AP Calculus AB

AP Calculus AB Curriculum

AP Calculus AB 

 

About the Course 

 

Explore the concepts, methods, and applications of differential and integral calculus. You’ll work to understand the theoretical basis and solve problems by applying your knowledge and skills. 

 
Skills You’ll Learn 

 

• Determining expressions and values using mathematical procedures and rules. 

• Connecting representations. 

• Justifying reasoning and solutions. 

• Using correct notation, language, and mathematical conventions to communicate results or solutions. 

 

Equivalency and Prerequisites 

 

College Course Equivalent 

A first-semester college calculus course devoted to topics in differential and integral calculus 

Recommended Prerequisites 

You should have successfully completed courses in which you studied algebra, geometry, trigonometry, analytic geometry, and elementary functions. Particularly, you should understand the properties of linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise-defined functions and know how to graph these functions and solve equations involving them. You should also be familiar with algebraic transformations, combinations, compositions, and inverses for general functions. 

 

Course Content 

 

The course content outlined below is organized into commonly taught units of study that provide one possible sequence for the course. Your teacher may choose to organize the course content differently based on local priorities and preferences. 

 

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. 

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. 

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions 

You’ll master using the chain rule, develop new differentiation techniques, and be introduced to higher-order derivatives. 

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. 

Unit 5: Analytical Applications of Differentiation 

After exploring relationships among the graphs of a function and its derivatives, you'll learn to apply calculus to solve optimization problems. 

Unit 6: Integration and Accumulation of Change 

You’ll learn to apply limits to define definite integrals and how the Fundamental Theorem connects integration and differentiation. You’ll apply properties of integrals and practice useful integration techniques. 

Unit 7: Differential Equations 

You’ll learn how to solve certain differential equations and apply that knowledge to deepen your understanding of exponential growth and decay. 

Unit 8: Applications of Integration 

You’ll make mathematical connections that will allow you to solve a wide range of problems involving net change over an interval of time and to find areas of regions or volumes of solids defined using functions. 


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