The difference between AP Calculus AB and BC is one of scope, not level of difficulty. AP Calculus AB includes techniques and applications of the derivative, the definite integral, and the Fundamental Theorem of Calculus. It is equivalent to at least a semester of calculus at most colleges and universities.  AP Calculus BC includes all topics in AP Calculus AB, as well as additional topics, such as differential and integral calculus (including parametric, polar, and vector functions) and series. It is equivalent to at least one year of calculus at most colleges and universities. AP Calculus BC is an extension of AP Calculus AB, and each course is challenging and demanding and requires a similar depth of understanding of topics. 

AP Calculus AB

Description

Students in this course will walk in the footsteps of Newton and Leibnitz. An interactive course framework combines with exciting on-line course delivery to make calculus an adventure. The course includes a study of limits, continuity, differentiation, and the integration of algebraic, trigonometric, and transcendental functions, as well as the applications of derivatives and integrals. 

Major Topics and Concepts

Semester 1

Review of Function Terminology and More
Graphing Calculators
Compositions and Transformations of Functions
Some Common Functions
Introduction to Limits
Properties of Limits
Limits Involving Infinity
Continuity
Applications of Limits
The Derivative
Rules of Differentiation
Trigonometric Derivatives and the Chain Rule
Inverse Functions
Exponential and Logarithmic Functions
Derivatives of Exponential, Logarithmic, and Inverse Trig Functions
Implicit Differentiation
Analyzing Functions Part I: Curve Sketching
Analyzing Functions Part II: Maximums and Minimums
Applied Maximum and Minimum Problems
Distance, Velocity, Acceleration, and Rectilinear Motion
Related Rates
The Mean-Value Theorem and L'Hôpital's Rule
Linearization

SEMESTER 2

Area Approximation and Riemann Sums
Introduction to the Definite Integral
The Fundamental Theorem of Calculus
Integrals and Antiderivatives
Integration by Substitution
The Definite Integral
Volume by Discs (Slicing)
Finding the Area Under and Between Curves
Average Value of a Function and Rectilinear Motion Revisited
Differential Equations – An Introduction
Initial Value Problems and Slope Fields  
Numerical Approximation Methods with Integrals
Exploring the Graphs of f, f Prime, and f Double Prime
Using Calculus with Data in a Table
Functions Defined By Integrals
AP Exam Review and Test Taking Tips and Practice