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Table of Contents
I. Equations and Inequalities
Expressions and Formulas
28m 56s
- Intro0:00
- Order of Operations0:51
- Variables and Algebraic Expressions0:57
- Order of Operations3:05
- Monomials5:25
- Examples5:37
- Constant, Coefficient, Degree, Power6:27
- Polynomials8:29
- Examples8:42
- Terms, Like Terms, Binomial, Trinomial8:59
- Formulas12:35
- Examples: Area, Volume, Surface Area12:50
- Lecture Example 115:50
- Lecture Example 221:31
- Additional Example 3-1
- Additional Example 4-2
Properties of Real Numbers
23m 45s
- Intro0:00
- Real Numbers0:15
- Rational Numbers0:40
- Irrational Numbers1:38
- Venn Diagram of the Real Numbers2:55
- Properties of Real Numbers6:49
- Commutative Property7:06
- Associative Property7:27
- Identity Property8:01
- Inverse Property8:42
- Distributive Property10:05
- Lecture Example 110:43
- Lecture Example 213:08
- Additional Example 3-1
- Additional Example 4-2
Solving Equations
24m 41s
- Intro0:00
- Translations0:11
- Example: Verbal to Algebraic Expressions0:44
- Properties of Equality2:51
- Reflexive, Symmetric, Transitive Properties2:58
- Addition, Subtraction, Multiplication, Division3:32
- Solving Equations6:09
- Example6:23
- Solving for a Variable8:49
- Example: Surface Area of a Cone8:58
- Lecture Example 111:06
- Lecture Example 212:39
- Additional Example 3-1
- Additional Example 4-2
Solving Absolute Value Equations
17m 36s
- Intro0:00
- Absolute Value Expressions0:10
- Example: Positive Distance0:15
- Absolute Value Equations1:07
- Examples1:18
- No Solutions2:54
- Example: Empty Set2:58
- Number of Solutions3:56
- Examples4:42
- Lecture Example 16:42
- Lecture Example 28:54
- Additional Example 3-1
- Additional Example 4-2
Solving Inequalities
19m 27s
- Intro0:00
- Properties of Inequality0:07
- Addition Property0:21
- Subtraction Property0:48
- Example1:02
- Multiplication Properties1:44
- Multiplying by a Positive Number1:48
- Example: Positive2:17
- Multiplying by a Negative Number2:25
- Example: Negative2:35
- Division Properties3:23
- Example: Positive3:32
- Example: Negative4:04
- Describing the Solution Set6:00
- Set Builder Notation6:15
- Graphing7:15
- Lecture Example 18:04
- Lecture Example 29:09
- Additional Example 3-1
- Additional Example 4-2
Solving Compound and Absolute Value Inequalities
24m 8s
- Intro0:00
- Compound Inequalities0:11
- Example0:33
- 'And' Inequality3:41
- Example: Set Intersection4:00
- 'Or' Inequality6:01
- Example: Set Union6:15
- Absolute Value Inequalities8:19
- Examples8:37
- Lecture Example 111:43
- Lecture Example 214:47
- Additional Example 3-1
- Additional Example 4-2
II. Linear Relations and Functions
Relations and Functions
38m 15s
- Intro0:00
- Coordinate Plane0:38
- Example: Origin and Quadrants0:44
- Relations4:08
- Example: Ordered Pairs4:14
- Domain and Range5:05
- Functions5:57
- Example: Mapping6:11
- One-to-One Functions9:58
- Example10:05
- Graphs of Relations13:42
- Example: Discrete and Continuous13:55
- Vertical Line Test16:26
- Examples16:38
- Equations, Relations, Functions19:38
- Example: Independent and Dependent Variables19:45
- Function Notation21:51
- Examples22:27
- Lecture Example 124:39
- Lecture Example 228:29
- Additional Example 3-1
- Additional Example 4-2
Linear Equations
12m 50s
- Intro0:00
