Mathematics·Advanced Placement
APCalculus AB
AP Calculus AB: Master the fundamentals of calculus and prepare for the AP Exam in May.
Built for the AP Exam
Every module sharpens the skills the College Board® tests. Sit the exam in May to earn potential college credit before you graduate.
About the course
Course Overview
AP Calculus AB offers students a comprehensive introduction to the core principles of calculus, focusing on concepts of limits, derivatives, integrals, and the Fundamental Theorem of Calculus. Designed to mirror a first-semester college calculus course, AP Calculus AB provides students with the mathematical foundation and problem-solving skills necessary for advanced studies in mathematics, physics, engineering, and other STEM fields.
In this course, students learn to analyze real-world situations through mathematical modeling, using derivatives to explore rates of change and integrals to understand accumulation. With hands-on practice and guided exploration, students gain a deep understanding of how calculus can describe motion, growth, and change in physical and theoretical contexts. Emphasis is placed on building a solid conceptual understanding, as well as proficiency in analytical, graphical, and numerical approaches to solving problems.
The course prepares students for the AP Exam in May, giving them the opportunity to earn college credit while honing critical thinking and problem-solving skills essential for future academic and professional success. With a focus on rigorous preparation, AP Calculus AB equips students with the confidence and knowledge to tackle complex mathematical concepts and apply them in real-life scenarios, setting a strong foundation for careers in STEM.
This course has been authorized by the College Board® to use the AP designation.
Want to take more AP classes? View our full [Online AP Program](https://www.excelhighschool.com/online-programs/advanced-placement-ap-courses-online/) to customize your academic path.
By the end of the course
Learning Objectives
- Determining expressions and values using mathematical procedures and rules
- Connecting representations
- Justifying reasoning and solutions
- Using correct notation, language, and mathematical conventions to communicate results or solutions
Course contents
What You'll Study
Limits and Continuity
Differentiation: Definition and Fundamental Properties
Differentiation: Composite, Implicit, and Inverse Functions
Contextual Applications of Differentiation
Analytical Applications of Differentiation
Integration and Accumulation of Change
Differential Equations
Applications of Integration
Earn your 1.0 credit in Calculus AB
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