AP Calculus Syallabus
Allen Park High School
Teacher: Mr. Youness Farokhrani
Room: C-3
Course: AP Calculus AB
Textbook: Calculus and Analytic Geometry, Thomas/Finney 9th Edition�1996
Course Description: AP Calculus is a college level course. The students may obtain college credit by taking the Advanced Placement examination. The course covers the study of limits, derivatives, integrals, and applications and modeling. TI-83+ or TI-84 graphing calculators are required for some problems and should be used regularly to reinforce, confirm, and assist in interpreting the results of written work or experimenting with other problems.
Course Outline:
Chapter: Preliminaries (students will work on assignments over the summer and take a test during the first week of school)
A. Functions
Graphs with and without using calculators.
Transformations of functions.
Trigonometric functions and identities.
Chapter 1: Limits and Continuity
A. Limits of Functions (including one-sided limits)
An intuitive understanding involving the limit process.
Calculating limits using algebra.
Estimating limits from graphs or tables of data.
B. Asymptotic and unbounded behavior
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.
C. Continuity as a property of functions
An intuitive understanding of continuity.
Understanding continuity in terms of limits.
Geometric understanding of the graphs of continuous functions (Intermediate Value Theorem and Extreme Value Theorem)
Chapter 2: Derivatives
A. Concepts of a derivative
Derivative presented graphically, 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.
B. Derivative at a point
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.
C. Derivative as a function
Corresponding characteristics of graphs of f and .
Relationship between the increasing and decreasing behavior of f and the sign of .
The Mean Value Theorem and its geometric consequences.
Equations involving derivatives.
D. Second derivative
Corresponding characteristics of graphs and
Relationship between the concavity of f and the sign of .
Points of inflection as places where concavity changes.
E. Computation of derivatives
Basic rules for the derivative of sums, products and quotients of functions.
Chain rule and implicit differentiation.
Chapter 3: Applications of derivatives
A. Analysis of curves.
B. Optimization, both absolute (global) and relative (local) extrema.
C. Modeling rates of change including related rates problems.
D. Use of implicit differentiation to find the derivative of an inverse function.
E. Interpretation of the derivative as a rate of change in varied applied contexts including velocity, speed and acceleration.
Chapter 4: Integration
A. Antiderivatives
Definitions of antiderivatives
Rules of integration.
Initial value problems of indefinite integrals.
B. The chain rule for antiderivatives
Simple substitutions.
Trigonometric integrals.
C. Definition of Definite Integral
Ramann sums
Trapezoid rule
D. Fundamental Theorem of Calculus
Properties of definite integral
Average value of function
E. Analyzing curves with antiderivates
Finding position given acceleration and initial values.
Finding position given the graph of velocity.
Chapter 5: Application of Integrals
A. Areas between Curves
Integration with respect to x.
Integration with respect to y.
B. Finding volume of solid
By slicing known cross sections
Disc method
Washer method
Shell method
Chapter 6: Transcendental Functions
A. Inverse functions
Derivative of Natural logarithm function.
Derivative and integral of y = ex
Integrals involving y = logax and y = ax
L�Hobital�s Rule (one day)
B. Growth and decay
Solving separable differential equations.
Studying the equation = ky and exponential growth.
Solving logistic differential equations.
Slope fields (two days). Use worksheets from other textbook.
Geometric interpretation of differential equations via slope fields and the relationship between slope fields and solution curves for differential equations
C. Inverse Trigonometric Functions (two days)
Derivatives of , , and .
Integrations of , , .
After the AP Exam
Chapter 7
A. Integration by parts
B. Partial fractions
Additionally, students will be given a large number of real-world applications; examples and problems which will enable them to create mathematical models that will help them understand and interpret the world in which they live.
Students should be able to adapt their knowledge and technique in order to solve other similar application problems. They will need to communicate both orally and in well-written explanations, the solutions to these problems.