- Linear Equations and Functions0:12
- Example: Linear Equation0:21
- Example: Linear Function1:16
- Standard Form2:13
- Examples2:43
- Graphing with Intercepts3:26
- Example: Intercepts3:51
- Lecture Example 16:25
- Lecture Example 27:53
- Additional Example 3-1
- Additional Example 4-2
Slope
20m 7s
- Intro0:00
- Definition of Slope0:23
- Interpretation of Slope2:19
- Example: 0 Slope and Undefined Slope2:25
- Example: Positive Slope4:04
- Example: Negative Slope4:43
- Parallel Lines6:16
- Perpendicular Lines7:15
- Lecture Example 18:20
- Lecture Example 210:45
- Additional Example 3-1
- Additional Example 4-2
Writing Linear Functions
27m 36s
- Intro0:00
- Slope Intercept Form0:08
- Origin of Form0:21
- Example2:08
- Point Slope Form3:47
- Origin of Form4:01
- Parallel and Perpendicular Lines5:36
- Example: Find Parallel Line5:58
- Lecture Example 18:27
- Lecture Example 212:08
- Additional Example 3-1
- Additional Example 4-2
Special Functions
24m 28s
- Intro0:00
- Step Functions0:13
- Graph0:21
- Example: Birthday Function2:32
- Absolute Value Functions5:21
- Graph5:27
- Piecewise Functions7:34
- Example7:38
- Lecture Example 110:20
- Lecture Example 214:38
- Additional Example 3-1
- Additional Example 4-2
Graphing Inequalities
30m 37s
- Intro0:00
- Graphing Linear Inequalities0:11
- Example: Linear Inequalities0:20
- Half Plane2:04
- Test Point2:53
- Graphing Absolute Value Inequalities5:38
- Example: Linear Inequalities5:49
- Example: Absolute Value8:23
- Lecture Example 111:39
- Lecture Example 214:50
- Additional Example 3-1
- Additional Example 4-2
III. Systems of Equations and Inequalities
Solving Systems of Equations by Graphing
21m 27s
- Intro0:00
- Systems of Equations0:14
- Solving by Graphing0:34
- Types of Systems1:07
- Independent (One Solution)2:02
- Dependent (Infinite Solutions)2:30
- Inconsistent (No Solutions, Parallel)3:37
- Lecture Example 14:52
- Lecture Example 28:42
- Additional Example 3-1
- Additional Example 4-2
Solving Systems of Equations Algebraically
31m 26s
- Intro0:00
- Solving by Substitution0:15
- Examples0:50
- Solving by Elimination4:19
- Examples4:27
- Solving by Multiplication7:24
- Examples7:37
- Inconsistent and Dependent Systems11:42
- Example: Spotting Differences12:07
- Lecture Example 115:00
- Lecture Example 217:35
- Additional Example 3-1
- Additional Example 4-2
Solving Systems of Inequalities by Graphing
20m 43s
- Intro0:00
- Solving by Graphing0:10
- Example: Single Inequality0:14
- No Solution4:16
- Example: No Solution4:25
- Lecture Example 16:25
- Lecture Example 28:23
- Additional Example 3-1
- Additional Example 4-2
Solving Systems of Equations in 3 Variables
21m 27s
- Intro0:00
- Solving Systems in Three Variables0:15
- Ordered Triple0:36
- Number of Solutions1:32
- Lecture Example 12:19
- Lecture Example 26:14
- Additional Example 3-1
- Additional Example 4-2
IV. Matrices
Basic Matrix Concepts
14m 8s
- Intro0:00
- What is a Matrix?0:33
- Example: Rectangular Array0:41
- Element1:52
- Examples: More Matrices2:04
- Dimensions3:40
- Examples4:53
- Special Matrices6:31
- (m x 1) Matrix6:36
- Square Matrix7:01
- Zero Matrix7:38
- Equal Matrices8:23
- Examples8:32
- Lecture Example 110:56
- Lecture Example 211:28
- Additional Example 3-1
- Additional Example 4-2
Matrix Operations
16m 40s
- Intro0:00
