College Algebra Online Course


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Thinkwell's College Algebra with Professor Edward Burger

College Algebra is the lowest level math course for college credit at most universities.  This course is an excellent supplement for students enrolled in a college algebra class, or students wanting to brush up on their algebra before taking precalculus or calculus course.

At the heart of the course is a series of entertaining video lessons by award-winning and Professor Edward Burger. Students universally love Professor Burger's ability to break down concepts and explain each example step by step, all while giving them the tips and that make algebra easy for anyone.

Coupled with concise review notes, problems, and step-by-step, automatically graded exercises, Thinkwell's complete online College Algebra course makes learning College Algebra a breeze, without a textbook!

The workbook (optional) comes with lecture notes, sample problems, and exercises so that you can study even when away from the computer.

Course Features

Video Lessons

279 engaging 5-10 minute video lessons
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Lesson Plan

Detailed, 36-week lesson plan and schedule
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Automatically graded exercises and tests with step-by-step feedback
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Notes & Sample Problems

Illustrated course notes, sample problems & solutions
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What Parents Are Saying. . .
"I purchased Thinkwell College Algebra for my daughter to use this year and she has loved it! Ed Burger is a fun and engaging professor. The price of the course is less than purchasing a textbook, test booklet, and answer key for some of the more popular texts available, and Thinkwell includes a great teacher! We will definitely be purchasing more products from Thinkwell!”
– Stephanie B
"This has turned out to be a wonderful curriculum for my son and I would highly recommend it to other families whose children's math abilities outpace their own. The curriculum provided him with high quality video instruction, which included a split screen format showing both the instructor and relevant visual aides and worked problems. My son is a 9th grader who succesfully completed the College Algebra program.”
– Lori K
"Professor Berger breathes life and humor into the dreaded, dry subject of math! (It's so fun to hear my daughters actually giggle during their algebra studies.) We have finished both intermediate and college algebra and have been very pleased with the results; the girls understood and retained much more than they did with our Teaching Textbooks experience. We're looking forward to American Government this fall.”
– Janine P
Course Overview

what you get

  • 12-month, online subscription to our complete College Algebra course
  • 36-week, day-by-day course lesson plan
  • 275+ course lessons, each with a streaming video
  • Illustrated notes
  • Automatically graded drill-and-practice exercises with step-by-step answer feedback
  • Sample problems and solutions
  • Chapter & Practice tests, a Midterm & Final Exam
  • Animated interactivities....and more!

how it works

  • Purchase Thinkwell's College Algebra through our online store
  • Create an account username and password which will give you access to the online College Algebra course section
  • Activate your 12-month subscription when you're ready
  • Login to the course website to access the online course materials, including streaming video lessons, exercises, quizzes, tests and more
  • Access your course anytime, anywhere, from any device
  • Your work is automatically tracked and updated in real-time
  • Grade reports and certificates of completion are available at request
About Thinkwell's College Algebra Author, Edward Burger

Learn from award-winning mathematician Dr. Edward Burger

It's like having a world-class college professor right by your side teaching you College Algebra.

  • "Global Hero in Education" by Microsoft Corporation
  • "America's Best Math Teacher" by Reader's Digest
  • Robert Foster Cherry Award Winner for Great Teaching
Thinkwell's College Algebra Table of Contents
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1. Prerequisites

