Algebra 2

Teacher: Shirly
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Introduction

0 Course Introduction 02:02

Function Properties

1 Lesson 1: Notations 14:12

Different notations are used in different areas of life depending on the audience. This lesson reviews the inequality notation and word descriptions.  Then we explore the new interval notation and how to use it.

1 Lesson 1: Notations Practice 19:20

Review of Practice

2 Lesson 2: Properties of Graphs 26:36

Properties of Graphs

3 Lesson 2: Properties of Graphs Practice 31:52

Review Practice

4 Lesson 3: Polynomial Properties 25:04

Properties determined from the equations.

5 Lesson 3: Polynomial Properties Practice 13:53

Review Practice

6 Lesson 4: End Behavior 22:19

Explore the relationship between the function and infinity.

7 Lesson 4: End Behavior Practice 10:01

Review Practice

Parent Functions

8 Lesson 5: Part 1: Parent Functions 04:50

This lessons introduces the following nine parent functions that are studied in greater detail later in the course: linear, absolute value, quadratic, square root, cubic, cube root, rational, exponential, and log. We learn how to recognize the type of parent function from a description, an equation, or a graph. Each of the notes videos are about 5 minutes long. The examples and review of practice problems videos are over 10 minutes each. Watch all of the videos first and take the notes. Then work the practice problems for all parts are in this lesson.

9 Lesson 5: Part 2: Quadratics 04:21

Introduction to the quadratic parent function.

10 Lesson 5: Part 3: Square Root 04:29

Introduction to square root parent functions

11 Lesson 5: Part 4: Absolute Value 04:56

Introduction to absolute value parent functions

12 Lesson 5: Part 5: Cubic 05:00

Introduction to cubic parent functions

13 Lesson 5: Part 6: Cube Roots 05:01

Introduction to cube root parent functions

14 Lesson 5: Part 7: Rational 06:38

Introduction to rational parent functions

15 Lesson 5: Part 8: Exponential 05:03

Introduction to exponential parent functions

16 Lesson 5: Part 9: Logs 06:24

Introduction to Log parent functions

17 Lesson 5: PF Examples 07:40

Examples based on notes from all parts

18 Lesson 5: Parent Function Practice 12:25

Practice problems using knowledge from all parts. Documents are in Part 1 of lesson.

19 Lesson 6: Transformations of Graphs 12:20

How changes in the parent function affect the graph and other properties. Notes & practice include work for parts 1 & 2.

20 Lesson 6: Transformation Practice 08:44

Review Practice

21 Lesson 7: Transformations with Equations 22:28

How changes in the equation affect the graph and other properties. All notes and practice are attached to part 1.

22 Lesson 7: Transformations with Equations Practice 25:37

Review Practice

Modeling Functions

23 Lesson 8: Scatterplots 14:18

Review of the relationship for collected data. and determining the type of function.

24 Lesson 8: Scatterplots Practice 06:26

Review Practice

25 Lesson 9: Finite Difference 16:09

Review of the relationship for collected data. and determining the type of function.

26 Lesson 9: Finite Difference Practice 10:28

Review practice

27 Lesson 10: Modeling Data 29:14

Finding the function that best fits the data to predict outcomes. TI-84 required.

28 Lesson 10: Modeling Data Practice 39:12

Review Practice

29 Lesson 11: Modeling Data Project 03:00

Short research activity applying modeling of data with real research.

Absolute Value Functions

30 Lesson 12: Absolute Value Equations 23:01

For the few absolutes in life we write equations.

31 Lesson 12: Part 1: Absolute Value Equations Practice 26:43

Review Practice

32 Lesson 12: Part 2: Absolute Value Equations Practice 15:19

Review Practice

33 Lesson 13: Compound Inequalities 13:04

In life things are not always equal.

34 Lesson 13: Compound Inequalities Practice 23:41

Review Practice

35 Lesson 14: Absolute Value Inequalities 15:19

Combining the absolute value function and inequalities give real world application.

36 Lesson 14: Absolute Value Inequalities Practice 26:43

Review Practice

37 Lesson 14: Absolute Value Inequalities Practice 2 15:19

Review word problem practice

38 Lesson 15: Absolute Value Inequalities Project 02:33

Short project designed to help students apply this knowledge to the real world.

Systems of Functions

39 Lesson 16: Solving Systems by Graphing 22:42

Review how to graph linear equations and use to solve systems.

40 Lesson 16: Solving Systems by Graphing Practice 15:54

Review Practice

41 Lesson 17: Solving Systems by Graphing Project 03:48

Brief project to apply knowledge to real world scenario.

