AP Calculus AB Syllabus Mr. Townsend NYOS Charter School Tutorials: Mornings M & TH
Course Website: www.tinyurl.com/mrtownsend Email address:
[email protected]
“To solve a problem is to make a discovery: a great problem means a great discovery but there is a grain of discovery in the solution of any problem. Your problem may be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.” -George Polya
Three Main Ideas Limit Derivative Integral
Students will develop their understanding of Calculus in four ways… 1) Numerically 2) Graphically 3) Algebraically 4) Verbally By successfully completing this course, you will be able to: Work with functions represented in a variety of ways and understand the connections among these representations. Understand the meaning of the derivative in terms of a rate of change and local linear approximation, and use derivatives to solve a variety of problems. Understand the relationship between the derivative and the definite integral. Communicate mathematics both orally and in well-written sentences to explain solutions to problems. Model a written description of a physical situation with a function, a differential equation, or an integral. Use technology to help solve problems, experiment, interpret results, and verify solutions. Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measure. Develop an appreciation for Calculus as a coherent body of knowledge and as a human accomplishment. It is a requirement that all students who complete this course take the AB level Advanced Placement Exam. Technology Requirement I will use a Texas Instruments 84 Plus graphing calculator in class regularly. You will want to have a graphing calculator as well, as there will not be calculators available for students to check out. We will use the calculator in a variety of ways including: Conduct explorations. Graph functions with arbitrary windows. Solve equations numerically. Analyze and interpret results. Justify and explain results of graphs and equations.
Grading Policies 10% Homework o Homework will be assigned each day in class. Mathematics is not a spectator sport; therefore success in Calculus will rely heavily on practice both in AND out of the classroom. 30% Quiz/Project o You can expect one/two quizzes per week and at least one project per quarter. Students will be informed of the material that will be assessed on the quiz at least one day prior to the administration of the quiz. The majority of the quiz problems will come directly from homework assignments. Projects will feature a grading rubric which will be made available via the course website at least one week prior to the due date of the project. 60% Test o You can expect a test about every two weeks. Tests will consist of both calculator and non-calculator sections with both multiple choice AND free response questions. A test review will be provided to students at least one day prior to the administration of the test. Late work will not be accepted in AP Calculus. The nature of the course is such that each topic builds upon the previous. Therefore, staying current on assignments is of vital importance to success in AP Calculus. Make up tests and quizzes will be arranged outside of class either before or after school. Academic Dishonesty Integrity is a positive attribute that we all possess and continually strengthen throughout our lives. I hope I will not have to question it. Cheating/copying on any assignment will result in a zero for that assignment for both the person copying and for the person who knowingly allowed you to cheat/copy. Parents and administrators will be notified in these situations. NYOS policy will be followed for all instances of academic dishonesty. Any talking or nonverbal communication (facial expressions, hand gestures, texting, etc…) during quizzes or tests will be considered cheating. Please be courteous to others as you complete your work. NYOS Policies I will adhere to all NYOS policies as specified in the Student Handbook. Policies on the school dress code, appropriate use of electronics (cell phones, laptops, etc…), tardies/absences, and code of conduct will be strictly adhered to. Textbooks/Resources Textbook: Calculus of a Single Variable 7th Edition by Larson, Hostetler, and Edwards. o This will be a primary source for AP Calculus. The textbook features 9 chapters and was chosen over other Calculus texts because of its rich explanations, Problem Solving section of each chapter, and clarity of visuals. o Each student will be issued a textbook that will be used as a resource and for practice problems for homework. Additionally, a textbook will be made available in the classroom. CollegeBoard o This site will be referenced routinely for its information regarding the AP Calculus AB test exam dates, fees, practice tests and more. Course Website o My website will feature resources such as daily assignment calendars, links to online textbooks, project grading rubrics, and downloadable assignments and activities. o www.tinyurl.com/mrtownsend Math Binder o I encourage you to keep an organized binder specifically for AP Calculus. Reviewing old notes, assignments, quizzes, and tests will help you succeed in this course. Organization is not something that comes easy to us all, so it is something we will work on together daily. Classmates o Contrary to popular belief, mathematics is a social endeavor and rarely do mathematicians work alone. I encourage and reward groups of students who study and learn together.
Course Outline Unit One: Limits and Their Properties (3 weeks)
Find limits graphically and numerically. Evaluate limits analytically. Continuity and one-sided limits Intermediate Value Theorem Infinite limits and vertical asymptotes
Unit Two: Differentiation and its Applications(10-13 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 Implicit differentiation Related Rates Extrema on an interval Rolle’s Theorem and the Mean Value Theorem Increasing and decreasing functions The First Derivative Test Concavity and points of inflection The Second Derivative Test Limits at Infinity (horizontal asymptotes) Summary of Curve Sketching (including monotonicity) Optimization problems Differentials Local linear approximations Antiderivatives and the indefinite integral
MIDTERM Mock-AP Exam with all four sections. Only material covered so far will be included on the midterm. Length of exam adjusted to fit the two-hour midterm time slot. Unit Three: Introduction to Integral Calculus (5-6 weeks)
Differential equations and slope fields 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 Separation of variables Growth and decay
Unit Four: Applications of Integration (2 weeks)
Area of a region between two curves Volume: Known cross-sections Volume: Disc method Volume: Washer method
Unit Five: AP Review (3 to 4 weeks) 2 full-length practice tests “Know Thy Enemy” Understanding the AP Test format and objectives Free-Response Workshop How to write a clear and concise explanation Overview of the year’s material Unit Six: Projects (3 to 4 weeks) Volume of a Known Cross Section Model o Build a three-dimensional model of an assigned solid and calculate its volume. Convert volume to weight and compare actual with calculated weight. Spread of Infectious Diseases o Model the spread of the H1N1 flu using various topics in Calculus. Use a spreadsheet and analytic Calculus to see what it would take for the H1N1 flu to become an epidemic. Calculus in Economics o Elasticity of demand is a measure used in economics to show the way that the quantity demanded of a good or service responds to a change in its price. In this activity, students learn about this measure and apply it to real-world situations. Final Exam covering the entire year
