ADVANCED PLACEMENT CALCULUS AB

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Course Code:
Honors Course Code:
AP Course Code: 1202310
Description:

An interactive text, graphing software and math symbol software combine with the exciting FLVS on-line course delivery to make Calculus an adventure. This course is designed to prepare the student for the AP Calculus AB exam given each year in May. With continuous enrollment, students can start the course and begin working on Calculus as early as spring of the previous year!

All AP courses are designed for students who are willing to accept the challenge of a rigorous academic curriculum. Additionally, AP courses are designed to provide students with a learning experience equivalent to that of a college course. Students should be prepared to dedicate time outside the course for reading and studying for the national exam in May.

Prerequisites: Algebra I and II, geometry, trigonometry and analytical geometry or pre-calculus

Estimated Completion Time: 2 segments / 32-36 weeks or 1 block/18 weeks

Major Topics and Concepts:

Segment 1

* Finding Limits Graphically and Numerically
* Evaluating Limits Analytically
* Continuity and One-Sided Limits
* Infinite Limits
* Differentiation
* The Derivative and Tangent Line Problem
* Basic Differentiation Rules and Rates of Change
* The Product and Quotient Rules and Higher Order Derivatives
* The Chain Rule
* Implicit Differentiation
* Related Rates
* Applications of Differentiation
* Extrema on an Interval
* Rolle's Theorem and the Mean Value Theorem
* Increasing and Decreasing Functions and the First Derivative Test
* Concavity and the Second Derivative Test
* Limits at Infinity
* Summary of Curve Sketching
* Optimization Problems
* Differentials

Segment 2

* Integration
* Antiderivatives and Indefinite Integration
* Area
* Riemann Sums and Definite Integrals
* The Fundamental Theorem of Calculus
* Integration by Substitution
* Numeric Integration
* The Integral as a Function
* Logarithmic, Exponential, and Other Transcendental Functions
* The Natural Logarithmic Function and Differentiation
* The Natural Logarithmic Function and Integration
* Inverse Functions
* Exponential Functions: Differentiation and Integration
* Bases other than e and Applications
* Differential Equations: Growth and Decay
* Differential Equations: Separation of Variables
* Inverse Trigonometric Functions and Differentiation
* Differential Equations: Slope Fields
* Applications of Integration
* Area of Region between Two Curves
* Volume: Disk Method
* Integration Techniques and L'Hopital's Rule
* Basic Integration Rules
* Integration by Parts
* Indeterminate Forms and L'Hopital's Rule

NOTE: FLVS courses are continually on a redevelopment cycle in order to respond to state standard changes, updates in technology and in the case of Advanced Placement courses, the new College Board criteria. This course is undergoing the redevelopment process with state certified subject matter expert(s) in 2007.

Course Assessment and
Participation Requirements:

Besides engaging students in challenging curriculum, VLACS guides students to reflect on their learning and to evaluate their progress through a variety of assessments. Assessments can be in the form of self-checks, practice lessons, multiple choice questions, free-response questions, matching questions, oral assessments, and discussions. Instructors evaluate progress and provide interventions through the variety of assessments built into a course, as well as through contact with the student in other venues.