AP Syllabus



AP? Calculus AB Syllabus 2014-15Olympic athletes undoubtedly have genetic gifts that help them triumph, but hard work in any field may matter more than innate talent. In fact, when we practice a certain skill, such as swinging a golf club, over and over again, we strengthen the connections between neurons in the brain and stimulate the formation of new connections. Practicing also stimulates the growth of myelin – protective insulation – around the neurons. As a result, the electrical impulses controlling the thoughts and movements needed to hit the ball became faster and more accurate. “Myelination makes the flow of information in the brain more efficient and coordinated,” says Dr. R. Douglas Fields.Experts talk about the benefits of “deep” or “deliberate” practice, which includes repetition of particular movement or musical passage, doing something extra slowly and working at a level that is slightly more challenging than what you can already do. “It’s a shame we call it ‘playing’ music, when it’s really work,” points out Dr. Robert Cutietta. “But if you never get over the hurdle of learning to play well, it’ll be hard to really enjoy it.” – Parents MagazineCourse OverviewBy 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 conclusions.? Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.? Develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.Technology RequirementWe will use a Texas Instruments 84 Plus graphing calculator in class regularly.. If you do not have the means to borrow or purchase a graphing calculator, I can let you borrow one, but please try to get one on your own, as there are a limited number available to loan.We will use the calculator in a variety of ways including:? Conduct explorations.? Graph functions within arbitrary windows.? Solve equations numerically.? Analyze and interpret results.? Justify and explain results of graphs and equations.Other SuppliesYou will need pencils, a TI-84 Plus, TI-84 Silver, TI-84C or TI Inspire calculator. I would also like for you to have a binder to keep notes in, as well as a pack of colored pencils.Primary TextFinney, Demana, Waits, Kennedy Calculus: Graphical, Numerical, Algebraic. Prentice Hall, 3rd EditionSupplemental TextBest, George, and J. Richard Luxe. Preparing for the (AB) AP Calculus Examination. Andover, MA.: Venture Publishing, 2004.A Balanced ApproachAs we began last year in Precalculus, we will emphasizes a “Rule of Four.” There are a variety of ways to approach and solve problems. The four ways one can investigate problems in mathematics are:? Numerical analysis (where data points are known, but not an equation)? Graphical analysis (where a graph is known, but again, not an equation)? Analytic/algebraic analysis (traditional equation and variable manipulation)? Verbal/written methods of representing problems (classic story problems as well as written justification of one’s thinking in solving a problem)Course OutlineWe will be following the sequence established in Calculus: Graphical, Numerical, Algebraic (3rd Edition) by Finney, Demana, Waits, and Kennedy. The timeline given is an estimate, as the actual time varies from year to year depending upon the time each class spends in exploration and discovery as well as the depth of discussions generated.We will begin with Chapter 2, but we will review prerequisites for Calculus found in Chapter 1 of the text. Multiple representations of functions will be stressed in this review. 1.1Lines1.2Functions and Graphs1.3Exponential Equations1.5Functions and Logarithms1.6Trigonometric FunctionsChapter 2 – Limits and Continuity (2-3 weeks)2.1Rates of Change and Limits2.2Limits Involving Infinity2.3Continuity2.4Rates of Change and Tangent Lines Chapter 3 – Derivatives (6-7 weeks)3.1Derivative of a Function3.2Differentiability3.3Rules for Differentiation3.4Velocity and Other Rates of Change3.5Derivatives of Trigonometric Functions3.6Chain Rule3.7Implicit Differentiation3.8Derivatives of Inverse Trigonometric Functions3.9Derivatives of Exponential and Logarithmic FunctionsChapter 4 – Applications of Derivatives (5-6 weeks)4.1Extreme Values of Functions4.2 Mean Value Theorem4.3Connecting f’ and f’’ with the Graph of f4.4Modeling and Optimization4.5Linearization and Newton’s Method4.6Related RatesChapter 5 – The Definite Integral (3-4 weeks)5.1Estimating with Finite Sums5.2Definite Integrals5.3Definite Integrals and Antiderivatives5.4Fundamental Theorem of Calculus5.5Trapezoidal RuleChapter 6 – Differential Equations and Mathematical Modeling (4-5 weeks)6.1Slope Fields and Euler’s Method6.2Antidifferentiation by Substitution6.4Exponential Growth and Decay6.5Logistic GrowthChapter 7 – Applications of Definite Integrals (2-3 weeks)7.1Integral as Net Change7.2Areas in the Plane7.3VolumesPedagogy:We will be learning in a variety of ways. Much of the time, we will be in groups, working together to solve and investigate problems and theorems, as well as justifying answers. We will investigate both multiple choice and free-response questions, in order to understand how to best answer them.Tests/Quizzes/Projects:Tests and quizzes will be cumulative, though with an emphasis on recent material. Calculators may be used on tests/quizzes unless otherwise announced. You are responsible for providing your own calculator – no loaners! There will be no make ups of quizzes or tests, as per math department policy. However, I will give you an additional test grade equal to your highest test score.Classwork/Homework:Classwork includes all bell-ringers, exit slips, notes, and examples done during class time. It is to be done in pencil on loose-leaf paper and kept in the “Classwork” section of your binder. Each day must be clearly labeled with the date and objective. Homework includes the assignments given for you to practice what you learned in class. It will be assigned almost daily. IF YOU DO NOT DO HOMEWORK, YOU WILL FAIL. I will check homework every day by stamping on a calendar. Calendars will be collected monthly for homework points.AttendanceYou are responsible for all work assigned/collected during any absence from class. I strongly suggest that you exchange email/phone information with a classmate so that you can find out what you have missed. You are responsible for making arrangements with your teacher for any tests/quizzes missed due to an excused absence. Tests/quizzes missed due to an unexcused absence will receive a score of zero.Grading:The grading scale will be:90-100 A80-89B70-79C60-69D 0–59FHomework quizzes will count for 25% of the quarter grade, major quizzes and tests will count for 75%.The semester grade will be calculated as follows: 45 % Quarter 145 % Quarter 210 % Semester ExamAll students are required to take the AP exam in May.Each problem you do in class will be graded on the following rubric:Score543210ACCURACY andSUPPORT OF ANSWERAnswer, work and explanation are 100% correct.Answer and/or work incorrect, explanation is correct.Answer and work incorrect, explanation is mostly correct.Some work correct, answer incorrect, explanation not correct.Less than half of work shown is correctORAnswer is 100% correct and NO WORK SHOWN.No work shown is correct.No explanation.Expectations 1) I expect you to behave like the adults that you are. 2) Be on time, geniuses. Each time you are late, you lose 1 point on a test.3) Please ask questions. Especially in this class. We will be talking about some pretty crazy stuff, so please ask. 4) When I ask the class a question and you know the answer, please raise your hand.5) Tutoring. I will give extra credit for going to tutoring. I will also give extra credit and service learning for being a tutor. See me about this on your own. Tutoring is every day during 8th period and after school. YOU WILL NEED TO GO TO TUTORING.7) Cheating. This is my biggest pet peeve. You have no idea how much cheating infuriates me! If I catch you cheating, I will give you a zero on that assignment. No questions, no reprieves. (Look it up). And no make ups.Instructor:Mr. Tim NuttleOffice Hours: After school and before school by appointment (room 101)Phone: 773-534-5100 ext. 22440, though email is betterE-Mail:tanuttle@cps.eduWebsite: ................
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