I. Equations and Inequalities 

Expressions and Formulas 
22:23 
 
Intro 
0:00  
 
Order of Operations 
0:19  
 
 Variable 
0:27  
 
 Algebraic Expression 
0:46  
 
 Term 
0:57  
 
 Example: Algebraic Expression 
1:25  
 
 Evaluate Inside Grouping Symbols 
1:55  
 
 Evaluate Powers 
2:30  
 
 Multiply/Divide Left to Right 
2:55  
 
 Add/Subtract Left to Right 
3:35  
 
Monomials 
4:40  
 
 Examples of Monomials 
4:52  
 
 Constant 
5:27  
 
 Coefficient 
5:46  
 
 Degree 
6:25  
 
 Power 
7:15  
 
Polynomials 
8:02  
 
 Examples of Polynomials 
8:24  
 
 Binomials, Trinomials, Monomials 
8:53  
 
 Term 
9:21  
 
 Like Terms 
10:02  
 
Formulas 
11:00  
 
 Example: Pythagorean Theorem 
11:15  
 
Example 1: Evaluate the Algebraic Expression 
11:50  
 
Example 2: Evaluate the Algebraic Expression 
14:38  
 
Example 3: Area of a Triangle 
19:11  
 
Example 4: Fahrenheit to Celsius 
20:41  

Properties of Real Numbers 
20:15 
 
Intro 
0:00  
 
Real Numbers 
0:07  
 
 Number Line 
0:15  
 
 Rational Numbers 
0:46  
 
 Irrational Numbers 
2:24  
 
Venn Diagram of Real Numbers 
4:03  
 
 Irrational Numbers 
5:00  
 
 Rational Numbers 
5:19  
 
 Real Number System 
5:27  
 
 Natural Numbers 
5:32  
 
 Whole Numbers 
5:53  
 
 Integers 
6:19  
 
 Fractions 
6:46  
 
Properties of Real Numbers 
7:15  
 
 Commutative Property 
7:34  
 
 Associative Property 
8:07  
 
 Identity Property 
9:04  
 
 Inverse Property 
9:53  
 
 Distributive Property 
11:03  
 
Example 1: What Set of Numbers? 
12:21  
 
Example 2: What Properties Are Used? 
13:56  
 
Example 3: Multiplicative Inverse 
16:00  
 
Example 4: Simplify Using Properties 
17:18  

Solving Equations 
19:10 
 
Intro 
0:00  
 
Translations 
0:06  
 
 Verbal Expressions and Algebraic Expressions 
0:13  
 
 Example: Sum of Two Numbers 
0:19  
 
 Example: Square of a Number 
1:33  
 
Properties of Equality 
3:20  
 
 Reflexive Property 
3:30  
 
 Symmetric Property 
3:42  
 
 Transitive Property 
4:01  
 
 Addition Property 
5:01  
 
 Subtraction Property 
5:37  
 
 Multiplication Property 
6:02  
 
 Division Property 
6:30  
 
Solving Equations 
6:58  
 
 Example: Using Properties 
7:18  
 
Solving for a Variable 
8:25  
 
 Example: Solve for Z 
8:34  
 
Example 1: Write Algebraic Expression 
10:15  
 
Example 2: Write Verbal Expression 
11:31  
 
Example 3: Solve the Equation 
14:05  
 
Example 4: Simplify Using Properties 
17:26  

Solving Absolute Value Equations 
17:31 
 
Intro 
0:00  
 
Absolute Value Expressions 
0:09  
 
 Distance from Zero 
0:18  
 
 Example: Absolute Value Expression 
0:24  
 
Absolute Value Equations 
1:50  
 
 Example: Absolute Value Equation 
2:00  
 
 Example: Isolate Expression 
3:13  
 
No Solution 
3:46  
 
 Empty Set 
3:58  
 
 Example: No Solution 
4:12  
 
Number of Solutions 
4:46  
 
 Check Each Solution 
4:57  
 
 Example: Two Solutions 
5:05  
 
 Example: No Solution 
6:18  
 
 Example: One Solution 
6:28  
 
Example 1: Evaluate for X 
7:16  
 
Example 2: Write Verbal Expression 
9:08  
 
Example 3: Solve the Equation 
12:18  
 
Example 4: Simplify Using Properties 
13:36  

Solving Inequalities 
17:14 
 
Intro 
0:00  
 
Properties of Inequalities 
0:08  
 
 Addition Property 
0:17  
 
 Example: Using Numbers 
0:30  
 
 Subtraction Property 
1:03  
 
 Example: Using Numbers 
1:19  
 
Multiplication Properties 
1:44  
 
 C>0 (Positive Number) 
1:50  
 
 Example: Using Numbers 
2:05  
 
 C<0 (Negative Number) 
2:40  
 
 Example: Using Numbers 
3:10  
 
Division Properties 
4:11  
 
 C>0 (Positive Number) 
4:15  
 
 Example: Using Numbers 
4:27  
 
 C<0 (Negative Number) 
5:21  
 
 Example: Using Numbers 
5:32  
 
Describing the Solution Set 
6:10  
 
 Example: Set Builder Notation 
6:26  
 
 Example: Graph (Closed Circle) 
7:08  
 
 Example: Graph (Open Circle) 
7:30  
 
Example 1: Solve the Inequality 
7:58  
 
Example 2: Solve the Inequality 
9:06  
 
Example 3: Solve the Inequality 
10:10  
 
Example 4: Solve the Inequality 
13:12  

Solving Compound and Absolute Value Inequalities 
25:00 
 
Intro 
0:00  
 
Compound Inequalities 
0:08  
 
 'And' and 'Or' 
0:13  
 
 Example: And 
0:22  
 
 Example: Or 
1:12  
 
'And' Inequality 
1:41  
 
 Intersection 
1:49  
 
 Example: Numbers 
2:08  
 
 Example: Inequality 
2:43  
 
'Or' Inequality 
4:35  
 
 Example: Union 
4:45  
 
 Example: Inequality 
5:53  
 
Absolute Value Inequalities 
7:19  
 
 Definition of Absolute Value 
7:33  
 
 Examples: Compound Inequalities 
8:30  
 
 Example: Complex Inequality 
12:21  
 
Example 1: Solve the Inequality 
12:54  
 
Example 2: Solve the Inequality 
17:21  
 
Example 3: Solve the Inequality 
18:54  
 
Example 4: Solve the Inequality 
22:15  
II. Linear Relations and Functions 

Relations and Functions 
32:05 
 
Intro 
0:00  
 
Coordinate Plane 
0:20  
 
 XCoordinate and YCoordinate 
0:30  
 
 Example: Coordinate Pairs 
0:37  
 
 Quadrants 
1:20  
 
Relations 
2:14  
 
 Domain and Range 
2:19  
 
 Set of Ordered Pairs 
2:29  
 
 As a Table 
2:51  
 
Functions 
4:21  
 
 One Element in Range 
4:32  
 
 Example: Mapping 
4:43  
 
 Example: Table and Map 
6:26  
 
OnetoOne Functions 
8:01  
 
 Example: OnetoOne 
8:22  
 
 Example: Not OnetoOne 
9:18  
 
Graphs of Relations 
11:01  
 
 Discrete and Continuous 
11:12  
 
 Example: Discrete 
11:22  
 
 Example: Continuous 
12:30  
 
Vertical Line Test 
14:09  
 
 Example: S Curve 
14:29  
 
 Example: Function 
16:15  
 
Equations, Relations, and Functions 
17:03  
 
 Independent Variable and Dependent Variable 
17:16  
 
Function Notation 
19:11  
 
 Example: Function Notation 
19:23  
 
Example 1: Domain and Range 
20:51  
 
Example 2: Discrete or Continuous 
23:03  
 
Example 3: Discrete or Continuous 
25:53  
 
Example 4: Function Notation 
30:05  

Linear Equations 
14:46 
 
Intro 
0:00  
 
Linear Equations and Functions 
0:07  
 
 Linear Equation 
0:19  
 
 Example: Linear Equation 
0:29  
 
 Example: Linear Function 
1:07  
 
Standard Form 
2:02  
 
 Integer Constants with No Common Factor 
2:08  
 
 Example: Standard Form 
2:27  
 
Graphing with Intercepts 
4:05  
 
 XIntercept and YIntercept 
4:12  
 
 Example: Intercepts 
4:26  
 
 Example: Graphing 
5:14  
 
Example 1: Linear Function 
7:53  
 
Example 2: Linear Function 
9:10  
 
Example 3: Standard Form 
10:04  
 
Example 4: Graph with Intercepts 
12:25  

Slope 
23:07 
 
Intro 
0:00  
 
Definition of Slope 
0:07  
 
 Change in Y / Change in X 
0:26  
 
 Example: Slope of Graph 
0:37  
 
Interpretation of Slope 
3:07  
 
 Horizontal Line (0 Slope) 
3:13  
 
 Vertical Line (Undefined Slope) 
4:52  
 
 Rises to Right (Positive Slope) 
6:36  
 
 Falls to Right (Negative Slope) 
6:53  
 
Parallel Lines 
7:18  
 
 Example: Not Vertical 
7:30  
 
 Example: Vertical 
7:58  
 
Perpendicular Lines 
8:31  
 
 Example: Perpendicular 
8:42  
 
Example 1: Slope of Line 
10:32  
 
Example 2: Graph Line 
11:45  
 
Example 3: Parallel to Graph 
13:37  
 
Example 4: Perpendicular to Graph 
17:57  

Writing Linear Functions 
23:05 
 
Intro 
0:00  
 
Slope Intercept Form 
0:11  
 
 m and b 
0:28  
 
 Example: Graph Using Slope Intercept 
0:43  
 
Point Slope Form 
2:41  
 
 Relation to Slope Formula 
3:03  
 
 Example: Point Slope Form 
4:36  
 
Parallel and Perpendicular Lines 
6:28  
 
 Review of Parallel and Perpendicular Lines 
6:31  
 
 Example: Parallel 
7:50  
 
 Example: Perpendicular 
9:58  
 
Example 1: Slope Intercept Form 
11:07  
 
Example 2: Slope Intercept Form 
13:07  
 
Example 3: Parallel 
15:49  
 
Example 4: Perpendicular 
18:42  

Special Functions 
31:05 
 
Intro 
0:00  
 
Step Functions 
0:07  
 
 Example: Apple Prices 
0:30  
 
Absolute Value Function 
4:55  
 
 Example: Absolute Value 
5:05  
 
Piecewise Functions 
9:08  
 
 Example: Piecewise 
9:27  
 
Example 1: Absolute Value Function 
14:00  
 
Example 2: Absolute Value Function 
20:39  
 
Example 3: Piecewise Function 
22:26  
 
Example 4: Step Function 
25:25  

Graphing Inequalities 
21:42 
 
Intro 
0:00  
 
Graphing Linear Inequalities 
0:07  
 
 Shaded Region 
0:19  
 
 Using Test Points 
0:32  
 
 Graph Corresponding Linear Function 
0:46  
 
 Dashed or Solid Lines 
0:59  
 
 Use Test Point 
1:21  
 
 Example: Linear Inequality 
1:58  
 
Graphing Absolute Value Inequalities 
4:50  
 
 Graph Corresponding Equations 
4:59  
 
 Use Test Point 
5:20  
 
 Example: Absolute Value Inequality 
5:38  
 
Example 1: Linear Inequality 
9:17  
 
Example 2: Linear Inequality 
11:56  
 
Example 3: Linear Inequality 
14:29  
 
Example 4: Absolute Value Inequality 
17:06  
III. Systems of Equations and Inequalities 