1.1 Introduction
1.1.1 Introduction to Algebra
1.1.2 The Top Ten List of Mistakes
1.2 Inequalities
1.2.1 Concepts of Inequality
1.2.2 Inequalities and Interval Notation
1.3 Absolute Value
1.3.1 Properties of Absolute Value
1.3.2 Evaluating Absolute Value Expressions
1.4 Exponents
1.4.1 An Introduction to Exponents
1.4.2 Evaluating Exponential Expressions
1.4.3 Applying the Rules of Exponents
1.4.4 Evaluating Expressions with Negative Exponents
1.5 Converting between Notations
1.5.1 Converting between Decimal and Scientific Notation
1.5.2 Converting Rational Exponents and Radicals
1.6 Radical Expressions
1.6.1 Simplifying Radical Expressions
1.6.2 Simplifying Radical Expressions with Variables
1.6.3 Rationalizing Denominators
1.7 Polynomial Expressions
1.7.1 Determining Components and Degree
1.7.2 Adding, Subtracting, and Multiplying Polynomials
1.7.3 Multiplying Big Products
1.7.4 Using Special Products
1.8 Factoring
1.8.1 Factoring Using the Greatest Common Factor
1.8.2 Factoring by Grouping
1.8.3 Factoring Trinomials Completely
1.9 Factoring Patterns
1.9.1 Factoring Perfect Square Trinomials
1.9.2 Factoring the Difference of Two Squares
1.9.3 Factoring Sums and Differences of Cubes
1.9.4 Factoring by Any Method
1.10 Rational Expressions
1.10.1 Rational Expressions and Domain
1.10.2 Working with Fractions
1.10.3 Writing Rational Expressions in Lowest Terms
1.11 Working with Rationals
1.11.1 Multiplying and Dividing Rational Expressions
1.11.2 Adding and Subtracting Rational Expressions
1.11.3 Rewriting Complex Fractions
1.12 Complex Numbers
1.12.1 Introducing and Writing Complex Numbers
1.12.2 Rewriting Powers of i
1.12.3 Adding and Subtracting Complex Numbers
1.12.4 Multiplying Complex Numbers
1.12.5 Dividing Complex Numbers

2. Equations and Inequalities

2.1 Linear Equations
2.1.1 An Introduction to Solving Equations
2.1.2 Solving a Linear Equation
2.1.3 Solving a Linear Equation with Rationals
2.1.4 Solving a Linear Equation That Has Restrictions
2.2 Word Problems with Linear Equations: Math Topics
2.2.1 An Introduction to Solving Word Problems
2.2.2 Solving for Perimeter
2.2.3 Solving a Linear Geometry Problem
2.2.4 Solving for Consecutive Numbers
2.2.5 Solving to Find the Average
2.3 Word Problems with Linear Equations: Applications
2.3.1 Solving for Constant Velocity
2.3.2 Solving a Problem about Work
2.3.3 Solving a Mixture Problem
2.3.4 Solving an Investment Problem
2.3.5 Solving Business Problems
2.4 Quadratic Equations: Some Solution Techniques
2.4.1 Solving Quadratics by Factoring
2.4.2 Solving Quadratics by Completing the Square
2.4.3 Completing the Square: Another Example
2.5 Quadratic Equations and the Quadratic Formula
2.5.1 Proving the Quadratic Formula
2.5.2 Using the Quadratic Formula
2.5.3 Predicting the Type of Solutions Using the Discriminant
2.6 Quadratic Equations: Special Topics
2.6.1 Solving for a Squared Variable
2.6.2 Finding Real Number Restrictions
2.6.3 Solving Fancy Quadratics
2.7 Word Problems with Quadratics: Math Topics
2.7.1 An Introduction to Word Problems with Quadratics
2.7.2 Solving a Quadratic Geometry Problem
2.7.3 Solving with the Pythagorean Theorem
2.8 Word Problems with Quadratics: Applications
2.8.1 Solving a Motion Problem
2.8.2 Solving a Projectile Problem
2.8.3 Solving Other Problems
2.9 Radical Equations
2.9.1 Determining Extraneous Roots
2.9.2 Solving an Equation Containing a Radical
2.9.3 Solving an Equation with Two Radicals
2.9.4 Solving an Equation with Rational Exponents
2.10 Variation
2.10.1 An Introduction to Variation
2.10.2 Direct Proportion
2.10.3 Inverse Proportion
2.11 Solving Inequalities
2.11.1 An Introduction to Solving Inequalities
2.11.2 Solving Compound Inequalities
2.11.3 More on Compound Inequalities
2.11.4 Solving Word Problems Involving Inequalities
2.12 Inequalities: Quadratics
2.12.1 Solving Quadratic Inequalities
2.12.2 Solving Quadratic Inequalities: Another Example
2.13 Inequalities: Rationals and Radicals
2.13.1 Solving Rational Inequalities
2.13.2 Solving Rational Inequalities: Another Example
2.13.3 Determining the Domains of Expressions with Radicals
2.14 Absolute Value
2.14.1 Matching Number Lines with Absolute Values
2.14.2 Solving Absolute Value Equations
2.14.3 Solving Equations with Two Absolute Value Expressions
2.14.4 Solving Absolute Value Inequalities
2.14.5 Solving Absolute Value Inequalities: More Examples