- Matrix Addition0:10
- Example1:07
- Matrix Subtraction2:12
- Example2:31
- Scalar Multiplication3:23
- Example4:05
- Properties of Matrix Operations5:31
- Commutative Property5:48
- Associative Property5:59
- Distributive Property6:34
- Lecture Example 17:03
- Lecture Example 28:15
- Additional Example 3-1
- Additional Example 4-2
Matrix Multiplication
22m 47s
- Intro0:00
- Dimension Requirement0:19
- Example0:45
- Matrix Multiplication1:35
- Example2:21
- Properties of Matrix Multiplication6:46
- Associative Property6:59
- Distributive Property7:15
- Commutative Property7:39
- Lecture Example 18:49
- Lecture Example 211:43
- Additional Example 3-1
- Additional Example 4-2
Determinants
25m 47s
- Intro0:00
- What is a Determinant0:15
- Determinant of a 2x2 Matrix0:56
- Difference from Matrices1:16
- Second Order Determinant1:38
- Example2:06
- Determinant of a 3x3 Matrix3:20
- Third Order Determinants3:25
- Origin of Equation (Minors)3:38
- Expansion by Minors6:05
- Example: 3x3 Matrix8:55
- Diagonal Method for 3x3 Matrix12:45
- Example12:55
- Lecture Example 117:03
- Lecture Example 217:42
- Additional Example 3-1
- Additional Example 4-2
Cramer's Rule
25m 42s
- Intro0:00
- System of 2 Equations in 2 Variables0:27
- Example1:20
- System of 3 Equations in 3 Variables3:10
- Example3:51
- Lecture Example 16:45
- Lecture Example 210:22
- Additional Example 3-1
- Additional Example 4-2
Identity and Inverse Matrices
27m 1s
- Intro0:00
- Identity Matrix0:10
- Example: 2x2 Matrix2:18
- Matrix Inverses4:40
- Example: Does Not Exist6:04
- Inverse of a 2x2 Matrix8:17
- Example9:38
- Lecture Example 113:19
- Lecture Example 215:57
- Additional Example 3-1
- Additional Example 4-2
Solving Systems of Equations with Matrices
28m 40s
- Intro0:00
- Matrix Equations0:22
- Example0:40
- Solving Systems of Equations4:20
- Example5:58
- Lecture Example 19:11
- Lecture Example 215:09
- Additional Example 3-1
- Additional Example 4-2
V. Quadratic Functions and Inequalities
Graphing Quadratic Equations
26m 36s
- Intro0:00
- Quadratic Functions0:10
- Parabola0:50
- Example: Opens Upward1:03
- Example: Opens Downward1:54
- Properties of Parabolas3:17
- Axis of Symmetry3:26
- Vertex4:05
- Example4:28
- Maximum and Minimum Values7:10
- Example: Upwards/Minimum7:32
- Example: Downwards/Maximum8:19
- Lecture Example 19:09
- Lecture Example 213:05
- Additional Example 3-1
- Additional Example 4-2
Solving Quadratic Equations by Graphing
19m 26s
- Intro0:00
- Quadratic Equations0:18
- Example: Standard Form0:55
- Solving by Graphing1:39
- Roots1:48
- Example: 2 Solutions1:56
- Example: 1 Solution2:39
- Example: 0 Solutions3:10
- Estimating Solutions3:55
- Example4:07
- Lecture Example 15:16
- Lecture Example 27:51
- Additional Example 3-1
- Additional Example 4-2
Solving Quadratic Equations by Factoring
17m 46s
- Intro0:00
- Factoring Techniques0:16
- Greatest Common Factor (GCF)0:29
- Difference of Two Squares1:45
- Perfect Square Trinomials2:07
- General Trinomials3:16
- Zero Product Rule4:50
- Example5:01
- Lecture Example 16:19
- Lecture Example 28:13
- Additional Example 3-1
- Additional Example 4-2
Imaginary and Complex Numbers
37m 41s
- Intro0:00
- Properties of Square Roots0:17
- Example: Product and Quotient Rules0:33
- Imaginary Numbers4:04
- Powers of Imaginary Numbers5:06
- Example6:27
