Understanding the Differences Between AP Calculus AB and BC

AP Calculus, designed to be comparable with college-level courses, is divided into two courses: AP Calculus AB and AP Calculus BC. These courses cover different content and depth, catering to students with varying levels of mathematical proficiency and interest in pursuing advanced mathematics in their future academic or professional endeavors.

AP Calculus AB

Content: The content of AP Calculus AB includes the fundamental concepts of calculus, such as limits, derivatives, and the Fundamental Theorem of Calculus. Additionally, it covers essential topics like integrals and basic differential equations.

Topics:

Functions, graphs, and limits Derivatives and their applications Definite and indefinite integrals Basic differential equations

Depth: AP Calculus AB generally focuses on the basic concepts and techniques of calculus. It does not delve into as many advanced topics as AP Calculus BC, making it a more manageable course for students who have a solid foundation in pre-calculus mathematics.

AP Calculus BC

Content: AP Calculus BC includes all the topics covered in AP Calculus AB, plus additional advanced concepts and more in-depth applications. This course provides a more comprehensive and deeper understanding of calculus, often intended for students who are preparing for college-level calculus courses.

Topics:

All topics from AP Calculus AB Parametric equations and polar coordinates Series and sequences Advanced integration techniques Taylor and Maclaurin series

Depth: AP Calculus BC is designed to provide a deeper understanding of calculus concepts, thus covering more complex topics and more advanced applications. This course is intended for students who have a strong background in pre-calculus mathematics and can handle more challenging material.

Summary

In essence, AP Calculus BC is a superset of AP Calculus AB. It not only encompasses all the topics covered in AP Calculus AB but also goes further into more complex topics and applications. Students taking AP Calculus BC are expected to have a stronger background in mathematics and the ability to handle more challenging material.

Choosing between the two courses depends on the student's level of mathematical proficiency, their future academic plans, and their interest in advanced calculus.