3. Relations and Functions

3.1 Graphing Basics
3.1.1 Using the Cartesian System
3.1.2 Thinking Visually
3.2 Relationships between Two Points
3.2.1 Finding the Distance between Two Points
3.2.2 Finding the Second Endpoint of a Segment
3.3 Relationships among Three Points
3.3.1 Collinearity and Distance
3.3.2 Triangles
3.4 Circles
3.4.1 Finding the Center-Radius Form of the Equation of a Circle
3.4.2 Finding the Center and Radius of a Circle
3.4.3 Decoding the Circle Formula
3.4.4 Solving Word Problems Involving Circles
3.5 Graphing Equations
3.5.1 Graphing Equations by Locating Points
3.5.2 Finding the x- and y-Intercepts of an Equation
3.6 Function Basics
3.6.1 Functions and the Vertical Line Test
3.6.2 Identifying Functions
3.6.3 Function Notation and Finding Function Values
3.7 Working with Functions
3.7.1 Determining Intervals Over Which a Function Is Increasing
3.7.2 Evaluating Piecewise-Defined Functions for Given Values
3.7.3 Solving Word Problems Involving Functions
3.8 Function Domain and Range
3.8.1 Finding the Domain and Range of a Function
3.8.2 Domain and Range: One Explicit Example
3.8.3 Satisfying the Domain of a Function
3.9 Linear Functions: Slope
3.9.1 An Introduction to Slope
3.9.2 Finding the Slope of a Line Given Two Points
3.9.3 Interpreting Slope from a Graph
3.9.4 Graphing a Line Using Point and Slope
3.10 Equations of a Line
3.10.1 Writing an Equation in Slope-Intercept Form
3.10.2 Writing an Equation Given Two Points
3.10.3 Writing an Equation in Point-Slope Form
3.10.4 Matching a Slope-Intercept Equation with Its Graph
3.10.5 Slope with Parallel and Perpendicular Lines
3.11 Linear Functions: Applications
3.11.1 Constructing Linear Function Models of a Set of Data
3.11.2 Linear Cost and Revenue Functions
3.12 Graphing Functions
3.12.1 Graphing Some Important Functions
3.12.2 Graphing Piecewise-Defined Functions
3.12.3 Matching Equations with Their Graphs
3.13 The Greatest Integer Function
3.13.1 The Greatest Integer Function
3.13.2 Graphing the Greatest Integer Function
3.14 Composite Functions
3.14.1 Using Operations on Functions
3.14.2 Composite Functions
3.14.3 Components of Composite Functions
3.14.4 Finding Functions That Form a Given Composite
3.14.5 Finding the Difference Quotient of a Function
3.15 Quadratic Functions: Basics
3.15.1 Deconstructing the Graph of a Quadratic Function
3.15.2 Nice-Looking Parabolas
3.15.3 Using Discriminants to Graph Parabolas
3.15.4 Maximum Height in the Real World
3.16 Quadratic Functions: The Vertex
3.16.1 Finding the Vertex by Completing the Square
3.16.2 Using the Vertex to Write the Quadratic Equation
3.16.3 Finding the Maximum or Minimum of a Quadratic
3.16.4 Graphing Parabolas
3.17 Manipulating Graphs: Shifts and Stretches
3.17.1 Shifting Curves along Axes
3.17.2 Shifting or Translating Curves along Axes
3.17.3 Stretching a Graph
3.17.4 Graphing Quadratics Using Patterns
3.18 Manipulating Graphs: Symmetry and Reflections
3.18.1 Determining Symmetry
3.18.2 Reflections
3.18.3 Reflecting Specific Functions

