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Calculus C

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Open to: Grades 9 - 12

Prerequisites: Qualifying math score and completion of AP Calculus AB or equivalent

Course Format: Individually Paced

Course Length: Typically 6 months

Recommended School Credit: This course is equivalent to the second half of a year long Calculus BC sequence.

Course Code: CAC

Course Description


This Calculus C 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 II course, intended for students who have already completed AP Calculus AB, or the first half of AP Calculus BC. While taking the Advanced Placement (AP) Calculus BC exam is not required, this course prepares students to succeed on the AP Calculus BC exam and subsequent courses.

This course starts with a review of the traditionally more difficult topics from Calculus AB and uses computer based interactives and homework assignments to help 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 assignments. 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 BC exam.  Instructors use virtual classroom software allowing video, voice, text, screen sharing and whiteboard interaction.

Topics include:

  • A review of differential calculus
  • Techniques of integration
  • Applications of integral calculus
  • Parametric equations and polar coordinates
  • Sequences and series
  • An introduction to differential equations

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

AP Calculus C Banner

Materials Needed

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:

Review of Differential Calculus

  • The Squeeze Theorem
  • Continuity and Discontinuity
  • Infinite Limits and Indeterminate Forms
  • Implicit Differentiation
  • Logarithmic Differentiation
  • Derivatives of Inverse Functions
  • Indeterminate Quotients and L'Hospital's Rule
  • Other Indeterminate Forms
  • Antiderivatives

Techniques of Integration

  • Review of Integration
  • The Fundamental Theorem of Calculus
  • Numerical Integration and Tables of Integrals
  • Integrals Involving Powers of Sine and Cosine
  • Integrals Involving Powers of Other Trigonometric Functions
  • An Introduction to Integration by Partial Fractions
  • Integration by Partial Fractions with Repeated Factors
  • Integration by Parts
  • An Introduction to Trigonometric Substitution
  • Trigonometric Substitution Strategy
  • Improper Integrals

Applications of Integration

  • Motion
  • Finding Area between Curves
  • The Average Value of a Function
  • Finding Volumes Using Cross-Sections
  • Disks, Washers, and Shells
  • Work
  • Moments and Centers of Mass
  • Arc Lengths and Functions

Parametric Equations and Polar Coordinates

  • Understanding Parametric Equations
  • Derivatives and Arc Length of Parametric Equations
  • Understanding Polar Coordinates
  • Polar Functions and Slope
  • Polar Functions and Area

Sequences and Series

  • Sequences
  • Infinite Series
  • Convergence and Divergence
  • The Integral Test and p-Series
  • The Comparison and Limit Comparison Test
  • The Alternating Series Test, Absolute and Conditional Convergence
  • The Ratio and Root Test

Applications of Series

  • Polynomial Approximations of Elementary Functions
  • Taylor and Maclaurin Polynomials
  • Taylor and Maclaurin Series
  • Power Series
  • Power Series Representations of Functions

Differential Equations

  • Separable Differential Equations
  • Direction Fields
  • Growth and Decay Problems
  • Euler's Method

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Sample Video 

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.

This course uses an online virtual classroom for discussions with the instructor. The classroom works on standard computers with the Adobe Connect Add-in or Adobe Flash plugin, and also tablets or handhelds that support the Adobe Connect Mobile appStudents who are unable to attend live sessions will need a computer with the Adobe Connect Add-in or Adobe Flash plugin installed to watch recorded meetings. The Adobe Connect Add-in, Adobe Flash plugin, and Adobe Connect Mobile app are available for free download. Students who do not have the Flash plug-in installed or enabled on their browsers will be prompted to download and install the Adobe Connect add-in when accessing the virtual classroom.


AP Calculus demo