Textbook and Resources:



AP Calculus BCMr. XiongRoom H110vxiong@Course Information: Welcome to 2nd term of Calculus - AP Calculus BC. This class is based on the curriculum set by AP Central and the College Board. This class is a college or university level course and the score you receive on the AP exam can count as credit at some institutions. The pace and workload of this class will be the same as a college course. This course will require you to work with functions represented in a variety of ways – graphically, numerically, analytically, and verbally. We will also look at the connections among these representations. It is the expectation that all students enrolled in this course will take the AP Calculus AB/BC exam. Textbook and Resources:Larson, Ron, and Bruce H. Edwards. Calculus of a Single Variable. 10th ed. Belmont, CA : Brooks/Cole 2014.It is your responsibility to take care of your assigned textbook. Students will be held financially responsible for any lost or damaged textbook or if you turn in a book that is not your assigned book. Supplemental materials include but are not limited to the following texts:Supplemental materials include the following texts:Foerster, Paul A. Calculus Explorations. Emeryville: Key Curriculum Press, 1998.Barron’s AP Calculus Study GuideD&S Practice Exams for AP CalculusPrinceton Review AP Calculus Study GuideWebsite:URL: The AP Central page provides several key articles (including those discussing the role of sign charts and solving differential equations) as well as an archive of past free-response questions, which will be used regularly throughout the course to familiarize students with the AP style of questioning.Students may go online to to access math tutors for additional help and work out solutions to all odd-numbered exercise through Calc Chat.Required Class Materials: Each student should bring the following items to class everyday: Textbook Pencil/ Color Pens / highlighters / rulers Line paper / Graph Paper 3-ring binder or notebook Whiteboard marker Graphing Calculator (mandatory). TI–83, TI–84 or TI–89 (preferred),Grading: Your grade in this course will be composed of the following:Homework/ Classwork/ Quizzes/projects: 10%Tests: 55%Semester Final: 35%Letter grades will be based on the following scale:90-100%= A80-89%= B70-79%= C60-69%= DBelow 60%= FFinal Exam Clause: Due to the importance of the final exam, the students’ final grade in the class cannot be more than one grade higher than the grade on the final exam. The following rules will prevail regardless of the student’s overall percentage: In order to earn a semester grade of A(-), the final exam grade must be at least a B(-). In order to earn a semester grade of B(-), the final exam grade must be at least a C(-). In order to earn a semester grade of C(-), the final exam grade must be at least a D(-). Parents and students may utilize the PowerSchool Portal to access grades online.Warm-up and Notes: There will be a warm-up written on the board at the beginning of each class period. Students are expected to be in their seat working on their warm-up when the bell rings. I will be lecturing on the course material nearly every day and students are required to take notes. Students will write all warm-up activities and notes in a notebook dedicated to this course. Homework/Classwork: This class will be taught like a college course – lecture, notes, and applied projects. It is imperative that you come to class, take good notes, and do your homework diligently. Expect homework every night. Homework is to be done neatly so that I can read it. Chances are if you can’t read it, then I can’t either. Work and diagrams must accompany every problem unless otherwise instructed. Remember the AP Exam is the goal that we are working towards and all work done in this class is a step towards this goal. Homework quizzes will be given frequently to provide a formative assessment of student understanding.ALL homework, quizzes, and test must show the aspects required on the AP exam – graphically, numerically, analytically, and verbally. All student work must follow these guidelines. Completed in pencilAll work is shown. Work is complete, neat, and organized with correct calculus words and notations. If you use a calculator to obtain an answer you must show the Calculus representation as to how you arrived to your answer.All graphs are completed on graph paperThe final solution is clearly statedAnswers must be exact or approximated to exactly 3 decimal places.Expect homework every night. Homework will be graded daily for completeness. Homework checks will be given periodically where students will write down and completely solve a few chosen questions from the homework. You may be required to present your solutions to the classAssessments: Homework quizzes will be given throughout each unit, with or without notice. Tests will be given at the end of a unit and always announced in advance. The students will take a comprehensive final exam at the end of the semester (including materials from Calculus AB). There will be no Unit Test-RetakesMost written assessments will consist of two parts – calculator and non-calculator. Each of these will also consist of multiple choice and free response questions. This is to prepare you for the actual AP exam format. Most tests will be graded 50% multiple choice and 50% free response. Multiple choice questions will require justification for credit. All free response questions will be of the format of 9 points per question. The free response questions will require you to justify and explain your thought process, in Calculus terms, how your solution was found – even with the use of a calculator. Each portion will be timed. I will make every effort to make every test and quiz with the same difficulty level equivalent to an AP type exam problem.AP Exam Final – Full AP ExamFree Response CalculatorFree Response Non-CalculatorMultiple Choice CalculatorMultiple Choice Non-CalculatorExtra Credit: Students are expected to do assigned work and study for tests to do well in the course. Extra credit assignments should not be expected. Academic Dishonesty: All Vista students are expected