- Complex Numbers7:21
- Real and Complex Numbers8:19
- Equality9:04
- Example9:17
- Addition and Subtraction9:43
- Example9:55
- Complex Plane11:38
- Example11:52
- Multiplication13:34
- Example13:43
- Division16:36
- Complex Conjugates16:45
- Example18:16
- Lecture Example 123:40
- Lecture Example 226:34
- Additional Example 3-1
- Additional Example 4-2
Completing the Square
16m 42s
- Intro0:00
- Square Root Property0:22
- Examples0:33
- Completing the Square1:48
- Example: Making into Perfect Square1:50
- Solve Equations3:43
- Example3:53
- Equations Where 'a' Not Equal to 16:47
- Example6:57
- Complex Solutions10:14
- Example10:22
- Lecture Example 111:30
- Lecture Example 212:34
- Additional Example 3-1
- Additional Example 4-2
Quadratic Formula and the Discriminant
17m 44s
- Intro0:00
- Quadratic Formula0:37
- Example0:56
- One Rational Root3:10
- Why It Works3:26
- Repeated/Double Root3:49
- Complex Solutions4:31
- Example4:50
- Discriminant7:19
- Discriminant Value and Root Type8:50
- Lecture Example 112:08
- Lecture Example 214:15
- Additional Example 3-1
- Additional Example 4-2
Analyzing the Graphs of Quadratic Functions
23m
- Intro0:00
- Vertex Form0:24
- Example1:56
- Significance of Coefficient 'a'3:15
- Example3:39
- Writing Quadratic Equations in Vertex Form4:51
- Examples5:19
- Lecture Example 18:14
- Lecture Example 210:22
- Additional Example 3-1
- Additional Example 4-2
Graphing and Solving Quadratic Inequalities
34m 38s
- Intro0:00
- Graphing Quadratic Inequalities1:14
- Example: Linear Inequality1:29
- Example: Quadratic Inequality3:11
- Solving Quadratic Inequalities6:32
- Example6:38
- Lecture Example 111:50
- Lecture Example 215:09
- Additional Example 3-1
- Additional Example 4-2
VI. Polynomial Functions
Properties of Exponents
20m 28s
- Intro0:00
- Simplifying Exponential Expressions0:32
- Negative Exponents0:54
- Example: Base 01:16
- Examples1:30
- Properties of Exponents2:22
- Base and Exponent2:52
- Lecture Example 18:29
- Lecture Example 210:58
- Additional Example 3-1
- Additional Example 4-2
Operations on Polynomials
16m 13s
- Intro0:00
- Adding and Subtracting Polynomials0:24
- Example: Signs0:34
- Multiplying Polynomials3:04
- Example3:12
- Lecture Example 16:40
- Lecture Example 27:21
- Additional Example 3-1
- Additional Example 4-2
Dividing Polynomials
29m 26s
- Intro0:00
- Dividing by a Monomial0:16
- Example0:28
- Long Division3:24
- Example: Missing Terms, Remainder3:49
- Example: Long Division6:51
- Synthetic Division10:13
- Example10:44
- Divisor in Synthetic Division13:18
- Example: Coefficient Not 113:30
- Lecture Example 116:41
- Lecture Example 218:22
- Additional Example 3-1
- Additional Example 4-2
Polynomial Functions
29m 34s
- Intro0:00
- Polynomial in One Variable0:17
- Degree n0:30
- Descending Order0:43
- Example: Leading Coefficient1:04
- Function Values3:31
- Example3:42
- Zeros of Polynomial Functions5:45
- Example: Zeros6:04
- End Behavior9:51
- Example: 4 Situations10:51
- Lecture Example 117:30
- Lecture Example 219:11
- Additional Example 3-1
- Additional Example 4-2
Analyzing Graphs of Polynomials
34m 36s
- Intro0:00
- Graphing Polynomial Functions0:09
- End Behavior0:19
- Examples: Degree and Sign of Polynomials1:13
- Location Principle4:50
- Example6:19
- Maximum and Minimum Points7:34
