AP Calculus AB - Syllabus

 AP Calculus AB

Teacher: Mr. Evans

Email: mark.evans@hcps.org (for large files email to, evans@scienceandmathacademy.com)

Webpage: www.scienceandmathacademy.com/academics/calculus/

Text: Finney, R. L., Demana, F. D., Waits, B. K., Kennedy, D. (2007). Calculus: Graphical, Numerical, Algebraic, 3^rd ed. Boston : Pearson Prentice Hall.

Course Description: This course is equivalent to a typical first semester college Calculus course. Topics covered will include limits, derivatives and their applications, and integrals and their applications. Students may receive college credit by taking the Advanced Placement Exam.

Course Objectives and Goals: My goal is to prepare students to be successful on the AP Calculus BC exam. To achieve this goal, students will gain a thorough understanding of the topics covered in the course outline.

Course Outline: The following is an outline of the topics we will cover and a rough estimate of the time we will spend on each chapter.

Prerequisites for Calculus
Time: 2 days
·         Test of chapter 1
·         Review of first test

Limits and Continuity
Time: 8 days
·         Lab: Limits of Functions
·         Develop an intuitive understanding of the nature of limits
·         Lay the foundation for the use of limits in calculus
·         Evaluate limits graphically, numerically, and algebraically
·         Rates of Change and Limits
·         Limits Involving Infinity
·         Continuity
·         Rates of Change and Tangent Lines
·         Test

Derivatives
Time: 12 days
·         Derivative of a Function
·         Differentiability
·         Rules for Differentiation
·         Velocity and Other Rates of Change
·         Derivatives of Trigonometric Functions
·         Chain Rule (Quiz on the section)
·         Implicit Differentiation
·         Derivatives of Inverse Trigonometric Functions
·         Derivatives of Exponential and Logarithmic Functions
·         Test

Applications of Derivatives
Time: 11 days
·         Extrema Values of Functions
·         Mean Value Theorem
·         Connecting f’ and f” with the Graph of f
·         Modeling and Optimization (Quiz on this section)
·         Linearization and Newton ’s Method
·         Related Rates
·         Test

The Definite Integral
Time: 9 days
·         Estimating with Finite Sums
·         Definite Integrals
·         Definite Integrals and Antiderivatives
·         Fundamental Theorem of Calculus
·         Trapezoidal Rule
·         Test

Differential Equations and Mathematical Modeling
Time: 8 days
·         Slope Fields and Euler’s Method (Quiz on this section)
·         Antidifferentiation by Substitution
·         Exponential Growth and Decay
·         Logistic Growth
·         Test

Applications of Definite Integrals
Time: 10 days
·         Integral As Net Change
·         Areas in the Plane
·         Volumes (Quiz on this section)
·         Applications from Science and Statistics
·         Test

AP Review
Time: 6 days
·         We will try many free-response questions from previous AP Calculus tests
·         We will review all previously covered topics

Grading:

• Daily Quizzes: There will be a daily quiz most days. It will consist of 3 questions and will be completed independently at the beginning of the period. Each quiz will be worth 9 points and the top 12 quizzes in a quarter will be counted.
• Tests: There will be a test at the conclusion of each chapter. Each test will be worth 100 points. There will be a non-calculator section and calculator section to every test.
• Quizzes: There will not be many regular quizzes. When we do have a quiz it will be worth 25 points. Expect a quiz on Chain Rule, Optimization, Slope Fields, and Volumes.
• Homework: Daily homework will be assigned every day. It will not be formally graded, unless students are not completing the homework. This is to prepare students for typical first and second year college math courses.
• Spirals: Spirals are take home quizzes that review material throughout the course. Each spiral is worth 20 points. Students will receive a spiral every 2-3 weeks. Spirals will be assigned on Monday’s or Tuesday’s and due on Friday (regardless of whether the class meets). If they are turned in on Wednesday you will receive 2 bonus points and on Thursday 1 bonus point. You may work with others students. You must show work.
• Projects: Projects will be worth 30-40 points. There will be at least 4 projects.

·         Portfolios: Due around the end of first semester and near the end of the year.

·         Related Rates: You will make an example problem, solve it, and make a model of the problem for visualization.

·         Volume: You will find the volume of a food item using calculus and teach your parents how to as well.

Note: Mr. Evans reserves the right to change grading policies as seen fit.

Calculators:

“The use of a graphing calculator in AP Calculus is considered an integral part of the course. Students should be using this technology on a regular basis so that they become adept at using their graphing calculators. Students should also have experience with the basic paper-and-pencil techniques of calculus and be able to apply them when technological tools are unavailable or inappropriate.” (Excerpt taken from the CollegeBoard, Calculus Course Description.)

You must have a graphing calculator that fits the following requirements (preferably a TI-84 or TI-89.)
·         Plot the graph of a function within an arbitrary viewing window
·         Find the zeros of functions (solve equations numerically)
·         Numerically calculate the derivative of a function, and
·         Numerically calculate the value of a definite integral.

• Be on time. Sharpen you pencil if necessary and get in your seat before the bell rings. If you are not in your seat when the bell rings, you are late.
• Be prepared for class. Bring a pencil, notebook, textbook (covered) and calculator.
• You will not be permitted to go to your locker during class.
• Use of the bathroom is a privilege that is allowed at the discretion of Mr. Evans. You will be permitted to use the restrooms on the third floor only.
• Make up work will be given for excused absences only. You will be allowed to make-up missed work according to the HCPS policy. It is your responsibility to see the teacher for the assignment.
• All work must be on time to be accepted for credit. Field trips, rehearsals, or any other absences known in advance are not an excuse for late work. Submit it early or give it to a classmate to submit it for you.