Section 1: Properties of Real Numbers |
|
Basic Types of Numbers |
30:41 |
| |
Intro |
0:00 | |
| |
Objectives |
0:07 | |
| |
Basic Types of Numbers |
0:36 | |
| |
| Natural Numbers |
1:02 | |
| |
| Whole Numbers |
1:29 | |
| |
| Integers |
2:04 | |
| |
| Rational Numbers |
2:38 | |
| |
| Irrational Numbers |
5:06 | |
| |
| Imaginary Numbers |
6:48 | |
| |
Basic Types of Numbers Cont. |
8:09 | |
| |
| The Big Picture |
8:10 | |
| |
| Real vs. Imaginary Numbers |
8:30 | |
| |
| Rational vs. Irrational Numbers |
8:48 | |
| |
Basic Types of Numbers Cont. |
10:55 | |
| |
| Number Line |
11:06 | |
| |
| Absolute Value |
11:44 | |
| |
| Inequalities |
12:39 | |
| |
Example 1 |
13:16 | |
| |
Example 2 |
17:30 | |
| |
Example 3 |
21:56 | |
| |
Example 4 |
24:27 | |
| |
Example 5 |
27:48 | |
|
Operations on Numbers |
19:26 |
| |
Intro |
0:00 | |
| |
Objectives |
0:06 | |
| |
Operations on Numbers |
0:25 | |
| |
| Addition |
0:53 | |
| |
| Subtraction |
1:33 | |
| |
| Multiplication & Division |
2:19 | |
| |
| Exponents |
3:24 | |
| |
| Bases |
4:04 | |
| |
| Square Roots |
4:59 | |
| |
| Principle Square Roots |
5:09 | |
| |
| Perfect Squares |
6:32 | |
| |
| Simplifying and Combining Roots |
6:52 | |
| |
Example 1 |
8:16 | |
| |
Example 2 |
12:30 | |
| |
Example 3 |
14:02 | |
| |
Example 4 |
16:27 | |
|
Order of Operations |
12:06 |
| |
Intro |
0:00 | |
| |
Objectives |
0:06 | |
| |
The Order of Operations |
0:25 | |
| |
| Work Inside Parentheses |
0:42 | |
| |
| Simplify Exponents |
0:52 | |
| |
| Multiplication & Division from Left to Right |
0:57 | |
| |
| Addition & Subtraction from Left to Right |
1:11 | |
| |
| Remember PEMDAS |
1:21 | |
| |
The Order of Operations Cont. |
2:27 | |
| |
| Example |
2:43 | |
| |
Example 1 |
3:55 | |
| |
Example 2 |
5:36 | |
| |
Example 3 |
7:35 | |
| |
Example 4 |
8:56 | |
|
Properties of Real Numbers |
18:52 |
| |
Intro |
0:00 | |
| |
Objectives |
0:07 | |
| |
The Properties of Real Numbers |
0:23 | |
| |
| Commutative Property of Addition and Multiplication |
0:44 | |
| |
| Associative Property of Addition and Multiplication |
1:50 | |
| |
| Distributive Property of Multiplication Over Addition |
3:20 | |
| |
| Division Property of Zero |
4:46 | |
| |
| Division Property of One |
5:23 | |
| |
| Multiplication Property of Zero |
5:56 | |
| |
| Multiplication Property of One |
6:17 | |
| |
| Addition Property of Zero |
6:29 | |
| |
| Why Are These Properties Important? |
6:53 | |
| |
Example 1 |
9:16 | |
| |
Example 2 |
13:04 | |
| |
Example 3 |
14:30 | |
| |
Example 4 |
16:57 | |
Section 2: Linear Equations |
|
The Vocabulary of Linear Equations |
12:22 |
| |
Intro |
0:00 | |
| |
Objectives |
0:09 | |
| |
The Vocabulary of Linear Equations |
0:44 | |
| |
| Variables |
0:52 | |
| |
| Terms |
1:09 | |
| |
| Coefficients |
1:40 | |
| |
| Like Terms |
2:18 | |
| |
| Examples of Like Terms |
2:37 | |
| |
| Expressions |
4:01 | |
| |
| Equations |
4:26 | |
| |
| Linear Equations |
5:04 | |
| |
| Solutions |
5:55 | |
| |
Example 1 |
6:16 | |
| |
Example 2 |
7:16 | |
| |
Example 3 |
8:45 | |
| |
Example 4 |
10:20 | |
|
Solving Linear Equations in One Variable |
28:52 |
| |
Intro |
0:00 | |
| |
Objectives |
0:08 | |
| |
Solving Linear Equations in One Variable |
0:34 | |
| |
| Conditional Cases |
0:51 | |
| |
| Identity Cases |
1:09 | |
