# AP Calculus AB

## Course Description

This AP Calculus course is designed with the intent for students to incorporate the concepts of all previous math courses and expand upon these concepts with the implementation of Limits. Emphasis is placed upon the multi-representational approach to calculus where problems and their solutions are explored and interpreted graphically, numerically, analytically and verbally. Students will also be required to explain their answers in written form and will be asked to compare their written response to the AP grading rubric and explain why they feel they should receive that grade. Students are required to use graphing calculators with the capabilities ascribed by the College Board: (apcentral.collegeboard.com). These calculators will be used in a variety of ways including multi-representation of equations (graphs and tables) and also for conducting explorations with various functions and how different values change the look of the function.

## Course Requirements

#### Grade Level

11 – 12

#### Materials

Graphing Calculator

Calculus, Volume 1 from OpenStax (Will be provided as a downloadable .pdf once in the course)

**Digital:**

ISBN-10: 1-947172-13-1

ISBN-13: 978-1-947172-13-5

Princeton Review AP Calculus AB Premium Prep, 2022

ISBN-10: 052557056X

ISBN-13: 978-0525570561

#### Duration

2 Semesters

#### Prerequisites

Pre-Calculus

#### Technology Skills

- Internet Access
- Word Processor
- Email Access

## Major Concepts

- Students should develop a deeper understanding of very small and very large numbers and a variety of ways to represent them.
- Representations should be used to model and interpret physical, social, and mathematical phenomena.
- Mathematical thinking should be communicated coherently and clearly to teachers, peers, and others.
- Students should be able to judge the meaning, utility, and reasonableness of the results of symbol manipulation, including those carried out by technology.
- Functions should be analyzed by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior.
- Students should be able to use the language of mathematics to express mathematical ideas incisively.
- The connection between derivatives, antiderivatives, and integrals.
- Theorems involving integrals including the Fundamental Theorem of Calculus and the Second Fundamental Theorem of Calculus.
- How to construct antiderivatives using graphs, numbers, and differential equations.
- Different types of functions require different methods of finding integrals
- When we can’t find an exact integral we can use approximation we can find approximate integrals when there is not a finite interval
- Use integrals to compute volumes of irregular shapes.
- Use integrals to solve differential equations.
- Use integrals to solve real world exponential growth and decay problems.
- The format and topics to be addressed on the AP Calculus BC Exam and be prepared to take the exam.