## AP Calculus AB – Mohammad Al-Khuffash

From: 150,00 $ / month

#### Available courses

#### Mohammad Al-Khuffash

High school Mathematics teacher

Course Type |
Full Course |
---|---|

Program | |

Level |
AP |

Subject |
Mathematics |

## Course Curriculum

**General**- Announcements
- AP Calculus AB - Course Syllabus

**Unit 1: Limits and Continuity (Big Ideas: Change, Limits, Analysis of Functions)**- 1.1 Introducing Calculus
- 1.2 Defining Limits
- 1.3 Finding Limits From Graphs
- 1.4 Finding Limits from Tables
- 1.5 Determining Limits Using Algebraic Properties of Limits
- 1.6 Determining Limits Using Algebraic Manipulation
- 1.7 Selecting Procedures for Determining Limits
- 1.8 Determining Limits Using the Squeeze Theorem
- 1.9 Connecting Multiple Representations of Limits
- 1.10 Exploring Types of Discontinuities
- 1.11 Defining Continuity at a Point
- 1.12 Confirming Continuity Over an Interval
- 1.13 Removing Discontinuities
- 1.14 Infinite Limits and Vertical Asymptotes
- 1.15 Limits at Infinity and Horizontal Asymptotes
- 1.16 Intermediate Value Theorem (IVT)

**Unit 2: Differentiation: Definition and Fundamental Properties (Big Ideas: Change, Limits, Analysis of Functions)**- 2.1 Defining Average and Instantaneous Rate of Change at a Point
- 2.2 Defining the Derivative of a Function and Using Derivative Notation
- 2.3 Estimating Derivatives of a Function at a Point
- 2.4 Connecting Differentiability and Continuity
- 2.5 Applying the Power Rule
- 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
- 2.7 Derivatives of cos(x), sin(x), e^x, and ln(x)
- 2.8 The Product Rule
- 2.9 The Quotient Rule
- 2.10 Derivatives of tan(x), cot(x), sec(x), and csc(x)

**Unit 3: Differentiation: Composite, Implicit, and Inverse Functions (Big Idea: Analysis of Functions)**- 3.1 The Chain Rule
- 3.2 Implicit Differentiation

## About Course

**Course Overview **

The AP Calculus AB course provides a comprehensive introduction to the concepts and techniques of calculus, focusing on limits, derivatives, and integrals. Students begin by exploring limits and continuity, which lay the groundwork for understanding how functions behave. They then learn to compute derivatives using various rules and apply them to real-world problems, such as optimization and rates of change. The course also covers integration, teaching students to find both indefinite and definite integrals while highlighting the Fundamental Theorem of Calculus, which connects differentiation and integration. Throughout the course, emphasis is placed on analytical methods, problem-solving skills, and the ability to communicate mathematical ideas effectively, all of which prepare students for the AP exam and further studies in mathematics and related fields.

## What you'll learn?

- Understanding limits and their role in determining function behavior.
- Calculating and applying derivatives to analyze rates of change and optimize functions.
- Learning to compute integrals and applying the Fundamental Theorem of Calculus to find areas and volumes.

## Material Includes

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