42 Lesson 18: Solving Systems of Inequalities 25:25

Review of graphing linear inequalities and using them to solve systems.

43 Lesson 19: Solving Systems of Inequalities 20:44

Word problems = applications of the math.

44 Lesson 19: Solving Systems of Inequalities Practice 30:37

Review practice

45 Lesson 20: Solving Systems using Substitution 12:23

Review of solving 2x2 systems from algebra 1.

46 Lesson 21: Solving Systems using Substitution 28:06

Using the substitution method to solve 3x3 systems.

47 Lesson 21: Solving Systems using Substitution Practice 38:47

Review practice

48 Lesson 22: Solve Systems using Elimination 17:24

Review of solving 2x2 systems from algebra 1.

49 Lesson 23: Solve Systems using Elimination 19:55

Using the Elimination method to solve 3x3 systems.

50 Lesson 23: Solve Systems using Elimination Practice 32:00

Review Practice

Matricies

51 Lesson 24: Properties of a Matrix 29:47

This is not about the movies! A matrix is another method for solving systems of equations.

52 Lesson 24: Properties of a Matrix Practice 17:51

Review Practice

53 Lesson 25: Determinant & Inverse 20:19

In order to use a matrix to solve, we have to find the determinant and the inverse of a matrix.

54 Lesson 25: Determinant & Inverse Practice 12:30

Review Practice

55 Lesson 26: Solving Systems using a Matrix 29:36

Finally the Solving! You need a TI-84 or TI-85 for this lesson. I will show how to solve by hand and by calculator.

56 Lesson 26: Solving Systems using a Matrix Practice 27:48

Review Practice

57 Lesson 26: Solving Systems using a Matrix Project 03:48

Food for thought activity from the bottom of the notes.

Factoring

58 Lesson 27: GCF 10:21

Review of Greatest Common Factor

59 Lesson 27: GCF Practice 18:52

Review Practice

60 Lesson 28: Factoring Simple Quadratics 14:08

factoring quadratics with a lead coefficient equal to one.

61 Lesson 28: Factoring Simple Quadratics Practice 39:43

Review Practice

62 Lesson 29: Factoring Complex Quadratics 24:10

Factoring quadratics with a lead coefficient not equal to one.

63 Lesson 29: Factoring Complex Quadratics Practice 21:29

Review Practice

64 Lesson 30: Factor Higher Polynomials 17:33

Factoring polynomials with a degree greater than two.

65 Lesson 30: Factor Higher Polynomials Practice 19:10

Review Practice

66 Lesson 31: Factor Perfect Cubes 11:58

There is a shortcut for perfect cubes! Here is the trick...

67 Lesson 31: Factor Perfect Cubes Practice 39:43

Review Practice

Quadratic Functions

68 Lesson 32: Quadratic Graph Properties 29:52

Explore finding the properties of a quadratic from graphs and real-world applications

69 Lesson 32: Quadratic Graph Properties Practice 23:57

Review Practice

70 Lesson 33: Complex Numbers 21:55

Identify and use complex numbers and root

71 Lesson 33: Complex Numbers Practice 16:54

Review Practice

72 Lesson 34: Quadratic Formula 15:23

Solve quadratic equations using the quadratic formula.

73 Lesson 34: Quadratic Formula Practice 28:43

Review Practice

74 Lesson 35: Complete the Square 17:43

Solve quadratic equations using the complete the square method.

75 Lesson 35: Complete the Square Practice 20:17

Review Practice

76 Lesson 36: Quadratic Inequalities 22:52

Solve quadratic inequalities using a table or a graph.

77 Lesson 36: Quadratic Inequalities Practice 29:55

Review Practice

78 Lesson 37: Quadratic Forms 19:02

Change from one form of the quadratic to another to find key information.

79 Lesson 37: Quadratic Forms Practice 29:48

Review Practice

80 Lesson 38: Write a Quadratic Equation 14:14

Write a quadratic given different pieces of information.

81 Lesson 38: Write a Quadratic Equation Practice 20:02

Review Practice

82 Lesson 39: Quadratic Project 02:42

Use the information from the Quadratic Lessons to fly to the moon...or at least throw a football on the moon.

Radical Functions

83 Lesson 40: Graphing Radicals 17:43

Graphing square root and cube root equations and inequalities.

