Calculus AB compatible with AP®*


Calculus AB compatible with AP®*

Award-winning professor Edward Burger teaches the fundamentals of AP® Calculus AB in a series of dynamic, comprehensive video lessons. You'll learn the calculus concepts you need to score a perfect 5 on the AP® Calculus AB exam.

The Printed Notes (optional) are the Thinkwell Calculus course notes printed in a color, on-the-go format.

*(AP® is a registered trademark of the College Board, which was not involved in the production of this product. This course is designed for self-study preparation for the AP® exam and has not been audited by the College Board.)

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Course Features

Video Lessons

173 engaging 5-20 minute video lessons
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Lesson Plan

Detailed, 38-week lesson plan and schedule
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Automatically graded practice and chapter tests
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Notes & Sample Problems

Illustrated course notes, sample problems & solutions
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What Parents Are Saying. . .
"My eldest daughter, now a college freshman, used Thinkwell's Precalculus and AP Calculus. With the help of Professor Ed Burger, she scored a perfect 5 on her AP exam and received full college credit! Ed Burger is humorous and organized. The course is very comprehensive."
– Barbara H
“We ordered a subscription of the Calculus for my son who was to retake the AP Calculus B/C exam after scoring a 3 the first time around. He watched the videos at his leisure, focusing on content that he needed to review. He ended up with a 5 on the AP exam thanks to Thinkwell. We highly recommend them!”
– Rebecca O
“Thinkwell Math is the best product out there for students headed into a math or science field in college. My son used Thinkwell Calculus, took the AP Calculus BC test, and scored a 5, allowing him to go directly into Calculus III in college. He loved Dr. Burger and learned so much from the course! My other children will be using it as well.”
– Linda
Course Overview

What you get

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

How it works

  • Purchase Thinkwell's Calculus AB compatible with AP® through our online store
  • Create an account username and password which will give you access to the online Calculus AB compatible with AP® 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, tests and more
  • Access your course anytime, anywhere, from any device
  • Your work is automatically tracked and updated in real-time
  • Transcripts, grade reports, and certificates of completion are available at request
Thinkwell's Calculus AB compatible with AP® 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 Calculus.

  • "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 Calculus AB compatible with AP® Table of Contents
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1. The Basics

1.1 Overview
1.1.1 An Introduction to Thinkwell Calculus
1.1.2 The Two Questions of Calculus
1.1.3 Average Rates of Change
1.1.4 How to Do Math
1.2 Precalculus Review
1.2.1 Functions
1.2.2 Graphing Lines
1.2.3 Parabolas
1.2.4 Some Non-Euclidean Geometry

2. Limits

2.1 The Concept of the Limit
2.1.1 Finding Rate of Change over an Interval
2.1.2 Finding Limits Graphically
2.1.3 The Formal Definition of a Limit
2.1.4 The Limit Laws, Part I
2.1.5 The Limit Laws, Part II
2.1.6 One-Sided Limits
2.1.7 The Squeeze Theorem
2.1.8 Continuity and Discontinuity
2.2 Evaluating Limits
2.2.1 Evaluating Limits
2.2.2 Limits and Indeterminate Forms
2.2.3 Two Techniques for Evaluating Limits
2.2.4 An Overview of Limits

3. An Introduction to Derivatives

3.1 Understanding the Derivative
3.1.1 Rates of Change, Secants, and Tangents
3.1.2 Finding Instantaneous Velocity
3.1.3 The Derivative
3.1.4 Differentiability
3.2 Using the Derivative
3.2.1 The Slope of a Tangent Line
3.2.2 Instantaneous Rate
3.2.3 The Equation of a Tangent Line
3.2.4 More on Instantaneous Rate
3.3 Some Special Derivatives
3.3.1 The Derivative of the Reciprocal Function
3.3.2 The Derivative of the Square Root Function

4. Computational Techniques

4.1 The Power Rule
4.1.1 A Shortcut for Finding Derivatives
4.1.2 A Quick Proof of the Power Rule
4.1.3 Uses of the Power Rule
4.2 The Product and Quotient Rules
4.2.1 The Product Rule
4.2.2 The Quotient Rule
4.3 The Chain Rule
4.3.1 An Introduction to the Chain Rule
4.3.2 Using the Chain Rule
4.3.3 Combining Computational Techniques

5. Special Functions

5.1 Trigonometric Functions
5.1.1 A Review of Trigonometry
5.1.2 Graphing Trigonometric Functions
5.1.3 The Derivatives of Trigonometric Functions
5.1.4 The Number Pi
5.2 Exponential Functions
5.2.1 Graphing Exponential Functions
5.2.2 Derivatives of Exponential Functions
5.3 Logarithmic Functions
5.3.1 Evaluating Logarithmic Functions
5.3.2 The Derivative of the Natural Log Function
5.3.3 Using the Derivative Rules with Transcendental Functions

