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# Algebra 2

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### Algebra 2 Details

Thinkwell's Algebra 2 with online videos and automatic grading gives your student the algebra help they need. Thinkwell's complete online Algebra 2 course makes solving algebra problems a breeze.

Thinkwell's video lessons feature award-winning teacher Edward Burger. Students love Professor Burger's ability to break down concepts and explain each example step by step, all while giving them the tips and tricks that make algebra easy for anyone.

Thinkwell's Algebra 2 has all the features your home school needs:

• Aligned to Algebra 2 National Math Standards
• More than 100 topics with 400+ engaging video lessons (see sample)
• 34-week lesson plan with daily assignments (see lesson plan)
• 128.8 available contact hours (What is this?)
• Printable Algebra 2 worksheets and answer keys for each subchapter and topic
(See sample worksheet - See sample answer key)
• 750+ automatically graded exercises allow you to track your progress
• 28 animated interactivities with audio
• Algebra 2 practice tests and final tests for all 14 chapters, as well as a midterm and a final
• Real-world application examples in both lectures and exercises
• Closed captioning for all video lessons
• Glossary of more than 250 mathematical terms
• Brand-new content to help students advance their mathematical knowledge:
• Linear equations, inequalities, and functions
• Linear systems in two and three dimensions
• Matrix operations
• Quadratic functions and complex numbers
• Polynomial, exponential, and logarithmic functions
• Rational and radical functions
• Graphing functions
• Conic sections
• Probability and statistics
• Arithmetic and geometric sequences and series
• Trigonometric functions, graphs, and identities

### About the Author

Edward Burger
Williams College

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest listed him in the "100 Best of America". After completing his tenure as Gaudino Scholar at Williams, he was named Lissack Professor for Social Responsibility and Personal Ethics. In 2010, he won the prestigious Robert Foster Cherry Award for Great Teaching.

Prof. Burger is the author of over 50 articles, videos, and books, including the trade book Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

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#### 1. Foundations for Functions

• 1.1 Properties and Operations
• 1.1.1 Sets of Numbers
• 1.1.2 Properties of Real Numbers
• 1.1.3 Square Roots
• 1.1.4 Simplifying Algebraic Expressions
• 1.1.5 Properties of Exponents and Scientific Notation
• 1.2 Introduction to Functions
• 1.2.1 Relations and Functions
• 1.2.2 Function Notation
• 1.2.3 Exploring Transformations
• 1.2.4 Introduction to Parent Functions

#### 2. Linear Functions

• 2.1 Linear Equations and Inequalities
• 2.1.1 Solving Linear Equations and Inequalities
• 2.1.2 Proportional Reasoning
• 2.1.3 Graphing Linear Functions
• 2.1.4 Writing Linear Functions
• 2.1.5 Linear Inequalities in Two Variables
• 2.2 Applying Linear Functions
• 2.2.1 Transforming Linear Functions
• 2.2.2 Curve Fitting With Linear Models
• 2.2.3 Solving Absolute-Value Equations and Inequalities
• 2.2.4 Absolute-Value Functions

#### 3. Linear Systems

• 3.1 Linear Systems in Two Dimensions
• 3.1.1 Using Graphs and Tables to Solve Linear Systems
• 3.1.2 Using Algebraic Methods to Solve Linear Systems
• 3.1.3 Solving Systems of Linear Inequalities
• 3.1.4 Linear Programming
• 3.2 Linear Systems in Three Dimensions
• 3.2.1 Linear Equations in Three Dimensions
• 3.2.2 Solving Linear Systems in Three Variables

#### 4. Matrices

• 4.1 Matrix Operations
• 4.1.1 Matrices and Data
• 4.1.2 Multiplying Matrices
• 4.1.3 Using Matrices to Transform Geometric Figures
• 4.2 Using Matrices to Solve Systems
• 4.2.1 Determinants and Cramer's Rule
• 4.2.2 Matrix Inverses and Solving Systems
• 4.2.3 Row Operations and Augmented Matrices

#### 5. Quadratic Functions

• 5.1 Quadratic Functions and Complex Numbers
• 5.1.1 Using Transformations to Graph Quadratic Functions
• 5.1.2 Properties of Quadratic Functions in Standard Form
• 5.1.3 Solving Quadratic Equations by Graphing and Factoring
• 5.1.4 Completing the Square
• 5.1.5 Complex Numbers and Roots
• 5.1.6 The Quadratic Formula
• 5.2 Applying Quadratic Functions
• 5.2.1 Solving Quadratic Inequalities
• 5.2.2 Curve Fitting with Quadratic Models
• 5.2.3 Operations with Complex Numbers

#### 6. Polynomial Functions

• 6.1 Operations with Polynomials
• 6.1.1 Polynomials
• 6.1.2 Adding and Subtracting Polynomials
• 6.1.3 Multiplying Polynomials
• 6.1.4 Factoring Polynomials
• 6.1.5 Dividing Polynomials
• 6.1.6 Synthetic Division and the Remainder and Factor Theorems
• 6.2 Roots and Graphs of Polynomial Functions
• 6.2.1 Finding Real Roots of Polynomial Equations
• 6.2.2 Fundamental Theorem of Algebra
• 6.2.3 Investigating Graphs of Polynomial Functions
• 6.2.4 Transforming Polynomial Functions
• 6.2.5 Curve Fitting with Polynomial Models