| |
| Contradiction Cases |
1:30 | |
| |
Solving Linear Equations in One Variable Cont. |
2:00 | |
| |
| Addition Property of Equality |
2:10 | |
| |
| Multiplication Property of Equality |
2:43 | |
| |
| Steps to Solve Linear Equations |
3:14 | |
| |
Example 1 |
4:22 | |
| |
Example 2 |
8:21 | |
| |
Example 3 |
12:32 | |
| |
Example 4 |
14:19 | |
| |
Example 5 |
17:25 | |
| |
Example 6 |
22:17 | |
|
Solving Formulas |
12:02 |
| |
Intro |
0:00 | |
| |
Objectives |
0:06 | |
| |
Solving Formulas |
0:18 | |
| |
| Formulas |
0:26 | |
| |
| Use the Same Properties as Solving Linear Equations |
1:36 | |
| |
| Addition Property of Equality |
1:55 | |
| |
| Multiplication Property of Equality |
1:58 | |
| |
| Steps to Solve Formulas |
2:43 | |
| |
Example 1 |
3:56 | |
| |
Example 2 |
6:09 | |
| |
Example 3 |
8:39 | |
|
Applications of Linear Equations |
28:41 |
| |
Intro |
0:00 | |
| |
Objectives |
0:10 | |
| |
Applications of Linear Equations |
0:43 | |
| |
| The Six-Step Method to Solving Word Problems |
0:55 | |
| |
| Common Terms |
3:12 | |
| |
Example 1 |
5:03 | |
| |
Example 2 |
9:40 | |
| |
Example 3 |
13:48 | |
| |
Example 4 |
17:58 | |
| |
Example 5 |
23:28 | |
|
Applications of Linear Equations, Motion & Mixtures |
24:26 |
| |
Intro |
0:00 | |
| |
Objectives |
0:21 | |
| |
Motion and Mixtures |
0:46 | |
| |
| Motion Problems: Distance, Rate, and Time |
1:06 | |
| |
| Mixture Problems: Amount, Percent, and Total |
1:27 | |
| |
| The Table Method |
1:58 | |
| |
| The Beaker Method |
3:38 | |
| |
Example 1 |
5:05 | |
| |
Example 2 |
9:44 | |
| |
Example 3 |
14:20 | |
| |
Example 4 |
19:13 | |
Section 3: Graphing |
|
Rectangular Coordinate System |
22:55 |
| |
Intro |
0:00 | |
| |
Objectives |
0:11 | |
| |
The Rectangular Coordinate System |
0:39 | |
| |
| The Cartesian Coordinate System |
0:40 | |
| |
| X-Axis |
0:54 | |
| |
| Y-Axis |
1:04 | |
| |
| Origin |
1:11 | |
| |
| Quadrants |
1:26 | |
| |
| Ordered Pairs |
2:10 | |
| |
Example 1 |
2:55 | |
| |
The Rectangular Coordinate System Cont. |
6:09 | |
| |
| X-Intercept |
6:45 | |
| |
| Y-Intercept |
6:55 | |
| |
| Relation of X-Values and Y-Values |
7:30 | |
| |
Example 2 |
11:03 | |
| |
Example 3 |
12:13 | |
| |
Example 4 |
14:10 | |
| |
Example 5 |
18:38 | |
|
Slope & Graphing |
27:58 |
| |
Intro |
0:00 | |
| |
Objectives |
0:11 | |
| |
Slope and Graphing |
0:48 | |
| |
| Standard Form |
1:14 | |
| |
Example 1 |
2:24 | |
| |
Slope and Graphing Cont. |
4:58 | |
| |
| Slope, m |
5:07 | |
| |
| Slope is Rise over Run |
6:11 | |
| |
| Don't Mix Up the Coordinates |
8:20 | |
| |
Example 2 |
9:39 | |
| |
Slope and Graphing Cont. |
14:26 | |
| |
| Slope-Intercept Form |
14:34 | |
| |
Example 3 |
16:55 | |
| |
Example 4 |
18:00 | |
| |
Slope and Graphing Cont. |
19:00 | |
| |
| Rewriting an Equation in Slope-Intercept Form |
19:39 | |
| |
| Rewriting an Equation in Standard Form |
20:09 | |
| |
| Slopes of Vertical & Horizontal Lines |
20:56 | |
| |
Example 5 |
22:49 | |
| |
Example 6 |
24:09 | |
| |
Example 7 |
25:59 | |
| |
Example 8 |
26:57 | |
|
Linear Equations in Two Variables |
20:36 |
| |
Intro |
0:00 | |
| |
Objectives |
0:13 | |
| |
Linear Equations in Two Variables |
0:36 | |
| |
| Point-Slope Form |
1:07 | |
| |
| Substitute in the Point and the Slope |
2:21 | |
| |
| Parallel Lines: Two Lines with the Same Slope |
