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# Courses

## AP Calculus AB

Pre-Requisites: Algebra I, Geometry, Algebra II, Pre-Calculus or Trigonometry/Analytical Geometry.
Credits: 1.0
Estimated Completion Time: 32-36 weeks

### Description

In AP Calculus AB, students walk in the footsteps of Newton and Leibnitz. This interactive course framework combines with an exciting on-line course delivery to make calculus an adventure. The course includes a study of limits, continuity, differentiation, integration, differential equations, and the applications of derivatives and integrals. This course consists of a full high school year of work that is comparable to calculus courses in colleges and universities. It is expected that students who take an AP course in calculus will seek college credit, college placement, or both, from institutions of higher learning. Most colleges and universities offer a sequence of several courses in calculus, and entering students are placed within this sequence according to the extent of their preparation, as measured by the results of an AP examination or other criteria.

### Major Topics and Concepts

Semester One

Module 01 - Limits and Continuity

• Using Limits to Analyze Instantaneous Change
• Estimating Limit Values from Graphs and Tables
• Determining Limits Using Algebraic Properties and Manipulation
• Selecting Procedures for Determining Limits
• Squeeze Theorem and Representations of Limits
• Determining Continuity and Exploring Discontinuity
• Connecting Limits, Infinity, and Asymptotes
• The Intermediate Value Theorem (IVT)

Module 02 - Differentiation: Definition and Fundamental Properties

• Average and Instantaneous Rates of Change and the Derivative Definition
• Determining Differentiability and Estimating Derivatives
• Derivative Rules: Constant, Sum, Difference, Constant Multiple, and Power
• The Product Rule and the Quotient Rule
• Derivatives of Trigonometric Functions
• Derivatives of Exponential and Logarithmic Functions

Module 03 - Differentiation: Composite, Implicit, and Inverse Functions

• The Chain Rule
• Implicit Differentiation
• Differentiating Inverse Functions
• Differentiating Inverse Trigonometric Functions
• Selecting Procedures for Calculating Derivatives
• Calculating Higher-Order Derivatives

Module 04 - Contextual Applications of Differentiation

• Interpreting and Applying the Derivative in Motion
• Rates of Change in Applied Contexts Other Than Motion
• Related Rates
• Approximating Values of a Function Using Local Linearity and Linearization
• L'Hospital's Rule

Segment Two

Module 05 - Analytical Applications of Differentiation

• Mean Value and Extreme Value Theorems
• Determining Function Behavior and the First Derivative Test
• Using the Candidates Test to Determine Absolute Extrema
• Determining Concavity of Functions and the Second Derivative Test
• Connecting Graphs of Functions and Their Derivatives
• Optimization Problems
• Exploring Behaviors of Implicit Relations

Module 06 - Integration and Accumulation of Change

• Exploring Accumulations of Change
• Riemann Sums and the Definite Integral
• Accumulation Functions Involving Area and the Fundamental Theorem of Calculus
• Applying Properties of Definite Integrals
• Finding Antiderivatives and Indefinite Integrals
• Integrating Using Substitution
• Integrating Functions Using Long Division and Completing the Square
• Selecting Techniques for Antidifferentiation

Module 07 - Differential Equations

• Solutions of Differential Equations
• Sketching and Reasoning Using Slope Fields
• Finding Solutions Using Separation of Variables
• Exponential Models with Differential Equations

Module 08 - Applications of Integration

• Average Value and Connecting Position, Velocity, and Acceleration Using Integrals
• Using Accumulation Functions and Definite Integrals in Applied Contexts
• Finding the Area Between Curves
• Finding the Area Between Curves That Intersect at More Than Two Points
• Volumes with Discs
• Volumes with Washers
• Volumes with Cross Sections