*At the end of each chapter, you will receive assignments that include related multiple choice and free response questions from previous AP exams.
Procedure and Technology:
I will go over a few challenging questions from their homework on the board. However, many of these problems will be answered by students for extra credit.
The classroom is equipped with a computer-linked TV monitor, making it easier to teach and review information with the class.
Students have access to two in-school computer labs, which are occasionally used for AP Test preparation during school hours.
There will be a variety of approaches and methods used to explain each topic outside of the text book. Power point technology will be employed in 2007 to teach some concepts, especially finding the area and volume of solids of rotations. These presentations are very beneficial, and will be very crucial to your performance. Thus, regular attendance is highly recommended.
Graphing calculators are used. A number of programs are linked to your calculators, including SHOWRAM, Trapezoid, and slope field. These programs provide greater understanding of the concepts.
Supplementary teaching materials will be provided to reinforce some topics, especially slope-field, which is not covered efficiently in the textbook.
Homework:
There will be assignments assigned for the following day.
Homework will be checked based on completeness.
Select problems from assignments or the course pack will be collected and graded for accuracy.
I will be available to provide help during my prep hour or after school.
Quizzes:
Periodically quizzes will be given from problems directly off of their homework or course pack.
Your response will be graded based on correctness of procedures, explanations, organization, and completeness.
Quizzes may cover 2 or 3 sections of a chapter. Quizzes are meant to be one assessment tool to better your understanding of the topic and increase your success on the final chapter test.
Tests:
Tests will usually be given after the completion of each chapter.
At least one day of review has been set aside for each test.
It is highly suggested that you understand all assignments, including the course pack assignments, related to each chapter.
After a short preliminary chapter review Chapters 1-6 will be completed.
Each chapter test will be worth 100 points.
Each test will consist of free-response and multiple-choice questions as wells as review questions from the course pack and previous chapters.
In the end of March or early April, students will work in an assigned group of selected students (consisting of average to superior academic achievers) on multiple-choice and free-response questions. Each group will be assigned a leader who is in charge of making sure that each member understands each assigned question from start to finish. A random member will be selected from each group to present his/her group�s approach to the assigned problem. Each group will be graded based on that individual�s work as well as the accomplishments of each group member. From multi-representational approaches, the best and shortest method will be suggested to be employed on the AP-test.
Grading: You will be given points for all assignments, but grades will be weighted with the following percentages.
Homework/quizzes 10%
Problems of the week from course pack 10%
Tests 60%
Final Exam 20%
An AP Practice test will be given in the end of April. This test follows the exact same directions as the AP test and will last 3 hours. Practice tests will be worth 300 points.
Absences:
The assignments are online. Homework is posted in class as well. If you are absent you should check the website from home or get the assignments from a classmate.
If you are absent for a test, you have to make it up as soon as possible.
No make-up tests/quizzes will be given during class time. It is your responsibility to schedule an appointment to make up any missing test.
You are highly encouraged not to miss the AP-Calculus class for any reason such as school activities, 5th grade camp, make-up tests, family vacations, helping other teachers, etc.
Grading Scale: Grades will be posted as often as possible.
97-100% A+ 77-79% C+
93-96% A 73-76% C
90-92% A- 70-72% C-
87-89% B+ 67-69% D+
83-86% B 63-66% D
80-82% B- 60-62% D-
Resources:
Appropriate web sites are utilized. These include:
AP Central: www.apcentral.collegeboard.com
Free response solutions, with scoring guidelines and the course outline are available here for teachers and students.
United Streaming: www.unitedstreaming.com
AP free response questions
Learning Library Express (through the Michigan E-library): www.mel.org
AP Calculus multiple-choice practice tests are employed through this site.
Math Demonstration web site from GCSU: http://mathdemos.gcsu.edu/mathdemos/shellmethod/
Volume calculation 3-D illustrations are provided.
AP Calculus review books are suggested for use by students.