Solving Systems of Equations by Graphing 
17:13 
 
Intro 
0:00  
 
Systems of Equations 
0:09  
 
 Example: Two Equations 
0:24  
 
Solving by Graphing 
0:53  
 
 Point of Intersection 
1:09  
 
Types of Systems 
2:29  
 
 Independent (Single Solution) 
2:34  
 
 Dependent (Infinite Solutions) 
3:05  
 
 Inconsistent (No Solution) 
4:23  
 
Example 1: Solve by Graphing 
5:20  
 
Example 2: Solve by Graphing 
9:10  
 
Example 3: Solve by Graphing 
12:27  
 
Example 4: Solve by Graphing 
14:54  

Solving Systems of Equations Algebraically 
23:53 
 
Intro 
0:00  
 
Solving by Substitution 
0:08  
 
 Example: System of Equations 
0:36  
 
Solving by Multiplication 
7:22  
 
 Extra Step of Multiplying 
7:38  
 
 Example: System of Equations 
8:00  
 
Inconsistent and Dependent Systems 
11:14  
 
 Variables Drop Out 
11:48  
 
 Inconsistent System (Never True) 
12:01  
 
 Constant Equals Constant 
12:53  
 
 Dependent System (Always True) 
13:11  
 
Example 1: Solve Algebraically 
13:58  
 
Example 2: Solve Algebraically 
15:52  
 
Example 3: Solve Algebraically 
17:54  
 
Example 4: Solve Algebraically 
21:40  

Solving Systems of Inequalities By Graphing 
27:12 
 
Intro 
0:00  
 
Solving by Graphing 
0:08  
 
 Graph Each Inequality 
0:25  
 
 Overlap 
0:35  
 
 Corresponding Linear Equations 
1:03  
 
 Test Point 
1:23  
 
 Example: System of Inequalities 
1:51  
 
No Solution 
7:06  
 
 Empty Set 
7:26  
 
 Example: No Solution 
7:34  
 
Example 1: Solve by Graphing 
10:27  
 
Example 2: Solve by Graphing 
13:30  
 
Example 3: Solve by Graphing 
17:19  
 
Example 4: Solve by Graphing 
23:23  

Solving Systems of Equations in Three Variables 
28:53 
 
Intro 
0:00  
 
Solving Systems in Three Variables 
0:17  
 
 Triple of Values 
0:31  
 
 Example: Three Variables 
0:56  
 
Number of Solutions 
5:55  
 
 One Solution 
6:08  
 
 No Solution 
6:24  
 
 Infinite Solutions 
7:06  
 
Example 1: Solve 3 Variables 
7:59  
 
Example 2: Solve 3 Variables 
13:50  
 
Example 3: Solve 3 Variables 
19:54  
 
Example 4: Solve 3 Variables 
25:50  
IV. Matrices 

Basic Matrix Concepts 
11:34 
 
Intro 
0:00  
 
What is a Matrix 
0:26  
 
 Brackets 
0:46  
 
 Designation 
1:21  
 
 Element 
1:47  
 
 Matrix Equations 
1:59  
 
Dimensions 
2:27  
 
 Rows (m) and Columns (n) 
2:37  
 
 Examples: Dimensions 
2:43  
 
Special Matrices 
4:22  
 
 Row Matrix 
4:32  
 
 Column Matrix 
5:00  
 
 Zero Matrix 
6:00  
 
Equal Matrices 
6:30  
 
 Example: Corresponding Elements 
6:36  
 
Example 1: Matrix Dimension 
8:12  
 
Example 2: Matrix Dimension 
9:03  
 
Example 3: Zero Matrix 
9:38  
 
Example 4: Row and Column Matrix 
10:26  

Matrix Operations 
21:36 
 
Intro 
0:00  
 
Matrix Addition 
0:18  
 
 Same Dimensions 
0:25  
 
 Example: Adding Matrices 
1:04  
 
Matrix Subtraction 
3:42  
 
 Same Dimensions 
3:48  
 
 Example: Subtracting Matrices 
4:04  
 
Scalar Multiplication 
6:08  
 
 Scalar Constant 
6:24  
 
 Example: Multiplying Matrices 
6:32  
 
Properties of Matrix Operations 
8:23  
 
 Commutative Property 
8:41  
 
 Associative Property 
9:08  
 
 Distributive Property 
9:44  
 
Example 1: Matrix Addition 
10:24  
 
Example 2: Matrix Subtraction 
11:58  
 
Example 3: Scalar Multiplication 
14:23  
 
Example 4: Matrix Properties 
16:09  

Matrix Multiplication 
29:36 
 
Intro 
0:00  
 
Dimension Requirement 
0:17  
 
 n = p 
0:24  
 
 Resulting Product Matrix (m x q) 
1:21  
 
 Example: Multiplication 
1:54  
 
Matrix Multiplication 
3:38  
 
 Example: Matrix Multiplication 
4:07  
 
Properties of Matrix Multiplication 
10:46  
 
 Associative Property 
11:00  
 
 Associative Property (Scalar) 
11:28  
 
 Distributive Property 
12:06  
 
 Distributive Property (Scalar) 
12:30  
 
Example 1: Possible Matrices 
13:31  
 
Example 2: Multiplying Matrices 
17:08  
 
Example 3: Multiplying Matrices 
20:41  
 
Example 4: Matrix Properties 
24:41  

Determinants 
33:13 
 
Intro 
0:00  
 
What is a Determinant 
0:13  
 
 Square Matrices 
0:23  
 
 Vertical Bars 
0:41  
 
Determinant of a 2x2 Matrix 
1:21  
 
 Second Order Determinant 
1:37  
 
 Formula 
1:45  
 
 Example: 2x2 Determinant 
1:58  
 
Determinant of a 3x3 Matrix 
2:50  
 
 Expansion by Minors 
3:08  
 
 Third Order Determinant 
3:19  
 
 Expanding Row One 
4:06  
 
 Example: 3x3 Determinant 
6:40  
 
Diagonal Method for 3x3 Matrices 
13:24  
 
 Example: Diagonal Method 
13:36  
 
Example 1: Determinant of 2x2 
18:59  
 
Example 2: Determinant of 3x3 
20:03  
 
Example 3: Determinant of 3x3 
25:35  
 
Example 4: Determinant of 3x3 
29:22  

Cramer's Rule 
28:25 
 
Intro 
0:00  
 
System of Two Equations in Two Variables 
0:16  
 
 One Variable 
0:50  
 
 Determinant of Denominator 
1:14  
 
 Determinants of Numerators 
2:23  
 
 Example: System of Equations 
3:34  
 
System of Three Equations in Three Variables 
7:06  
 
 Determinant of Denominator 
7:17  
 
 Determinants of Numerators 
7:52  
 
Example 1: Two Equations 
8:57  
 
Example 2: Two Equations 
13:21  
 
Example 3: Three Equations 
17:11  
 
Example 4: Three Equations 
23:43  

Identity and Inverse Matrices 
22:25 
 
Intro 
0:00  
 
Identity Matrix 
0:13  
 
 Example: 2x2 Identity Matrix 
0:30  
 
 Example: 4x4 Identity Matrix 
0:50  
 
 Properties of Identity Matrices 
1:24  
 
 Example: Multiplying Identity Matrix 
2:52  
 
Matrix Inverses 
