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MARUTHI RAMPALLYWOODLAND HIGHAP Calculus AB SyllabusEmail: maruthi.rampally @henry.k12.ga.usTutoring times: 3:15-4:00 pm Prerequisites: Pre-Calculus and Teacher recommendation Textbook: CALCULUS by Ron Larson, Paul Battaglia Required Materials: Graphing calculator (TI-Nspire is preferred), 3-ring binder to be used exclusively for Calculus class, supplemental review materials to prepare for AP test: AP Calculus AB 5 Steps to a 5 by William Ma, and Barron’s “How to Prepare for the AP Exam: Calculus” (recommended).Course Description: This is a rigorous course for the mathematically advanced student capable of college-level work. In order to enroll in the course, students must have successfully completed Pre-Calculus. All students enrolled in this course are required to take the Advanced Placement Calculus AB Examination administered by the College board in the spring. 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. You will 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 and also understand the relationship between the derivative and the definite integral. Students will be able to communicate mathematics both orally and in well-written sentences to explain solutions to problems and 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. Course Outline: Review Basic algebra skills - simplifying expressions, factoring, operations with polynomials Graphs and models - intercepts, symmetry, points of intersections, models for data Linear models and rates of change - slopes, equations, graphing, parallel and perpendicular Functions and their graphs - notation, domain, range, transformations, classification, and combinations (Students must be able to graph certain parent functions with and without the aid of a graphing calculator). Fitting models to data - linear, quadratic, exponential, logarithmic and trigonometric using a graphing calculator Review of trigonometric functions Limits of a function Understanding of the limit process Instantaneous velocity Finding limits algebraically Continuous functions Evaluate one sided limits Limits involving infinity Asymptotic and unbounded behavior Comparing relative magnitudes of functions and their rates of change (exponential growth, polynomial growth, and logarithmic growth) Concept of the derivative Concept of the derivative presented geometrically, numerically, and analytically Derivative defined as the limit of the difference quotient Slopes, tangent lines, and derivatives Differentiation rules Velocity, speed and other rates of change Find derivative by slope of tangent lines, rate of change of a function, and instantaneous velocity Derivatives of trigonometric functions Derivatives of logarithmic and exponential functions Relationship between differentiability and continuity Slope of a curve at a point Chain rule, product rule, and quotient rule Implicit differentiation and fractional powers Logarithmic differentiation Instantaneous rates of change as the limit of average rate of change Applications of derivatives Curve sketching involving derivatives and sign lines Use first derivative test (intervals of increasing/decreasing functions and relative extrema) Use second derivative test (intervals of concavity and inflection points) Corresponding characteristics of f and f’ Relationship between the increasing and decreasing behavior of f and the sign of f’ Corresponding characteristics of the graphs of f, f’, and f’’ Relationship between concavity of f and the sign of f’’ Points of inflection as places where concavity changes Optimization (absolute and relative) Modeling rates of change (related rates problems) Graphing summary (roots, domain, range, asymptotes, symmetry, extrema, and concavity) Integrals Understand the concept of area under a curve using a Riemann sum over equal subdivisions Use the limit of the Riemann sum to calculate a definite integral Definition of derivative and antiderivatives Fundamental Theorem of Calculus Use calculator to compute definite integrals Techniques of integration (integration by parts, partial fractions) Integration of trigonometric functions Numeric Integration (Trapezoidal Rule and Simpson’s Rule) Solve differentiable equations with separable variables Slope fields Applications of integration Use definite integrals to find area under a curve Use definite integrals to find area between two curves Volumes of solids of revolution (disk and washer method) Cylindrical shells Average value of a function Volumes of solids with known cross sections Review/Test Preparation Remaining time prior to the administration of the AP examination is spent reviewing past AP multiple choice and free response questions, and taking practice exams. These are assigned as homework as well as assessed through quizzes and tests. Multiple-choice & Free-response practice - Test taking strategies are emphasized Individual and group practice are both used Rubrics are reviewed so students see the need for complete answers Student Objectives: It is my goal that students in this class will learn strategies and develop the skills and techniques necessary to becoming a good problem-solver and a logical and analytical thinker. Students should be able to make connections among the different representations of functions (graphical, numerical, analytical and verbal). Although it is not required, my expectation is that everyone taking AP Calculus also takes the AP exam. Ultimately, the exposure to this kind of mathematics is good for you and will serve you well in whatever endeavors you pursue. I hope you get a taste of the expectations and the rigor of a college-level Calculus course. Classroom activities: Students are expected to participate regularly in class discussions. Daily assignments will be checked by the teacher and corrected as a class. Students will assist in reviewing the previous lesson by asking and answering questions and presenting problems in a small-group or whole class settings. Students may also, on occasion, work together in small groups to solve problems, complete an activity, or develop a project. For example, in developing the concept of optimization, students are asked to construct a paper box of maximum volume from a rectangle. Each group has a unique rectangle. Groups may communicate about processes and strategies, but not identical answers. Classroom Participation: Students will be expected not only to articulate their own solutions, but to respond to the solutions that classmates have presented. Classroom discussions are essential for students to develop conceptually. Students will be expected to verbalize their solutions, their mathematical thought processes, and to ask insightful questions daily in class. In addition, students will frequently be given mathematical labs and explorations where active participation is critical for students to develop and in-depth conceptual understanding. During these explorations, students will use their graphing calculators to help explore, interpret, and verify solutions. Homework: Homework is given daily and I expect that it is completed daily. Homework is designed to enhance skills developed in class and is typically not graded on correctness but completeness. Some problems are extremely challenging, but I will always expect you to try something intelligent. Students’ work should be THEIR work only, but study groups are encouraged. Students will have my contact information if homework help is needed at night. There are also several online resources dedicated to calculus homework help. Homework is collected in chunks after several concepts have been covered. Please, do your homework completely and turn it in ON TIME. Late homework will not be accepted. Assessment: Students will be assessed on daily assignments, projects, quizzes and tests all including AP Exam items. Quizzes will be given after one or two sections have been covered. Major tests will occur at the end of each unit. After a sufficient number of calculus concepts have been covered, students will be assigned weekly AP problem sets. These sets will include multiple choice questions as well as free response items. The problem sets will be take-home assessments. Students are required to show all of their work or explain all of their processes to receive credit on each item of the problem set. The Problem Sets will alternate between calculator active and calculator prohibitive. Questions regarding these sets must be addressed before or after school. Calculators: Students are required to obtain a graphing calculator for this course. While many operations should be done without the aid of a calculator, several calculus problems require the support of technology to arrive at a solution. This course will teach students how to use the calculator to examine graphs, experiment, interpret results and solve problems. The four required functionalities of a graphing calculator for this course are: Finding a root Sketching a function in a specified window Approximating the derivative at a point using numerical methods Approximating the value of a definite integral using numerical methods Students are also required to make connections between the graphs of functions and their analysis, and conclusions about the behavior of functions when using a graphing calculator. As with the AP exam, portions of each unit test will require the use of a graphing calculator and other portions will prohibit its use. Grading Scale: Summative Assessments:Tests ,Quizzes, Projects 40% Practice work:Classwork, Homework, Formative assessments 40% Final Exam 20% **NOTE: In accordance with county policy 10 points will be added to the students’ final grade at the end of the school year. Please this portion, sign and return acknowledging that you’ve read and understand the contents of the AP Calculus AB Course Syllabus. Student’s Name: _________________________________Signature:____________________ Parent/Guardian’s Name : _____________________ Signature:________________________ Phone Number(s): __________________ (H) ___________________(C) Email Address: _____________________________________________ ................
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