6. Implicit Differentiation and the Inverse Function

6.1 Implicit Differentiation Basics
6.1.1 An Introduction to Implicit Differentiation
6.1.2 Finding the Derivative Implicitly
6.2 Applying Implicit Differentiation
6.2.1 Using Implicit Differentiation
6.2.2 Applying Implicit Differentiation
6.3 Inverse Functions
6.3.1 The Exponential and Natural Log Functions
6.3.2 Differentiating Logarithmic Functions
6.3.3 Logarithmic Differentiation
6.3.4 The Basics of Inverse Functions
6.3.5 Finding the Inverse of a Function
6.4 The Calculus of Inverse Functions
6.4.1 Derivatives of Inverse Functions
6.5 Inverse Trigonometric Functions
6.5.1 The Inverse Sine, Cosine, and Tangent Functions
6.5.2 The Inverse Secant, Cosecant, and Cotangent Functions
6.5.3 Evaluating Inverse Trigonometric Functions
6.6 The Calculus of Inverse Trigonometric Functions
6.6.1 Derivatives of Inverse Trigonometric Functions
6.7 The Hyperbolic Functions
6.7.1 Defining the Hyperbolic Functions
6.7.2 Hyperbolic Identities
6.7.3 Derivatives of Hyperbolic Functions

7. Applications of Differentiation

7.1 Position and Velocity
7.1.1 Acceleration and the Derivative
7.1.2 Solving Word Problems Involving Distance and Velocity
7.2 Linear Approximation
7.2.1 Higher-Order Derivatives and Linear Approximation
7.2.2 Using the Tangent Line Approximation Formula
7.2.3 Newton's Method
7.3 Optimization
7.3.1 The Connection Between Slope and Optimization
7.3.2 The Fence Problem
7.3.3 The Box Problem
7.3.4 The Can Problem
7.3.5 The Wire-Cutting Problem
7.4 Related Rates
7.4.1 The Pebble Problem
7.4.2 The Ladder Problem
7.4.3 The Baseball Problem
7.4.4 The Blimp Problem
7.4.5 Math Anxiety

8. Curve Sketching

8.1 Introduction
8.1.1 An Introduction to Curve Sketching
8.1.2 Three Big Theorems
8.1.3 Morale Moment
8.2 Critical Points
8.2.1 Critical Points
8.2.2 Maximum and Minimum
8.2.3 Regions Where a Function Increases or Decreases
8.2.4 The First Derivative Test
8.2.5 Math Magic
8.3 Concavity
8.3.1 Concavity and Inflection Points
8.3.2 Using the Second Derivative to Examine Concavity
8.3.3 The Möbius Band
8.4 Graphing Using the Derivative
8.4.1 Graphs of Polynomial Functions
8.4.2 Cusp Points and the Derivative
8.4.3 Domain-Restricted Functions and the Derivative
8.4.4 The Second Derivative Test
8.5 Asymptotes
8.5.1 Vertical Asymptotes
8.5.2 Horizontal Asymptotes and Infinite Limits
8.5.3 Graphing Functions with Asymptotes
8.5.4 Functions with Asymptotes and Holes
8.5.5 Functions with Asymptotes and Critical Points

9. The Basics of Integration

9.1 Antiderivatives
9.1.1 Antidifferentiation
9.1.2 Antiderivatives of Powers of x
9.1.3 Antiderivatives of Trigonometric and Exponential Functions
9.2 Integration by Substitution
9.2.1 Undoing the Chain Rule
9.2.2 Integrating Polynomials by Substitution
9.3 Illustrating Integration by Substitution
9.3.1 Integrating Composite Trigonometric Functions by Substitution
9.3.2 Integrating Composite Exponential and Rational Functions by Substitution
9.3.3 More Integrating Trigonometric Functions by Substitution
9.3.4 Choosing Effective Function Decompositions
9.4 The Fundamental Theorem of Calculus
9.4.1 Approximating Areas of Plane Regions
9.4.2 Areas, Riemann Sums, and Definite Integrals
9.4.3 The Fundamental Theorem of Calculus, Part I
9.4.4 The Fundamental Theorem of Calculus, Part II
9.4.5 Illustrating the Fundamental Theorem of Calculus
9.4.6 Evaluating Definite Integrals
9.5 Trigonometric Substitution Strategy
9.5.1 An Overview of Trigonometric Substitution Strategy
9.5.2 Trigonometric Substitution Involving a Definite Integral: Part One
9.5.3 Trigonometric Substitution Involving a Definite Integral: Part Two
9.6 Numerical Integration
9.6.1 Deriving the Trapezoidal Rule
9.6.2 An Example of the Trapezoidal Rule

