AP Calculus AB
Course Long Plan
Brief Description of Course
After completing AP Calculus it is my hope that students will develop an appreciation of Calculus and of its many applications. It
is also my hope that they will be proud of their accomplishment and the effort required to develop their skills. In their daily
work students will analyze and make connections between the concepts of Calculus using the "rule of four"; graphical,
numerical, analytical, and verbal. I sense students frustration learning Calculus because of its abstract nature. It is my goal that
through class discussion,demonstration, and projects, combined with repeated practice, students will develop the confidence
and required skills that will enable them be successful.
Unit Information
Unit Name or Timeframe:
Unit 1 (7 days)
Preparation for Calculus
Content and/or Skills Taught:
1 Graphs and Models
2 Linear Models and Rates of Change
3 Functions and Their Graphs
4 Fitting Models to Data
Major Assignments and/or Assessments:
Section problems and applications
Unit Name or Timeframe:
Unit 2 (15 days)
Limits and Their Properties
Content and/or Skills Taught:
1 A Preview of Calculus
2 Finding limits Graphically and Numerically
3 Evaluating Limits Analytically
4 Continuity and One-Sided Limits
5 Infinite Limits
6 Graphs and Limits of Trigonometric Functions
Major Assignments and/or Assessments:
Section problems and applications
Calculator use of charts, tables, and graphs to analyze and interpret the meaning of limits
Unit Name or Timeframe:
Unit 3 (25 days)
Differentiation
Content and/or Skills Taught:
1 Basic differentiation rules and rates of change
2 Product and quotient rules and higher-order derivatives
3 The Chain Rule
4 Implicit Differentiation
5 Related Rates
Major Assignments and/or Assessments:
Section problems and applications
Unit Name or Timeframe:
Unit 4 (20 days)
Applications of Differentiation
Content and/or Skills Taught:
1 Extrema on an interval
2 Rolle's Theorem and the Mean Value Theorem
3 Increasing and Decreasing Functions and the First Derivative Test
4 Concavity and the Second Derivative Test
5 Limits at Infinity
6 Curve Sketching
7 Optimization Problems
8 Newton's Method
9 Differentials
Major Assignments and/or Assessments:
Section problems and applications
Sunrise/sunset project (See additional information)
Unit Name or Timeframe:
Unit 5 (15 days)
Integration
Content and/or Skills Taught:
1 Antiderivatives and Indefinite Integration
2 Area
3 Riemann Sums and Definite Integrals
4 The Fundamental Theorem of Calculus
5 Integration Rules
6 Integration by Substitution
7 Integration by Parts
8 Trigonometric Integrals
9 Numerical Integration
Major Assignments and/or Assessments:
Section problems and applications
Unit Name or Timeframe:
Unit 6 (15 days)
Logarithmic, Exponential, and Other Transcendental Functions
Content and/or Skills Taught:
1 Natural Logarithmic Function: Differentiation
2 Natural Logarithmic Function: Integration
3 Inverse Functions
4 Exponential Functions: Differentiation and Integration
5 Inverse Trigonometric Functions: Differentiation
6 Inverse Trigonometric Functions: Integration
Major Assignments and/or Assessments:
Section problems and applications
Unit Name or Timeframe:
Unit 7 (10 days)
Differential Equations
Content and/or Skills Taught:
1 Slope Fields and Euler's Method
2 Differential Equations: Growth and Decay
3 Separation of Variables and the Logistic Equation
Major Assignments and/or Assessments:
Section problems and applications
Unit Name or Timeframe:
Unit 8 (10 days)
Applications of Integration
Content and/or Skills Taught:
1 Area of a Region Between Two Curves
2 Volume: The Disk Method
3 Volume: The Shell Method
4 Arc Length and Surfaces of Revolution
Major Assignments and/or Assessments:
Section problems and applications
Egg project (See additional information)
Alternate Approaches
Textbooks/Course Materials
Textbooks
Author:Larson, Ron
Title:Calculus of a Single Variable
Publisher:Houghton Mifflin Company
Published Date:19 January, 2005
Other Course Materials
Material Type:Primary Source
Description:TI-84 Plus or another similar graphing calculator
Material Type:Other
Description:Multiple-Choice & Free-Response Question in Preparation for the AP Calculus (AB) Examination.