84 Lesson 40: Graphing Radicals Practice 27:29

Review Practice

85 Lesson 41: Add & Subtract Radicals 21:43

Add and subtract square roots and cube roots

86 Lesson 41: Add & Subtract Radical Practice 17:49

Review Practice

87 Lesson 42: Multiply & Divide Radicals 14:14

Multiply, divide, and simplify square roots and cube roots

88 Lesson 42: Multiply Radical Practice 21:22

Review Practice

89 Lesson 42: Divide Radical Practice 19:28

Review Practice

90 Lesson 43: Solve Radical Equations 14:53

Solve square root and cube root equations

91 Lesson 43: Solve Radical Equations Practice 20:31

Review Practice

92 Lesson 44: Solve Radical Inequalities 19:48

Solve and graph radical inequalities

93 Lesson 44: Solve Radical Inequalities Practice 29:55

Review Practice

94 Lesson 45: Radical Scenarios 11:53

Square root functions in the world

95 Lesson 45: Radical Scenarios Practice 23:49

Review Practice

96 Lesson 46: Radical Project 01:20

Application Project

Polynomial Functions

97 Lesson 47: Simplify Polynomials 21:02

Add and Subtract polynomial expressions

98 Lesson 47: Simplify Polynomials Practice 17:14

Review Practice

99 Lesson 48: Polynomial Multiplication 18:42

Multiplying polynomials of all shapes and sizes

100 Lesson 48: Polynomial Multiplication Practice 16:32

Review practice

101 Lesson 49: Pascal's Triangle 21:01

A shortcut method for multiplying binomials to a power.

102 Lesson 49: Pascal's Triangle Practice 16:38

Review Practice

103 Lesson 50: Long Division 18:31

First method to dividing polynomials.

104 Lesson 50: Long Division Practice 15:32

Review Practice

105 Lesson 51: Synthetic Division 29:43

Shortcut division process and theorems that can be used instead of long division.

106 Lesson 51: Synthetic Division Practice 21:15

Review Practice

107 Lesson 52: Polynomial Project 02:16

Use all of the polynomial lessons, including end behaviors and graphs from the beginning.

Rational Functions

108 Lesson 53: Variation 17:02

Direct, inverse and joint variation and how it describes real world relationships.

109 Lesson 53: Variation Practice 29:11

Review Practice

110 Lesson 54: Add & Subtract Rational 28:56

Add & subtract rational expressions in order to simplify

111 Lesson 54: Add & Subtract Rational Practice 33:48

Review Practice

112 Lesson 55: Simplify Rationals 10:36

Simplify rational expressions

113 Lesson 55: Simplify Rationals Practice 16:42

Review Practice

114 Lesson 56: Multiply Rationals 14:22

Simplify & multiply rational expressions

115 Lesson 56: Multiply Rationals Practice 20:44

Review Practice

116 Lesson 57: Divide Rationals 17:14

Divide & simplify rational expressions

117 Lesson 57: Divide Rationals Practice 22:59

Review Practice

118 Lesson 58: Solve Rational Equations 26:32

find the solution for the rational equations

119 Lesson 58: Solve Rational Equations Practice 33:45

Review Practice

120 Lesson 59: Graphing Rational Parent Function 25:27

Identify key information and graph the parent function form of the rational equation.

121 Lesson 59: Graphing Rationals PF Practice 19:53

Review Pratice

122 Lesson 60: Graph Standard Rationals 29:57

Identify key information and graph the standard form of the rational equation.

123 Lesson 60: Graph Standard Rationals Practice 47:30

Review Practice

124 Lesson 61: Rational Scenarios 20:49

How are rational functions used in the real world?

125 Lesson 61: Rational Scenarios Practice 30:37

Review Practice

126 Lesson 62: Rational Project 01:55

Optional application project

Exponential Functions

127 Lesson 63: Rational Exponents 16:08

How are exponents and radicals are the same thing?

128 Lesson 63: Rational Exponents Practice 19:07

Review Practice

129 Lesson 64: Multiplying Exponents 17:44

What to do with exponents when multiplying?

130 Lesson 64: Multiplying Exponents Practice 17:38

Review Practice

131 Lesson 65: Dividing Exponents 14:18

What to do with exponents when dividing?

132 Lesson 65: Dividing Exponents Practice 22:08

Review Practice

133 Lesson 66: Zero & Negative Exponents 17:55

Review of zero exponents. What to do with negative exponents?

134 Lesson 66: Zero & Negative Exponents Practice 14:16

Review Practice

135 Lesson 67: Graphing Exponential Functions 13:04

How to transform the graphs of exponential functions using points.