5:30  
 
 Writing Matrix Inverse 
6:07  
 
Inverse of a 2x2 Matrix 
6:39  
 
 Example: 2x2 Matrix 
7:31  
 
Example 1: Inverse Matrix 
10:18  
 
Example 2: Find the Inverse Matrix 
13:04  
 
Example 3: Find the Inverse Matrix 
17:53  
 
Example 4: Find the Inverse Matrix 
20:44  

Solving Systems of Equations Using Matrices 
22:32 
 
Intro 
0:00  
 
Matrix Equations 
0:11  
 
 Example: System of Equations 
0:21  
 
Solving Systems of Equations 
4:01  
 
 Isolate x 
4:16  
 
 Example: Using Numbers 
5:10  
 
 Multiplicative Inverse 
5:54  
 
Example 1: Write as Matrix Equation 
7:18  
 
Example 2: Use Matrix Equations 
9:12  
 
Example 3: Use Matrix Equations 
15:06  
 
Example 4: Use Matrix Equations 
19:35  
V. Quadratic Functions and Inequalities 

Graphing Quadratic Functions 
31:48 
 
Intro 
0:00  
 
Quadratic Functions 
0:12  
 
 A is Zero 
0:27  
 
 Example: Parabola 
0:45  
 
Properties of Parabolas 
2:08  
 
 Axis of Symmetry 
2:11  
 
 Vertex 
2:32  
 
 Example: Parabola 
2:48  
 
Minimum and Maximum Values 
9:02  
 
 Positive or Negative 
9:28  
 
 Upward or Downward 
9:58  
 
 Example: Minimum 
10:31  
 
 Example: Maximum 
11:16  
 
Example 1: Axis of Symmetry, Vertex, Graph 
12:41  
 
Example 2: Axis of Symmetry, Vertex, Graph 
17:25  
 
Example 3: Minimum or Maximum 
21:47  
 
Example 4: Minimum or Maximum 
27:09  

Solving Quadratic Equations by Graphing 
27:03 
 
Intro 
0:00  
 
Quadratic Equations 
0:16  
 
 Standard Form 
0:18  
 
 Example: Quadratic Equation 
0:47  
 
Solving by Graphing 
1:41  
 
 Roots (xIntercepts) 
1:48  
 
 Example: Number of Solutions 
2:12  
 
Estimating Solutions 
9:23  
 
 Example: Integer Solutions 
9:30  
 
 Example: Estimating 
9:53  
 
Example 1: Solve by Graphing 
10:52  
 
Example 2: Solve by Graphing 
15:10  
 
Example 1: Solve by Graphing 
17:50  
 
Example 1: Solve by Graphing 
20:54  

Solving Quadratic Equations by Factoring 
19:53 
 
Intro 
0:00  
 
Factoring Techniques 
0:15  
 
 Greatest Common Factor (GCF) 
0:37  
 
 Difference of Two Squares 
1:48  
 
 Perfect Square Trinomials 
2:30  
 
 General Trinomials 
3:09  
 
Zero Product Rule 
5:22  
 
 Example: Zero Product 
5:53  
 
Example 1: Solve by Factoring 
7:46  
 
Example 1: Solve by Factoring 
9:48  
 
Example 1: Solve by Factoring 
12:34  
 
Example 1: Solve by Factoring 
15:28  

Imaginary and Complex Numbers 
35:45 
 
Intro 
0:00  
 
Properties of Square Roots 
0:10  
 
 Product Property 
0:26  
 
 Example: Product Property 
0:56  
 
 Quotient Property 
2:17  
 
 Example: Quotient Property 
2:35  
 
Imaginary Numbers 
3:12  
 
 Imaginary 'i' 
3:51  
 
 Examples: Imaginary Number 
4:22  
 
Complex Numbers 
7:23  
 
 Real Part and Imaginary Part 
7:33  
 
 Examples: Complex Numbers 
7:57  
 
Equality 
9:37  
 
 Example: Equal Complex Numbers 
9:52  
 
Addition and Subtraction 
10:12  
 
 Examples: Adding Complex Numbers 
10:25  
 
Complex Plane 
13:32  
 
 Horizontal Axis (Real) 
13:49  
 
 Vertical Axis (Imaginary) 
13:59  
 
 Example: Labeling 
14:11  
 
Multiplication 
15:57  
 
 Example: FOIL Method 
16:03  
 
Division 
18:37  
 
 Complex Conjugates 
18:45  
 
 Conjugate Pairs 
19:10  
 
 Example: Dividing Complex Numbers 
20:00  
 
Example 1: Simplify Complex Number 
24:50  
 
Example 2: Simplify Complex Number 
27:56  
 
Example 3: Multiply Complex Numbers 
29:27  
 
Example 3: Dividing Complex Numbers 
31:48  

Completing the Square 
27:11 
 
Intro 
0:00  
 
Square Root Property 
0:12  
 
 Example: Perfect Square 
0:38  
 
 Example: Perfect Square Trinomial 
3:00  
 
Completing the Square 
4:39  
 
 Constant Term 
4:50  
 
 Example: Complete the Square 
5:04  
 
Solve Equations 
6:42  
 
 Add to Both Sides 
6:59  
 
 Example: Complete the Square 
7:07  
 
Equations Where 'a' Not Equal to 1 
10:58  
 
 Divide by Coefficient 
11:08  
 
 Example: Complete the Square 
11:24  
 
Complex Solutions 
14:05  
 
 Real and Imaginary 
14:14  
 
 Example: Complex Solution 
14:35  
 
Example 1: Square Root Property 
18:31  
 
Example 2: Complete the Square 
19:15  
 
Example 3: Complete the Square 
20:40  
 
Example 4: Complete the Square 
23:56  

Quadratic Formula and the Discriminant 
22:48 
 
Intro 
0:00  
 
Quadratic Formula 
0:21  
 
 Standard Form 
0:29  
 
 Example: Quadratic Formula 
0:57  
 
One Rational Root 
3:00  
 
 Example: One Root 
3:31  
 
Complex Solutions 
6:16  
 
 Complex Conjugate 
6:28  
 
 Example: Complex Solution 
7:15  
 
Discriminant 
9:42  
 
 Positive Discriminant 
10:03  
 
 Perfect Square (Rational) 
10:51  
 
 Not Perfect Square (2 Irrational) 
11:27  
 
 Negative Discriminant 
12:28  
 
 Zero Discriminant 
12:57  
 
Example 1: Quadratic Formula 
13:50  
 
Example 2: Quadratic Formula 
16:03  
 
Example 3: Quadratic Formula 
19:00  
 
Example 4: Discriminant 
21:33  

Analyzing the Graphs of Quadratic Functions 
30:07 
 
Intro 
0:00  
 
Vertex Form 
0:12  
 
 H and K 
0:32  
 
 Axis of Symmetry 
0:36  
 
 Vertex 
0:42  
 
 Example: Origin 
1:00  
 
 Example: k = 2 
2:12  
 
 Example: h = 1 
4:27  
 
Significance of Coefficient 'a' 
7:13  
 
 Example: a > 1 
7:25  
 
 Example: a < 1 
8:18  
 
 Example: a > 0 
8:51  
 
 Example: a < 0 
9:05  
 
Writing Quadratic Equations in Vertex Form 
10:22  
 
 Standard Form to Vertex Form 
10:35  
 
 Example: Standard Form 
11:02  
 
 Example: 'a' Term Not 1 
14:42  
 