I use this book as part of the review for the AP Exam, and the course final.
Material Type:Other
Description:Calculus Explorations by Paul A. Foerster
I use worksheets from this book for students to acquire hands-on practice. These exercises require students to work in any one
of a variety of ways: graphical, numerical, analytical, or verbal. Many times students are asked to make connections between
the four types of representations.
Material Type:Other
Description:A Watched Cup Never Cools; Lab Activities for Calculus & Precalculus by Ellen Kamischke
Students become very engaged in these fun lab activites. They get practice analyzing data, writing lab reports, and using
technology.
Material Type:Other
Description:Professional Development Workshop Materials
Exam Resources and Program Information
I use the multiple choice practice questions and free response questions for students.
Websites
URL:http://archives.math.utk.edu/visual.calculus/5/are
Description:I use this site to introduce and reinforce concepts. This is also a good site for student to use at home as a turorial.
URL:apcentral.collegeboard.com
Description:This site is an excellent resource for students. Students take the practice AP test from this site to get further
practice doing AP type questions.
Periodicals
Additional Information
Requirement:Teaching Strategies
How Course Meets Requirement:I expect students to come to class prepared to learn each day as I come prepared to teach. I
try not to have a full day of class lecture. Rather, I give students smaller bits of lecture combined with problem sets of
increasing difficulty. I try to keep students engaged by leading them through a variety of problems ranging in difficulty till they
feel confident in their ability. As each new concept is introduced, I help students relate new information to previous information.
There is homework each day, even if it is only a few problems or correcting previous work. I encourage students to do both
classwork and homework with a partner discussing and comparing answers and work for each problem.
As much as I can I try to create activites where students can work, learn,and ask questions in a non-threatening environment.
Depending on the material, students will work in teams at the board. This activity engages students and helps them to see a
variety of problem solving methods. Additionally, this method allows me to watch students as they work and to be available for
questions or point out errors sooner rather than later.
Students integrate technology into their work starting with pre-calculus review on the first day of class. I encourage them to
use the calculator as a tool to represent information, check their work, and learn, evaluate new information.
Requirement:Student Evaluation
How Course Meets Requirement:I expect students to take notes daily and to apply the examples to their homework. We grade
and discuss homework daily. At times students hand in selected problems for grading and credit.
I give quizzes over "sets of related knowledge". At times students take partner quizzes. These have been surprisingly beneficial
to students and enlightening to me. I often overhear knowledgeable discussions depicting student ability that may not
neccessarily show itself on an evaluation.
Students are graded throughout the course according to AP standards with regard to rounding, justification, and detail of work.
Each chapter test has two parts, multiple choice and free response. Generally, students can expect 2-3 quizzes and a final
chapter test for each chapter.
As we proceed through the course I give students retired AP free-response questions. Some are used as examples and many
are used as an evaluation tool. This prepares students for the level of detail required for the AP test.
Requirement:Projects
How Course Meets Requirement:In addition to the daily problems that require students to analyze information I give them
larger projects that encapsulate bodies of knowledge.
The Sunrise/Sunset project incorporates information found about the change in daylight hours in one city during a one year
period. Students have to use their calculators to make a scatter plot and do regression analysis to obtain an equation of the
data. Through a series of questions students analyze the information and confirm their estimates using calculus. Students are
required to compile their information in order to present, display the data and findings to the class.
The Eggsactly Right project is a culminating activity that students enjoy. Once again they are required to generate data,
analyze and interpret the data. Students communicate their findings in the form of a 1 page lab report as well as a poster
showing graphs, equations, and analysis. Students are required to create a graph showing the top arc of a hard boiled egg.
They then estimate the volume of the egg using water displacement. Using their calculator they create as many regression
equations as needed to represent a good model of the arc of the egg. Students then use integral analysis to compare actual
results with their estimates. For extra credit they can find the surface area of the egg using calculus methods.