- Example: Relative Maximum and Relative Minimum7:44
- Lecture Example 110:17
- Lecture Example 215:13
- Additional Example 3-1
- Additional Example 4-2
Solving Polynomial Equations
19m 23s
- Intro0:00
- Factoring Polynomials0:08
- Example: Greatest Common Factor (GCF)0:40
- Example: Perfect Square Trinomials1:30
- Example: General Trinomials2:48
- Sum and Difference of Two Cubes3:25
- Example4:18
- Quadratic Form6:20
- Lecture Example 17:30
- Lecture Example 210:43
- Additional Example 3-1
- Additional Example 4-2
Remainder and Factor Theorems
27m 52s
- Intro0:00
- Remainder Theorem0:04
- Quotient and Remainder0:30
- Examples1:34
- Synthetic Substitution5:04
- Example5:28
- Factor Theorem10:00
- Factoring Polynomials11:21
- Example11:51
- Lecture Example 116:38
- Lecture Example 218:41
- Additional Example 3-1
- Additional Example 4-2
Roots and Zeros
31m 4s
- Intro0:00
- Numbers of Roots0:10
- Example: Real and Complex Roots0:23
- Descartes' Rule of Signs3:43
- Example: Positive Real Roots4:58
- Example: Negative Real Roots8:00
- Finding the Roots12:11
- Conjugate Roots13:24
- Lecture Example 115:41
- Lecture Example 219:41
- Additional Example 3-1
- Additional Example 4-2
Rational Zero Theorem
29m 27s
- Intro0:00
- Equation0:14
- Leading Coefficient and Constant Term0:30
- Example2:15
- Leading Coefficient Equal to 18:08
- Example9:20
- Finding Rational Zeros11:48
- Lecture Example 112:10
- Lecture Example 215:59
- Additional Example 3-1
- Additional Example 4-2
VII. Rational Equations and Inequalities
Operations on Functions
35m 12s
- Intro0:00
- Arithmetic Operations0:12
- Example: Domain0:25
- Composition of Functions7:35
- Example7:55
- Composition is Not Commutative17:13
- Example18:18
- Lecture Example 121:51
- Lecture Example 224:25
- Additional Example 3-1
- Additional Example 4-2
Inverse Functions and Relations
18m 12s
- Intro0:00
- Inverse of a Relation0:24
- Example: Ordered Pairs0:33
- Inverse of a Function2:15
- Procedure to Construct an Inverse Function4:28
- Example: Inverse Function4:58
- Example: Inverse Function 27:31
- Inverses and Compositions8:41
- Lecture Example 19:59
- Lecture Example 210:45
- Additional Example 3-1
- Additional Example 4-2
Square Root Functions and Inequalities
26m 24s
- Intro0:00
- Square Root Functions0:06
- Example: Not Square Root Function0:23
- Example: Square Root Function1:17
- Graphing Square Root Functions3:11
- Example: Radicand3:21
- Square Root Inequalities6:51
- Example7:13
- Lecture Example 111:27
- Lecture Example 214:05
- Additional Example 3-1
- Additional Example 4-2
nth Roots
24m 6s
- Intro0:00
- Definition of the nth Root0:13
- Example0:36
- Principal nth Root2:18
- Index3:04
- Examples3:20
- Using Absolute Values6:25
- Examples6:52
- Lecture Example 111:26
- Lecture Example 213:17
- Additional Example 3-1
- Additional Example 4-2
Operations with Radical Expressions
34m 38s
- Intro0:00
- Properties of Radicals0:22
- Example1:37
- Simplifying Radical Expressions2:58
- Examples3:24
- Rationalizing Denominators4:08
- Examples4:18
- Conjugate Radical Expressions8:01
- Example8:09
- Adding and Subtracting Radicals11:23
- Examples11:44
- Multiplying Radicals12:57
- Examples13:03
- Lecture Example 116:53
- Lecture Example 220:11
- Additional Example 3-1
- Additional Example 4-2
Rational Exponents
24m 36s
- Intro0:00
