 
  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  
   Additional Example 3 5:07 
   Additional Example 4 6:38 

X. 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 
   Additional Example 3 4:26 
   Additional Example 4 6:27 
  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 
   Additional Example 3 2:35 
   Additional Example 4 4:48 
  Circles 17:33
   Intro 0:00 
   What are Circles 0:17 
    Center, Radius 0:37 
   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 
   Additional Example 3 2:25 
   Additional Example 4 4:00 
  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 
   Additional Example 3 4:58 
   Additional Example 4 5:50 
  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 
   Additional Example 3 8:20 
   Additional Example 4 2:59 
  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 
   Additional Example 3 6:26 
   Additional Example 4 4:15 
  Solving Quadratic Systems 28:18
   Intro 0:00 
   Linear Quadratic Systems 0:04 
    Example 0:28 
   Solutions 3:13 
   Quadratic Quadratic System 3:36 
    Example: Elimination 3:45 
   Solutions 7:34 
   Systems of Quadratic Inequalities 7:55 
    Example 8:07 
   Lecture Example 1 11:10 
   Lecture Example 2 16:12 
   Additional Example 3 4:29 
   Additional Example 4 3:34 

XI. 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 
   Additional Example 3 3:36 
   Additional Example 4 5:01 
  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 
   Additional Example 3 4:07 
   Additional Example 4 5:01 
  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 
   Additional Example 3 2:33 
   Additional Example 4 5:18 
  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 
   Additional Example 3 4:06 
   Additional Example 4 4:37 
  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 
   Additional Example 3 2:21 
   Additional Example 4 3:21 
  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 
   Additional Example 3 3:06 
   Additional Example 4 2:52 
  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 
   Additional Example 3 5:24 
   Additional Example 4 5:29 
  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 
   Additional Example 3 5:07 
   Additional Example 4 1:31