AP CALCULUS AB COURSE SYLLABUS Course Description: Our study of calculus, the mathematics of motion and change, is divided into two major topics: differential and integral calculus. Differential calculus enables us to calculate rates of change, to find the slope of a curve, and to calculate velocities and accelerations of moving bodies. Integral calculus is used to find the area of an irregular region in a plane, to measure lengths of curves, and to calculate centers of mass of arbitrary solids. Course Objectives: This course is intended to provide you with a sound understanding of the concepts of calculus. You will study limits, derivatives, and integrals, and applications of all of these ideas. Your study will be based on a balanced approach. You will be asked to solve graphically, support numerically, confirm analytically, and solve algebraically, all while applying calculus to problem situations. I want you to be able to present the solutions both verbally and precisely written. An AP Calculus AB course is typically equivalent to one semester of college calculus. Therefore, you should prepare for this class as if you were in college. This class will demand a lot of your time and commitment. What I expect from you are the following: (1) Do ALL your work, (2) Come prepared for class everyday, and (3) Study!! Essential questions: 1. What is Calculus? 2. How do we find the instantaneous rate of change (velocity)? Applications: An object is dropped. How long will it take to fall? How fast will it be going when it falls? What is the most efficient way to package my product? 3. How do we find the area and/or volume of exotic shapes? Applications: What is the area of the rotor in a Wankel engine? How fast will a wound heal? How do I construct an arch dam? What is the volume of a fuel tank?
Instructor: Mr. Goncalves Classroom: Room 401 Schedule: Monday & Wednesday 2 nd period Tuesday & Thursday 7 th period Friday 1 st period Extra help hours: 7:40 to 8:25 AM Tuesday Friday 3:00 to 4:00 PM Wednesday and Thursday Contact Information: Phone: Office (212) 772-1220 E-Mail: ggoncalves@erhsnyc.net Required Materials: Primary Textbook: Finney, Demana, Waits, Kennedy. Calculus: Graphical, Numerical, Algebraic: AP Edition. Boston: Pearson Prentice Hall, 1st edition, 2003. Secondary Textbook: Larson/Edwards. Calculus of a Single Variable AP Edition, Florence: Cengage Learning, 9 th edition, 2010. Calculator - TI-83 or TI-84 required Each student must have his/her own graphing calculator. Pencil and eraser Ink is not allowed on any assignment or test. Composition book It is suggested that students have a Composition book to keep all daily notes, examples, homework, and AP Calculus problems that will be assigned during the year. Folder or Binder It is suggested that students have a folder to keep all graded assignments, handouts, and practice AP problems. Expectations: You can expect 100% from me because I am expecting 100% from you. Be on time and prepared for class everyday. Do not come late and always do your Homework.
Classroom Procedures: Homework is given daily and counts for 10% of your grade. If have any questions about it see me in the morning or after school hours. In addition, homework packets will be given at the end of each chapter to reinforce the material learned. Late Homework assignments will NOT be accepted. Quizzes will be given weekly and unannounced. Quizzes will require you to memorize formulas, definitions and to interpret questions. They count for 30% of your grade. Tests count for 50% of your grade. I am planning to give 2 or 3 tests every marking period and they will be cumulative. There are no test corrections. Extra Credit will be given sporadically on our website. Weekly AM Quizzes will be administered before class during the month of April. The format will be 5 multiple choice questions, with the potential to earn up to1 point on your final average. 4 th Marking Period Pre-Exam April Madness!! Dates Assignments Weight 04/01 05/03 Friday exams 60% 80% Homework assignments 20% Afternoon sessions from 3:15 to 5:00 PM 20% 20% Post-Exam 05/-05 06/10 Group project and presentation Research assignments Calculus BC topics Details Breakdown: Your last marking period (04/01 06/10) will be divided into two parts: Pre-exam and Post-exam. The first part counts for 60% of your 4 th Marking Period grade and the second part 40%. Pre-exam: In the first part tests count for 60%, HW assignments 20%, and attendance/participation 20% of your grade. You are required to come in the afternoon from 3:15 pm to 5 pm Tuesday through Thursday every week until the day prior to the exam. This is to prepare you for the AP Calculus Exam that will be administrated on May 4 th 2011, Wednesday at 8:00 am. Post-exam: After the AP Calculus exam, your grade is composed of: (1) coming to class on time and (2) participating in all activities. Work is not accepted if completed in ink This includes homework, tests, quizzes, and everything else assigned in class. You should expect to write a lot in this class since you will be able to interpret the questions from a geometric, analytically, and numerically point of view. ERHS Academic Honesty Requirement: ERHS Academic Honesty Requirements apply to all assigned material in this class. This includes homework, quizzes, tests, projects, extra credit work, and anything else assigned. Failure to do your own work, or providing work to others, will result in a zero for the assignment and a referral to the Principal.