10. Applications of Integration

10.1 Motion
10.1.1 Antiderivatives and Motion
10.1.2 Gravity and Vertical Motion
10.1.3 Solving Vertical Motion Problems
10.2 Finding the Area between Two Curves
10.2.1 The Area between Two Curves
10.2.2 Limits of Integration and Area
10.2.3 Common Mistakes to Avoid When Finding Areas
10.2.4 Regions Bound by Several Curves
10.3 Integrating with Respect to y
10.3.1 Finding Areas by Integrating with Respect to y: Part One
10.3.2 Finding Areas by Integrating with Respect to y: Part Two
10.3.3 Area, Integration by Substitution, and Trigonometry
10.4 The Average Value of a Function
10.4.1 Finding the Average Value of a Function
10.5 Finding Volumes Using Cross-Sections
10.5.1 Finding Volumes Using Cross-Sectional Slices
10.5.2 An Example of Finding Cross-Sectional Volumes
10.6 Disks and Washers
10.6.1 Solids of Revolution
10.6.2 The Disk Method along the y-Axis
10.6.3 A Transcendental Example of the Disk Method
10.6.4 The Washer Method across the x-Axis
10.6.5 The Washer Method across the y-Axis
10.7 Shells
10.7.1 Introducing the Shell Method
10.7.2 Why Shells Can Be Better Than Washers
10.7.3 The Shell Method: Integrating with Respect to y
10.8 Work
10.8.1 An Introduction to Work
10.8.2 Calculating Work
10.8.3 Hooke's Law
10.9 Moments and Centers of Mass
10.9.1 Center of Mass
10.9.2 The Center of Mass of a Thin Plate
10.10 Arc Lengths and Functions
10.10.1 An Introduction to Arc Length
10.10.2 Finding Arc Lengths of Curves Given by Functions

11. Differential Equations

11.1 Separable Differential Equations
11.1.1 An Introduction to Differential Equations
11.1.2 Solving Separable Differential Equations
11.1.3 Finding a Particular Solution
11.1.4 Direction Fields
11.1.5 Euler's Method for Solving Differential Equations Numerically
11.2 Growth and Decay Problems
11.2.1 Exponential Growth
11.2.2 Logistic Growth
11.2.3 Radioactive Decay

12. L'Hôpital's Rule and Improper Integrals

12.1 Indeterminate Quotients
12.1.1 Indeterminate Forms
12.1.2 An Introduction to L'Hôpital's Rule
12.1.3 Basic Uses of L'Hôpital's Rule
12.1.4 More Exotic Examples of Indeterminate Forms
12.2 Other Indeterminate Forms
12.2.1 L'Hôpital's Rule and Indeterminate Products
12.2.2 L'Hôpital's Rule and Indeterminate Differences
12.2.3 L'Hôpital's Rule and One to the Infinite Power
12.2.4 Another Example of One to the Infinite Power
12.3 Improper Integrals
12.3.1 The First Type of Improper Integral
12.3.2 The Second Type of Improper Integral
12.3.3 Infinite Limits of Integration, Convergence, and Divergence

13. Math Fun

13.1 Paradoxes
13.1.1 An Introduction to Paradoxes
13.1.2 Paradoxes and Air Safety
13.1.3 Newcomb's Paradox
13.1.4 Zeno's Paradox
13.2 Sequences
13.2.1 Fibonacci Numbers
13.2.2 The Golden Ratio
13.3 The Close of Calculus AB
13.3.1 A Glimpse Into Calculus II
Frequently Asked Questions for Thinkwell's Calculus AB compatible with AP®

How do Thinkwell courses work?

Your student watches a 5-10 minute online video lesson, completes the automatically graded exercises for the topic with instant correct-answer feedback, then moves 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 entire course.

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.

Is Thinkwell Calculus AB® compatible with AP® certified by the College Board®?

The College Board® states at their website: “The AP Course Audit process is designed to review AP courses in their entirety, so only schools (whether brick-and-mortar or virtual) can submit course syllabi for review.” Since Thinkwell is a publisher and not a school, our materials can’t be certified. We strive to make this distinction, which is why you see this statement: AP® is a registered trademark of the College Board, which was not involved in its production. This course is designed for self-study preparation for the AP® exam and has not been audited by the College Board®.

Does my student get school credit for Thinkwell Calculus AB®?

No, only schools are accredited and Thinkwell is not a school, though many accredited schools use Thinkwell. Getting AP® credit is accomplished by taking the AP exam®.

What’s the difference between the Thinkwell Calculus course and the separate AP® versions?

The content of Thinkwell’s Calculus is very similar to the AB and BC course versions. So in a sense, you may feel like you’re getting a two-for-one deal, which is great. However, the College Board offers the Calculus AB & BC exams these ways: 1) Take the CAL AB exam only, 2) Take the CAL AB & BC exams sequentially (one each year), or 3) Skip the CAL AB and take the BC since it includes AB. Therefore, for #1 use our AB course, for #2 use our AB course then our BC course next year, and for #3 use our regular CAL course so you get both semesters in one year.

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

You can purchase extra time in one-month, three-month, and six-month increments.

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 Calculus AB®?

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

Can I see my grade?

Thinkwell courses track 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?

You can contact to request a file with your student's grades.

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?

The exercises are multiple choice and they are graded automatically with correct answer solutions.

Is there a guarantee?

Yes, we offer a full refund within three business days of purchase, no questions asked.

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.

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