to adhere to the rules of responsible scholarship, requiring all student grades to be earned honestly through hard work and good study habits. More information about the consequences for students who violate Vista’s Academic Honesty Agreement is available on the Academic Dishonesty Policy page of the school websiteCitizenship: Citizenship is reported separately from the academic grades. Course citizenship includes both work habits and attitude/behavior – excessive tardies and unexcused absences will negatively impact a student’s citizenship. Good citizenship is vital to a positive productive school environment. Please refer to the student handbook or Vista’s website for information on citizenship marks.Tutoring: Please come and see me if you need help. I will be sure to find a time that works for both of us. Afterschool sessions may be required in reviewing for the AP Exam. A mock exam may be given prior to the AP Exam.AP Exam: Thursday, May 5For more information on AP Exam fees and fee reductions visit: Policy: Vista tardy policy will be enforced in my classroom –refer to hand book for detailsMake-ups: If you have an excused absence, it is the students’ responsibility to inquire about missed work and to schedule a time to make up that work. Any work assigned before the student’s absence and due on the day of the absence is due the first day the student returns to school unless other arrangements have been made. One day will be given for each absence to allow students to complete work they have missed due to absence. All work must be made up, including: notes, classwork, homework, quizzes and tests. All make-up work will be administered during lunch or before school. Any work not made up by the required date will receive no credit. Any work missed due to a school activity must be completed and received on the due date. Students should request work several days ahead of time if they are expecting to be absent.Cell Phones: Cell phones should not be used in class as it interrupts the educational environment. Students’ phones will be confiscated if they are using them for any reason during class time. The first time the phone will be returned at the end of the school day. After that offense, the parent will be contacted and will have to come to the office to pick up the student’s phone.Classroom Rules: Students are expected to follow the guidelines/expectations outlined in the student handbook. In order to create a safe and positive classroom environment, we expect you to always: BE SAFE: Keep hands, feet, and objects to yourselfBE RESPONSIBLE: Be on time in your seat when the bell ringsBe prepared to learn by bringing materials, and participate, No gum or food, except waterSharpen your pencils before the bell ringsDo not cheatBE RESPECTFUL: Be a good listener - Avoid interrupting when other people are talkingUse appropriate languageDo not distract other students from learningFollow directionsDo not leave your desk without asking permission, even to throw away trash or sharpen your pencilWorking on other subjects is permitted only if you have finished your math assignmentAP Calculus BC Syllabus2015I have read the “rules and expectation” sheet for Mr. Xiong’ Calculus course. I will help monitor his/her progress in this course through the PowerSchool Portal at least every other week. I will make sure that he/she has all the proper supplies needed for this class in order to succeed. If I have any questions concerning my child’s progress in this course, I will e-mail Mr. Xiong (vxiong@).Keep a copy of the procedures in your math binder/notebook for reference but turn in the signature portion below for my records. Thank you.___________________________________________________________________Name of Parent/Guardian (Print) Parent Signature ______________DateI have read the “rules and expectation” sheet for Mr. Xiong’ Calculus course with my teacher. I realize the things I must do to be successful in this course. I promise to work hard and do my best. If I need help I will make it a point to go see Mr. Xiong, ask my parents for help, or go to tutoring.___________________________________________________________________Name of Student (Print) Signature of Student___________________DatePlease fill in the following contact information: Phone number:___________________________Parent Email:___________________________Student Email: ___________________________Preferred school to home communication method: (circle one) phone / emailDo you have internet access at home? ____ Are you able to print documents at home? _____Please use the back to comments (Is there anything you would like me to be aware of?).Pedagogical Practices:Graphical, Numerical, Analytical, and Verbal UnderstandingIt is my practice to provide continuous multiple representations for the conceptual development of calculus. Students are expected to understand topics graphically, numerically, and analytically and be able to explain their answers verbally using “Calculus” terms. Students are presented with a great deal of material to assist their complex understanding of calculus. The textbook delivers numerous problems which require an analytical understanding of concepts. These problems are supplemented with additional problems that utilize graphs and data tables to emphasize graphical and numerical understanding of key concepts. Conceptual understanding is emphasized at least as much as the algorithms of integration and differentiation. Justification, using the language of calculus, is a critical component of both instruction and assessment. More and more frequently, a student is expected to respond to “AP-like” questions within small group discussion, assignments, quizzes and exams. Students must justify their answers to questions both verbally and in written sentences using proper “Calculus” language. Understanding takes priority over computation. Advanced Placement questions are dealt with weekly. From the time that a topic is taught, an appropriate test question is presented to them in class. Often, they self-grade these questions to enhance their understanding of the approach the readers take to scoring their exams and reinforce their