4:05 | |
| |
| Perpendicular Lines: Slopes are Negative Reciprocals of Each Other |
4:39 | |
| |
| Perpendicular Lines: Product of Slopes is -1 |
5:24 | |
| |
Example 1 |
6:02 | |
| |
Example 2 |
7:50 | |
| |
Example 3 |
10:49 | |
| |
Example 4 |
13:26 | |
| |
Example 5 |
15:30 | |
| |
Example 6 |
17:43 | |
Section 4: Functions |
|
Introduction to Functions |
21:24 |
| |
Intro |
0:00 | |
| |
Objectives |
0:07 | |
| |
Introduction to Functions |
0:58 | |
| |
| Relations |
1:03 | |
| |
| Functions |
1:37 | |
| |
| Independent Variables |
2:00 | |
| |
| Dependent Variables |
2:11 | |
| |
| Function Notation |
2:21 | |
| |
Function |
3:43 | |
| |
| Input and Output |
3:53 | |
| |
Introduction to Functions Cont. |
4:45 | |
| |
| Domain |
4:46 | |
| |
| Range |
4:55 | |
| |
| Functions Represented by a Diagram |
6:41 | |
| |
| Natural Domain |
9:11 | |
| |
| Evaluating Functions |
12:02 | |
| |
Example 1 |
13:13 | |
| |
Example 2 |
15:03 | |
| |
Example 3 |
16:18 | |
| |
Example 4 |
19:54 | |
|
Graphing Functions |
16:12 |
| |
Intro |
0:00 | |
| |
Objectives |
0:09 | |
| |
Graphing Functions |
0:54 | |
| |
| Using Slope-Intercept Form |
1:56 | |
| |
| Vertical Line Test |
2:58 | |
| |
| Determining the Domain |
4:20 | |
| |
| Determining the Range |
5:43 | |
| |
Example 1 |
6:06 | |
| |
Example 2 |
7:18 | |
| |
Example 3 |
8:31 | |
| |
Example 4 |
11:04 | |
Section 5: Systems of Linear Equations |
|
Systems of Linear Equations |
25:54 |
| |
Intro |
0:00 | |
| |
Objectives |
0:13 | |
| |
Systems of Linear Equations |
0:46 | |
| |
| System of Equations |
0:51 | |
| |
| System of Linear Equations |
1:15 | |
| |
| Solutions |
1:35 | |
| |
| Points as Solutions |
1:53 | |
| |
| Finding Solutions Graphically |
5:13 | |
| |
Example 1 |
6:37 | |
| |
Example 2 |
12:07 | |
| |
Systems of Linear Equations Cont. |
17:01 | |
| |
| One Solution, No Solution, or Infinite Solutions |
17:10 | |
| |
Example 3 |
18:31 | |
| |
Example 4 |
22:37 | |
|
Solving a System Using Substitution |
20:01 |
| |
Intro |
0:00 | |
| |
Objectives |
0:09 | |
| |
Solving a System Using Substitution |
0:32 | |
| |
| Substitution Method |
1:24 | |
| |
| Substitution Example |
2:35 | |
| |
| One Solution, No Solution, or Infinite Solutions |
7:50 | |
| |
Example 1 |
9:45 | |
| |
Example 2 |
12:48 | |
| |
Example 3 |
15:01 | |
| |
Example 4 |
17:30 | |
|
Solving a System Using Elimination |
19:40 |
| |
Intro |
0:00 | |
| |
Objectives |
0:09 | |
| |
Solving a System Using Elimination |
0:27 | |
| |
| Elimination Method |
0:42 | |
| |
| Elimination Example |
2:01 | |
| |
| One Solution, No Solution, or Infinite Solutions |
7:05 | |
| |
Example 1 |
8:53 | |
| |
Example 2 |
11:46 | |
| |
Example 3 |
15:37 | |
| |
Example 4 |
17:45 | |
|
Applications of Systems of Equations |
24:34 |
| |
Intro |
0:00 | |
| |
Objectives |
0:12 | |
| |
Applications of Systems of Equations |
0:30 | |
| |
| Word Problems |
1:31 | |
| |
Example 1 |
2:17 | |
| |
Example 2 |
7:55 | |
| |
Example 3 |
13:07 | |
| |
Example 4 |
17:15 | |
Section 6: Inequalities |
|
Solving Linear Inequalities in One Variable |
17:13 |
| |
Intro |
0:00 | |
| |
Objectives |
0:08 | |
| |
Solving Linear Inequalities in One Variable |
0:37 | |
| |
| Inequality Expressions |
0:46 | |
| |
| Linear Inequality Solution Notations |
3:40 | |
| |