Example 1: Vertex Form 
19:47  
 
Example 2: Vertex Form 
22:09  
 
Example 3: Vertex Form 
24:32  
 
Example 4: Vertex Form 
28:23  

Graphing and Solving Quadratic Inequalities 
27:05 
 
Intro 
0:00  
 
Graphing Quadratic Inequalities 
0:11  
 
 Test Point 
0:18  
 
 Example: Quadratic Inequality 
0:29  
 
Solving Quadratic Inequalities 
3:57  
 
 Example: Parameter 
4:24  
 
Example 1: Graph Inequality 
11:16  
 
Example 2: Solve Inequality 
14:27  
 
Example 3: Graph Inequality 
19:14  
 
Example 4: Solve Inequality 
23:48  
VI. Polynomial Functions 

Properties of Exponents 
19:29 
 
Intro 
0:00  
 
Simplifying Exponential Expressions 
0:09  
 
 Monomial Simplest Form 
0:19  
 
Negative Exponents 
1:07  
 
 Examples: Simple 
1:34  
 
Properties of Exponents 
3:06  
 
 Negative Exponents 
3:13  
 
 Multiplying Same Base 
3:24  
 
 Dividing Same Base 
3:45  
 
 Raising Power to a Power 
4:33  
 
 Parentheses (Multiplying) 
5:11  
 
 Parentheses (Dividing) 
5:47  
 
 Raising to 0th Power 
6:15  
 
Example 1: Simplify Exponents 
7:59  
 
Example 2: Simplify Exponents 
10:41  
 
Example 3: Simplify Exponents 
14:11  
 
Example 4: Simplify Exponents 
18:04  

Operations on Polynomials 
13:27 
 
Intro 
0:00  
 
Adding and Subtracting Polynomials 
0:13  
 
 Like Terms and Like Monomials 
0:23  
 
 Examples: Adding Monomials 
1:14  
 
Multiplying Polynomials 
3:40  
 
 Distributive Property 
3:44  
 
 Example: Monomial by Polynomial 
4:06  
 
Example 1: Simplify Polynomials 
5:47  
 
Example 2: Simplify Polynomials 
6:28  
 
Example 3: Simplify Polynomials 
8:38  
 
Example 4: Simplify Polynomials 
10:47  

Dividing Polynomials 
31:11 
 
Intro 
0:00  
 
Dividing by a Monomial 
0:13  
 
 Example: Numbers 
0:26  
 
 Example: Polynomial by a Monomial 
1:18  
 
Long Division 
2:28  
 
 Remainder Term 
2:41  
 
 Example: Dividing with Numbers 
3:04  
 
 Example: With Polynomials 
5:01  
 
 Example: Missing Terms 
7:58  
 
Synthetic Division 
11:44  
 
 Restriction 
12:04  
 
 Example: Divisor in Form 
12:20  
 
Divisor in Synthetic Division 
15:54  
 
 Example: Coefficient to 1 
16:07  
 
Example 1: Divide Polynomials 
17:10  
 
Example 2: Divide Polynomials 
19:08  
 
Example 3: Synthetic Division 
21:42  
 
Example 4: Synthetic Division 
25:09  

Polynomial Functions 
22:30 
 
Intro 
0:00  
 
Polynomial in One Variable 
0:13  
 
 Leading Coefficient 
0:27  
 
 Example: Polynomial 
1:18  
 
 Degree 
1:31  
 
Polynomial Functions 
2:57  
 
 Example: Function 
3:13  
 
Function Values 
3:33  
 
 Example: Numerical Values 
3:53  
 
 Example: Algebraic Expressions 
5:11  
 
Zeros of Polynomial Functions 
5:50  
 
 Odd Degree 
6:04  
 
 Even Degree 
7:29  
 
End Behavior 
8:28  
 
 Even Degrees 
9:09  
 
 Example: Leading Coefficient +/ 
9:23  
 
 Odd Degrees 
12:51  
 
 Example: Leading Coefficient +/ 
13:00  
 
Example 1: Degree and Leading Coefficient 
15:03  
 
Example 2: Polynomial Function 
15:56  
 
Example 3: Polynomial Function 
17:34  
 
Example 4: End Behavior 
19:53  

Analyzing Graphs of Polynomial Functions 
33:29 
 
Intro 
0:00  
 
Graphing Polynomial Functions 
0:11  
 
 Example: Table and End Behavior 
0:39  
 
Location Principle 
4:43  
 
 Zero Between Two Points 
5:03  
 
 Example: Location Principle 
5:21  
 
Maximum and Minimum Points 
8:40  
 
 Relative Maximum and Relative Minimum 
9:16  
 
 Example: Number of Relative Max/Min 
11:11  
 
Example 1: Graph Polynomial Function 
11:57  
 
Example 2: Graph Polynomial Function 
16:19  
 
Example 3: Graph Polynomial Function 
23:27  
 
Example 4: Graph Polynomial Function 
28:35  

Solving Polynomial Functions 
21:10 
 
Intro 
0:00  
 
Factoring Polynomials 
0:06  
 
 Greatest Common Factor (GCF) 
0:25  
 
 Difference of Two Squares 
1:14  
 
 Perfect Square Trinomials 
2:07  
 
 General Trinomials 
2:57  
 
 Grouping 
4:32  
 
Sum and Difference of Two Cubes 
6:03  
 
 Examples: Two Cubes 
6:14  
 
Quadratic Form 
8:22  
 
 Example: Quadratic Form 
8:44  
 
Example 1: Factor Polynomial 
12:03  
 
Example 2: Factor Polynomial 
13:54  
 
Example 3: Quadratic Form 
15:33  
 
Example 4: Solve Polynomial Function 
17:24  

Remainder and Factor Theorems 
31:21 
 
Intro 
0:00  
 
Remainder Theorem 
0:07  
 
 Checking Work 
0:22  
 
 Dividend and Divisor in Theorem 
1:12  
 
 Example: f(a) 
2:05  
 
Synthetic Substitution 
5:43  
 
 Example: Polynomial Function 
6:15  
 
Factor Theorem 
9:54  
 
 Example: Numbers 
10:16  
 
 Example: Confirm Factor 
11:27  
 
Factoring Polynomials 
14:48  
 
 Example: 3rd Degree Polynomial 
15:07  
 
Example 1: Remainder Theorem 
19:17  
 
Example 2: Other Factors 
21:57  
 
Example 3: Remainder Theorem 
25:52  
 
Example 4: Other Factors 
28:21  

Roots and Zeros 
31:27 
 
Intro 
0:00  
 
Number of Roots 
0:08  
 
 Not Nature of Roots 
0:18  
 
 Example: Real and Complex Roots 
0:25  
 
Descartes' Rule of Signs 
2:05  
 
 Positive Real Roots 
2:21  
 
 Example: Positive 
2:39  
 
 Negative Real Roots 
5:44  
 
 Example: Negative 
6:06  
 
Finding the Roots 
9:59  
 
 Example: Combination of Real and Complex 
10:07  
 
Conjugate Roots 
13:18  
 
 Example: Conjugate Roots 
13:50  
 
Example 1: Solve Polynomial 
16:03  
 
Example 2: Solve Polynomial 
18:36  
 
Example 3: Possible Combinations 
23:13  
 
Example 4: Possible Combinations 
27:11  

Rational Zero Theorem 
