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AP® Calculus BC | Extended | 2021-22

Students in Classroom

AP Calculus BC | Extended is a live online class for homeschool and traditional high school students who have previously completed AP Calculus AB. This year-long course covers the content equivalent to a second-semester college calculus course and is intended for students who have already learned the basics of differential and integral calculus.


Unlike a traditional AP Calculus BC class--which includes the content of AB (first semester) and BC (second semester)--our AP Calculus BC | Extended class picks up where AB instruction concluded. It spreads the BC content over an entire year, offering a less intensive pacing and more thorough coverage of the topics typically covered in the second semester of a traditional AP Calculus BC class. Those topics include advanced integration techniques, infinite series, parametric equations, polar coordinates and vectors. Students will be fully prepared to take the AP Calculus BC exam by the end of this class. 


Up to three classes will be available each week:

  • The first class consists of recorded instruction by the instructor, where she will introduce new material that students will be learning that week.

  • The second class is an optional live office hour offered mid-week on Wednesdays for those students who need more individual help.

  • The third class is a live problem session designed to help students solve problems based on the weekly assignments and concepts learned in the week's instruction.

Class Details

  • AP Calculus BC | Extended is a College Board-approved class.

    • This class is designed for students who have previously taken AP Calculus AB who do not need extensive review of AB material (which is the entire first semester of a traditional AP Calculus BC class).

    • This class will cover the second semester content of a traditional AP Calculus BC class and spread it over a full year so that it can be covered at a more moderate pace.  

  • Dates: August 16, 2021 to May 9, 2022 (the AP exam).

    • See our FAQ for a complete list of days, times, and breaks for 2021-22.

  • Live class: Thursday | 1-2 p.m. Eastern

  • Office hours: Wednesday | 5-6 p.m. Eastern (as needed)

  • Live and Recorded: All live classes will be held on Zoom.

    • Recorded instruction opens up each Monday. Live problem sessions are held on Thursdays.

    • Optional office hours are offered on Wednesdays as needed.

    • Students who attend live Thursday classes are asked to please keep their webcams on.

    • Live sessions will be recorded for those who miss classes or who prefer to watch some or all as recordings.

  • For age/grade guidelines, prerequisites, and class-fit recommendations for all classes, please see our FAQ page.


Class Content

This class will cover topics in a second semester college calculus class:

  • Brief review of differential and integral calculus.

  • Advanced integration techniques and improper integrals.

  • Infinite Series: Series convergence and divergence, Taylor and Maclaurin Series and polynomials.

  • Parametric Equations.

  • Polar Coordinates.

  • Vectors and introduction to Vector Calculus


Flexibility and Collaboration

Each week, the instructor will post a summary of upcoming concepts in the Blue Tent online classroom along with links to helpful websites and resources related to the topics to be covered.


  • The year-long AP Calculus BC | Extended class will be taught at a slower pace than a regular college class. However, it is still a college-level class, and the material will be conceptually challenging.

  • Students will need to be disciplined about accessing the instructor's recorded instruction at the beginning of each week and working through the assignments during the week in order to come prepared to the live problem session on Fridays.

  • Recorded instruction will open up each Monday, and live problem sessions will be held on Fridays. Live office hours are offered on Wednesdays as needed, usually around exam time to give students extra review and more detailed feedback on problems.

    • This combination of recorded instruction and live interaction gives students more flexibility and permits the instructor to go into more detail in her recorded instruction than a one-hour lecture would allow.

  • Most student/teacher interaction takes place in problem sessions, and the live meetings on Friday are a key component of the class.

    • During the live problem sessions, students will have the opportunity to ask questions about the material they covered during the week, and the instructor will present problems and problem solving approaches relevant to each topic.

  • Students will be interacting with their classmates during live sessions as well as in text-based discussion forums in their Blue Tent classroom. In the class forums, students can post questions about reading assignments or homework, answer other students' questions, or post solutions to problems.

  • The instructor will be available to answer questions on homework assignments throughout each week via WebAssign, on the discussion forums, or via email


The textbook for this class is Calculus for AP by Ron Larson and Paul Battaglia.


  • This is an excellent textbook designed specifically for the AP curriculum framework and exam. While it covers all the topics a calculus student will need to succeed in subsequent calculus courses, its emphasis is placed on AP exam material, and AP-style problem practices are provided in each chapter.

  • Students will be assigned weekly homework through WebAssign--an interactive platform with features such as Read It, Master It, and Watch it links that will direct students to the relevant section in the textbook (Read It), provide another version of the same problem, with step-by-step guidance (Master It), or offer a short video tutorial on the problem (Watch it).

  • An electronic version of the textbook will be available through WebAssign.

  • Through the Blue Tent OnLoan program, students can borrow a hard-copy of the class textbook for use during the year, so they can utilize both interactive and print resources in a manner that fits their needs and preferences

The AP Calculus instructor, Shin Yen, has successfully taught calculus to many bright students over the years, and she looks forward to working with future students to nurture their interest in mathematics and prepare them for success.

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