AP Calculus AB is an Advanced Placement calculus course taken by high school students around the world, most of whom study at schools with an American curriculum. The course is traditionally taken after precalculus and is the first calculus course offered at most schools except for the regular calculus class. The Pre-Advanced Placement pathway for math will help prepare students for further Advanced Placement classes and exams.
Purpose
According to the College Board,
An AP course in calculus consists of a full high school academic year of work that is comparable to calculus courses in colleges and universities. It is expected that students who take an AP course in calculus will seek college credit, college placement, or both, from institutions of higher learning.
The AP Program includes specifications for two calculus courses and the exam for each course. The two courses and the two corresponding exams are designated as Calculus AB and Calculus BC. Calculus AB can be offered as an AP course by any school that can organize a curriculum for students with mathematical ability.
Course content
The material includes the study and application of differentiation and integration, and graphical analysis including limits, asymptotes, and continuity. An AP Calculus AB course is typically equivalent to one semester of college calculus. More specifically, the topics are
Analysis of graphs (predicting and explaining behavior)
Limits of functions (one and two sided)
Asymptotic and unbounded behavior
Continuity
Derivatives
Concept
At a point
As a function
Applications
Second derivatives
Integrals
Interpretations
Properties
Applications
Techniques
Numerical approximations
Fundamental theorem of calculus
Antidifferentation