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AP Calculus BC is an extended version of Calculus AB—it includes everything from AB and then goes even deeper. If you’re planning to take this course, you probably already know it’s one of the most advanced AP math classes available. From curve sketching to parametric equations and infinite series, there’s a lot to cover.
At TestprepKart, our AP Calculus BC coaching is designed to help you manage this challenging course with confidence. We focus on building a strong foundation, making difficult topics easier to understand, and preparing you to perform well in both the multiple-choice and free-response sections of the exam.
Let’s walk through what the course looks like and how we help you stay ahead.
The AP Calculus BC curriculum includes 10 units. While some of these are shared with Calculus AB, others—like parametric equations and series—are unique to BC. We’ve structured our sessions to spend more time on units with higher exam weight.
| Unit No. | Unit Title | Estimated Hours | Exam Weighting | Topics Covered |
| 1 | Limits and Continuity | 10 hours | 4–7% | Limits, continuity, one-sided limits, limits at infinity, Intermediate Value Theorem |
| 2 | Differentiation: Definition and Basic Rules | 12 hours | 7–12% | Derivatives at a point, rules of differentiation (power, product, quotient), higher-order derivatives |
| 3 | Differentiation: Composite, Implicit, and Inverse Functions | 12 hours | 9–13% | Chain rule, implicit differentiation, inverse functions, related rates |
| 4 | Contextual Applications of Derivatives | 15 hours | 6–12% | Motion, optimization, linear approximations, differentials, Mean Value Theorem |
| 5 | Analytical Applications of Derivatives | 15 hours | 15–18% | Curve sketching (extrema, concavity), first and second derivative tests, inflection points |
| 6 | Integration and Accumulation of Change | 15 hours | 17–20% | Riemann sums, definite/indefinite integrals, accumulation functions, FTC Part 1 & 2 |
| 7 | Differential Equations | 8 hours | 6–10% | Slope fields, separable differential equations, exponential/logistic models |
| 8 | Applications of Integration | 13 hours | 10–15% | Area under curves, volume of solids (disks, washers, shells), average value of a function |
| 9 | Parametric, Polar, and Vector Functions | 10 hours | 10–15% | Parametric equations, arc length, polar and vector-valued functions and their derivatives |
| 10 | Infinite Sequences and Series | 15 hours | 17–18% | Convergence tests (geometric, p-series, comparison), Taylor and Maclaurin series, radius and interval of convergence |
Along with the syllabus, we are also giving you a bonus TestprepKart eBook. This is not an academic textbook. It’s more of a helpful guide that answers many common questions students have about AP exams.
If you’re an NRI student, or if you’re not sure how AP scores work, or you’re confused between AP, IB, and A-Levels, this eBook will really help you.
What’s inside this guide:
Calculus BC adds several advanced topics that students haven’t seen before—like polar coordinates and series. This can make the course feel overwhelming, especially without proper planning.
Some students try to give equal time to every unit, but certain chapters like Integration and Series carry much more weight on the exam. Time management becomes critical.
If your base from AB topics like derivatives and integrals isn’t strong, it becomes harder to understand BC-specific content such as vector functions or convergence tests.
The exam often requires interpreting graphs or solving real-world application questions. These can be difficult without regular practice in a guided setting.
Knowing the content is one thing—writing clean, complete, and accurate FRQs is another. Many students lose points due to unclear reasoning or missed justifications.
We prioritize high-weight units like Integration, Series, and Parametric/Polar functions. This ensures you get enough time and practice on the areas that matter most.
We make sure you’re confident with AB-level content before moving to BC-specific units. This layered approach helps you connect concepts more easily.
Regular quizzes, mock tests, and assignments keep you on track. You’ll get detailed feedback so you always know what’s working and what needs attention.
You’ll learn how to solve both question types using proper methods. We cover past AP problems and teach you how to show your work clearly in the FRQ section.
We focus on why things work, not just shortcuts. This deeper understanding makes problem-solving more flexible and helps retain concepts longer.
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