The Comprehensive Guide to AP Calculus BC

Welcome to the ‘AP Calculus BC Guide’, a comprehensive resource for mathematically inclined high school students seeking a challenge beyond AP Calculus AB. Not only does taking AP Calculus BC allow students to take more advanced courses in math and sciences and earn college credit, like AP Calculus AB does, it also allows students to explore advanced mathematical concepts not typically covered in math courses such as infinite series and polar coordinates.

In this comprehensive AP Calculus BC Guide, we have broken down AP Calculus BC into 3 sections: Prerequisites & Materials, Course Topics, and Exam & Preparation. This guide is designed to provide you with a thorough understanding of all aspects of the AP Calculus BC course.

General Information:

AP Calculus BC is a rigorous calculus course part of the Advanced Placement (AP) series. At the end of the course, students take an AP final exam. A good score on the AP Calculus BC exam can let the student skip introductory calculus courses in university or place into accelerated courses. 

Exam Info:

All information for the exam can be found on the College Board’s page for AP Calculus BC

Date: Monday, May 13th, 2024

Structure and Breakdown

Multiple Choice Section (50% exam weight):

  • Part A (60 mins)
    • 30 multiple choice questions 
  • Part B (45 mins)
    • 15 multiple choice questions Free Response Questions 

FRQs (50% exam weight):

  • Part A (30 mins)
    • 2 long form questions, work is shown 
  • Part B (60 mins)
    • 4 long form questions, work is shown

Total Duration: 3 hrs 15 mins

Official Practice Problems

Historical Exam Results

AP exam scores range between a 1 and a 5, with a 3 or higher being a passing mark and accepted for credit in many colleges, though requirements vary by institution.

2023 Statistics:

76% of students passed the exam

41% of students scored a 5

A full score breakdown of AP Calculus BC and other AP exams can be found here.

Prerequisites, Materials, and Topics

Prerequisites & Materials

Before you take AP Calculus BC, it is important to understand what you need to have taken before. Additionally, you should also understand what textbooks and other materials, such as calculators, you may need. For a deeper look into that, check out our article on Prerequisites for Calculus

Topics

The AP Calculus BC curriculum covers various foundational calculus topics in 5 main categories: Limits and Continuity, Differentiation, Integration, Differential Equations and BC Topics. To understand these topics more in-depth, read our article on What is Calculus. “BC Topics” refers to the advanced calculus topics found in the AP Calculus BC curriculum but not in the AP Calculus AB curriculum.

TopicUnitExam Weightage
Limits and ContinuityLimits and Continuity6%
DifferentiationDefinition and Fundamental Properties30%
Composite, Implicit and Inverse Properties
Contextual Applications of Differentiation
Analytical Applications of Differentiation
IntegrationIntegration and Accumulation of Change27%
Applications of Integration
Differential EquationsDifferential Equations8%
BC TopicsParametric Equations, Polar Coordinates, and Vector Valued Functions29%
Infinite Sequences and Series
Full descriptions of units and exam weightages can be found on the College Board’s official page

It is important to note that, although a large portion of AP Calc BC covers topics also found in AP Calc AB, the level and pace at which they are covered will be different. For example, although integration is covered in both AB and BC, the latter covers more techniques and goes more into depth. Additionally, as AP Calc BC has more material to cover, the course tends to bee faster paced, while AP Calc AB’s curriculum focuses on the fundamentals of calculus.

Exam

Exams Preparation

To prepare for the exam, you should:

  • Use I Aced Calculus resources such as:
    • Practice decks for each topic to reinforce key ideas
    • Calculator tips to understand how to be efficient during the exam
    • Problem sets and practice tests to track growth and prepare for both course exams and the AP exam
    • Videos to gain a more in-depth understanding of the material
    • One-on-one tutors who will work to identify areas of growth and reinforce understanding of tricky concepts
  • Use physical resources such as a reputable textbook approved by the College Board. Students can find an extensive, though not exhaustive, list on College Board’s webpage. Other trusted sources include those by Larson & Stuart and Barrons AP.

Conclusion

Following these steps can increase your confidence and competence in AP Calculus BC. Remember that AP Calculus BC is not only a challenging course but also a rewarding one. By taking this course, you can develop your mathematical skills, enhance your critical thinking, and prepare yourself for college-level math courses. We hope that this guide has helped you understand the content of AP Calculus BC and how to succeed in the course. Good luck!

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