| Inequalities |
3:51 | |
| |
| Interval Notation |
4:04 | |
| |
| Number Lines |
4:43 | |
| |
| Set Builder Notation |
5:24 | |
| |
| Use Same Techniques as Solving Equations |
6:59 | |
| |
| 'Flip' the Sign when Multiplying or Dividing by a Negative Number |
7:12 | |
| |
| 'Flip' Example |
7:50 | |
| |
Example 1 |
8:54 | |
| |
Example 2 |
11:40 | |
| |
Example 3 |
14:01 | |
|
Compound Inequalities |
16:13 |
| |
Intro |
0:00 | |
| |
Objectives |
0:07 | |
| |
Compound Inequalities |
0:37 | |
| |
| 'And' vs. 'Or' |
0:44 | |
| |
| 'And' |
3:24 | |
| |
| 'Or' |
3:35 | |
| |
| 'And' Symbol, or Intersection |
3:51 | |
| |
| 'Or' Symbol, or Union |
4:13 | |
| |
| Inequalities |
4:41 | |
| |
Example 1 |
6:22 | |
| |
Example 2 |
9:30 | |
| |
Example 3 |
11:27 | |
| |
Example 4 |
13:49 | |
|
Solving Equations with Absolute Values |
14:12 |
| |
Intro |
0:00 | |
| |
Objectives |
0:08 | |
| |
Solve Equations with Absolute Values |
0:18 | |
| |
Solve Equations with Absolute Values Cont. |
1:11 | |
| |
| Steps to Solving Equations with Absolute Values |
2:21 | |
| |
Example 1 |
3:23 | |
| |
Example 2 |
6:34 | |
| |
Example 3 |
10:12 | |
|
Inequalities with Absolute Values |
17:07 |
| |
Intro |
0:00 | |
| |
Objectives |
0:07 | |
| |
Inequalities with Absolute Values |
0:23 | |
| |
| Recall
|
2:08 | |
| |
Example 1 |
3:39 | |
| |
Example 2 |
6:06 | |
| |
Example 3 |
8:14 | |
| |
Example 4 |
10:29 | |
| |
Example 5 |
13:29 | |
|
Graphing Inequalities in Two Variables |
15:33 |
| |
Intro |
0:00 | |
| |
Objectives |
0:07 | |
| |
Graphing Inequalities in Two Variables |
0:32 | |
| |
| Split Graph into Two Regions |
1:53 | |
| |
Graphing Inequalities |
5:44 | |
| |
| Test Points |
6:20 | |
| |
Example 1 |
7:11 | |
| |
Example 2 |
10:17 | |
| |
Example 3 |
13:06 | |
|
Systems of Inequalities |
21:13 |
| |
Intro |
0:00 | |
| |
Objectives |
0:08 | |
| |
Systems of Inequalities |
0:24 | |
| |
| Test Points |
1:10 | |
| |
| Steps to Solve Systems of Inequalities |
1:25 | |
| |
Example 1 |
2:23 | |
| |
Example 2 |
7:28 | |
| |
Example 3 |
12:51 | |
Section 7: Polynomials |
|
Integer Exponents |
44:51 |
| |
Intro |
0:00 | |
| |
Objectives |
0:09 | |
| |
Integer Exponents |
0:42 | |
| |
| Exponents 'Package' Multiplication |
1:25 | |
| |
Example 1 |
2:00 | |
| |
Example 2 |
3:13 | |
| |
Integer Exponents Cont. |
4:50 | |
| |
| Product Rule for Exponents |
4:51 | |
| |
Example 3 |
7:16 | |
| |
Example 4 |
10:15 | |
| |
Integer Exponents Cont. |
13:13 | |
| |
| Power Rule for Exponents |
13:14 | |
| |
| Power Rule with Multiplication and Division |
15:33 | |
| |
Example 5 |
16:18 | |
| |
Integer Exponents Cont. |
20:04 | |
| |
Example 6 |
20:41 | |
| |
Integer Exponents Cont. |
25:52 | |
| |
| Zero Exponent Rule |
25:53 | |
| |
| Quotient Rule |
28:24 | |
| |
| Negative Exponents |
30:14 | |
| |
| Negative Exponent Rule |
32:27 | |
| |
Example 7 |
34:05 | |
| |
Example 8 |
36:15 | |
| |
Example 9 |
39:33 | |
| |
Example 10 |
43:16 | |
|
Adding & Subtracting Polynomials |
18:33 |
| |
Intro |
0:00 | |
| |
Objectives |
0:07 | |
| |
Adding and Subtracting Polynomials |
0:25 | |
| |
| Terms |
0:33 | |
| |
| Coefficients |
0:51 | |
| |
| Leading Coefficients |
1:13 | |
| |
| Like Terms |
1:29 | |
| |
| Polynomials |
2:21 | |
| |
| Monomials, Binomials, Trinomials, and Polynomials |
5:41 | |
| |
| Degrees |
