# AP Calculus AB, 1st Semester

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```					                             AP Calculus AB, 1st Semester

Teachers: Jean Richardson, Laurie Lombardi, Laura Kimbro
Text: Calculus: Graphical, Numerical, Algebraic, Scott Foresman/Addison Wesley
Cost: \$61.47

Prerequisite: Precalculus
Class Web Page: http://home.comcast.net/~lombardi03/

Textbook                                      Tests:           50%
Notebook (work needs to be saved ALL year)                     Quizzes:         20%
Graphing Calculator (any type approved for AP                   HW & Free
test)                                      Responses:       10%
Final Exam:      20%

is higher.

* Ten points will be added to your average to account for AP course status.

** AP Calculus AB Exam Date: Wednesday, May 5, 2010

*** All students who do not take the AP exam will take an in class AP style
test on the same date.

Curricular goals interwoven throughout the mathematics program are that students will:
learn to communicate mathematically (QCC)
learn to use mathematics in their daily lives (QCC)
become proficient with appropriate computational tools and techniques (QCC)
learn to reason mathematically (QCC)
become mathematical problem solvers (QCC)

These goals will provide the direction for assessment and instruction. Attainment of these goals is
facilitated by the students’ demonstration of the following Academic Knowledge and Skills (AKS).

Number crunching and symbol manipulation are only small parts of learning calculus. One of the major
goals in this course is for students to learn how to use precise language to describe these concepts and the
relationships between ideas.

Course Planner
The course covers all topics associated with Functions, Graphs, and Limits and Derivatives; as delineated
in the Calculus AB Topic Outline in the AP Calculus Course Description.

Chapter 1: Prerequisites for Calculus This is not covered in class. Students are expected to
• Elementary functions:
o Linear, power, exponential/logarithmic, trigonometric/inverse trigonometric
• Getting familiar with the graphing calculator

Chapter 2: Limits and Continuity (17 days)
• an intuitive understanding of the limiting process
• calculating limits using algebra
• estimating limits from graphs or tables of data
AP Calculus AB, 1st Semester
•   understanding asymptotes in terms of graphical behavior
•   describing asymptotic behavior in terms of limits involving infinity
•   comparing relative magnitudes of functions and their rates of change
•   understanding continuity in terms of limits
•   geometric understanding of graphs of continuous functions (Intermediate Value Theorem and
Extreme Value Theorem)
•   derivative presented geometrically, numerically and analytically
•   derivative interpreted as an instantaneous rate of change
•   slope of a curve at a point
•   tangent line to a curve at a point and local linear approximation
•   instantaneous rate of change as the limit of average rate of change
•   approximate rate of change from graphs and tables of values

Chapter 3: Derivatives (36 days)
• estimate limits from graphs or tables of data
• derivative presented geometrically, numerically and analytically
• derivative interpreted as an instantaneous rate of change
• derivative defined as the limit of the difference quotient
• relationship between differentiability and continuity
• corresponding characteristics of graphs of f and f
• slope of a curve at a point
• tangent line to a curve at a point and local linear approximation
• instantaneous rate of change as the limit of average rate of change
• approximate rate of change from graphs and tables of values
• equations involving derivatives
• use of implicit differentiation to find the derivative of an inverse function
• interpretation of the derivative as a rate of change in varied applied contexts, including
velocity, speed and acceleration
• knowledge of derivatives of basic functions, including power, exponential, logarithmic,
trigonometric and inverse trigonometric functions
• basic rules for the derivative of sums, products, and quotients of functions
• chain rule and implicit differentiation

Chapter 4: Applications of Derivatives (29 days)
• geometric understanding of graphs of continuous functions (Intermediate Value Theorem and
Extreme Value Theorem)
• slope of a curve at a point
• tangent line to a curve at a point and local linear approximation
• relationship between the increasing and decreasing behavior of f and the sign of f
• the Mean Value Theorem and its geometric consequences
• equations involving derivatives
• corresponding characteristics of graphs of f, f’ and f”
• relationships between the concavity of f and the sign of f”
• points of inflection as places where concavity changes
• analysis of curves, including the notions of monotonicity and concavity
• optimization, both absolute (global) and relative (local) extreme
• modeling rates of change, including related rates problems
• interpretation of the derivative as a rate of change in varied applied contexts, including
velocity, speed and acceleration
• antiderivatives following directly from derivatives of basic functions
• finding specific antiderivatives using initial conditions, including applications to motion
along a line

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