31:16 
 
Intro 
0:00  
 
Equation 
0:08  
 
 List of Possibilities 
0:16  
 
 Equation with Constant and Leading Coefficient 
1:04  
 
 Example: Rational Zero 
2:46  
 
Leading Coefficient Equal to One 
7:19  
 
 Equation with Leading Coefficient of One 
7:34  
 
 Example: Coefficient Equal to 1 
8:45  
 
Finding Rational Zeros 
12:58  
 
 Division with Remainder Zero 
13:32  
 
Example 1: Possible Rational Zeros 
14:20  
 
Example 2: Possible Rational Zeros 
16:02  
 
Example 3: Possible Rational Zeros 
19:58  
 
Example 4: Find All Zeros 
22:06  
VII. Radical Expressions and Inequalities 

Operations on Functions 
34:30 
 
Intro 
0:00  
 
Arithmetic Operations 
0:07  
 
 Domain 
0:16  
 
 Intersection 
0:24  
 
 Denominator is Zero 
0:49  
 
 Example: Operations 
1:02  
 
Composition of Functions 
7:18  
 
 Notation 
7:48  
 
 Right to Left 
8:18  
 
 Example: Composition 
8:48  
 
Composition is Not Commutative 
17:23  
 
 Example: Not Commutative 
17:51  
 
Example 1: Function Operations 
20:55  
 
Example 2: Function Operations 
24:34  
 
Example 3: Compositions 
27:51  
 
Example 4: Function Operations 
31:09  

Inverse Functions and Relations 
22:42 
 
Intro 
0:00  
 
Inverse of a Relation 
0:14  
 
 Example: Ordered Pairs 
0:56  
 
Inverse of a Function 
3:24  
 
 Domain and Range Switched 
3:52  
 
 Example: Inverse 
4:28  
 
Procedure to Construct an Inverse Function 
6:42  
 
 f(x) to y 
6:42  
 
 Interchange x and y 
6:59  
 
 Solve for y 
7:06  
 
 Write Inverse f(x) for y 
7:14  
 
 Example: Inverse Function 
7:25  
 
 Example: Inverse Function 2 
8:48  
 
Inverses and Compositions 
10:44  
 
 Example: Inverse Composition 
11:46  
 
Example 1: Inverse Relation 
14:49  
 
Example 2: Inverse of Function 
15:40  
 
Example 3: Inverse of Function 
17:06  
 
Example 4: Inverse Functions 
18:55  

Square Root Functions and Inequalities 
30:04 
 
Intro 
0:00  
 
Square Root Functions 
0:07  
 
 Examples: Square Root Function 
0:16  
 
 Example: Not Square Root Function 
0:46  
 
 Radicand 
1:12  
 
 Example: Restriction 
1:31  
 
Graphing Square Root Functions 
3:42  
 
 Example: Graphing 
3:49  
 
Square Root Inequalities 
8:47  
 
 Same Technique 
9:00  
 
 Example: Square Root Inequality 
9:20  
 
Example 1: Graph Square Root Function 
15:19  
 
Example 2: Graph Square Root Function 
18:03  
 
Example 3: Graph Square Root Function 
22:41  
 
Example 4: Square Root Inequalities 
25:37  

nth Roots 
20:46 
 
Intro 
0:00  
 
Definition of the nth Root 
0:07  
 
 Example: 5th Root 
0:20  
 
 Example: 6th Root 
0:51  
 
Principal nth Root 
1:39  
 
 Example: Principal Roots 
2:06  
 
Using Absolute Values 
5:58  
 
 Example: Square Root 
6:18  
 
 Example: 6th Root 
8:40  
 
 Example: Negative 
10:15  
 
Example 1: Simplify Radicals 
12:23  
 
Example 2: Simplify Radicals 
13:29  
 
Example 3: Simplify Radicals 
16:07  
 
Example 4: Simplify Radicals 
18:18  

Operations with Radical Expressions 
41:11 
 
Intro 
0:00  
 
Properties of Radicals 
0:16  
 
 Quotient Property 
0:29  
 
 Example: Quotient 
1:00  
 
 Example: Product Property 
1:47  
 
Simplifying Radical Expressions 
3:24  
 
 Radicand No nth Powers 
3:47  
 
 Radicand No Fractions 
6:33  
 
 No Radicals in Denominator 
7:16  
 
Rationalizing Denominators 
8:27  
 
 Example: Radicand nth Power 
9:05  
 
Conjugate Radical Expressions 
11:47  
 
 Conjugates 
12:07  
 
 Example: Conjugate Radical Expression 
13:11  
 
Adding and Subtracting Radicals 
16:12  
 
 Same Index, Same Radicand 
16:20  
 
 Example: Like Radicals 
16:28  
 
Multiplying Radicals 
19:04  
 
 Distributive Property 
19:10  
 
 Example: Multiplying Radicals 
19:20  
 
Example 1: Simplify Radical 
24:11  
 
Example 2: Simplify Radicals 
28:43  
 
Example 3: Simplify Radicals 
32:00  
 
Example 4: Simplify Radical 
36:34  

Rational Exponents 
30:45 
 
Intro 
0:00  
 
Definition 1 
0:20  
 
 Example: Using Numbers 
0:39  
 
 Example: NonNegative 
2:46  
 
 Example: Odd 
3:34  
 
Definition 2 
4:32  
 
 Restriction 
4:52  
 
 Example: Relate to Definition 1 
5:04  
 
 Example: m Not 1 
5:31  
 
Simplifying Expressions 
7:53  
 
 Multiplication 
8:31  
 
 Division 
9:29  
 
 Multiply Exponents 
10:08  
 
 Raised Power 
11:05  
 
 Zero Power 
11:29  
 
 Negative Power 
11:49  
 
Simplified Form 
13:52  
 
 Complex Fraction 
14:16  
 
 Negative Exponents 
14:40  
 
 Example: More Complicated 
15:14  
 
Example 1: Write as Radical 
19:03  
 
Example 2: Write with Rational Exponents 
20:40  
 
Example 3: Complex Fraction 
22:09  
 
Example 4: Complex Fraction 
26:22  

Solving Radical Equations and Inequalities 
31:27 
 
Intro 
0:00  
 
Radical Equations 
0:11  
 
 Variables in Radicands 
0:22  
 
 Example: Radical Equation 
1:06  
 
 Example: Complex Equation 
2:42  
 
Extraneous Roots 
7:21  
 
 Squaring Technique 
7:35  
 
 Double Check 
7:44  
 
 Example: Extraneous 
8:21  
 
Eliminating nth Roots 
10:04  
 
 Isolate and Raise Power 
10:14  
 
 Example: nth Root 
10:27  
 
Radical Inequalities 
11:27  
 
 Restriction: Index is Even 
11:53  
 
 Example: Radical Inequality 
12:29  
 
Example 1: Solve Radical Equation 
15:41  
 
Example 2: Solve Radical Equation 
17:44  
 
Example 3: Solve Radical Inequality 
20:24  
 
Example 4: Solve Radical Equation 
24:34  
VIII. Rational Equations and Inequalities 