- Definition 10:24
- nth Root0:44
- Example: Even1:29
- Definition 22:55
- Simplifying Expressions3:20
- Examples3:40
- Simplified Form7:07
- Example7:32
- Lecture Example 18:18
- Lecture Example 210:20
- Additional Example 3-1
- Additional Example 4-2
Solving Radical Equations and Inequalities
38m 46s
- Intro0:00
- Radical Equations0:23
- Examples0:34
- Example: Radical Equation4:47
- Extraneous Roots12:29
- Eliminating nth Roots14:28
- Examples14:54
- Radical Inequalities16:38
- Example17:18
- Lecture Example 120:28
- Lecture Example 222:57
- Additional Example 3-1
- Additional Example 4-2
VIII. Radical Expressions and Equations
Multiplying and Dividing Rational Expressions
30m 11s
- Intro0:00
- Simplifying Rational Expressions0:12
- Examples: Rational Expressions0:31
- Factoring -13:26
- Example3:33
- Multiplying and Dividing Rational Expressions4:50
- Multiplying5:08
- Dividing5:16
- Example6:10
- Factoring9:13
- Example9:33
- Complex Fractions13:15
- Example13:27
- Lecture Example 115:36
- Lecture Example 218:25
- Additional Example 3-1
- Additional Example 4-2
Adding and Subtracting Rational Exprsesions
51m 53s
- Intro0:00
- Example: Fractions0:22
- Least Common Multiple (LCM)1:36
- Example2:07
- Adding and Subtracting7:56
- Least Common Denominator (LCD)8:01
- Example: Fractions8:14
- Example: Rational Expression10:23
- Equivalent Fractions13:45
- Example14:20
- Simplifying Complex Fractions20:03
- Example20:28
- Lecture Example 126:34
- Lecture Example 231:06
- Additional Example 3-1
- Additional Example 4-2
Graphing Rational Functions
45m 13s
- Intro0:00
- Rational Functions0:35
- Example0:57
- Breaks in Continuity2:48
- Discontinuities3:19
- Example: Excluded Values3:52
- Graphs and Discontinuities4:36
- Example: Hole Discontinuity6:07
- Example: Asymptote8:53
- Horizontal Asymptotes13:34
- Example13:54
- Lecture Example 117:58
- Lecture Example 220:29
- Additional Example 3-1
- Additional Example 4-2
Direct, Joint, and Inverse Variation
21m 49s
- Intro0:00
- Direct Variation0:16
- Constant of Variation0:44
- Graph of Direct Variation1:28
- Example: Straight Line1:36
- Joint Variation2:55
- Inverse Variation4:17
- Example4:50
- Graph of Inverse Variation5:35
- Example6:00
- Proportions8:00
- Example9:28
- Lecture Example 112:32
- Lecture Example 214:26
- Additional Example 3-1
- Additional Example 4-2
Solving Rational Equations and Inequalities
53m 21s
- Intro0:00
- Rational Equations0:15
- Example: Not Rational Equation0:26
- Example: X in Denominator0:38
- Example: LCD1:08
- Example: Rational Equations5:19
- Extraneous Solutions12:08
- Example12:42
- Rational Inequalities15:31
- Example15:45
- Example: Rational Inequalities12:05
- Lecture Example 132:06
- Lecture Example 235:18
- Additional Example 3-1
- Additional Example 4-2
IX. Exponential and Logarithmic Relations
Exponential Functions
28m 22s
- Intro0:00
- What is an Exponential Function?0:11
- Exponent and Base0:38
- Graphing Exponential Functions1:31
- Example1:34
- Properties4:05
- Growth and Decay9:38
- Equations10:32
- Example11:05
- Inequalities13:00
- Example14:29
- Lecture Example 116:48
- Lecture Example 218:50
- Additional Example 3-1
- Additional Example 4-2
Logarithms and Logarithmic Functions
36m 31s
- Intro0:00
- What are Logarithms?0:17
- Examples1:30
- Logarithmic Functions4:09