7:00 | |
| |
| Evaluating Polynomials |
8:12 | |
| |
Adding and Subtracting Polynomials Cont. |
9:25 | |
| |
Example 1 |
11:48 | |
| |
Example 2 |
13:00 | |
| |
Example 3 |
14:41 | |
| |
Example 4 |
16:15 | |
|
Multiplying Polynomials |
25:07 |
| |
Intro |
0:00 | |
| |
Objectives |
0:06 | |
| |
Multiplying Polynomials |
0:41 | |
| |
| Distributive Property |
1:00 | |
| |
Example 1 |
2:49 | |
| |
Multiplying Polynomials Cont. |
8:22 | |
| |
| Organize Terms with a Table |
8:23 | |
| |
Example 2 |
13:40 | |
| |
Multiplying Polynomials Cont. |
16:33 | |
| |
| Multiplying Binomials with FOIL |
16:48 | |
| |
Example 3 |
18:49 | |
| |
Example 4 |
20:04 | |
| |
Example 5 |
21:42 | |
|
Dividing Polynomials |
44:56 |
| |
Intro |
0:00 | |
| |
Objectives |
0:07 | |
| |
Dividing Polynomials |
0:29 | |
| |
| Dividing Polynomials by Monomials |
2:10 | |
| |
| Dividing Polynomials by Polynomials |
2:59 | |
| |
| Dividing Numbers |
4:09 | |
| |
| Dividing Polynomials Example |
8:39 | |
| |
Example 1 |
12:35 | |
| |
Example 2 |
14:40 | |
| |
Example 3 |
16:45 | |
| |
Example 4 |
21:13 | |
| |
Example 5 |
24:33 | |
| |
Example 6 |
29:02 | |
| |
| Dividing Polynomials with Synthetic Division Method |
33:36 | |
| |
Example 7 |
38:43 | |
| |
Example 8 |
42:24 | |
Section 8: Factoring Polynomials |
|
Greatest Common Factor & Factor by Grouping |
28:27 |
| |
Intro |
0:00 | |
| |
Objectives |
0:09 | |
| |
Greatest Common Factor |
0:31 | |
| |
| Factoring |
0:40 | |
| |
| Greatest Common Factor (GCF) |
1:48 | |
| |
| GCF for Polynomials |
3:28 | |
| |
| Factoring Polynomials |
6:45 | |
| |
| Prime |
8:21 | |
| |
Example 1 |
9:14 | |
| |
Factor by Grouping |
14:30 | |
| |
| Steps to Factor by Grouping |
17:03 | |
| |
Example 2 |
17:43 | |
| |
Example 3 |
19:20 | |
| |
Example 4 |
20:41 | |
| |
Example 5 |
22:29 | |
| |
Example 6 |
26:11 | |
|
Factoring Trinomials |
21:44 |
| |
Intro |
0:00 | |
| |
Objectives |
0:06 | |
| |
Factoring Trinomials |
0:25 | |
| |
| Recall FOIL |
0:26 | |
| |
| Factor a Trinomial by Reversing FOIL |
1:52 | |
| |
| Tips when Using Reverse FOIL |
5:31 | |
| |
Example 1 |
7:04 | |
| |
Example 2 |
9:09 | |
| |
Example 3 |
11:15 | |
| |
Example 4 |
13:41 | |
| |
Factoring Trinomials Cont. |
15:50 | |
| |
Example 5 |
18:42 | |
|
Factoring Trinomials Using the AC Method |
30:09 |
| |
Intro |
0:00 | |
| |
Objectives |
0:08 | |
| |
Factoring Trinomials Using the AC Method |
0:27 | |
| |
| Factoring when Leading Term has Coefficient Other Than 1 |
1:07 | |
| |
| Reversing FOIL |
1:18 | |
| |
Example 1 |
1:46 | |
| |
Example 2 |
4:28 | |
| |
Factoring Trinomials Using the AC Method Cont. |
7:45 | |
| |
| The AC Method |
8:03 | |
| |
| Steps to Using the AC Method |
8:19 | |
| |
| Tips on Using the AC Method |
9:29 | |
| |
Example 3 |
10:45 | |
| |
Example 4 |
16:50 | |
| |
Example 5 |
21:08 | |
| |
Example 6 |
24:58 | |
|
Special Factoring Techniques |
30:14 |
| |
Intro |
0:00 | |
| |
Objectives |
0:07 | |
| |
Special Factoring Techniques |
0:26 | |
| |
| Difference of Squares |
1:46 | |
| |
| Perfect Square Trinomials |
2:38 | |
| |
| No Sum of Squares |
3:32 | |
| |
Special Factoring Techniques Cont. |
4:03 | |
| |
| Difference of Squares Example |
4:04 | |
| |
| Perfect Square Trinomials Example |
5:29 | |
| |
Example 1 |
7:31 | |
| |
Example 2 |
9:59 | |
| |