136 Lesson 67: Graphing Exponential Functions Practice 18:13

Review Practice

137 Lesson 68: Compound Interest 12:58

How can I make more money?

138 Lesson 68: Compound Interest Practice 13:17

Review Practice

139 Lesson 69: Growth & Decay 12:24

Exponential growth and decay in life.

140 Lesson 69: Growth & Decay Practice 13:17

Review Practice

141 Lesson 70: Exponential Models 23:07

Using data to find answers and the exponential equations.

142 Lesson 70: Exponential Models Practice 28:56

Review Practice

143 Lesson 71: Exponential Projects 02:02

Investment project and medicine vs. bacteria project.

Log Functions

144 Lesson 72: Introduction to Logs 22:22

Introduction to logarithm functions, converting logs to exponents, and solving very simple logs.

145 Lesson 72: Introduction to Logs Practice 19:14

Review Practice

146 Lesson 73: Expanding Logs 16:36

Expand and solve logs

147 Lesson 73: Expanding Logs Practice 15:43

Review Practice

148 Lesson 74: Condense Logs 13:12

Condensing logs and solving

149 Lesson 74: Condense Logs Practice 21:23

Review Practice

150 Lesson 75: Change of Base 17:22

How to change the base of a log to use the preprogrammed calculator buttons.

151 Lesson 75: Change of Base Practice 19:23

Review Practice

152 Lesson 76: Solving Log Equations 21:22

How to solve 3 different types of logarithm equations.

153 Lesson 76: Solving Log Equations Practice 25:33

Review Practice

154 Lesson 77: Graphing Log Functions 18:42

How to accurately graph log equations and inequalities.

155 Lesson 77: Graphing Log Functions Practice 21:15

Review Practice

156 Lesson 78: Log Scenarios 23:58

Applications of Log in real world scenarios

157 Lesson 78: Log Scenarios Practice 22:03

Review Practice

158 Lesson 79: Log Scenarios Project 02:04

Research and apply what you have learned about logs.

159 Lesson 80: Log Models 14:41

Modeling Log equations and inequalities

160 Lesson 80: Log Models Practice 10:08

Review Practice

Non-Parent Functions

161 Lesson 81: Composite Functions 20:23

A new notation for combining functions and simplifying functions.

162 Lesson 81: Composite Functions Practice 26:35

Review Practice

163 Lesson 82: Inverse Functions 24:38

Inverse is like opposite. Find the opposite of this function.

164 Lesson 82: Inverse Functions Practice 32:09

Review Practice

165 Lesson 83: Piecewise Functions 28:20

Functions with domain restrictions and different pieces on the graph.

166 Lesson 83: Piecewise Functions Practice 18:31

Review Practice

Final Exams

167 Final Exams 00:00

The fall final exam includes the following units: Functions, Parent Functions, Modeling, Absolute Value, Systems, Matrices, Factoring, and Quadratics.

 

The spring final exam includes the following units: Radicals, Polynomials, Rationals, Exponents, Logs, and Non-parent functions.

Course Description:

In this course I guide the students step by step through applying the fundamental skills of mathematics to such topics as functions, equations and inequalities, radicals and rational expressions, logarithmic and exponential relationships, quadratic and polynomial equations, and matrices. The student will be introduced to key concepts and theories that provide a foundation for further study in mathematics (College Algebra, PreCalculus, Calculus, and beyond) and increases students’ mathematic literacy, problem solving, and critical thinking skills. Real world scenarios will be used to introduce and expand upon the topics discussed in each unit. Use of graphing calculators will be incorporated into many of the lessons.

 

Course Goals:

Upon completion of this course student will know how to recognize, graph, perform operations (add, subtract, multiply, divide), solve, and apply each parent function. Additionally students will be prepared for PreCalculus (or Geometry which is also a prerequisite for PreCal).

 

Target Audience:

This course is intended for students that have completed Algebra 1 and Math grades 6-8. Geometry is optional, but should be completed before taking Precalculus. Students will be using a TI-84 or TI-85 calculator as part of the lessons.

 

Course Includes:

52.6 Hours of Video (lessons and working of practice problems)

14 Units

83 Video Lessons

83 Exercise Review Videos (where I go over each exercise problem step by step)

73 Outlined notes, Practice Problems and Paper Quizzes (each lesson)

10 Project Lessons (no quizzes)

82 Short Tests (paper & electronic for each lesson)

82 Test Answer Keys (for parents)

2 Paper Final Exams

Parent resources for each lesson include pdf keys of notes, practice problems, paper quizzes and electronic quiz keys.

