AP Calculus Online Exam Preparation

AP® Calculus BC

Course description:

AP® Calculus BC is equivalent to a two semester college course in Calculus. This course is intended to prepare students to take the AP® Calculus BC exam.  As such, the curriculum of this course follows the recommendations of the College Board for a university level, introductory Calculus course.  This course will address:

  1. Pre-requisites for Calculus
  2. Limits and continuity
  3. Derivatives, including limit definition of derivatives, rules of differentiation, derivatives of trigonometric functions, the Chain Rule, implicity differentiation, derivates of inverse trigonometric functions, and derivatives of exponential and logarithmic functions
  4. Applications of derivatives, including optimization, related rates, curve sketching, the Mean Value Theorem's, linearization and Newton's Method
  5. Integration, including the definite and indefinite integral, the Fundamental Theorem of Calculus, Trapezoidal Rule and estimating with finite sums
  6. Differential equations and modeling, including slope fields, anti-differentiaion by subsitution, anti-differentiation by parts, exponential growth and decay, logistic growth
  7. Applications of integration, including areas in the plane, volume by shells, volume by discs, and curve length
  8. Sequences, L'Hopital's rule and improper integrals
  9. Infinite series, including power series, Taylor Series, Taylor's Theorem, and convergence
  10. Parametric, vector, and polar functions



Students wishing to enroll in AP® Calculus BC will find it beneficial to have taken a pre-calculus course and/or to have completed four years of high school math courses.  The College Board recommends that students have studied algebra, geometry, trigonometry, and functions, including linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric and piecewise-defined functions.  Additionally, students should be familiar with concepts as they pertain to functions: domain, range, odd, even, periodic, symmetry, zeros, intercepts and know the values of trigonometric functions at 0, π/6, π/4, π/3, π/2, and their multiples (College Board, 2011).  AP Calculus BC is typically a more challenging course than AP Calculus AB. 

Textbook and curricular materials:

Learning Activities:

Taking AP® Calculus BC online can help making learning more individualized, allowing students to work efficiently through the course material. A individualized study plan is developed within the course software, which indicates areas of mastery as well as those in need of additional review. This allows students to take control of their learning. In MyMathLab, powered by BlackBoard, an interactive, electronic textbook along with video presentations of course content, animated tutorials, discussion boards, quizzes and exams are available 24hours a day/7 days a week.

The purpose of feedback to the student is to inform the student when they have demonstrated mastery of course objectives and to highlight areas that require further study.  The instructor evaluates the quality of students’ work and participation in the course and communicates this to the student via email and the course’s electronic grade book. 


Catherine Bliss received her Ph.D. in Mathematical Sciences from the University of Vermont where received the Kenney Award and the for Outstanding Work in Graduate Mathematics, the Complex Systems Fellowship and the Sang Kil Nam Scholarship. She has taught Calculus for many years, both in high schools (AP Calculus), colleges and universities. Her students have earned excellent scores on the AP exams. Catherine has also conducted research in Mathematical Ecology to simulate species interactions in stream communities, to model an invasive plant species and to predict ecosystem states in a sea urchin fishery. Catherine's students report that she welcomes their questions and explains difficult concepts in easy to understand terms.

Cost & Dates:

The tuition cost of this course, taken over two-semesters, is $540. To see a list of our currently open courses, please visit our Costs & Dates page.


We try our best to match students with appropriate courses. As such, we ask that you complete an application before enrolling in our course. Once our staff have reviewed your application, you will then be sent an acceptance letter (via email) with payment and login information.

*AP® and Advanced Placement® Program are trademarks of the College Board which was not involved in the production of this website. All courses are participating in the rigorous AP® Course Audit. Courses designated as AP have been approved for the current year. Courses designated as AP* are currently being reviewed by the College Board.