4. Polynomial and Rational Functions

4.1 Polynomials: Long Division
4.1.1 Using Long Division with Polynomials
4.1.2 Long Division: Another Example
4.2 Polynomials: Synthetic Division
4.2.1 Using Synthetic Division with Polynomials
4.2.2 More Synthetic Division
4.3 The Remainder Theorem
4.3.1 The Remainder Theorem
4.3.2 More on the Remainder Theorem
4.4 The Factor Theorem
4.4.1 The Factor Theorem and Its Uses
4.4.2 Factoring a Polynomial Given a Zero
4.5 The Rational Root Theorem
4.5.1 Presenting the Rational Zero Theorem
4.5.2 Considering Possible Solutions
4.6 Zeros of Polynomials
4.6.1 Finding Polynomials Given Zeros, Degree, and One Point
4.6.2 Finding all Zeros and Multiplicities of a Polynomial
4.6.3 Finding the Real Zeros for a Polynomial
4.6.4 Using Descartes' Rule of Signs
4.6.5 Finding the Zeros of a Polynomial from Start to Finish
4.7 Graphing Polynomials
4.7.1 Matching Graphs to Polynomial Functions
4.7.2 Sketching the Graphs of Basic Polynomial Functions
4.8 Rational Functions
4.8.1 Understanding Rational Functions
4.8.2 Basic Rational Functions
4.9 Graphing Rational Functions
4.9.1 Vertical Asymptotes
4.9.2 Horizontal Asymptotes
4.9.3 Graphing Rational Functions
4.9.4 Graphing Rational Functions: More Examples

5. Exponential and Logarithmic Functions

5.1 Function Inverses
5.1.1 Understanding Inverse Functions
5.1.2 The Horizontal Line Test
5.1.3 Are Two Functions Inverses of Each Other?
5.1.4 Graphing the Inverse
5.2 Finding Function Inverses
5.2.1 Finding the Inverse of a Function
5.2.2 Finding the Inverse of a Function with Higher Powers
5.3 Exponential Functions
5.3.1 An Introduction to Exponential Functions
5.3.2 Graphing Exponential Functions: Useful Patterns
5.3.3 Graphing Exponential Functions: More Examples
5.4 Applying Exponential Functions
5.4.1 Using Properties of Exponents to Solve Exponential Equations
5.4.2 Finding Present Value and Future Value
5.4.3 Finding an Interest Rate to Match Given Goals
5.5 The Number e
5.5.1 e
5.5.2 Applying Exponential Functions
5.6 Logarithmic Functions
5.6.1 An Introduction to Logarithmic Functions
5.6.2 Converting between Exponential and Logarithmic Functions
5.7 Solving Logarithmic Functions
5.7.1 Finding the Value of a Logarithmic Function
5.7.2 Solving for x in Logarithmic Equations
5.7.3 Graphing Logarithmic Functions
5.7.4 Matching Logarithmic Functions with Their Graphs
5.8 Properties of Logarithms
5.8.1 Properties of Logarithms
5.8.2 Expanding a Logarithmic Expression Using Properties
5.8.3 Combining Logarithmic Expressions
5.9 Evaluating Logarithmic Functions
5.9.1 Evaluating Logarithmic Functions Using a Calculator
5.9.2 Using the Change of Base Formula
5.10 Applying Logarithmic Functions
5.10.1 The Richter Scale
5.10.2 The Distance Modulus Formula
5.11 Solving Exponential and Logarithmic Equations
5.11.1 Solving Exponential Equations
5.11.2 Solving Logarithmic Equations
5.11.3 Solving Equations with Logarithmic Exponents
5.12 Applying Exponents and Logarithms
5.12.1 Compound Interest
5.12.2 Predicting Change
5.13 Word Problems Involving Exponential Growth and Decay
5.13.1 An Introduction to Exponential Growth and Decay
5.13.2 Half-Life
5.13.3 Newton's Law of Cooling
5.13.4 Continuously Compounded Interest