Multiplying and Dividing Rational Expressions 
40:54 
 
Intro 
0:00  
 
Simplifying Rational Expressions 
0:22  
 
 Algebraic Fraction 
0:29  
 
 Examples: Rational Expressions 
0:49  
 
 Example: GCF 
1:33  
 
 Example: Simplify Rational Expression 
2:26  
 
Factoring 1 
4:04  
 
 Example: Simplify with 1 
4:19  
 
Multiplying and Dividing Rational Expressions 
6:59  
 
 Multiplying and Dividing 
7:28  
 
 Example: Multiplying Rational Expressions 
8:36  
 
 Example: Dividing Rational Expressions 
11:20  
 
Factoring 
14:01  
 
 Factoring Polynomials 
14:19  
 
 Example: Factoring 
14:35  
 
Complex Fractions 
18:22  
 
 Example: Numbers 
18:37  
 
 Example: Algebraic Complex Fractions 
19:25  
 
Example 1: Simplify Rational Expression 
25:56  
 
Example 2: Simplify Rational Expression 
29:34  
 
Example 3: Simplify Rational Expression 
31:39  
 
Example 4: Simplify Rational Expression 
37:50  

Adding and Subtracting Rational Expressions 
55:04 
 
Intro 
0:00  
 
Least Common Multiple (LCM) 
0:27  
 
 Examples: LCM of Numbers 
0:43  
 
 Example: LCM of Polynomials 
4:02  
 
Adding and Subtracting 
7:55  
 
 Least Common Denominator (LCD) 
8:07  
 
 Example: Numbers 
8:17  
 
 Example: Rational Expressions 
11:03  
 
 Equivalent Fractions 
15:22  
 
Simplifying Complex Fractions 
21:19  
 
 Example: Previous Lessons 
21:36  
 
 Example: More Complex 
22:53  
 
Example 1: Find LCM 
28:30  
 
Example 2: Add Rational Expressions 
31:44  
 
Example 3: Subtract Rational Expressions 
39:18  
 
Example 4: Simplify Rational Expression 
38:26  

Graphing Rational Functions 
57:13 
 
Intro 
0:00  
 
Rational Functions 
0:18  
 
 Restriction 
0:34  
 
 Example: Rational Function 
0:51  
 
Breaks in Continuity 
2:52  
 
 Example: Continuous Function 
3:10  
 
 Discontinuities 
3:30  
 
 Example: Excluded Values 
4:37  
 
Graphs and Discontinuities 
5:02  
 
 Common Binomial Factor (Hole) 
5:08  
 
 Example: Common Factor 
5:31  
 
 Asymptote 
10:06  
 
 Example: Vertical Asymptote 
11:08  
 
Horizontal Asymptotes 
20:00  
 
 Example: Horizontal Asymptote 
20:25  
 
Example 1: Holes and Vertical Asymptotes 
26:12  
 
Example 2: Graph Rational Faction 
28:35  
 
Example 3: Graph Rational Faction 
39:23  
 
Example 4: Graph Rational Faction 
47:28  

Direct, Joint, and Inverse Variation 
20:21 
 
Intro 
0:00  
 
Direct Variation 
0:07  
 
 Constant of Variation 
0:25  
 
Graph of Constant Variation 
1:26  
 
 Slope is Constant k 
1:35  
 
 Example: Straight Lines 
1:41  
 
Joint Variation 
2:48  
 
 Three Variables 
2:52  
 
Inverse Variation 
3:38  
 
 Rewritten Form 
3:52  
 
 Examples in Biology 
4:22  
 
Graph of Inverse Variation 
4:51  
 
 Asymptotes are Axes 
5:12  
 
 Example: Inverse Variation 
5:40  
 
Proportions 
10:11  
 
 Direct Variation 
10:25  
 
 Inverse Variation 
11:32  
 
Example 1: Type of Variation 
12:42  
 
Example 2: Direct Variation 
14:13  
 
Example 3: Joint Variation 
16:24  
 
Example 4: Graph Rational Faction 
18:50  

Solving Rational Equations and Inequalities 
55:14 
 
Intro 
0:00  
 
Rational Equations 
0:15  
 
 Example: Algebraic Fraction 
0:26  
 
 Least Common Denominator 
0:49  
 
 Example: Simple Rational Equation 
1:22  
 
 Example: Solve Rational Equation 
5:40  
 
Extraneous Solutions 
9:31  
 
 Double check 
10:00  
 
 No Solution 
10:38  
 
 Example: Extraneous 
10:44  
 
Rational Inequalities 
14:01  
 
 Excluded Values 
14:31  
 
 Solve Related Equation 
14:49  
 
 Find Intervals 
14:58  
 
 Use Test Values 
15:25  
 
 Example: Rational Inequality 
15:51  
 
 Example: Rational Inequality 2 
17:07  
 
Example 1: Rational Equation 
28:50  
 
Example 2: Rational Equation 
33:51  
 
Example 3: Rational Equation 
38:19  
 
Example 4: Rational Inequality 
46:49  
IX. Exponential and Logarithmic Relations 

