BOOKER T. WASHINGTON SENIOR HIGH SCHOOL Syllabus Course Title: AP Calculus BC Instructor: Mora, Mariana

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1 BOOKER T. WASHINGTON SENIOR HIGH SCHOOL Syllabus Course Title: AP Calculus BC Instructor: Mora, Mariana The objective of the AP Calculus course during this year is to engage students in enjoyable activities that promote interest in mathematics. I provide them with key concepts to pull the students to have success in future mathematic courses and I try to get them to ask the questions. I rarely, if ever, tell students that some new concept or type of problem is easy. I d rather they feel a sense of accomplishment from being able to tackle hard concepts and problems than feel frustration at being stumped by even the easy ones. This course also helps them with a strong foundation for the math and science courses they will take in college. This course is taught with the use of Interactive software and websites that provide the students with the home learning necessary for the development of their knowledge and the use of Smart Board that is the equipment that our school has to help the teacher develop their class. Primary Textbook Finney, Ross L., Franklin Demana, Bert Waits, and Daniel Kennedy. Calculus: Graphical, Numerical, Algebraic. Copyright 1999 Addison Wesley Logmnan Course Topics: CHAPTER 1: Functions The course teaches all topics associated with functions, and graphs of polynomial and other rational, trigonometric, inverse trigonometric, exponential, and logarithmic functions. A. A review of Basic Functions B. Lines C. Properties of Functions D. Inverses E. Translations and Reflections F. Parametric Equations CHAPTER 2: Limits and Continuity The course teaches all topics associated with intuitive definitions; one-sided limits; functions becoming infinite; asymptotes and graphs; limits of a quotient; and the definition of continuity; kinds of discontinuities; theorems about continuous functions; rational Function, extreme Value, intermediate Value, and Intermediate Value Theorems. A. Functions and Asymptotes B. Evaluating Limits as x approaches a Finite Number e. C. Evaluating Limits as x approaches +, - infinite. D. Special limits E. Evaluating Limits of a Piecewise-Defined Function F. Continuity of Function

2 CHAPTER 3: The Derivative The course teaches all topics associated with definition of derivatives as the limit of a difference quotient and as instantaneous rate of change; formulas; composite functions and the chain rule; defensibility and continuality; estimating a derivative numerically and graphically; implicit differentiation; derivative of inverse functions; the Mean Value theorem; recognizing a given limit as a derivative. A. The derivative of a function B. The average rate of Change of a function on an interval C. The definition of the derivative D. Rules for Derivatives E. Recognizing the form of the derivative F. The equation of a tangent line G. Differentiability and continuity H. Particular motion I. Implicit differentiation J. Related Rates K. Derivative of Parametric equations CHAPTER 4: Applications of Differential Calculus The course teaches all topics associated with slope; critical points; average velocity; tangents and normals, increasing and decreasing function; using the first and second derivative for the following; local max or min, inflection points, curve sketching, global max or min and optimization problems; relating a function and its derivatives graphically; motion along a line; local linearization and its use in approximating a function; related rates. A. Three Theorems: The extreme value Theorem. Rolle s Theorem, and mean value theorem. B. Critical Value C. Concavity and the second derivative D. Curve sketching and the graphing calculator E. Optimization CHAPTER 5: techniques and Applications of Antidifferentiation The course teaches all topics associated with definite integral as the limit of a Riemann sum; area; definition of definite integral; properties of the definite integral; Riemann sums using rectangles or trapezoids in equal subdivisions; comparing approximating sums; average value of a function; Fundamental theorem of Calculus; graphing a function from its derivative (revisited); interpreting ln x as an area. The course teaches all topics associated with area of a region, including between two curves; volume of a solid of known cross sections, including a solid of revolution. A. Antiderivatives B. Area under a curve: Approximation by Riemann Sums C. The Fundamental theorem of Calculus (FTC). D. The Accumulation fundamental theorem part two of the Fundamental theorem (FTC).

3 E. Integration by the change of variable or u-substitution Method F. Applications of the integral: Average value of a function G. Volumes H. The trapezoidal rule I. Arc Length and Area of a Surface of Revolution CHAPTER 6: Separable Differential Equations and slope fields The course teaches all topics associated with basis definitions; slope fields, solving first order separable differential equations analytically; exponential growth and decay. A. Separable differential Equations B. Slope Fields C. The connection between a slope field and its differential equation. CHAPTER 7: Methods of Integration The course teaches all topics associated with basis definitions of Integration by parts, the methods of partial fraction and improper integrals A. Integration by parts B. Integration by the method of Partial fractions C. Improper Integrals CHAPTER 8: Polynomial Approximations and infinite series The course teaches all topics associated with basis definitions of sequence of partial sum, and convergence is defined in terms of the limit of the sequence of partial form sums, Taylor polynomial approximation with graphical demonstration convergence of p- series, power series. A. Introduction B. Sigma Notation C. Derivation of the Taylor Polynomial Formula D. Finding new polynomials from old. E. Error formula for Taylor Polynomial Approximation F. Sequences and Series G. Power Series CHAPTER 9: Logistic Growth, Euler s method, and other BC Topics The course teaches all topics associated with basis definitions; the logistic growth model, Euler s approximation, L Hospita s rules and Polar curves. A. The logistic Growth Model B. Euler s Approximation Methods C. Logarithmic Differentiation D. L Hopital s Rule E. Polar Curves Teaching Strategies I introduce each chapter with a discovery lesson. I think that exploration and discovery are great ways for students to learn, because these methods help students have more ownership in the material being covered than they would use a traditional lecture approach. The discovery lessons are done in groups of two students.

