The Difference Between AP Calculus AB and BC
You might now be beginning to choose potential AP® courses for the upcoming school year. Some AP courses seem similar in name but cover different content and skills. In this post, we’ll break down the similarities and differences between AP Calculus AB and AP Calculus BC.
What are AP Calculus AB and AP Calculus BC?
AP Calculus AB is an introductory college-level course in calculus that explores the concepts and applications of differential and integral calculus. This AP course culminates in an AP Exam that’s designed to test your understanding of the theoretical basis of course content and your ability to solve problems by applying your knowledge and skills.
AP Calculus BC is similar to AP Calculus AB. It explores the same concepts and applications, only it adds a few new topics. In other words, AP Calculus BC covers more content than AP Calculus AB, though both courses require you to apply the same skills.
How AP Calculus AB and AP Calculus BC are similar
The two courses cover content and skills that are introduced in a first-semester calculus course at the college level. All topics in the eight units of AP Calculus AB are included in AP Calculus BC.
These are the topics taught in both courses:
- Limits and continuity (Unit 1)
- Differentiation: Definition and fundamental properties (Unit 2)
- Differentiation: Composite, implicit, and inverse functions (Unit 3)
- Contextual applications of differentiation (Unit 4)
- Analytical applications of differentiation (Unit 5)
- Integration and accumulation of change (Unit 6)
- Differential equations (Unit 7)
- Applications of integration (Unit 8)
Because both courses and exams cover many of the same topics, the prerequisites needed for both courses and exams are comparable. Recommended mathematics courses to take before either AP Calculus AB or AP Calculus BC include those in which you study algebra, geometry, trigonometry, analytic geometry, and elementary functions.
How AP Calculus AB and AP Calculus BC are different
AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes.
All topics in the eight units of AP Calculus AB are also included in AP Calculus BC. However, AP Calculus BC contains two additional units (Units 9 and 10), plus some extra topics in Units 6─8.
These topics are only taught in AP Calculus BC:
- Additional techniques of integration (Unit 6)
- Euler's method and logistic models with differential equations (Unit 7)
- Arc length and distance traveled along a smooth curve (Unit 8)
- Parametric equations, polar coordinates, and vector-valued functions (Unit 9)
- Infinite sequences and series (Unit 10)