- Graph of the Logarithmic Function4:52
- Properties9:08
- Inverse Property10:47
- Equations11:44
- Example12:11
- Inequalities14:45
- Equations with Logarithms on Both Sides17:00
- Example17:18
- Inequalities with Logarithms on Both Sides19:17
- Example19:32
- Lecture Example 120:31
- Lecture Example 222:38
- Additional Example 3-1
- Additional Example 4-2
Properties of Logarithms
29m 50s
- Intro0:00
- Product Property0:08
- Example0:26
- Quotient Property1:06
- Example1:12
- Power Rule3:29
- Example3:33
- Equations5:43
- Example6:19
- Lecture Example 112:19
- Lecture Example 216:13
- Additional Example 3-1
- Additional Example 4-2
Common Logarithms
27m 10s
- Intro0:00
- What are Common Logarithms?0:54
- Base 100:58
- Equations2:00
- Examples2:22
- Inequalities5:35
- Example5:42
- Change of Base9:23
- Example10:09
- Lecture Example 112:04
- Lecture Example 215:16
- Additional Example 3-1
- Additional Example 4-2
Base 'e' and Natural Logarithms
19m 52s
- Intro0:00
- The Number 'e'0:32
- Natural Base0:44
- Euler1:12
- Natural Exponential Function1:38
- Natural Log Function2:44
- Growth and Decay2:55
- Natural Logarithms3:16
- Graph (Inverse)3:34
- Equations and Inequalities4:49
- Lecture Example 17:21
- Lecture Example 29:10
- Additional Example 3-1
- Additional Example 4-2
Exponential Growth and Decay
28m 10s
- Intro0:00
- Decay0:15
- Fixed Percentage0:24
- Rate of Decay2:35
- Scientific Model of Decay (Exponential Decay)4:17
- Graph5:19
- Growth6:19
- Rate of Growth6:36
- Scientific Model of Growth (Exponential Growth)6:41
- Graph6:48
- Lecture Example 17:48
- Additional Example 3-1
- Additional Example 4-2
X. Conic Sections
Midpoint and Distance Formulas
29m 35s
- Intro0:00
- Midpoint Formula0:35
- Distance Formula1:42
- Example2:52
- Lecture Example 13:40
- Lecture Example 26:37
- Additional Example 3-1
- Additional Example 4-2
Parabolas
26m 11s
- Intro0:00
- What is a Parabola?0:21
- Focus and Directrix0:33
- Axis of Symmetry1:41
- Vertex2:03
- Example2:15
- Standard Form3:11
- Upward and Downward4:07
- Graphing Parabolas5:24
- Example6:32
- Latus Rectum7:37
- Horizontal Parabolas9:10
- Focus and Direction12:31
- Lecture Example 113:11
- Lecture Example 216:46
- Additional Example 3-1
- Additional Example 4-2
Circles
17m 33s
- Intro0:00
- What are Circles0:17
- Center, Radius0:37
- Equation (Standard Form)0:46
- Graphing1:21
- Center Not at Origin1:53
- Example2:06
- Lecture Example 14:16
- Lecture Example 28:22
- Additional Example 3-1
- Additional Example 4-2
Ellipses
38m 57s
- Intro0:00
- What are Ellipses?0:59
- Foci1:04
- Properties3:47
- Major Axis, Minor Axis4:03
- Standard Form7:22
- Example8:05
- Vertical Major Axis10:12
- Example10:40
- Graphing Ellipses13:33
- Example: Completing the Square14:04
- Equation with Center at (h,k)17:25
- Example17:53
- Lecture Example 119:36
- Lecture Example 223:52
- Additional Example 3-1
- Additional Example 4-2
Hyperbolas
37m 59s
- Intro0:00
- What are Hyperbolas?1:09
- Properties2:35
- Transverse Axis, Conjugate Axis2:57
- Center, Vertices3:54
- Standard Form4:33
- Vertical Transverse Axis6:35
- Asymptotes10:17
- Graphing Hyperbolas13:44
- Example17:23
- Equation with Center at (h,k)18:20
- Lecture Example 120:19
- Lecture Example 223:25
- Additional Example 3-1
- Additional Example 4-2
Conic Sections
23m 10s
