【国际数学联盟】AP COURSE CONTENT AND DETAILS.pdf

AP Course Content Unit 1: Limits and Continuity You’ll start to explore how limits will allow you to solve problems involving change and to better understand mathematical reasoning about functions. Topics may include:  How limits help us to handle change at an instant  Definition and properties of limits in various representations  Definitions of continuity of a function at a point and over a domain  Asymptotes and limits at infinity  Reasoning using the Squeeze theorem and the Intermediate Value Theorem On The Exam 4%–7% of exam score  Unit 2: Differentiation: Definition and Fundamental Properties You’ll apply limits to define the derivative, become skillful at determining derivatives, and continue to develop mathematical reasoning skills. Topics may include:  Defining the derivative of a function at a point and as a function  Connecting differentiability and continuity  Determining derivatives for elementary functions  Applying differentiation rules On The Exam 4%–7% of exam score Unit 3: Differentiation: Composite, Implicit, and Inverse Functions You’ll master using the chain rule, develop new differentiation tech niques, and be introduced to higher-order derivatives. Topics may include:  The chain rule for differentiating composite functions  Implicit differentiation  Differentiation of general and particular inverse functions  Determining higher-order derivatives of functions On The Exam 4%–7% of exam score Unit 4: Contextual Applications of Differentiation You’ll apply derivatives to set up and solve real-world problems involving instantaneous rates of change and use mathematical reasoning to determine limits of certain indeterminate forms. Topics may include:  Identifying relevant mathematical information in verbal representations of real-world problems involving rates of change  Applying understa