Grading Policy: Criteria for computing grades: Weight Exams 50% Quizzes 30% Homework/ NEAT Notebook 10% Class Participation/Group Activity 10% Make-Up Work: Missing class is not an excuse to not take a test or a quiz. If you miss a test or quiz it is your responsibility to schedule a re-take. If you miss class for any reason, plan on staying after school to get caught up. Do not expect there to be time in class for catch-up help. AP Exam Cost: The cost for the AP Calculus exam is $88. This may be a large amount for you to come up with at once in the spring, especially if you plan to take multiple AP exams. I suggest saving for it over the course of the year, and then when it is time to take the exam you already have the money set aside. See Ms. Cohen to make payment arrangements and/or ask for more information. Math Must-Dos: Come to class prepared. Bring your notebook, pencils, paper, and calculator every day. Do your Homework! Have fun!
Course Outline: Unit One: Are You Ready for Calculus? Preparation for Calculus (2 weeks) Linear Models and Rates of Change Functions and their Graphs Exponential and Logarithmic Rules Trigonometry Functions Unit Two: What is your Limit? Limits and Their Properties (3-4 weeks) Find limits graphically and numerically Evaluate limits analytically Continuity and one-sided limits Intermediate Value Theorem: It ain t a sandwich unless there s something between the bread Infinite limits and vertical asymptotes Limits at Infinity (horizontal asymptotes) Unit Three: How is My Deriving? Differentiation (8-9 weeks) The derivative and the tangent line problem Differentiability and continuity Basic differentiation rules and rates of change (average and instantaneous) Product and Quotient Rules and Higher Order derivatives The Chain Rule: S & M Made Easy Implicit differentiation: Let s Be Oblique Related Rates: You Change, I Change Extrema on an interval Rolle s Theorem and the Mean Value Theorem Increasing and decreasing functions The First Derivative Test: How to Doodle Like an Expert Concavity and points of inflection The Second Derivative Test Summary of Curve Sketching (including monotonic functions) Optimization problems Differentials Local linear approximations Unit Four: Doing It All Backward: Introduction to Integral Calculus (4-5 weeks) Antiderivatives and indefinite integration Differential equations Position, velocity, acceleration problems Reimann sums Definite integrals solved using geometric formulas Properties of definite integrals Trapezoidal Rule The Fundamental Theorem of Calculus Average value of a function Second Fundamental Theorem of Calculus
Integration using u-substitution Displacement and definite integrals Unit Five: Doing That Calc Thing To Exponents and Logs: Transcendental Functions (2-3 weeks) The Natural Logarithmic Function and Differentiation The Natural Logarithmic Function and Integration Inverse Functions Exponential Functions: Differentiation and Integration Bases other than e and applications Differential equations: Growth and decay Differential equations: Separation of variables Differential equations: Slope fields Inverse trigonometric functions and Differentiation Inverse trigonometric functions and Integration Unit Six: Applications of Integration (2 weeks) Area of a region between two curves Volume: Known cross-sections Volume: Disc method Volume: Washer method