AP Calculus AB vs. AP Calculus BC
Advanced Placement (AP) Calculus AB and AP Calculus BC are introductory, yet separate, college-level math courses that introduce the fundamentals of differential and integral calculus. There are three (3) conceptual ideas that form the foundation of the AP Calculus AB and AP Calculus BC content: 1) rates of change; 2) limits; and 3) analysis of functions. In addition to the content, the AP Calculus AB and AP Calculus BC courses focus on the mathematical practices shown below. These skills will also be tested in both AP exams.
The Prerequisite
Math is a cumulative subject, which means that understanding the basic concepts is crucial in order to build on them and master more advanced concepts. AP Calculus AB and AP Calculus BC require students to already have mastered precalculus. A strong foundation on functions, geometry, trigonometry and algebra is essential. The step-up from precalculus to AP Calculus AB or AP Calculus BC is significant. Therefore, only students that achieved strong grades in Honors Precalculus are recommended to take AP Calculus AB or AP Calculus BC. Students should also be aware that since there is so much material to cover in AP Calculus AB and AP Calculus BC, there won't be enough time to review precalculus content.
The Options
AP Calculus AB and AP Calculus BC are year-long APs. Students are usually given the choice to take either AP Calculus AB or AP Calculus BC in 11th or 12th grade in high school after the completion of precalculus. Students are also allowed to take AP Calculus AB in 11th grade then AP Calculus BC in 12th grade. Self-study students must ensure that the precalculus skills and content are mastered before attempting to learn AP Calculus AB or AP Calculus BC. Taking both AP Calculus AB and AP Calculus BC exams in the same year is not permitted by College Board. Furthermore, the AP Calculus BC exam allows for a special score structure, where students are given an AP Calculus AB subscore in addition to their AP Calculus BC score. More information can be found on the College Board website here.
The Content
AP Calculus AB and AP Calculus BC explore similar topics within differential and integral calculus. There are eight (8) units, which are detailed in the table below within AP Calculus AB. These eight (8) units are also covered in AP Calculus BC. However, AP Calculus BC covers additional topics within Units 6-8 and introduces two (2) extra units. Since AP Calculus BC covers more content in the same amount of time as AP Calculus AB, the teaching pace will be significantly quicker. Therefore, students taking AP Calculus BC must be prepared for the challenges of learning the larger quantity of content, which requires much more time and effort to master.
The following table details the AP Calculus AB and AP Calculus BC content. Created by Presidio Education®, 2022.
| Unit Breakdown: AP Calculus AB vs. AP Calculus BC | ||
|---|---|---|
| Units | AP Calculus AB | AP Calculus BC |
| 1 | Limits and continuity | Limits and continuity |
| 2 | Differentiation: Definition and fundamental properties | Differentiation: Definition and fundamental properties |
| 3 | Differentiation: Composite, implicit, and inverse functions | Differentiation: Composite, implicit, and inverse functions |
| 4 | Contextual applications of differentiation | Contextual applications of differentiation |
| 5 | Analytical applications of differentiation | Analytical applications of differentiation |
| 6 | Integration and accumulation of change | Integration and accumulation of change (additional techniques of integration) |
| 7 | Differential equations | Differential equations (Euler's method and logistic models with differential equations) |
| 8 | Applications of integration | Applications of integration (arc length and distance traveled along a smooth curve) |
| 9 | – | Parametric equations, polar coordinates and vector-valued functions |
| 10 | – | Infinite sequences and series |
Almost all of the content covered in AP Calculus AB and AP Calculus BC should be entirely new to students. Therefore, most students and parents may underestimate the time, effort and skills required to master the content. The applications of differential and integral calculus (Units 4, 5 and 8) are particularly challenging as they require the mastery of the basics that are covered in Units 2, 3 and 6. Furthermore, no formula sheet is given in the exam. Students are expected to memorize an overwhelming quantity of formulas. Students hoping to take AP Calculus AB or AP Calculus BC are strongly encouraged to enroll in summer training the year before the May AP exams. This will better prepare students and reduce the pressure and workload during the school year. AP Calculus BC is the most challenging math AP. Consequently, only students that have demonstrated high-level math skills and have a passion for math are recommended to take AP Calculus BC.
The Exam Format
Both AP Calculus AB and AP Calculus BC exam formats are the same. However, they differ slightly from other AP exams. There are four (4) sections in the AP Calculus AB and AP Calculus BC exams. There are sections that require graphing calculators and sections that do not permit calculators. Each exam is three (3) hours and 15 minutes in length. The full details of the AP Calculus AB and AP Calculus BC exams can be found in the table below.
The following table details the AP Calculus AB and AP Calculus BC exams. Created by Presidio Education®, 2022.
| Exam Format Breakdown: AP Calculus AB vs. AP Calculus BC | |||||
|---|---|---|---|---|---|
| Sections | Question Types | Calculator | Questions | Exam Weight | Time |
| 1A | Multiple-Choice | No | 30 | 33.3% | 60 minutes |
| 1B | Multiple-Choice | Yes | 15 | 16.7% | 45 minutes |
| 2A | Free-Response | Yes | 2 | 16.7% | 30 minutes |
| 2B | Free-Response | No | 4 | 33.3% | 60 minutes |
| Total | 51 | 100% | 3 hours, 15 minutes | ||
Note that the total exam percentage for the sections that do not permit calculators is 66.6% and the total exam percentage for the calculator permitted sections is 33.4%. Students must learn to apply the AP Calculus concepts without depending on the graphing calculator. However, learning how to efficiently use the graphing calculator will also be crucial. Click here for more details on the College Board May 2022 AP exam calculator policy.
Get in Touch with Us
Navigating the nuances of the various AP exams can be daunting for students or parents. Here, at Presidio Education®, our experienced faculty is more than willing to help. We strongly encourage students or parents to get in touch with us as early as possible. Planning for AP training should not be left to the last minute. Please do not hesitate to contact us if you have any questions or would like more information on private classes.