4 Graphing Calculator Many of the discovery lessons rely heavily on the use of the graphing calculators. The calculator helps students develop a visual understanding of the material that they would not otherwise have. My students use the TI-83 graphing calculator almost every day in class for explorations and in assignments to analyze functions and justify solutions. For example, the students use the calculator to approximate the values of derivatives and definite integrals obtained through analytical means in order to verify that the answers are reasonable. However, many homework problems and about half of the problems on quizzes and tests are done without the use of the graphing calculator. Since the AP Exam is half calculator and half non-calculator, I feel that it is very important for students to have practice working problems both ways. We spend time in class discussions talking about the types of questions that they must know how to work with their calculators and the types of questions that they must know how to work without their calculators. We also discuss the techniques needed to use the calculator most efficiently (storing functions in the y = screen, storing values that will be used later in the problem, etc.). Materials (Students are required to bring materials to class every day): Notebook Pencil, no pens. A scientific Calculator. Lined Paper and Graph Paper. Classroom Rules: No eating or drinking is allowed in class. Remain seated until I dismiss the class. Do not stand by the door. Be respectful to everyone in class. Hall passes are to be used for emergency purpose only. Grading Criteria: Attendance: Students cannot learn unless they are present and good attendance usually results in success. Students must request make-up work upon their immediate return to class. Students will be allowed one day for every excused absence to make up their work. Makeup work is due one week after your absence. Any student, who has accumulated ten or more absences for the entire school year will receive a NC (no credit), if they are passing the class. Tardies: Detentions will be assigned to anyone who is late. BEFORE the bell rings you must be seated and ready to do your Do it Now during the first 10 minutes Homework: Students should expect homework every day and it will be due the next class session. Assignments will be assessed regularly and unannounced. Parents, please make sure your child is doing their homework. Testing: Each nine week grade consists of just do it, homework, Class assignment and participation (10%), class work (20%), quizzes (30%), and tests and project (40%). Homework is assigned after every class period, and quizzes are given after completing two sections. The unit tests, including the midterm and final exam, are similar to the AP Exam format. Students are given a class work grade for completing Exploration activities and warm-up activities and a participation grade for participating in class discussions and

5 presenting problems to the class. Written reports are included in their homework grade. Sample AP Exams are given throughout the year as another form of assessment. Grades will result by averaging Letter grades will be assigned as follows: It is the responsibility of the student to seek extra help whenever necessary. Tutoring is usually offered after school, free of charge, Monday through Thursday, 2:30 to 3:30 for clarification of their knowledge where I can work on individual problems and clear their understanding of different topics. Interim progress reports, failure notices and report cards are sent home periodically with the student to keep parents informed of their son/daughter s progress.. AP Exams A % Outstanding Progress 4 B % Above Average Progress 3 C % Average Progress 2 D % Lowest Acceptable Progress 1 F 0 59 % Failure 0 I 0 Incomplete (secondary only) 0 The Calculus BC Exam seeks to assess how well a student has mastered the concepts and techniques of the subject matter of the corresponding course. The exam consists of two sections, as described below. Section I: a multiple-choice section testing proficiency in a wide variety of topics Section II: a free-response section requiring the student to demonstrate the ability to solve problems involving a more extended chain of reasoning. Calculus BC: Section I Section I consists of 45 multiple-choice questions. Part A contains 28 questions and does not allow the use of a calculator. Part B contains 17 questions and requires a graphing calculator for some questions. Part A consists of 28 questions (55 minutes). In this section of the exam, as a correction for guessing, one-fourth of the number of questions answered incorrectly will be subtracted from the number of questions answered correctly. Part B consists of 17 questions (50 minutes). In this section of the exam, as a correction for guessing, one-fourth of the number of questions answered incorrectly will be subtracted from the number of questions answered correctly

6 Calculus BC: Section II Section II consists of six free-response problems in 90 minutes. Part A of the free-response section (two problems in 30 minutes) requires the use of a graphing calculator. Part B of the free-response (four problems in 60 minutes) does not allow the use of a calculator. During the second timed potion of the free-response section (Part B), students are permitted to continue work on problems in Part A but they are not permitted to use a calculator during this time. AP Calculus (both AB and BC) [MC corrects ¼ (MC wrong)] * 1.2 = MC score; max 54 points 6 FR questions, each out of 9 points = FR score; max 54 points ~ = 5 ~55-69 = 4 ~40-54 = 3 ~25-39=2 ~0-24=1 SPECIFIC RANGES VARY FROM YEAR-TO-YEAR, BUT THE NUMBERS ARE APPROXIMATELY GOOD. In addition, you can view your child s attendance and daily progress in class by going to the teacher s grade book at the following internet address:

AP Calculus AB. Nevada Academic Standards that are assessable at the local level only.

AP Calculus AB. Nevada Academic Standards that are assessable at the local level only. Calculus AB Priority Keys Aligned with Nevada Standards MA I MI L S MA represents a Major content area. Any concept labeled MA is something of central importance to the entire class/curriculum; it is a