Example 3 |
11:47 | |
| |
Example 4 |
15:09 | |
| |
Special Factoring Techniques Cont. |
19:07 | |
| |
| Sum of Cubes and Difference of Cubes |
19:08 | |
| |
Example 5 |
23:13 | |
| |
Example 6 |
26:12 | |
Section 9: Quadratic Equations |
|
Solving Quadratic Equations by Factoring |
23:38 |
| |
Intro |
0:00 | |
| |
Objectives |
0:08 | |
| |
Solving Quadratic Equations by Factoring |
0:19 | |
| |
| Quadratic Equations |
0:20 | |
| |
| Zero Factor Property |
1:39 | |
| |
| Zero Factor Property Example |
2:34 | |
| |
Example 1 |
4:00 | |
| |
Solving Quadratic Equations by Factoring Cont. |
5:54 | |
| |
Example 2 |
7:28 | |
| |
Example 3 |
11:09 | |
| |
Example 4 |
14:22 | |
| |
Solving Quadratic Equations by Factoring Cont. |
18:17 | |
| |
| Higher Degree Polynomial Equations |
18:18 | |
| |
Example 5 |
20:22 | |
|
Solving Quadratic Equations |
29:27 |
| |
Intro |
0:00 | |
| |
Objectives |
0:12 | |
| |
Solving Quadratic Equations |
0:29 | |
| |
| Linear Factors |
0:38 | |
| |
| Not All Quadratics Factor Easily |
1:22 | |
| |
| Principle of Square Roots |
3:36 | |
| |
| Completing the Square |
4:50 | |
| |
| Steps for Using Completing the Square |
5:15 | |
| |
| Completing the Square Works on All Quadratic Equations |
6:41 | |
| |
| The Quadratic Formula |
7:28 | |
| |
| Discriminants |
8:25 | |
| |
| Solving Quadratic Equations - Summary |
10:11 | |
| |
Example 1 |
11:54 | |
| |
Example 2 |
13:03 | |
| |
Example 3 |
16:30 | |
| |
Example 4 |
21:29 | |
| |
Example 5 |
25:07 | |
|
Equations in Quadratic Form |
16:47 |
| |
Intro |
0:00 | |
| |
Objectives |
0:08 | |
| |
Equations in Quadratic Form |
0:24 | |
| |
| Using a Substitution |
0:53 | |
| |
| U-Substitution |
1:26 | |
| |
Example 1 |
2:07 | |
| |
Example 2 |
5:36 | |
| |
Example 3 |
8:31 | |
| |
Example 4 |
11:14 | |
|
Quadratic Formulas & Applications |
29:04 |
| |
Intro |
0:00 | |
| |
Objectives |
0:09 | |
| |
Quadratic Formulas and Applications |
0:35 | |
| |
| Squared Variable |
0:40 | |
| |
| Principle of Square Roots |
0:51 | |
| |
Example 1 |
1:09 | |
| |
Example 2 |
2:04 | |
| |
Quadratic Formulas and Applications Cont. |
3:34 | |
| |
Example 3 |
4:42 | |
| |
Example 4 |
13:33 | |
| |
Example 5 |
20:50 | |
|
Graphs of Quadratics |
26:53 |
| |
Intro |
0:00 | |
| |
Objectives |
0:06 | |
| |
Graphs of Quadratics |
0:39 | |
| |
| Axis of Symmetry |
1:46 | |
| |
| Vertex |
2:12 | |
| |
| Transformations |
2:57 | |
| |
| Graphing in Quadratic Standard Form |
3:23 | |
| |
Example 1 |
5:06 | |
| |
Example 2 |
6:02 | |
| |
Example 3 |
9:07 | |
| |
Graphs of Quadratics Cont. |
11:26 | |
| |
| Completing the Square |
12:02 | |
| |
| Vertex Shortcut |
12:16 | |
| |
Example 4 |
13:49 | |
| |
Example 5 |
17:25 | |
| |
Example 6 |
20:07 | |
| |
Example 7 |
23:43 | |
|
Polynomial Inequalities |
21:42 |
| |
Intro |
0:00 | |
| |
Objectives |
0:07 | |
| |
Polynomial Inequalities |
0:30 | |
| |
| Solving Polynomial Inequalities |
1:20 | |
| |
Example 1 |
2:45 | |
| |
Polynomial Inequalities Cont. |
5:12 | |
| |
| Larger Polynomials |
5:13 | |
| |
| Positive or Negative Intervals |
7:16 | |
| |
Example 2 |
9:01 | |
| |
Example 3 |
13:53 | |
Section 10: Rational Equations |
|
Multiply & Divide Rational Expressions |
26:41 |
| |
Intro |
0:00 | |
| |
Objectives |
0:09 | |
| |
Multiply and Divide Rational Expressions |
0:44 | |
