Revised AP Calculus AB syllabus.docx by hedongchenchen


									2011 – 2012 Porter High School

                                          AP Calculus AB Syllabus
Prerequisite: Pre-Cal or Dual Credit College Algebra & Trig                        Cherish Reilly
                                                                                   5th & 10th Period Conference
                                                                                   Ext. 5770
Course Overview
Upon successful completion, students should be able to:

       Work with functions represented graphically, numerically, analytically, or verbally and understand the
        connections between these representations.
       Understand the concept of limits and continuity.
       Use the derivative to solve a variety of problems.
       Recognize the uses of the definite integral as a limit of Reimann sums, as a net accumulation of a rate of
        change, and as Trapezoid approximations.
       Use technology to help solve problems, experiment, interpret results, and verify conclusions.
       Find the derivative and integral of trigonometric, logarithmic and exponential functions.
       Calculate the area between two curves.
       Model problem situations using limits, derivatives, indefinite integrals, and definite integrals.
       Communicate solutions to mathematical problems both verbally and in written sentences.

Primary Textbook
Finley, Demana, Waits, Kennedy. Calculus ~ Graphical, Numerical, Algebraic.Third Edition. Pearson/Prantice Hall

The TI-84 Plus graphing calculator will be used in class regularly to help maximize the learning process. It is strongly
suggested that you have your own graphing calculator to be used at home as well as in future math classes. A class
set will be provided and there will be a few available for extended checkout.

Graphing calculators help students conduct explorations, graph functions, solve equations numerically, analyze and
interpret results, and justify and explain results of graphs and equations.

Notebook Paper
TI-83 or TI-84 Calculator (classroom set provided)

Grading Scale
10% Homework
30% Daily Work: class work & quizzes
60% Tests: 4 Major Grades per 9 weeks
2011 – 2012 Porter High School

Tutorials & AP Lounge
My Classroom (J113):   Mornings: Tuesday & Friday 6:50 – 7:20
                       Afternoon tutoring can be scheduled
AP Lounge: Dates to be announced (LMC3 in library)

Re-Testing Policy
Any student who makes below 70 on a major grade, may take a retest if the following requirements are met:
       1. The student must attend at least 2 tutoring sessions provided by the teacher.
       2. The retest must be taken no more than 2 weeks from the original date of the test AND must be
           completed within the grading period.

Topic Outline
Units will consist of daily note taking, frequent assignments, various quizzes, and end of unit tests. Fall and spring
semester finals are also given.
Unit 1: Relations, Functions, Graphs, & Geometric Transformations (August/September)
     Slope of a line as rate of change
     Parallel and Perpendicular Lines
     Domain and range of a function
     Piecewise functions
     Composition of functions
     Inverse functions
     Exponential and Logarithmic functions
     Domain and range of trig functions
     Graphs and transformations of trig functions

Unit 2: Limits & Continuity (September)
     Describe, define, calculate, and apply properties of limits
     Asymptotic behavior of limits involving infinity
     Calculate limits at infinity and identify the vertical and horizontal asymptotes
     Sandwich Theorem
     Removable, jump and infinite discontinuity
     Calculate the average and instantaneous speed

Unit 3: Limits & Concepts of the Derivative (September/October)
     Definition of a derivative as a limit of the difference quotient
       Interpret a derivative as an instantaneous rate of change
       Relationship between differentiability and continuity

Unit 4: Differentiation (October/November)
     Rules for derivatives – constant, power, sum, difference, product, & quotient rules
2011 – 2012 Porter High School

       Slope of a curve at a point
       Tangent line to a curve at a point
       Evaluate the derivative of a trig function
       Implicit differentiation
       Understanding and applying the Chain Rule
       Compare characteristics of f and f’
       Mean Value Theorem (MVT)

Unit 5: Applications of Derivatives (December)
     Extreme values and local extrema
     Points of inflections as places where concavity changes
     First derivative test
     Second derivative test
     Characteristics of f, f’, f’’ and the relationship between them
     Optimization
     Implicit differentiation to find the derivative of an inverse function
     Derivative of an Inverse, Exponential, Logarithmic, and Trig function

Unit 6: Integration (January/February)
     Basic antiderivative rules
     Area under a curve using Riemann sums (left, right, midpoint)
     Average Value Theorem
     Antiderivatives by substitution
     How and when to use integration by parts
     Integrate Exponential and Logarithmic functions
     Trapezoidal rule to approximate a definite integral

Unit 7: Volumes of solids (February/March)
     Area between two curves
     Volumes of solids using the disc method
     Volumes of solids using the washer method
     Volumes of solids using the cross section method

Unit 8: Differential Equations & Slope Fields (March)
     Solve separable differential equations
     Differential equations to solve growth and decay problems
     Draw slope field of a given derivative
     Recognize the function given its slope field

Unit 9: AP Test Review (April/May)
     Multiple-choice practice
     Free-response practice
2011 – 2012 Porter High School

Unit 10: After the Exam (May)
     Develop and present a Calculus Project
     Look at college math requirements

Cooperative Learning
I encourage cooperative learning during class. It is beneficial for students to work together as well as independently
to solve complex problems. I believe that classroom situations should help prepare students for the working
environment and students should be able to read and write mathematics and be able to determine if an answer is
reasonable. Cooperative learning helps to foster student exploration and discovery.

Teaching Strategies
There are four types of problem solving approaches that are emphasized in mathematics: numerical analysis,
graphical analysis, analytic/algebraic analysis, and verbal/written analysis. Developing all four skills will help students
master important calculus concepts.

Average and instantaneous rates of change:
A golf ball is dropped from a balcony of a two story building. What is the average speed during the first second of
fall? Find the speed of the ball at the instant t = 1. Note: a dense solid object dropped from rest to fall freely near
the surface of the earth will fall y  x 2 .

Sandwich Theorem:
Students graph y1  x 2 , y2   x 2 , y3  sin( 1 ) in radian mode on the graphing calculator. The limit as x
approaches 0 of each function is explored in an attempt to “see” the limit as x approaches 0 of x 2  sin( 1 ) .

AP Calculus AB is an advanced mathematics class and I expect my students to put forth more than the necessary
effort to excel in this course. A solid grasp of the main concepts will greatly benefit students in their future
mathematics courses. One of the main goals of this class is passing the AP Exam. This will help position students for
acceptance into a multitude of universities as well as gain valuable college credit which helps to save students
money. In order to reach this goal I expect a great deal from my students. Here is a plan to excel:
       Attend class regularly.
       Be prepared to work hard each day.
       Ask questions.
       Take good notes.
       Do your homework.
       Use all resources available to you.
       Review your notes, don’t wait till the last minute.
       Form a study group that meets regularly to do the homework and study for tests

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