 

Working Sequence:

Step 1) Watch the explanatory video-lesson.

Step 2) Download the practice worksheets (Documents Section) and work on the activities.

Step 3) Watch the Exercise Review Video where I review each problem step-by-step.

Step 4) Take the online test for the lesson. The system will auto-correct. Answer key is provided under the Resources Section (only for parents)

Step 5) Once we finish the unit, we move on to the next unit. Be sure you understood the content and you worked on the activities before moving to another unit. 

You can repeat steps 2 and 3 as many times as you like until you gain mastery of the topic. Each topic should take you 2 to 3 days on average to complete.

 

Course Topics:

Function Properties

Parent Functions

Modeling Fucntions

Absolute Value Functions

Systems of Functions

Matrices

Factoring

Quadratic Functions

Radical Functions

Polynomial Functions

Rational Functions

Exponential Functions

Log Functions

Non-Parent Functions

 

  • Teacher: Shirly
  • Areas of expertise: Aerospace Engineer: Algebra 1, 2, 3 and PreCalculus
  • Education: Bachelor of Science from Texas A&M University
  • Interests: Art, crafts, music, sewing, painting, cooking, and scrapbooking
  • Skills: teaching, organizing, and innovation
  • Associations: LDS
  • Issues I care about: Having a high moral character.

My life is a journey. I enjoy the steps I make and see the world around me a little differently each time I learn something new. I spent 10 years in the Aerospace industry and worked on the International Space Station and the Apache helicopter programs. I have learned many things and want to share them with you.

Lesson 1: Notations Resources

Keys for Notes, Practice, and Quiz

Lesson 2: Graph Properties

Lesson 3: Properties of Equations

Lesson 4: End Behaviors

Lesson 5: Parent Functions

Lesson 6 & 7: Transformations of PF

Lesson 8 & 9: Scatterplots & Finite Difference

Lesson 10: Modeling Functions

Lesson 12: Absolute Value Equations

Lesson 13: Compound Inequalities

Lesson 14 & 15: Absolute Value Inequalities

Lesson 16 & 17: Graphing Systems

Lesson 18 & 19: Graph Inequalities

Lesson 20 & 21: Solve by Substitution

Lesson 22 & 23: Solve by Elimination

Lesson 24: Matrix Properties

Lesson 25: Determinant & Inverse Matrix

Lesson 26: Solving Systems using Matricies

Lesson 27: GCF

Lesson 28: Simple Factor

Lesson 29: Complex Factor

Lesson 30: Factor Higher Polynomials

Lesson 31: Factor Perfect Cubes

Lesson 32: Quadratic Properties

Lesson 33: Complex Numbers

Lesson 34: Quadratic Formula

Lesson 35: Complete the Square

Lesson 36: Quadratic Inequality

Lesson 37: Quadratic Forms

Lesson 38: Write Quadratic Equations

Lesson 40: Graphing Radicals

Lesson 41: Add & Subtract Radicals

Lesson 42: Multiply & Divide Radicals

Lesson 43: Solve Radical Equations

Lesson 44: Solve Radical Inequalities

Lesson 45: Radical Scenarios

Lesson 47: Simplify Polynomials

Lesson 48: Polynomial Multiplication

Lesson 49: Pascal's Triangle

Lesson 50 & 51: Polynomial Division

Long & Synthetic Division

Lesson 53: Variation

Lesson 54: Add & Subtract Rationals

Lesson 55: Simplify Rationals

Lesson 56: Multiply Rationals

Lesson 57: Divide Rationals

Lesson 58: Solve Rational Equations

Lesson 59 & 60: Graphing Rationals

Parent function & standard form keys

Lesson 61: Rational Scenarios

Lesson 63: Rational Exponents

Lesson 64: Multiplying Exponents

Lesson 65: Dividing Exponents

Lesson 66: Zero & Negative Exponents

Lesson 67: Graphing Exponential Functions

Lesson 68 & 69: Exponential Scenarios

Lesson 70: Exponential Models

Lesson 72: Introduction to Logs

Lesson 73: Expanding Logs

Lesson 74: Condense Logs

Lesson 75: Change of Base

Lesson 76: Solving Log Equations

Lesson 77: Graphing Log Functions

Lesson 78: Log Scenarios

Lesson 80: Log Models

Lesson 81: Composite Functions

Lesson 82: Inverse Functions

Lesson 83: Piecewise Functions

Final Exams

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