AP Calculus AB vs. BC: Understanding the Difference

Calculus equations on a chalkboard
Updated:
January 30, 2024
4 min read
Contents

”Rohan

Reviewed by:

Former Admissions Committee Member, Columbia University

Reviewed: 01/30/24

Thinking about taking advanced calculus in high school? What’s the difference between AP Calculus AB and BC? We’ll break down everything you need to know about AP Calculus AB vs. BC to help you decide which one is best for you!

As a student preparing for college, you’ve probably heard about the opportunity to take college-level courses through programs like AP or IB. If you’re looking to challenge yourself academically, advanced math courses like AP Calculus AB and BC are often go-to options. But what are the differences between them?

Both AP classes are designed to challenge and prepare you for college-level mathematics, but they differ in their depth and breadth of topics. In this article, we'll explore the difference between AP Calculus AB and BC to help you make an informed decision and set you on the path to success in your mathematics studies.

What Is AP Calculus AB?

AP Calculus AB provides a comprehensive introduction to the fundamental principles of calculus. It is designed to help students develop a deep understanding of differential and integral calculus and their real-world applications.

Course Content

AP Calculus AB is equivalent to a calculus course students would take in the first semester of their freshman year of college. This AP course explores the following topics:

  1. Limits and Continuity
  2. Differentiation: Definition and Fundamental Properties
  3. Differentiation: Composite, Implicit, and Inverse Functions
  4. Contextual Applications of Differentiation
  5. Analytical Applications of Differentiation
  6. Integration and Accumulation of Change
  7. Differential Equations
  8. Applications of Integration

Students will also learn how to use technology, such as graphing calculators, to solve complex problems and visualize mathematical concepts.

Prerequisites

While there are no official prerequisites for AP Calculus AB, it is recommended that students have a solid strong foundation in topics such as:

  • Algebra 
  • Geometry and analytic geometry
  • Trigonometry
  • Limits and Continuity
  • Differentiation
  • Integration

Students should also have strong problem-solving skills and be comfortable working with functions, equations, and graphs. If you already have a strong grasp of the fundamentals covered in this course, you may be interested in the advanced topics explored in AP Calculus BC.

math equations on blackboard

What Is AP Calculus BC?

AP Calculus BC builds on the principles introduced in AP Calculus AB. Below we’ll take a closer look at the wide range of topics you’ll encounter in this AP course. 

Course Content

AP Calculus BC is designed to provide students with a comprehensive understanding of calculus and its applications. The course covers all the topics included in AP Calculus AB, but it also goes beyond that to cover additional concepts such as infinite sequences and series, and parametric equations, polar coordinates, and vector-valued functions.

Prerequisites

To enroll in AP Calculus BC, students should have completed Algebra II and Geometry courses, and be familiar with trigonometric functions and their properties. Students should also be familiar with the prerequisites needed for AP Calculus AB, as AP Calculus BC covers all the topics in AP Calculus AB.

Make sure to study the additional topics outlined earlier, as they are a significant part of the AP Calculus BC curriculum. The course is challenging but rewarding for students who are up to the task. Similar to AP Calculus AB, this course has its own exam that tests your understanding of concepts and problem-solving abilities.

AP Calculus AB vs. AP Calculus BC: What Is the Difference?

The main difference between AP Calculus AB and AP Calculus BC is the depth and breadth of the material they cover. AP Calculus AB focuses on the first semester of calculus (Calculus I), while AP Calculus BC covers both the first and second semesters or a full year of calculus (Calculus I and II combined).

In simpler terms, AP Calculus AB covers the basics of calculus, while AP Calculus BC takes those basics and adds more advanced concepts. 

So, if you take AP Calculus BC, you'll learn everything that's in AP Calculus AB, plus some extras like infinite sequences, series, parametric equations, polar coordinates, and vector-valued functions. 

Fundamental Similarities and Key Differences

Let's discuss the fundamental similarities and key differences between AP Calculus AB and AP Calculus BC:

Fundamental Similarities

  • Pre-calculus Prerequisite: Both AP Calculus AB and AP Calculus BC require students to have completed a pre-calculus course as a prerequisite.
  • Calculus I: Both courses cover the fundamentals of Calculus I, which is the introductory level of calculus.
  • Shared Topics: All the topics covered in AP Calculus AB are also included in AP Calculus BC. This means that if you study Calculus BC, you will cover everything taught in Calculus AB.

