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AP - Math and Computer Science

AP Calculus AB

It’s been said that change is the only true constant. Calculus helps make sense of change by grappling with questions that inspire thinkers from around the globe, across time, and in many disciplines. Can change occur in an instant? When is the next solar eclipse or the turning point for an economy? In AP Calculus AB, you’ll develop a deeper understanding of mathematical principles that can help you answer questions such as these.

College Board

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.

Asymptotes and limits at infinity

Definition and properties of limits in various representations

Definitions of continuity of a function at a point and over a domain

How limits help us to handle change at an instant

Reasoning using the Squeeze theorem and the Intermediate Value Theorem

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.

Applying differentiation rules

Connecting differentiability and continuity

Defining the derivative of a function at a point and as a function

Determining derivatives for elementary functions

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.

Determining higher-order derivatives of functions

Differentiation of general and particular inverse functions

Implicit differentiation

The chain rule for differentiating composite functions

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.

Applying understandings of differentiation to problems involving motion

Generalizing understandings of motion problems to other situations involving rates of change

Identifying relevant mathematical information in verbal representations of real-world problems involving rates of change

Local linearity and approximation

L’Hospital’s rule

Solving related rates problems

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.

Behaviors of Implicit relations

Derivatives and properties of functions

How to solve optimization problems

How to use the first derivative test, second derivative test, and candidates test

Mean Value Theorem and Extreme Value Theorem

Sketching graphs of functions and their derivatives

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.

Accumulation functions, the Fundamental Theorem of Calculus, and definite integrals

Antiderivatives and indefinite integrals

Approximating integrals using Riemann Sums

Properties of integrals and integration techniques

Using definite integrals to determine accumulated change over an interval

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.

Deriving and applying a model for exponential growth and decay

Interpreting verbal descriptions of change as separable differential equations

Sketching slope fields and families of solution curves

Solving separable differential equations to find general and particular solutions

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.