AP Calculus BC

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Course option: Live

Grade: Varies | Successful completion of Honors or AP Precalculus

Course dates: August 17, 2026 to May 2027 (AP exam)

Course length: Traditional, full year

Live Sessions - attendance required: Tuesdays and Thursdays | 12-1 p.m. Eastern

Course size: 20 students

Instructor: Dr. Kyle Barker

Cost: $875

Dr. Kyle Barker - AP Calculus AB & AP Calculus BC kylebarker.blueten[at]gmail.com

More about Dr. Kyle Barker

Dr. Barker teaches for Blue Tent Online (BTO) and is an applied mathematician with a strong commitment to clear, rigorous instruction. He earned his PhD in Applied Mathematics from the University of Arkansas at Little Rock, where he now serves as an Assistant Professor and the Graduate Coordinator. His interest in mathematics grew from an early fascination with how quantitative patterns help explain scientific and real-world phenomena.

Dr. Barker has more than ten years of teaching experience, working with students in AP Calculus, concurrent credit courses, and advanced competition preparation for the AMC, AIME, and the Putnam Exam. He focuses on helping students develop strong reasoning skills, mathematical confidence, and a deeper understanding of why ideas work the way they do.

In addition to teaching, Dr. Barker is an active researcher and a recognized expert in traveling waves and numerical methods for partial differential equations. His published work includes contributions on monotone traveling waves and p-biharmonic maps, reflecting his interest in the mathematical structures underlying complex dynamical systems.

Outside of academics, Dr. Barker enjoys growing peppers, making hot sauce, and spending time with his wife and their son, Benny.

See the 2025 AP Calculus BC exam scores our students earned HERE

Course Details

This live online AP Calculus BC course is for high school homeschoolers as well as other high school students who are supplementing their math skills.

This AP Calculus BC course complies with the AP course audit and has been approved by the College Board (CB). The CB has designed this year-long class to cover the content of AP Calculus AB in the first semester and the content of AP Calculus BC in the second semester and is taught at the pace of a two-semester college course. It is designed for students with a very strong math background since it will require discipline to take on its rigor.

Prerequisites

Students must have completed the equivalent of the high school math sequence: Algebra 1, Geometry, Algebra 2/Trigonometry,
Students must be familiar with all advanced topics in algebra, trigonometry, analytic geometry, elementary functions: linear, polynomial, rational, transcendental (trigonometric, exponential and logarithmic), inverse functions, and piece-wise defined functions.

Assessment

Beginning in early June, the instructor will send all registered students a questionnaire and diagnostic assessment to help them gauge whether some additional summer prep will be helpful.
A summer prep module will be available to students who need to refresh or reinforce necessary math concepts prior to the start of class.

Format

Students share an interactive online classroom and meet live on Zoom.
Students who attend live classes are expected to keep their webcams on.
Live classes will be recorded for those who miss classes or prefer to watch later.
All work will be handwritten and instructor graded.
There will be two live teacher-led meetings each week:
- One meeting: focuses on content and theory, and the
- Second meeting: focuses on solving calculus problems similar to the concepts taught in the recorded instruction and practiced in the weekly assignments.
- Active participation is required.
Office Hours (Optional):
- Friday, 12-1 p.m. Eastern
  - Students can receive help with assignments, prepare for upcoming quizzes or exams, and ask questions as needed.
- One-on-one scheduled times by appointment only
Average weekly time estimate: 8-10 hours, including recorded and live instruction
All Blue Tent live math classes are NCAA-approve
See our FAQs for:
- age/grade guidelines, prerequisites, and class fit recommendations
- a complete list of days, times, and breaks
- a list of CA charter schools where these courses are a-g approved

Course Content

This course will cover topics in both a first and second semester college calculus course:

Limits and their properties
Differentiation and applications of differentiation
Integration and applications of integration
Differential equations.
Advanced integration techniques, L’Hopital’s Rule and improper integrals
Infinite Series: Series convergence and divergence, Taylor and Maclaurin Series and polynomials.
Parametric equations, Polar coordinates and vectors

Foundational Elements

The AP Calculus BC online classroom will open each week with some combination of the following:

Weekly announcements
One or more 20-40 minute instructor-recorded lectures for every textbook section covered that week
- Since AP Calculus BC is taught at the pace of a college course, students will need to be disciplined about accessing the 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 Thursdays.
- A combination of recorded instruction and live interaction gives students more flexibility and permits the instructor to go into more detail in the recorded instruction than a one-hour lecture would allow.
Additional resources will help students with the calculus content covered that week
Quizzes or exams, if scheduled for the week
Free response questions (FRQs)
- Students will start learning to write answers to Free Response Questions (FRQs) from Chapter 1.
- All FRQs are graded by the instructor (not self-graded by the students)
- Detailed feedback is provided so the student can learn to write well-thought-out responses to FRQs.
- Corrections are allowed to give students an opportunity to learn from their mistakes and earn points back!
Live sessions:
- Most student/teacher interaction takes place in the problem sessions, and those live meetings 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 class forums they will post questions about reading assignments or homework, answer other students' questions, or post solutions to problems.
- There will also be one or more TAs available to help.

Course Goals

Develop a deep understanding of calculus concepts by learning to represent problems and solutions graphically, numerically, algebraically, and verbally, and by making connections between these different forms.
Use technology, including graphing calculators and Desmos, to explore functions, test conjectures, visualize behavior, and support mathematical reasoning rather than replace it.
Strengthen mathematical communication by explaining reasoning clearly in writing and discussion, using correct notation, and justifying conclusions.
Prepare for college-level mathematics by developing persistence, precision, and confidence when working with challenging multi-step problems.
Apply calculus to real-world contexts in science, engineering, and economics by modeling change, interpreting results, and evaluating assumptions.

The course is organized around the following foundational concepts of calculus:

Limits: Students will gain a solid, intuitive understanding of limits and be able to compute one-sided limits, limits at infinity, infinity limits and the limit of a sequence.
Derivatives: Students will learn to use different definitions of the derivative and be able to apply derivative rules and properties. Students will also become familiar with a variety of real-world applications of the derivative, including related rates, optimization, and growth and decay models.
Integrals and the Fundamental Theorem of Calculus: Students will gain a firm understanding of area, volume and motion applications of integrals as well as the use of the definite integral as an accumulation function. The relationship between integration and differentiation as expressed in the Fundamental Theorem of Calculus will also be emphasized.
Series: Students will become familiar with various methods for determining convergence and divergence of a series. Subsequently, students will learn to use power series to approximate an arbitrary function near a specific value. The generalization to Taylor and Maclaurin series for approximating common functions will also be studied.
The main components of Calculus BC are advanced integration techniques, sequences and series, and polynomial approximations. Calculus BC also extends all the content learned in Calculus AB to different types of equations (polar, parametric and vector-valued).