Calculus AB Curriculum
Introduction to the Calculus AB Curriculum
The Calculus AB curriculum is designed to give high school students a comprehensive introduction to differential and integral calculus, preparing them for both the Calculus AB Exam and future college-level calculus courses. Covering eight units, the course explores essential concepts such as limit values, derivative test, definite integrals, and the Fundamental Theorem of Calculus.
Through topics like implicit and inverse functions, differentiation definition and fundamental properties, contextual applications of differentiation, and the Mean Value Theorem, the course lays a solid foundation for understanding analytical applications and solving complex differential equations. The curriculum also covers the Squeeze Theorem, Intermediate Value Theorem, and integration techniques, ensuring students are well-prepared for the free response section and multiple-choice portions of the AP exam.
Limits & Continuity
Applications of Derivatives
Differential Equations
What’s the Difference Between AB and BC Calculus — and Why It Matters
Many students and parents wonder about the difference between AP Calculus AB and AP Calculus BC. While both are part of the AP program and cover introductory calculus, the Calculus AB curriculum focuses on the foundational aspects of differential and integral calculus, including topics like implicit differentiation, the Fundamental Theorem, definite integrals, and contextual applications of differentiation.
In contrast, AP Calculus BC builds on Calculus AB and dives deeper, adding additional units such as integration techniques, series, parametric equations, and more advanced differential equations. Essentially, Calculus AB covers the first semester of college calculus, while BC Calculus often equates to a full year.
Mastering the AP Calculus AB curriculum gives students a strong foundation in critical mathematical concepts like composite, implicit, and inverse functions, which are used in real-world fields such as engineering, computer science, economics, and medicine. Understanding derivatives, limits, and integrals isn’t just about passing the AP exam—it’s about developing the ability to model real-world problems, analyze data, and think logically under pressure.
From calculating rates of change in a business model to interpreting motion in physics, calculus plays a key role in everyday decision-making and future career success. Whether students move on to AP Calculus BC, other college math courses, or use these skills in life applications, AP Calculus AB provides the essential tools to succeed.
Prepare for the Calculus AB Exam with Confidence
This Calculus AB curriculum not only prepares students to succeed on the AP Calculus AB exam, but also equips them with the analytical thinking and problem-solving skills needed for success in advanced placement programs and college credit opportunities. With units like Unit 2 Differentiation Definition, Unit 3 Differentiation Composite Implicit, and in-depth instruction on composite, implicit, and inverse functions, students gain a complete understanding of introductory calculus.
Whether exploring contextual applications or mastering inverse trigonometric functions, students are guided through the complexities of calculus AB with clarity and support. This course is a cornerstone of the AP program, enabling learners to develop mastery in differential calculus, integral calculus, and beyond—while earning valuable preparation for AP Calculus BC or additional calculus courses in college.