#### 7. Exponential and Logarithmic Functions

• 7.1 Exponential Functions and Logarithms
• 7.1.1 Exponential Functions, Growth, and Decay
• 7.1.2 Inverses of Relations and Functions
• 7.1.3 Logarithmic Functions
• 7.1.4 Properties of Logarithms
• 7.2 Applying Exponential and Logarithmic Functions
• 7.2.1 Exponential and Logarithmic Equations and Inequalities
• 7.2.2 The Natural Base, e
• 7.2.3 Transforming Exponential and Logarithmic Functions
• 7.2.4 Curve Fitting With Exponential and Logarithmic Models

#### 8. Rational and Radical Functions

• 8.1 Rational Functions
• 8.1.1 Variation Functions
• 8.1.2 Multiplying and Dividing Rational Expressions
• 8.1.3 Adding and Subtracting Rational Expressions
• 8.1.4 Rational Functions
• 8.1.5 Solving Rational Equations and Inequalities
• 8.2 Radical Functions
• 8.2.1 Radical Expressions and Rational Exponents
• 8.2.2 Radical Functions
• 8.2.3 Solving Radical Equations and Inequalities

#### 9. Properties and Attributes of Functions

• 9.1 Functions and Their Graphs
• 9.1.1 Multiple Representations of Functions
• 9.1.2 Piecewise Functions
• 9.1.3 Transforming Functions
• 9.2 Functional Relationships
• 9.2.1 Operations with Functions
• 9.2.2 Functions and Their Inverses
• 9.2.3 Modeling Real-World Data

#### 10. Conic Sections

• 10.1 Understanding Conic Sections
• 10.1.1 Introduction to Conic Sections
• 10.1.2 Circles
• 10.1.3 Ellipses
• 10.1.4 Hyperbolas
• 10.1.5 Parabolas
• 10.2 Applying Conic Sections
• 10.2.1 Identifying Conic Sections
• 10.2.2 Solving Nonlinear Systems

#### 11. Probability and Statistics

• 11.1 Probability
• 11.1.1 Permutations and Combinations
• 11.1.2 Theoretical and Experimental Probability
• 11.1.3 Independent and Dependent Events
• 11.1.4 Compound Events
• 11.2 Data Analysis and Statistics
• 11.2.1 Measures of Central Tendency and Variation
• 11.2.2 Binomial Distributions

#### 12. Sequences and Series

• 12.1 Exploring Arithmetic Sequences and Series
• 12.1.1 Introduction to Sequences
• 12.1.2 Series and Summation Notation
• 12.1.3 Arithmetic Sequences and Series
• 12.2 Exploring Geometric Sequences and Series
• 12.2.1 Geometric Sequences and Series
• 12.2.2 Mathematical Induction and Infinite Geometric Series

#### 13. Trigonometric Functions

• 13.1 Introduction to Trigonometric Functions
• 13.1.1 Right-Angle Trigonometry
• 13.1.2 Angles of Rotation
• 13.1.3 The Unit Circle
• 13.1.4 Inverses of Trigonometric Functions
• 13.2 Applying Trigonometric Functions
• 13.2.1 The Law of Sines
• 13.2.2 The Law of Cosines

#### 14. Trigonometric Graphs and Identities

• 14.1 Exploring Trigonometric Graphs
• 14.1.1 Graphs of Sine and Cosine
• 14.1.2 Graphs of Other Trigonometric Functions
• 14.2 Trigonometric Identities
• 14.2.1 Fundamental Trigonometric Identities
• 14.2.2 Sum and Difference Identities
• 14.2.3 Double-Angle and Half-Angle Identities
• 14.2.4 Solving Trigonometric Equations

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### Testimonials

It is wonderful to have the checklist of each lesson for my daughter to see her progress, and for me to have an easy evaluation for our homeschool program. It is so nice not to be the one grading her.
When I use Thinkwell, the retention rate of what I've learned is significantly increased. I would say that Thinkwell not only makes the material easier to digest but creates a fun way to actually learn math.
Thinkwell turns learning into enjoyment, only you learn so much more!
Thinkwell contains all the necessary components for you to gain a thorough understanding of the course. The lectures are there, the notes are there, and the quizzes are there. It's a complete package.
Throughout the Thinkwell lectures, I never got lost. I never got confused. I was able to understand... The lecture section is outstanding.
Thinkwell is a program that allows students like me to learn these subjects while still keeping us entertained. Good job, Thinkwell.
- Annette J.
- Sung L.
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- Spencer R.
Professor Burger is passionate about Math and he is able to transmit his passion and clear thinking through his lectures. I could understand not only the concepts and HOW to solve the problems, but WHY we solve them in a certain way... You meet just a few of those instructors in a lifetime.
I have recommended them to many friends, all of whom have used them with great success. Dr. Burger's sense of humor really adds to the class and makes it particularly engaging for my son.
Our family has enjoyed the format and scope of the Thinkwell course we've used in our homeschool program. It is well organized, easy to use and has been an asset to our homeschool curriculum.
Thinkwell is a great resource, with videos, notes, sample problems, and animations to help students understand the material and solve problems.
Thinkwell is better than a textbook because it is more interactive! Instead of just droning over a book, a virtual person actually comes and teaches it to you.
Thinkwell is a WONDERFUL tool for learning... The transcripts and supplemental materials are very helpful in explaining the material and they make studying for the exams an absolute breeze.
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