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  
 
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  
Section 2: 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  
 
OnetoOne 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  
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  
 
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  
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  
 
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  
Section 5: 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  
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  
 
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  
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  
 
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  
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  
 
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  
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  
 
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  
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  
 
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  
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  
 
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  