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AP Calculus AB

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Open to: Grades 8 - 12

Eligibility: CTY-level or Advanced CTY-level math score required

Prerequisites: Successful completion of Precalculus or the equivalent

Course Format: Individually Paced

Course Length: Typically 6 Months

Recommended School Credit: This is an AP Calculus course, equivalent to a year-long Calculus AB sequence.

Course Code: CAB

Course Description


This AP Calculus AB course is an online and individually-paced course covering topics in single variable differential and integral calculus typically found in a first-year college Calculus I course.  While taking the Advanced Placement (AP) Calculus AB exam is not required, this course prepares students to succeed on the AP Calculus AB exam and subsequent courses that draw on material from this course. Computer based interactives and homework assignments help to reinforce concepts taught in the course.

Each student is assigned to a CTY instructor to help them during their course. Students can contact their instructor via email with any questions or concerns at any time. Students actively engage with the lectures, interact with online resources, and solve many practice problems through homework. Videos in the course are provided by Thinkwell.

Live one-on-one online review sessions can be scheduled as well to prepare for the graded assessments, which include homework, midterm exams, and a cumulative final. Exams contain both multiple choice and free response questions modeled after the AP Calculus AB exam.  Instructors use virtual classroom software allowing video, voice, text, screen sharing and whiteboard interaction.

This course has been reviewed and approved by the College Board to use the "AP" designation.

Topics include:

  • Precalculus Review
  • Limits and Continuity
  • Derivatives
  • Applications of the Derivative
  • Implicit Differentiation
  • L'Hospital's Rule
  • Curve Sketching
  • Related Rates
  • Integration
  • Applications of Integration
  • Differential Equations

For a detailed list of topics, click the "List of Topics" tab.

AP Calculus AB banner

Materials Needed

A textbook is not required for this course.
A graphing calculator is required, such as:

  • TI-83 PLUS
  • TI-84 PLUS
  • TI-85
  • TI-86
  • TI-89*


To see a full list of allowable calculators, visit the College Board website to view the AP Calculus calculator policy.

Full List of Topics

List of Topics

Upon successful completion of the course, students will be able to demonstrate mastery over the following topics:

Precalculus Review

  • Overview
  • Functions and Graphing
  • Exponential Functions
  • Inverse Functions
  • Evaluating Logarithmic Functions
  • Trigonometry Review


  • The Concept of the Limit
  • Calculating Limits
  • The Squeeze Theorem
  • Continuity and Discontinuity
  • Infinite Limits and Indeterminate Forms

An Introduction to Derivatives

  • Understanding the Derivative
  • Using the Derivative
  • Some Special Derivatives

Computational Techniques

  • The Power Rule
  • The Product and Quotient Rules
  • The Chain Rule

Derivatives of Special Functions

  • Derivatives of Trigonometric Functions
  • Derivatives of Exponential Functions
  • Derivatives of Logarithmic Functions

Implicit Differentiation and L'Hospital's Rule

  • Implicit Differentiation Basics
  • Applying Implicit Differentiation
  • Differentiating Logarithms
  • Logarithmic Differentiation
  • Derivatives of Inverse Functions
  • Inverse Trigonometric Functions
  • Derivatives of Inverse Trigonometric Functions
  • Indeterminate Quotients
  • Other Indeterminate Forms and L'Hospital's Rule

Applications of the Derivative

  • Position and Velocity
  • Linear Approximation and Newton's Method
  • Optimization
  • Related Rates

Curve Sketching

  • An Introduction to Curve Sketching
  • Critical Points
  • Concavity and Inflection Points
  • Graphing Using the Derivative
  • Graphing Functions with Asymptotes

The Basics of Integration

  • Antiderivatives
  • Integration by Substitution
  • Illustrating Integration by Substitution
  • The Fundamental Theorem of Calculus
  • Numerical Integration

Applications of Integration

  • Motion
  • Finding the Area between Two Curves
  • Integrating with Respect to y
  • The Average Value of a Function
  • Finding Volumes Using Cross-Sections
  • Disks and Washers
  • Shells

Differential Equations

  • Separable Differential Equations
  • Direction Fields
  • Growth and Decay Problems


Sample Video Lecture

Sample Video

Click on the image below to view the online demo.

AP Calculus demo

Technical Requirements

This course requires a properly maintained computer with high-speed internet access and an up-to-date web browser (such as Chrome or Firefox). The student must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.

Zoom online virtual classroom
This course uses an online virtual classroom for discussions with the instructor. The classroom works on standard computers with the Zoom desktop client and also tablets or handhelds that support the Zoom Mobile app. Students who are unable to attend live sessions will need a computer with the Zoom desktop client installed to watch recorded meetings. The Zoom desktop client and Zoom Mobile App are both available for free download.

This course uses Respondus LockDown Browser proctoring software for designated assessments. LockDown Browser is a client application that is installed to a local computer. Visit the Respondus website for system requirements.

While Chromebook can be used to progress through the course, all exams must be completed on a PC or Mac.