| |
| Rational Numbers |
0:55 | |
| |
| Dividing by Zero |
1:45 | |
| |
| Canceling Extra Factors |
2:43 | |
| |
| Negative Signs in Fractions |
4:52 | |
| |
| Multiplying Fractions |
6:26 | |
| |
| Dividing Fractions |
7:17 | |
| |
Example 1 |
8:04 | |
| |
Example 2 |
14:01 | |
| |
Example 3 |
16:23 | |
| |
Example 4 |
18:56 | |
| |
Example 5 |
22:43 | |
|
Adding & Subtracting Rational Expressions |
20:24 |
| |
Intro |
0:00 | |
| |
Objectives |
0:07 | |
| |
Adding and Subtracting Rational Expressions |
0:41 | |
| |
| Common Denominators |
0:52 | |
| |
| Common Denominator Examples |
1:14 | |
| |
| Steps to Adding and Subtracting Rational Expressions |
2:39 | |
| |
Example 1 |
3:34 | |
| |
Example 2 |
5:27 | |
| |
Adding and Subtracting Rational Expressions Cont. |
6:57 | |
| |
| Least Common Denominators |
6:58 | |
| |
| Transitioning from Fractions to Rational Expressions |
9:08 | |
| |
| Identifying Least Common Denominators for Rational Expressions |
9:56 | |
| |
| Subtracting vs. Adding |
10:41 | |
| |
Example 3 |
11:19 | |
| |
Example 4 |
12:36 | |
| |
Example 5 |
15:08 | |
| |
Example 6 |
16:46 | |
|
Complex Fractions |
18:23 |
| |
Intro |
0:00 | |
| |
Objectives |
0:09 | |
| |
Complex Fractions |
00:37 | |
| |
| Dividing to Simplify Complex Fractions |
1:10 | |
| |
Example 1 |
2:03 | |
| |
Example 2 |
3:58 | |
| |
Complex Fractions Cont. |
9:15 | |
| |
| Using the Least Common Denominator to Simplify Complex Fractions |
9:16 | |
| |
| Both Methods Lead to the Same Answer |
10:07 | |
| |
Example 3 |
10:42 | |
| |
Example 4 |
14:28 | |
|
Solving Rational Equations |
16:24 |
| |
Intro |
0:00 | |
| |
Objectives |
0:07 | |
| |
Solving Rational Equations |
0:23 | |
| |
| Isolate the Specified Variable |
1:23 | |
| |
Example 1 |
1:58 | |
| |
Example 2 |
5:00 | |
| |
Example 3 |
8:23 | |
| |
Example 4 |
13:25 | |
|
Rational Inequalities |
18:54 |
| |
Intro |
0:00 | |
| |
Objectives |
0:06 | |
| |
Rational Inequalities |
0:18 | |
| |
| Testing Intervals for Rational Inequalities |
0:38 | |
| |
| Steps to Solving Rational Inequalities |
1:05 | |
| |
| Tips to Solving Rational Inequalities |
2:27 | |
| |
Example 1 |
3:33 | |
| |
Example 2 |
12:21 | |
|
Applications of Rational Expressions |
20:20 |
| |
Intro |
0:00 | |
| |
Objectives |
0:07 | |
| |
Applications of Rational Expressions |
0:27 | |
| |
| Work Problems |
1:05 | |
| |
Example 1 |
2:58 | |
| |
Example 2 |
6:45 | |
| |
Example 3 |
13:17 | |
| |
Example 4 |
16:37 | |
|
Variation & Proportion |
27:04 |
| |
Intro |
0:00 | |
| |
Objectives |
0:10 | |
| |
Variation and Proportion |
0:34 | |
| |
| Variation |
0:35 | |
| |
| Inverse Variation |
1:01 | |
| |
| Direct Variation |
1:10 | |
| |
| Setting Up Proportions |
1:31 | |
| |
Example 1 |
2:27 | |
| |
Example 2 |
5:36 | |
| |
Variation and Proportion Cont. |
8:29 | |
| |
| Inverse Variation |
8:30 | |
| |
Example 3 |
9:20 | |
| |
Variation and Proportion Cont. |
12:41 | |
| |
| Constant of Proportionality |
12:42 | |
| |
Example 4 |
13:59 | |
| |
Variation and Proportion Cont. |
16:17 | |
| |
| Varies Directly as the nth Power |
16:30 | |
| |
| Varies Inversely as the nth Power |
16:53 | |
| |
| Varies Jointly |
17:09 | |
| |
| Combining Variation Models |
17:36 | |
| |
Example 5 |
19:09 | |
| |
Example 6 |
22:10 | |
Section 11: Radical Equations |
|
