AP Calculus AB

Limits, derivatives, and integrals

AP Calculus AB is a first course in the mathematics of change — the two great ideas of the derivative (an instantaneous rate) and the integral (an accumulated total), bound together by the Fundamental Theorem of Calculus. This journey walks the College Board's eight-unit framework from the ground up: how limits make 'instantaneous' rigorous, how to differentiate any function you can write, how derivatives describe motion and shape, how integration accumulates change, how differential equations model growth, and how to turn all of it into points on the exam's multiple-choice and free-response sections. Master these and the language of physics, engineering, economics, and every quantitative science becomes readable.