AP Calculus AB

# AP Calculus AB #

2022–2023

## Summer Work #

I recommend completing the Get ready for AP Calculus course on Khan Academy.

## Course Description #

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. You’ll learn how to determine expressions and values using mathematical procedures and rules; connect representations; justify reasoning and solutions; and use correct notation, language, and mathematical conventions to communicate results or solutions

## AP Exam #

The AP exams is 3 hours and 15 minute long and include 45 multiple-choice questions and 6 free-response questions. A calculator is not permitted on 30 of the multiple-choice questions and 4 of the free-response questions. The exam takes place on Monday, May 8 at 8 a.m.

## Units of Study #

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.
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.
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.
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.
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.
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.
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.
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.

## Miscellaneous #

We will use the book Calculus: Graphical, Numerical, Algebraic (AP ed., 5th ed.) as reference and for homework assignments, though I recommend Khan Academy as a first stop for any extra practice. They have both an AP Calculus AB course and a Get ready for AP Calculus course. I suggest reviewing the latter prior to any new chapter.

You will also have access to TI-84 Plus calculators in class, and an emulator of the same is on your Chromebooks. Purchasing your own is not a bad idea if you have the means, but not required in any way shape or form. I still have a TI-89 from my freshman year of college over 20 years ago, so it’s worth considering if you anticipate using it after this course. For a list of acceptable calculators, see this list from College Board. You want calculators with an asterisk after their name.

Also …

• Grading is point-based. Homework assignments are worth 1 point, quizzes 10 points and exams 25.
• Homework is due at the end of the chapter, but zeroes will go in the grade book in the meantime
• Late homework loses two percentage points per day with a floor of 70%