Unformatted text preview: f
‘integrating the area of each slice’
Determine the type of cross section
(triangle, semicircle, square, etc.)
and its relationship to the given
function or set of functions
Create an expression for the area of
each slice in terms of the function to
be used as the integrand
Set up and evaluate integrals to find
volume
Sketch a slope field given a
derivative in terms of x, y or both
Visualize the position functions that
differ by a constant (change in
vertical shift)
Understand the process behind
finding a solution to a differential
equation given an initial condition;
i.e. separating the variable, taking
the antiderivative, etc. NJ CCCS Strands &
Indicators 4.1
4.2
4.3
4.5 A,B,C
A,B,C,D
A,B,C,D
A,B,C,D,E,F 4.1
4.2
4.3
4.5 A,B,C
A1,A3,C,D
A,B,C,D
A,B,C,D,E,F Suggested
Timeframe
(in blocks)
3 2 Course Objective(s)
Review applications of
differential equations Student Objectives
•
• • Recall finding solutions to
differential equations
Apply knowledge to problems
involving compound interest,
population growth, Newton’s Law of
Cooling, Law of Exponential Change
and halflife
Apply Euler’s Method of
Approximation NJ CCCS Strands &
Indicators 4.1
4.2
4.3
4.5 A,B,C
A1,A3,C,D
A,B,C,D
A,B,C,D,E,F Suggested
Timeframe
(in blocks)
3 RESOURCES
• Textbook: :Calculus: Graphical, Numerical, Algebraic
Finney,Demana,Waits,Kennedy
Addison Wesley, 1999 • Supplementary Materials
Workbooks
D & S Marketing Workbooks
8th Edition, Edited by David Lederman, 2004
Barron’s “How to Prepare for the AP Calculus Exam”
6th Edition, Edited by Shirley O. Hockett, 1998
Reference HandOuts
TI89 Titanium: Calculator Extraordinaire
Trigonometry: Unit Circle with Exact Radian Values, Identities
Derivative and Integral Identities
Various Supplements from AP Central
Websites
www.collegeboard.com: provides information about AP exams
http://archives.math.utk.edu/visual.calculus/: an extremely
thorough site for precalculus through integral calculus with
accompanying tutorials, practice problems, interactive quizzes and
animations
http://online.math.uh.edu/HoustonACT/: contains Powerpoint
presentations for each section correlating to our text book
www.calculushelp.com/funstuff/phobe.html: animated
explanations of the first two chapters of calculus
www.calculusabc.com: teacher and student resources containing
multiple choice problems for each unit and well as a forum for
teachers to exchange teaching ideas
http://clem.mscd.edu/~talmanl/APCalculus.html: FRQ solutions,
explanations, links to number of other sites and much more! www.pen.k12.va.us/Div/Winchester/jhhs/math/lessons/calculus.html:
calculus lesson plans & activities
Technology (Software/Equipment)
Geometer’s Sketchpad
Winplot
Various Online Tutorials/Animations
Smartboard© Technology
Calculators
TI83, TI89 Titanium with associated software and programs
Additional Teacher Resources
All resources and files available through College Board’s AP Central as well
as a large bank of websites, journal and magazine articles, and newsletters
Barton, et. al. Preparing for the Calculus AP Exam with Calculus:
Graphical, Numerical, Algebraic. (Finney/Demana/Waits/Kennedy),
Pearson, 2006.
Kennedy, Dan. Teacher’s Guide – AP Calculus. The College Board.
Lifshitz, Maxine. Amsco’s AP Calculus AB/BC, Amsco School
Publications, Inc. 2004
Lipp, Alan. Visualizing Differential Equations with Slope Fields.
Little Book of Big Ideas, People’s Publishing Group. 2006.
McMullin, Lin. Teaching AP Calculus, 2nd Edition; D&S Marketing
Systems, Inc. 2005
Ralph, Bill. Journey Through Calculus. Brooks, Cole. 2000.
Stewart, James. Calculus Concepts and Contexts, 3rd Edition.
Thompson, Brooks/Cole. 2005.
2004 – 2005 Professional Development for AP Calculus—Special
Topic: Differential Equations. Workshop Materials, College Board.
2005 Professional Development & Workshops Available for Teaches:
“Teaching AP Calculus” Sponsored by the College Board. This
program is offered through the College Board
itself or through public and private institutions throughout the
school year
AP Calculus Roundtable, Summit, NJ (biannual meetings):
Past readers share concerns and suggestions toward the FreeResponse Questions Discussion of common errors and discrepancies
Breakdown of the test for scoring
AP Calculus ListServe through AP Central: open discussion on
methods and specific problems
Full AP Exams: MultipleChoice and FRQ: 2003, 1998, 1997, 1993,
1988, 1985
FreeResponse Questions:
1985 – 2007 (both forms, when applicable) with Scoring Guides
The Princeton Review: Cracking the AP Calculus AB Exam
Additional Practice Exams from Student and Teacher Resources ACTIVITIES
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• Lecture
Class discussions
Student presentations
Cooperative Learning structures
Guided practice
Technology infusion
Learning Styles activities
Brainbased activities
Differentiated Instruction
State and standardized test preparation
Homework review
AP Test Preparation: Exams and practice exercises ASSESSMENT
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• Tests
Quizzes
Homework
InClass assignments
Presentations
Class participation
Midterm/final exams...
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Full Document
 Spring '10
 Zalla
 Calculus, Derivative, AP Calculus, Student Objectives, NJ CCCS

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