Exponential Functions 
35:58 
 
Intro 
0:00  
 
What is an Exponential Function? 
0:12  
 
 Restriction on b 
0:31  
 
 Base 
0:46  
 
 Example: Exponents as Bases 
0:56  
 
 Variables as Exponents 
1:12  
 
 Example: Exponential Function 
1:50  
 
Graphing Exponential Functions 
2:33  
 
 Example: Using Table 
2:49  
 
Properties 
11:52  
 
 Continuous and One to One 
12:00  
 
 Domain is All Real Numbers 
13:14  
 
 XAxis Asymptote 
13:55  
 
 YIntercept 
14:02  
 
 Reflection Across YAxis 
14:31  
 
Growth and Decay 
15:06  
 
 Exponential Growth 
15:10  
 
 Real Life Examples 
15:41  
 
 Example: Growth 
15:52  
 
 Example: Decay 
16:12  
 
 Real Life Examples 
16:30  
 
Equations 
17:32  
 
 Bases are Same 
18:05  
 
 Examples: Variables as Exponents 
18:20  
 
Inequalities 
21:29  
 
 Property 
21:51  
 
 Example: Inequality 
22:37  
 
Example 1: Graph Exponential Function 
24:05  
 
Example 2: Growth or Decay 
27:50  
 
Example 3: Exponential Equation 
29:31  
 
Example 4: Exponential Inequality 
32:54  

Logarithms and Logarithmic Functions 
45:54 
 
Intro 
0:00  
 
What are Logarithms? 
0:08  
 
 Restrictions 
0:15  
 
 Written Form 
0:26  
 
 Logarithms are Exponents 
0:52  
 
 Example: Logarithms 
1:49  
 
Logarithmic Functions 
5:14  
 
 Same Restrictions 
5:30  
 
 Inverses 
5:53  
 
 Example: Logarithmic Function 
6:24  
 
Graph of the Logarithmic Function 
9:20  
 
 Example: Using Table 
9:35  
 
Properties 
15:09  
 
 Continuous and One to One 
15:14  
 
 Domain 
15:36  
 
 Range 
15:56  
 
 YAxis is Asymptote 
16:02  
 
 X Intercept 
16:12  
 
Inverse Property 
16:57  
 
 Compositions of Functions 
17:10  
 
Equations 
18:30  
 
 Example: Logarithmic Equation 
19:13  
 
Inequalities 
20:36  
 
 Properties 
20:47  
 
 Example: Logarithmic Inequality 
21:40  
 
Equations with Logarithms on Both Sides 
24:43  
 
 Property 
24:51  
 
 Example: Both Sides 
25:23  
 
Inequalities with Logarithms on Both Sides 
26:52  
 
 Property 
27:02  
 
 Example: Both Sides 
28:05  
 
Example 1: Solve Log Equation 
31:52  
 
Example 2: Solve Log Equation 
33:53  
 
Example 3: Solve Log Equation 
36:15  
 
Example 4: Solve Log Inequality 
39:19  

Properties of Logarithms 
28:43 
 
Intro 
0:00  
 
Product Property 
0:08  
 
 Example: Product 
0:46  
 
Quotient Property 
2:40  
 
 Example: Quotient 
2:59  
 
Power Property 
3:51  
 
 Moved Exponent 
4:07  
 
 Example: Power 
4:37  
 
Equations 
5:15  
 
 Example: Use Properties 
5:58  
 
Example 1: Simplify Log 
11:17  
 
Example 2: Single Log 
15:54  
 
Example 3: Solve Log Equation 
18:48  
 
Example 4: Solve Log Equation 
22:13  

Common Logarithms 
25:23 
 
Intro 
0:00  
 
What are Common Logarithms? 
0:10  
 
 Real World Applications 
0:16  
 
 Base Not Written 
0:27  
 
 Example: Base 10 
0:39  
 
Equations 
1:47  
 
 Example: Same Base 
1:56  
 
 Example: Different Base 
2:37  
 
Inequalities 
6:07  
 
 Multiplying/Dividing Inequality 
6:21  
 
 Example: Log Inequality 
6:54  
 
Change of Base 
12:45  
 
 Base 10 
13:24  
 
 Example: Change of Base 
14:05  
 
Example 1: Log Equation 
15:21  
 
Example 2: Common Logs 
17:13  
 
Example 3: Log Equation 
18:22  
 
Example 4: Log Inequality 
21:52  

Base e and Natural Logarithms 
21:14 
 
Intro 
0:00  
 
Number e 
0:09  
 
 Natural Base 
0:21  
 
 Growth/Decay 
0:33  
 
 Example: Exponential Function 
0:53  
 
Natural Logarithms 
1:11  
 
 ln x 
1:19  
 
 Inverse and Identity Function 
1:39  
 
 Example: Inverse Composition 
1:55  
 
Equations and Inequalities 
4:39  
 
 Extraneous Solutions 
5:30  
 
 Examples: Natural Log Equations 
5:48  
 
Example 1: Natural Log Equation 
9:08  
 
Example 2: Natural Log Equation 
10:37  
 
Example 3: Natural Log Inequality 
16:54  
 
Example 4: Natural Log Inequality 
18:16  

Exponential Growth and Decay 
24:30 
 
Intro 
0:00  
 
Decay 
0:17  
 
 Decreases by Fixed Percentage 
0:23  
 
 Rate of Decay 
0:56  
 
 Example: Finance 
1:34  
 
Scientific Model of Decay 
3:37  
 
 Exponential Decay 
3:45  
 
 Radioactive Decay 
4:13  
 
 Example: Half Life 
5:33  
 
Growth 
9:06  
 
 Increases by Fixed Percentage 
9:18  
 
 Example: Finance 
10:09  
 
Scientific Model of Growth 
11:35  
 
 Population Growth 
12:04  
 
 Example: Growth 
12:20  
 
Example 1: Computer Price 
14:00  
 
Example 2: Stock Price 
15:46  
 
Example 3: Medicine Disintegration 
19:10  
 
Example 4: Population Growth 
22:33  
X. Conic Sections 

Midpoint and Distance Formulas 
32:42 
 
Intro 
0:00  
 
Midpoint Formula 
0:15  
 
 Example: Midpoint 
0:30  
 
Distance Formula 
2:30  
 
 Example: Distance 
2:52  
 
Example 1: Midpoint and Distance 
4:58  
 
Example 2: Midpoint and Distance 
8:07  
 
Example 3: Median Length 
18:51  
 
Example 4: Perimeter and Area 
23:36  

Parabolas 
41:27 
 
Intro 
0:00  
 
What is a Parabola? 
0:20  
 
 Definition of a Parabola 
0:29  
 
 Focus 
0:59  
 
 Directrix 
1:15  
 
 Axis of Symmetry 
3:08  
 
Vertex 
3:33  
 
 Minimum or Maximum 
3:44  
 
Standard Form 
4:59  
 
 Horizontal Parabolas 
5:08  
 
 Vertex Form 
5:19  
 
 Upward or Downward 
5:41  
 
 Example: Standard Form 
6:06  
 
Graphing Parabolas 
8:31  
 
 Shifting 
8:51  
 
 Example: Completing the Square 
9:22  
 
 Symmetry and Translation 
12:18  
 
 Example: Graph Parabola 
12:40  
 
Latus Rectum 
17:13  
 
 Length 
18:15  
 
 Example: Latus Rectum 
18:35  
 
Horizontal Parabolas 
18:57  
 
 Not Functions 
20:08  
 
 Example: Horizontal Parabola 
21:21  
 
Focus and Directrix 
24:11  
 
 Horizontal 
24:48  
 
Example 1: Parabola Standard Form 
25:12  
 
Example 2: Graph Parabola 
30:00  
 
Example 3: Graph Parabola 
33:13  
 
Example 4: Parabola Equation 
37:28  

Circles 
21:03 
 
Intro 
0:00  
 
What are Circles? 
0:08  
 
 Example: Equidistant 
0:17  
 
 Radius 
0:32  
 
Equation of a Circle 
0:44  
 
 Example: Standard Form 
1:11  
 
Graphing Circles 
1:47  
 
 Example: Circle 
1:56  
 
Center Not at Origin 
3:07  
 
 Example: Completing the Square 
3:51  
 
Example 1: Equation of Circle 
6:44  
 
Example 2: Center and Radius 
11:51  
 
Example 3: Radius 
15:08  
 
Example 4: Equation of Circle 
16:57  

Ellipses 
46:51 
 
Intro 
0:00  
 
What Are Ellipses? 
0:11  
 
 Foci 
0:23  
 
Properties of Ellipses 
1:43  
 
 Major Axis, Minor Axis 
1:47  
 
 Center 
