Subject: Mathematics

AP Calculus AB

AP Calculus AB: Master the fundamentals of calculus and prepare for the AP Exam in May.

Course Type: Advanced Placement

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Credits: 1.0

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Course Description

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 to customize your academic path.

Course 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

Starting is Easy

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Course Contents

Module TitleModule Topic(s)
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

Recommended Prerequisites

Algebra 1

Credits: 1.0

Course Type: Standard High School

Course Subject: Mathematics

Algebra 2

Credits: 1.0

Course Type: Standard High School

Course Subject: Mathematics

Geometry

Credits: 1.0

Course Type: Standard High School

Course Subject: Mathematics

Pre-Calculus

Credits: 1.0

Course Type: Standard High School

Course Subject: Mathematics

Carnegie Credits Explained: Our Approach vs. Trimester Credits

Carnegie Credit System
Excel High School follows the Carnegie Credit system, a widely recognized method of measuring student progress based on instructional hours. A single Carnegie credit reflects approximately 120 hours of coursework, typically completed over a full academic year.

Carnegie Credit vs. Trimester Credit
While Carnegie credits are awarded based on total hours over a year, trimester credits divide the school year into three terms. In a trimester system, students complete courses in shorter, intensive sessions, often earning partial credits (e.g., 0.33 or 0.5 per term). In contrast, Excel’s use of Carnegie credits ensures students have ample time to engage deeply with the material and develop a well-rounded understanding at a consistent pace.

Accreditation You Can Trust

Recognized & Respected Nationwide

At Excel High School, we are proud to be regionally accredited by Cognia, along with additional accreditations from NCA, SACS, NWAC, and the Middle States Association. Our programs meet the same rigorous standards as public schools, giving you the confidence of earning a well-respected diploma.

Global Recognition for Our Accredited Diplomas

Excel High School’s regionally accredited diploma is accepted by colleges and universities around the world. With our recognized accreditation, you can confidently pursue higher education wherever your journey takes you.

Accreditation You Can Trust

Recognized & Respected Nationwide

At Excel High School, we are proud to be regionally accredited by Cognia, along with additional accreditations from NCA, SACS, NWAC, and the Middle States Association. Our programs meet the same rigorous standards as public schools, giving you the confidence of earning a well-respected diploma.

Global Recognition for Our Accredited Diplomas

Excel High School’s regionally accredited diploma is accepted by colleges and universities around the world. With our recognized accreditation, you can confidently pursue higher education wherever your journey takes you.