Exploring the differences between Calculus AB vs BC, this guide offers an in-depth comparison of the two popular AP Calculus courses. Both AP Calculus AB and BC are top choices for high school students seeking a challenging mathematical curriculum. In 2022 alone, a combined total of 420,000 students enrolled in these courses, reflecting their popularity. While they share similarities, such as offering college credit and introducing students to advanced calculus concepts, there are distinct differences in their curriculums and exams.
In this blog, we will compare and contrast the AP Calculus AB and BC courses.
Prerequisites
In comparing Calculus AB vs BC, we find that both AP Calculus courses have similar prerequisites. Typically, students have completed Algebra II and/or Precalculus before enrolling in either Calculus AB or BC. For a deeper look into that, check out our article on Prerequisites for Calculus.
Curriculums
For the most part, both classes have very similar curricula, but BC is regarded as an extension of AB; AB does not touch some of the content covered by BC. The list of topics found in BC but not AB are:
- Integration by Parts
- Integration by Partial Fractions
- Improper Integrals
- Euler’s Method
- Logistic Modeling
- Arc Length
- Parametric Equations, Polar Coordinates, and Vector-Valued Functions (Unit 9)
- Infinite Sequences and Series (Unit 10)
These topics are typically found between Calculus 2 and the beginning of Calculus 3 in college and thus are significantly more advanced than other topics. in AB.
Due to these differences in the curriculum, AP Calculus BC is more rigorous than AB–it is also faster paced because despite having more content, it is covered in the same amount of time as the AB content. Thus, the workload is more demanding as more is expected of a BC student.
The Exams
AB:
45 Multiple Choice Questions (50% of score), 105 minutes
- Part A:
- 30 no calculator questions
- 60 minutes
- Part B:
- 15 calculator questions
- 45 minutes
6 Free Response Questions (50% of score), 90 minutes
- Part A:
- 2 calculator questions
- 30 minutes
- Part B:
- 4 no calculator questions
- 60 minutes
BC:
45 Multiple Choice Questions (50% of score), 105 minutes
- Part A:
- 30 no calculator questions
- 60 minutes
- Part B:
- 15 calculator questions
- 45 minutes
6 Free Response Questions (50% of score), 90 minutes
- Part A:
- 2 calculator questions
- 30 minutes
- Part B:
- 4 no calculator questions
- 60 minutes
The AB and BC exams are both three hours and fifteen minutes, but BC covers a wider range of topics. 60% of the BC exam counts towards an “AB subscore”, which implies how well you performed on the AB topics of the exam. Here is a table comparing the weightings of each unit in AB to the weightings in BC.
| Topic | Unit | AB Exam Weighting | BC Exam Weighting |
|---|---|---|---|
| Limits and Continuity | Limits and Continuity | 11% | 6% |
| Differentiation | Definition and Fundamental Properties | 49% | 30% |
| Composite, Implicit and Inverse Properties | |||
| Contextual Applications of Differentiation | |||
| Analytical Applications of Differentiation | |||
| Integration | Integration and Accumulation of Change | 31% | 27% |
| Applications of Integration | |||
| Differential Equations | Differential Equations | 9% | 8% |
| BC Topics | Parametric Equations, Polar Coordinates, and Vector Valued Functions | – | 29% |
| Infinite Sequences and Series |
By passing the exam with a 4 or higher, most colleges will award credit for taking either AB or BC; colleges typically award at least twice as many credits for BC because BC covers two semesters of college calculus, whereas AB covers only the first semester.
Conclusion
AP Calculus BC and AB are two of the most challenging math courses offered in high school, but they have their similarities and differences. Here is a table that summarizes their relationship:
| Section | Calculus AB | Calculus BC |
|---|---|---|
| Prerequisites | Algebra II and Precalculus | Algebra II and Precalculus |
| Curriculum | Limits and Continuity, Differentiation, Integration, and Differential Equations | AB Topics + Other Methods and Applications of Integration, Non-Cartesian Coordinates, Sequences and Series |
| Exam | 3 hours and 15 minutes, 45 MCQ and 6 FRQ | 3 hours and 15 minutes, 45 MCQ and 6 FRQ; has an AB Subscore |
| College Credit | Yes | Yes; typically awarded more |
If you are a student seeking a career in STEM, it is recommended to take BC instead of AB to gain a foundation in both Calculus 1 and Calculus 2. If you only need Calculus 1 for your major, you may find AB more suitable. Both courses develop mathematical skills, enhance critical thinking, and prepare students for college-level math courses. We hope that this guide has helped you understand the difference between AP Calculus AB and BC. Good luck!
