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

**CONTENTS**

### 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. In particular, 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.

**About Exams **

Both the paper and digital versions of the AP Calculus AB Exam will be full length and measure the full range of skills and knowledge specified in the course and exam description (CED).

The paper exams will follow the typical multiple-choice and free-response format given in the CED. The digital exam will take the same amount of time as the paper exam, but the free-response questions will be adapted to include responses and explanations that can be easily typed with a computer keyboard, and will not require you to type mathematical symbols, to draw, or to create graphs. The digital exam app will include any symbols you would need to type your responses. No handwritten or photographed work will be accepted.

On the paper exam, calculators are not allowed in Section 1 Part A and Section 2 Part B, per the AP Exam Calculator Policy. On the digital exam, calculators will be allowed on all sections of the exam.

There are differences between the paper and digital versions of some 2021 AP Exams, and those variations differ by course. The information below applies to AP Calculus AB only.

For more information, see the brochure below.

#### Contents

**Unit 1: Limits and Continuity**- Unit 2: Differentiation: Definition and Fundamental Properties
- Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
- Unit 4: Contextual Applications of Differentiation
- Unit 5: Analytical Applications of Differentiation
- Unit 6: Integration and Accumulation of Change
- Unit 7: Differential Equations
- Unit 8: Applications of Integration