Course: AP Calculus [AB] [Overview] - Math Thought

Courses: AP Calculus AB

[Cal1] (03) Applications of Derivatives

[Cal1] (05) Integration Basics

[Cal1] (06) Applications of Integrals

This course prepares high school students planning to take the Calculus AB Advanced Placement exam. For more information about this exam, please click here. Students will study the main ideas found in differential calculus: limits, derivatives, and basic integration. By the end of the course, students will be able to demonstrate an adequate understanding of these topics.

To be successful in this course, students must be proficient in precalculus. Students may forgo enrolling in a precalculus course provided they have a strong background in algebra 2 and trigonometry. Please review the prerequisite before enrolling in this course. Students will not be able to complete the course without having a strong background in these subjects. The topics discussed in AP Calculus AB are equivalent to those found in a semester college-level calculus 1 course. Consequently, those who score a 3 on the exam may qualify for college credit, whereas some colleges require at least a 4 on the exam.

Course Description:

This course prepares high school students planning to take the Calculus AB Advanced Placement exam. For more information about this exam please click here. Students will study the main ideas found in differential calculus: limits, derivatives, and basic integration. By the end of the course, students will be able to demonstrate an adequate understanding of these topics.

Prerequisite: Precalculus.

Duration: 15 weeks
Study Time: 6-8 hours per week
Classes: 40 Lectures
Prerequisite: Precalculus
Level: Intermediate
Virtual Lectures
Practice Problems
Exam Prep Questions

Course Topics

Limits

The idea of a limit
Calculating limits
Squeeze Theorem
Infinite Limits
Indeterminate Forms
L’Hospital’s Rule
Continuity

Fundamentals of Derivatives

Average Rate of Change
Instantaneous Rate of Change
Properties of Derivatives
Derivatives of Special Functions
- Trigonometric Functions
- Exponential Functions
- Logarithmic Functions

Computing Derivatives

The Power Rule
The Product Rule
The Quotient Rule
The Chain Rule

Advanced Techniques

Implicit Differentiation
Logarithmic Differentiation
Inverse Trigonometric Functions

Derivative Applications

Optimization
Related Rates, I
Related Rates, II
Motion
- Position
- Velocity
- Acceleration
Linear Approximation

Curve Sketching

Critical Points
Monotonicity of Functions
- Increasing, Decreasing
Inflection Points
Concavity
Relative and Absolute Extrema
- First Derivative Test
- Second Derivative Test
Graphing Functions
Interpreting Graphs

Basic Integration

Antiderivatives
- Indefinite Integrals
Fundamental Theorem of Calculus
- Definite Integrals
Basic Properties of Integrals
Integrals of Basic Functions
Integration by substitution
Numerical Integration
- Left-Hand Rule
- Right-Hand Rule
- Midpoint Rule
- Trapezoidal Rule
- Simpson’s Rule

Integrals Application

The Area of an Enclosed Region
- Vertical Simple Regions
- Horizontal Simple Regions
The Average Value of a Function
Volumes
- Disk/Washer Method
- Shell Method
- Non-rotational Symmetries
  - Cross-sections

Basic Differential Equations

Separable Differential Equations
Graphing and Understanding Slope Fields
Growth and Decay Problems

Techniques of Integration

U-Substitution
Integration By Parts
Trigonometric Integrals
Trigonometric Substitution
Partial Fractions
Improper Integrals
Numerical Integration
- Left-Hand Rule
- Right-Hand Rule
- Midpoint Rule
- Trapezoidal Rule
- Simpson’s Rule