Key Differences

  • Course Duration: AP Calculus AB focuses solely on the first semester of calculus (Calculus I). In contrast, AP Calculus BC covers both the first and second semesters or a full year of calculus (Calculus I and II courses combined).
  • Additional Concepts: Calculus BC goes beyond Calculus AB by introducing additional mathematical concepts. These additional topics include infinite sequences and series, parametric equations, polar coordinates, and vector-valued functions.
  • Pace of Learning: Due to the inclusion of more advanced concepts, Calculus BC is generally a more fast-paced and challenging course compared to Calculus AB.
  • Specific Units: Calculus AB typically covers three main sections: functions, derivatives, and integrals. Calculus BC includes these units but also adds an extra unit that focuses on polynomial approximations, series of constants, and the Taylor series.

While both Calculus AB and Calculus BC cover the fundamentals of calculus, Calculus BC is a more comprehensive and advanced course that includes additional topics and is taught at a faster pace. It's important to choose the course that aligns with your mathematical interests and goals. 

Calculus AB Calculus BC
Functions, Limits and Graphs Functions, Limits, and Graphs
Derivatives Derivatives
Applications of Derivatives Applications of Derivatives
Integrals Integrals
Applications of Integrals Applications of Integrals
Polynomial Approximations and Series
Series and Constants
Taylor Series

AP Calculus AB or AP Calculus BC: Which Should You Choose?

When deciding between AP Calculus AB vs. AP Calculus BC, it's important to consider which one is best suited for your academic goals. 

While both courses cover calculus topics, AP Calculus BC is more advanced and challenging than AP Calculus AB. Therefore, students who aim to pursue more rigorous college degrees and programs may find Calculus BC to be a better fit.

One significant benefit of securing a good score in AP Calculus BC is that it signals to college admissions committees that you are well-prepared and have a strong aptitude for college-level mathematics. This credential is especially helpful for students who plan to pursue competitive degrees in STEM programs and majors. 

Taking AP exams allows you to earn college credit and skip certain courses in college. AP Calculus BC typically grants more math credit in college than AP Calculus AB, which is helpful for those who want to jump into advanced math courses sooner.

If you're confident in your math abilities and have done well in pre-calculus classes, you may want to consider taking AP Calculus BC. However, AP Calculus AB is a good option for applicants who want an AP credential in mathematics at a relatively lower difficulty. AP Statistics is another good option. 

While AP Calculus AB covers fewer topics and concepts than AP Calculus BC, it still teaches core calculus concepts that will provide you with the fundamentals needed for tougher math courses in college.

Ultimately, the decision between AP Calculus AB vs. AP Calculus BC depends on your academic goals and math abilities. Consider your future degree programs and your confidence level in mathematics when deciding which course is right for you.

FAQs: AP Calculus AB vs. BC

Still have more questions? Take a look at our answers to these frequently asked questions to help you calculate your next steps! 

1. Is AP Calculus AB or BC Harder?

AP Calculus BC is considered more challenging because it covers all the topics covered in AP Calculus AB, includes additional topics, and is taught at a faster pace.

2. Is It Better to Take AP Calculus AB or BC?

That depends largely on your own circumstances and plans for college. In essence, AP Calculus AB is more suitable for students who want a good foundation in mathematics but are not pursuing a degree containing advanced mathematics. Calculus BC has more depth in content and gives a more advantageous edge for competitive degrees. 

3. Is AP Calculus BC the Hardest AP?

It is difficult but not necessarily the hardest among AP courses, especially if you look at the score distributions. 

In 2023, 78.5% of students who took AP Calculus BC got a final exam score of 3 or higher, with 43.5% of all those test-takers getting a 5. However, there are certainly harder classes, like Physics 1, and United States History. 

4. Is AP Calculus AB Worth It?

Yes, it is an excellent way to showcase your mathematical abilities without having to be too stressed and having more flexibility in your schedule. It is also a great fit if you’re aiming for programs that aren’t too math-heavy. 

5. Can I Take Both AP Calculus AB and AP Calculus BC?

No, the College Board explicitly states you may not take both exams within the same year. You must make a choice and decide which one suits you better. 

Final Thoughts

Choosing the right AP class is a crucial first step for students aiming to make the most of their college application. Hopefully, this article has cleared up some confusion about the difference between AP Calculus AB and BC.

Both AP Calculus courses require a lot of effort, but successfully completing either one can be invaluable in the college admissions process. So, whichever course you choose, put your best foot forward, and you'll reap the rewards. Best of luck!

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