6. Systems of Equations

6.1 Linear Systems of Equations
6.1.1 An Introduction to Linear Systems
6.1.2 Solving Systems with Substitution
6.1.3 Solving Systems by Elimination
6.2 Linear Systems in Three Variables
6.2.1 An Introduction to Linear Systems in Three Variables
6.2.2 Solving Linear Systems in Three Variables
6.2.3 Solving Inconsistent Systems
6.2.4 Solving Dependent Systems
6.2.5 Solving Systems with Two Equations
6.3 Applying Linear Systems
6.3.1 Investments
6.3.2 Solving with Partial Fractions
6.4 Nonlinear Systems of Equations
6.4.1 Solving Nonlinear Systems Using Elimination
6.4.2 Solving Nonlinear Systems with Substitution
6.5 Matrices
6.5.1 An Introduction to Matrices
6.5.2 The Arithmetic of Matrices
6.5.3 Multiplying Matrices by a Scalar
6.5.4 Multiplying Matrices
6.5.5 Multiplying Matrices: Can They Multiply?
6.6 The Gauss-Jordan Method of Solving Matrices
6.6.1 Using the Gauss-Jordan Method
6.6.2 Using Gauss-Jordan: Another Example
6.7 Evaluating Determinants
6.7.1 Evaluating 2x2 Determinants
6.7.2 Evaluating nxn Determinants
6.7.3 Applying Determinants
6.8 Cramer's Rule
6.8.1 Using Cramer's Rule
6.8.2 Using Cramer's Rule in a 3x3 Matrix
6.9 Inverses and Matrices
6.9.1 An Introduction to Inverses
6.9.2 Inverses: 2x2 Matrices
6.9.3 Another Look at 2x2 Inverses
6.9.4 Inverses: 3x3 Matrices
6.9.5 Solving a System of Equations with Inverses
6.10 Working with Inequalities
6.10.1 An Introduction to Graphing Linear Inequalities
6.10.2 Graphing Linear and Nonlinear Inequalities
6.10.3 Graphing the Solution Set of a System of Inequalities
6.11 Linear Programming
6.11.1 Solving for Maxima-Minima
6.11.2 Applying Linear Programming

7. Conic Sections

7.1 Parabolas
7.1.1 An Introduction to Conic Sections
7.1.2 An Introduction to Parabolas
7.1.3 Determining Information about a Parabola from Its Equation
7.1.4 Writing an Equation for a Parabola
7.2 Ellipses
7.2.1 An Introduction to Ellipses
7.2.2 Finding the Equation for an Ellipse
7.2.3 Applying Ellipses: Satellites
7.3 Hyperbolas
7.3.1 An Introduction to Hyperbolas
7.3.2 Finding the Equation for a Hyperbola
7.3.3 Applying Hyperbolas: Navigation
7.4 Conic Sections
7.4.1 Identifying a Conic
7.4.2 Name That Conic

8. Further Topics in Algebra

8.1 The Binomial Theorem
8.1.1 Using the Binomial Theorem
8.1.2 Binomial Coefficients
8.2 Sequences
8.2.1 Understanding Sequence Problems
8.2.2 Solving Problems Involving Arithmetic Sequences
8.2.3 Solving Problems Involving Geometric Sequences
8.3 Induction
8.3.1 Proving Formulas Using Mathematical Induction
8.3.2 Examples of Induction
8.4 Combinations and Probability
8.4.1 Solving Problems Involving Permutations
8.4.2 Solving Problems Involving Combinations
8.4.3 Independent Events
8.4.4 Inclusive and Exclusive Events

9. Conclusion

9.1 Conclusion
9.1.1 Final Close
Frequently Asked Questions for Thinkwell's College Algebra

How do Thinkwell courses work?

Your student watches a 5-10 minute online video lesson and then completes the automatically graded exercises for the topic. You'll get instant correct-answer feedback. Then move on to the next lesson! The courses are self-paced, or you can use the daily lesson plans. Just like a textbook, you can choose where to start and end, or follow the standard table of contents.

When does my 12-month online subscription start?

It starts when you're ready. You can have instant access to your online subscription when you purchase online, or you can purchase now and start later.