Rational Exponents |
14:32 |
| |
Intro |
0:00 | |
| |
Objectives |
0:07 | |
| |
Rational Exponents |
0:32 | |
| |
| Power on Top, Root on Bottom |
1:05 | |
| |
Example 1 |
1:37 | |
| |
Rational Exponents Cont. |
4:04 | |
| |
| Using Rules from Exponents for Radicals as Exponents |
4:05 | |
| |
| Combining Terms Under a Single Root |
4:50 | |
| |
Example 2 |
5:21 | |
| |
Example 3 |
7:39 | |
| |
Example 4 |
11:23 | |
| |
Example 5 |
13:14 | |
|
Simplify Rational Exponents |
15:12 |
| |
Intro |
0:00 | |
| |
Objectives |
0:07 | |
| |
Simplify Rational Exponents |
0:25 | |
| |
| Product Rule for Radicals |
0:26 | |
| |
| Product Rule to Simplify Square Roots |
1:11 | |
| |
| Quotient Rule for Radicals |
1:42 | |
| |
| Applications of Product and Quotient Rules |
2:17 | |
| |
| Higher Roots |
2:48 | |
| |
Example 1 |
3:39 | |
| |
Example 2 |
6:35 | |
| |
Example 3 |
8:41 | |
| |
Example 4 |
11:09 | |
|
Adding & Subtracting Radicals |
17:22 |
| |
Intro |
0:00 | |
| |
Objectives |
0:07 | |
| |
Adding and Subtracting Radicals |
0:33 | |
| |
| Like Terms |
1:29 | |
| |
| Bases and Exponents May be Different |
2:02 | |
| |
| Bases and Powers Must be Same when Adding and Subtracting |
2:42 | |
| |
| Add Radicals' Coefficients |
3:55 | |
| |
Example 1 |
4:47 | |
| |
Example 2 |
6:00 | |
| |
Adding and Subtracting Radicals Cont. |
7:10 | |
| |
| Simplify the Bases to Look the Same |
7:25 | |
| |
Example 3 |
8:23 | |
| |
Example 4 |
11:45 | |
| |
Example 5 |
15:10 | |
|
Multiply & Divide Radicals |
19:24 |
| |
Intro |
0:00 | |
| |
Objectives |
0:08 | |
| |
Multiply and Divide Radicals |
0:25 | |
| |
| Rules for Working With Radicals |
0:26 | |
| |
| Using FOIL for Radicals |
1:11 | |
| |
| Dont Distribute Powers |
2:54 | |
| |
| Dividing Radical Expressions |
4:25 | |
| |
| Rationalizing Denominators |
6:40 | |
| |
Example 1 |
7:22 | |
| |
Example 2 |
8:32 | |
| |
Multiply and Divide Radicals Cont. |
9:23 | |
| |
| Rationalizing Denominators with Higher Roots |
9:25 | |
| |
Example 3 |
10:51 | |
| |
Example 4 |
11:53 | |
| |
Multiply and Divide Radicals Cont. |
13:13 | |
| |
| Rationalizing Denominators with Conjugates |
13:14 | |
| |
Example 5 |
15:52 | |
| |
Example 6 |
17:25 | |
|
Solving Radical Equations |
15:05 |
| |
Intro |
0:00 | |
| |
Objectives |
0:07 | |
| |
Solving Radical Equations |
0:17 | |
| |
| Radical Equations |
0:18 | |
| |
| Isolate the Roots and Raise to Power |
0:34 | |
| |
Example 1 |
1:13 | |
| |
Example 2 |
3:09 | |
| |
Solving Radical Equations Cont. |
7:04 | |
| |
| Solving Radical Equations with More than One Radical |
7:05 | |
| |
Example 3 |
7:54 | |
| |
Example 4 |
13:07 | |
|
Complex Numbers |
29:16 |
| |
Intro |
0:00 | |
| |
Objectives |
0:06 | |
| |
Complex Numbers |
1:05 | |
| |
| Imaginary Numbers |
1:08 | |
| |
| Complex Numbers |
2:27 | |
| |
| Real Parts |
2:48 | |
| |
| Imaginary Parts |
2:51 | |
| |
| Commutative, Associative, and Distributive Properties |
3:35 | |
| |
| Adding and Subtracting Complex Numbers |
4:04 | |
| |
| Multiplying Complex Numbers |
6:16 | |
| |
| Dividing Complex Numbers |
8:59 | |
| |
| Complex Conjugate |
9:07 | |
| |
| Simplifying Powers of i |
14:34 | |
| |
| Shortcut for Simplifying Powers of i |
18:33 | |
| |
Example 1 |
21:14 | |
| |
Example 2 |
22:15 | |
| |
Example 3 |
23:38 | |
| |
Example 4 |
26:33 | |