- Intro0:00
- What are Conic Sections?2:16
- Standard Form2:58
- Example5:29
- Identifying Conic Sections6:14
- Example6:55
- Lecture Example 18:55
- Lecture Example 211:18
- Additional Example 3-1
- Additional Example 4-2
Solving Quadratic Systems
28m 18s
- Intro0:00
- Linear Quadratic Systems0:04
- Example0:28
- Solutions3:13
- Quadratic Quadratic System3:36
- Example: Elimination3:45
- Solutions7:34
- Systems of Quadratic Inequalities7:55
- Example8:07
- Lecture Example 111:10
- Lecture Example 216:12
- Additional Example 3-1
- Additional Example 4-2
XI. Sequences and Series
Arithmetic Sequences
27m 44s
- Intro0:00
- Sequences0:27
- Example: Term0:36
- Arithmetic Sequence2:13
- Common Difference2:22
- Example2:35
- Formula for nth Term3:39
- Example4:29
- Equation for nth Term5:58
- Example6:10
- Arithmetic Means7:40
- Example8:13
- Lecture Example 114:08
- Lecture Example 215:35
- Additional Example 3-1
- Additional Example 4-2
Arithmetic Series
29m 12s
- Intro0:00
- What are Arithmetic Series?0:22
- Example: Sequence0:29
- Example: Common Difference (d)0:35
- Sum of Arithmetic Series2:52
- Example3:44
- Sigma Notation6:10
- Example6:48
- Lecture Example 18:32
- Lecture Example 212:39
- Additional Example 3-1
- Additional Example 4-2
Geometric Sequences
24m 52s
- Intro0:00
- What are Geometric Sequences?0:20
- Common Ratio1:03
- Example1:20
- nth Term of a Geometric Sequence3:39
- Geometric Means4:16
- Example: Missing Term5:06
- Lecture Example 18:09
- Lecture Example 211:42
- Additional Example 3-1
- Additional Example 4-2
Geometric Series
27m 2s
- Intro0:00
- What are Geometric Series?0:20
- Example: Common Ratio1:00
- Sum of Geometric Series2:27
- Example4:01
- Sigma Notation4:56
- Example: Index5:24
- Example6:20
- Another Sum Formula7:51
- Specific Terms9:19
- Lecture Example 111:15
- Lecture Example 214:30
- Additional Example 3-1
- Additional Example 4-2
Infinite Geometric Series
24m 1s
- Intro0:00
- What are Infinite Geometric Series?0:35
- Partial Sums of the Infinite Series1:17
- Example1:24
- Sum of an Infinite Geometric Series3:16
- Convergent Series3:25
- Example4:17
- Sigma Notation5:31
- Example5:43
- Repeating Decimals6:38
- Example6:48
- Lecture Example 19:33
- Lecture Example 211:20
- Additional Example 3-1
- Additional Example 4-2
Recursion and Special Sequences
17m 11s
- Intro0:00
- Fibonacci Sequence0:17
- Example: Fibonacci Sequence0:36
- Example: Recursive Formula2:38
- Iteration3:40
- Example4:57
- Lecture Example 17:10
- Lecture Example 29:03
- Additional Example 3-1
- Additional Example 4-2
Binomial Theorem
38m 25s
- Intro0:00
- Pascal's Triangle0:11
- General Form2:43
- Properties7:01
- Binomial Theorem9:20
- Example11:47
- Finding a Specific Term16:24
- Example16:32
- Lecture Example 120:35
- Lecture Example 223:30
- Additional Example 3-1
- Additional Example 4-2
Proof and Mathematical Induction
19m 53s
- Intro0:00
- Math Induction Principle0:19
- Example0:29
- Counter Examples5:00
- Example5:14
- Lecture Example 17:16
- Lecture Example 210:53
- Additional Example 3-1
- Additional Example 4-2
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For more information, please see full course syllabus of Algebra 2
For more information, please see full course syllabus of Algebra 2
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