What math courses should a student take?

A typical sequence of secondary math courses completed by a college-bound student is: Grade 6 Math > Grade 7 Math > Grade 8 Math > Algebra 1 > Geometry > Algebra 2 > Precalculus. For students looking to include Calculus as part of their high school curriculum and are able to complete Grade 7 Math in 6th grade, the sequence can be: Grade 7 Math > Prealgebra > Algebra 1 > Geometry > Algebra 2 > Precalculus > Calculus.

Is Thinkwell’s College Algebra a college course?

Yes, typically College Algebra is the lowest credit math course at a 4 -year college.

Does my student get school credit for Thinkwell’s College Algebra?

No, only schools are accredited and Thinkwell is not a school, though many accredited schools use Thinkwell.

Does Thinkwell College Algebra meet state standards?

College Algebra is not a high school course so state standards do not apply.

What if my student needs access to the course for more than 12 months?

You can extend your subscription for $19.95/month.

Can I share access with more than one student?

The courses are designed and licensed to accommodate one student per username and password; additional students need to purchase online access. This allows parents to keep track of each student's progress and grades.

How long does it take to complete Thinkwell’s College Algebra course?

The pace of your course is up to you, but most college students will schedule one semester.

Can I see my grade?

Thinkwell’s course software tracks everything your student does. When logged in, your student can click "My Grades" to see their progress.

How are grades calculated?

The course grade is calculated this way: Chapter Tests 33.3%, Midterm: 33.3%, Final: 33.3%.

What is acceptable performance on the exams?

As a homeschool parent, you decide the level of performance you want your student to achieve; the course does not limit access to topics based on performance on prior topics.

Can I get a transcript?

Yes, there's a final grade report print option in the My Grades section. Contact with any questions.

What if I change my mind and want to do a different math course, can I change?

If you discover that you should be in a different course, contact within one week of purchase and we will move you to the appropriate course.

Can I print the exercises?

Yes, but completing the exercises online provides immediate correct answer feedback and automatic scoring, so we recommend answering the exercises online.

Are exercises multiple choice?

Most of the exercises are multiple choice and they are graded automatically with correct answer solutions.

Is Thinkwell's College Algebra Math built on "continuous review?"

Thinkwell's College Algebra is carefully constructed to build on previous knowledge, reinforcing key concepts every step of the way. It is not only a reflection of empirically effective instruction, but also reflects Dr Burger’s philosophies learned over a career of teaching mathematics, emphasizing a solid foundation that addresses why students need to learn certain concepts. Finally, Thinkwell College Algebra is intentionally designed to work for a wide variety of learning styles.

What is Thinkwell's Refund Policy?

We offer a full refund of 12-month subscription purchases within 14 days of purchase, no questions asked. For Essential Review courses, the refund period is 3 days. Optional printed materials are printed on demand and the sales are final.

How does my school review this course?

Should your school need to review a Thinkwell course for any reason, have the school contact and we can provide them access to a demo site.

Do I get credits for a Thinkwell course?

Generally, only schools can award credits, and Thinkwell is not a school. We can provide you with a certificate of completion and a grade report. However, if you’re pursuing credit with a particular school or institution, it might be helpful to know that Thinkwell math courses are accredited by the Western Association of Schools and Colleges (WASC) as a Supplementary Education Program. For California students, Thinkwell is also an approved A-G online publisher.

Is Thinkwell math conceptual or procedural?

Thinkwell’s approach to teaching and learning mathematics blends conceptual understanding with procedural fluency. Overall, we aim to strike a balance between concepts and procedures in our content which allows students to develop the skills and knowledge needed for success in mathematics. We recognize the importance of building a strong conceptual foundation when learning math. Prof. Burger emphasizes the "why" behind mathematical principles in the video lectures so that our students can develop a comprehensive understanding of the ideas underpinning the subject. We also believe in the benefits of procedural fluency, recognizing that mathematical proficiency requires not only understanding but also the ability to apply procedures accurately and efficiently. Through systematic practice, students master various mathematical techniques, ensuring they can solve problems confidently and accurately.

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