1:54  
 
 Length of Major Axis and Minor Axis 
3:21  
 
Standard Form 
5:33  
 
 Example: Standard Form of Ellipse 
6:09  
 
Vertical Major Axis 
9:14  
 
 Example: Vertical Major Axis 
9:46  
 
Graphing Ellipses 
12:51  
 
 Complete the Square and Symmetry 
13:00  
 
 Example: Graphing Ellipse 
13:16  
 
Equation with Center at (h, k) 
19:57  
 
 Horizontal and Vertical 
20:14  
 
 Difference 
20:27  
 
 Example: Center at (h, k) 
20:55  
 
Example 1: Equation of Ellipse 
24:05  
 
Example 2: Equation of Ellipse 
27:57  
 
Example 3: Equation of Ellipse 
32:32  
 
Example 4: Graph Ellipse 
38:27  

Hyperbolas 
38:15 
 
Intro 
0:00  
 
What are Hyperbolas? 
0:12  
 
 Two Branches 
0:18  
 
 Foci 
0:38  
 
Properties 
2:00  
 
 Transverse Axis and Conjugate Axis 
2:06  
 
 Vertices 
2:46  
 
 Length of Transverse Axis 
3:14  
 
 Distance Between Foci 
3:31  
 
 Length of Conjugate Axis 
3:38  
 
Standard Form 
5:45  
 
 Vertex Location 
6:36  
 
 Known Points 
6:52  
 
Vertical Transverse Axis 
7:26  
 
 Vertex Location 
7:50  
 
Asymptotes 
8:36  
 
 Vertex Location 
8:56  
 
 Rectangle 
9:28  
 
 Diagonals 
10:29  
 
Graphing Hyperbolas 
12:58  
 
 Example: Hyperbola 
13:16  
 
Equation with Center at (h, k) 
16:32  
 
 Example: Center at (h, k) 
17:21  
 
Example 1: Equation of Hyperbola 
19:20  
 
Example 2: Equation of Hyperbola 
22:48  
 
Example 3: Graph Hyperbola 
26:05  
 
Example 4: Equation of Hyperbola 
36:29  

Conic Sections 
18:43 
 
Intro 
0:00  
 
Conic Sections 
0:16  
 
 Double Cone Sections 
0:24  
 
Standard Form 
1:27  
 
 General Form 
1:37  
 
Identify Conic Sections 
2:16  
 
 B = 0 
2:50  
 
 X and Y 
3:22  
 
Identify Conic Sections, Cont. 
4:46  
 
 Parabola 
5:17  
 
 Circle 
5:51  
 
 Ellipse 
6:31  
 
 Hyperbola 
7:10  
 
Example 1: Identify Conic Section 
8:01  
 
Example 2: Identify Conic Section 
11:03  
 
Example 3: Identify Conic Section 
11:38  
 
Example 4: Identify Conic Section 
14:50  

Solving Quadratic Systems 
47:04 
 
Intro 
0:00  
 
Linear Quadratic Systems 
0:22  
 
 Example: Linear Quadratic System 
0:45  
 
Solutions 
2:49  
 
 Graphs of Possible Solutions 
3:10  
 
Quadratic Quadratic System 
4:10  
 
 Example: Elimination 
4:21  
 
Solutions 
11:39  
 
 Example: 0, 1, 2, 3, 4 Solutions 
11:50  
 
Systems of Quadratic Inequalities 
12:48  
 
 Example: Quadratic Inequality 
13:09  
 
Example 1: Solve Quadratic System 
21:42  
 
Example 2: Solve Quadratic System 
29:13  
 
Example 3: Solve Quadratic System 
35:02  
 
Example 4: Solve Quadratic Inequality 
40:29  
XI. Sequences and Series 

Arithmetic Sequences 
21:16 
 
Intro 
0:00  
 
Sequences 
0:10  
 
 General Form of Sequence 
0:16  
 
 Example: Finite/Infinite Sequences 
0:33  
 
Arithmetic Sequences 
0:28  
 
 Common Difference 
2:41  
 
 Example: Arithmetic Sequence 
2:50  
 
Formula for the nth Term 
3:51  
 
 Example: nth Term 
4:32  
 
Equation for the nth Term 
6:37  
 
 Example: Using Formula 
6:56  
 
Arithmetic Means 
9:47  
 
 Example: Arithmetic Means 
10:16  
 
Example 1: nth Term 
12:38  
 
Example 2: Arithmetic Means 
13:49  
 
Example 3: Arithmetic Means 
16:12  
 
Example 4: nth Term 
18:26  

Arithmetic Series 
21:36 
 
Intro 
0:00  
 
What are Arithmetic Series? 
0:11  
 
 Common Difference 
0:28  
 
 Example: Arithmetic Sequence 
0:43  
 
 Example: Arithmetic Series 
1:09  
 
 Finite/Infinite Series 
1:36  
 
Sum of Arithmetic Series 
2:27  
 
 Example: Sum 
3:21  
 
Sigma Notation 
5:53  
 
 Index 
6:14  
 
 Example: Sigma Notation 
7:14  
 
Example 1: First Term 
9:00  
 
Example 2: Three Terms 
10:52  
 
Example 3: Sum of Series 
14:14  
 
Example 4: Sum of Series 
18:13  

Geometric Sequences 
23:03 
 
Intro 
0:00  
 
Geometric Sequences 
0:11  
 
 Common Difference 
0:38  
 
 Common Ratio 
1:08  
 
 Example: Geometric Sequence 
2:38  
 
nth Term of a Geometric Sequence 
4:41  
 
 Example: nth Term 
4:56  
 
Geometric Means 
6:51  
 
 Example: Geometric Mean 
7:09  
 
Example 1: 9th Term 
12:04  
 
Example 2: Geometric Means 
15:18  
 
Example 3: nth Term 
18:32  
 
Example 4: Three Terms 
20:59  

Geometric Series 
22:43 
 
Intro 
0:00  
 
What are Geometric Series? 
0:11  
 
 List of Numbers 
0:24  
 
 Example: Geometric Series 
1:12  
 
Sum of Geometric Series 
2:16  
 
 Example: Sum of Geometric Series 
2:41  
 
Sigma Notation 
4:21  
 
 Lower Index, Upper Index 
4:38  
 
 Example: Sigma Notation 
4:57  
 
Another Sum Formula 
6:08  
 
 Example: n Unknown 
6:28  
 
Specific Terms 
7:41  
 
 Sum Formula 
7:56  
 
 Example: Specific Term 
8:11  
 
Example 1: Sum of Geometric Series 
10:02  
 
Example 2: Sum of 8 Terms 
14:15  
 
Example 3: Sum of Geometric Series 
18:23  
 
Example 4: First Term 
20:16  

Infinite Geometric Series 
18:32 
 
Intro 
0:00  
 
What are Infinite Geometric Series 
0:10  
 
 Example: Finite 
0:29  
 
 Example: Infinite 
0:51  
 
 Partial Sums 
1:09  
 
 Formula 
1:37  
 
Sum of an Infinite Geometric Series 
2:39  
 
 Convergent Series 
2:58  
 
 Example: Sum of Convergent Series 
3:28  
 
Sigma Notation 
7:31  
 
 Example: Sigma 
8:17  
 
Repeating Decimals 
8:42  
 
 Example: Repeating Decimal 
8:53  
 
Example 1: Sum of Infinite Geometric Series 
12:15  
 
Example 2: Repeating Decimal 
13:24  
 
Example 3: Sum of Infinite Geometric Series 
15:14  
 
Example 4: Repeating Decimal 
16:48  

Recursion and Special Sequences 
14:34 
 
Intro 
0:00  
 
Fibonacci Sequence 
0:05  
 
 Background of Fibonacci 
0:23  
 
 Recursive Formula 
0:37  
 
 Fibonacci Sequence 
0:52  
 
 Example: Recursive Formula 
2:18  
 
Iteration 
3:49  
 
 Example: Iteration 
4:30  
 
Example 1: Five Terms 
7:08  
 
Example 2: Three Terms 
9:00  
 
Example 3: Five Terms 
10:38  
 
Example 4: Three Iterates 
12:41  

Binomial Theorem 
48:30 
 
Intro 
0:00  
 
Pascal's Triangle 
0:06  
 
 Expand Binomial 
0:13  
 
 Pascal's Triangle 
4:26  
 
Properties 
6:52  
 
 Example: Properties of Binomials 
6:58  
 
Factorials 
9:11  
 
 Product 
9:28  
 
 Example: Factorial 
9:45  
 
Binomial Theorem 
11:08  
 
 Example: Binomial Theorem 
13:48  
 
Finding a Specific Term 
18:36  
 
 Example: Specific Term 
19:26  
 
Example 1: Expand 
24:39  
 
Example 2: Fourth Term 
30:26  
 
Example 3: Five Terms 
36:13  
 
Example 4: Three Iterates 
45:07  