Skip Navigation

We are unable to take calls at this time, though your questions are important to us. Please send them to for the quickest response. Thank you.

AP Calculus AB (NCAA Approved)

Arrow image that is used as button to enroll in courses. Enroll in this Course

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: Session Based. See calendar for session dates and application deadlines.

Course Length: 30 weeks

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

Student Expectations: Students are strongly encouraged to work at least 1 hour a day, 5 days a week.

Course Code: CABY

Course Description


This AP Calculus AB course is an online 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. Online interactives and assignments help to reinforce concepts taught in the course. Exams contain both multiple choice and free response questions modeled after the AP Calculus AB exam. 

Online course materials, such as videos, notes, interactive webpages, and practice problems with solutions, are provided for the student. Students are expected to watch videos and review notes regularly. Each student is assigned to a CTY instructor to help them during their course. Videos in the course are provided by Thinkwell.

In this course, participation in forums and synchronous online virtual sessions are required as part of the final grade. Discussion forums are located within the course where students will be required to respond to a given prompt and then comment on responses by other students. Online sessions, led by a CTY instructor, are held in Adobe Connect, which allows for video, voice, text, screen sharing, and whiteboard interaction. 

Students can contact their instructors via email with questions or concerns at any time. Live one-on-one online review sessions can be scheduled as well, to prepare for the graded assessments, which include homework, chapter exams, and a cumulative midterm and final.

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.

Note: For flexible pacing, please view the course description in the individually paced format: AP Calculus AB. Both versions cover the same concepts but differ in approach. This session-based version is NCAA approved.

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.