understanding of proper written justifications of answers. The extensive library of questions from the College Board as well as problems from additional resources offers a plethora of options to present to the student. They work frequently in small groups to encourage peer interaction and the language of calculus. Groups often present their solutions to the class in an effort to practice the written and verbal understanding of topics. Graphing CalculatorsGraphing calculators are used extensively throughout the course. Students will use them to solve an equation, collect data to model calculus concepts, and represent functions graphically. Students must be able to use the calculator to find roots of equations, discuss domain and range, and the graphical characteristics of an even and odd function. Within the topics of Limits and Continuity, a graphing calculator is used to analyze limits both numerically, using tables, and graphically, using the zoom feature. Piecewise and rational functions are graphed to discuss continuity and discontinuity. Students are taught to use the integration and differentiation capabilities to confirm analytical response. Some examples of graphing calculator activities include the following:Using a graphic calculator, students must explore and explain partial sums and explore convergence and divergence graphically. They compare series convergence or divergence and the sequence that generated the series. This provides the student an inductive way to discover the nth test for divergence. Students are required to show an understanding of convergence both analytically and graphically through this exercise. Students must justify their answers through written sentences and present their results to the class verbally.Using a graphing calculator, the students will model the spread of a flu virus using their knowledge of logistic growth functions, regression, differentiation, and integration. The students collect numerical data on the spread of the flu using a random generator. The graph of the total number infected is analyzed, as well as the graph of the derivative. Students run a regression on data to find the proportional constant. Then they integrate the differential equation, using partial fractions to create the logistical curve. They are then given actual data from the Center for the Disease Control and perform the same process using actual data. Results of the exercise must be justified in writing using sentences.Course OutlineBlock Schedule – 90 minutes per day for 89 days = 1 year on traditional scheduleUnit 1 - Calculus AB Review: Limits and Differentiation - 10 Days LimitsRates of Change – Tangents, velocities, and other rates of changeLimits at a Point – One sided limits, two sided limits, limits that do not existTangents and Velocity - two points to find tangent (secant line), instantaneous velocity and average velocity.Limits at Infinity –Asymptotes, infinite limits at infinity,, , limits algebraically and graphicallyCalculating Limits using Limit Laws – Limit Laws to find algebraically, direct substitution, greatest integer function, Squeeze Theorem, estimating limits from graphs or tables of dataPrecise Definition of Limits - - proofs and definition of limitsContinuity – Definition of continuity, graphical representation of continuity, continuity in terms of limits, jump discontinuity, removable discontinuity, infinite discontinuity, The Intermediate Value Theorem.DifferentiationDefinition of Derivative as a Limit Definition of Differentiable – If , then the function is differentiable at point “c”, functions that are continuous but not differentiable, Derivative Notation and derivatives with respect to different variablesRules for Differentiation – Power rule, product rule, quotient rule, chain ruleHigher Derivatives – 1st, 2nd, 3rd, and nth derivatives of functions, correlation using position, velocity, acceleration, and jerkDerivative of Trig Functions – Derivatives of sine, cosine, tangent, cosecant, secant and cotangentImplicit Differentiation – Differentiating with respect to x when y and x are present in the functionSeparable Differentiable Functions – solving equations using separable differentiable functions, specifically, exponential growth and y’=kyRelated Rates – Differentiating functions with respect to time, applications of related ratesSlope Fields – Introduction to slope fields, analyze graph of derivative using slope fields, translating graphs of f’(x) to f(x) and f(x) to f’(x) with initial conditionsRelated rates project (see student activity 1)Extreme Value TheoremFirst Derivative Test – Absolute and Local ExtremaSecond Derivative Test – Determine concavity and points of inflectionMean Value Theorem – Rolle’s Theorem and Mean Value Theorem and applicationsCurve Sketching – Sketching the graph of a f(x), f’(x), and f’’(x) using the first and second derivative tests to determine intervals of increasing/decreasing, local/absolute max and min, concavity, and points of inflection Use of the calculator to find derivatives, zeros, extremaNewton’s Method of Approximation - Using Newton’s iterative process to find an approximation of a root both graphically and algebraicallyOptimization Problems – Finding max and min to maximize or minimizeUnit 2 - Review of Integration Techniques (13 Days)Area between two curvesVolumeVolume of known cross sectionsThe Integral as Net ChangeFundamental Theorem of CalculusArc lengthSurface AreaApplications to particle motionApplications in Physics, including the integral as Work, Total Fluid Force, and CentroidUnit 3– Advanced Integration (13 Days)Integration by PartsTrigonometric IntegralsTrigonometric SubstitutionIntegration by Partial FractionsL’Hopitals Rule and its applicationImproper Integrals and their convergence or divergence, including the use of L’Hopital’s RuleApplication of new techniques in context of finding area, centroid, volume, including applications to motion on a line.Unit 4 – Sequences and Series (23 Days)SequencesConvergence and Divergence of sequences.Definition of series as a sequence of partial sums and convergence of series is defined as the convergence of the sequence of partial sumsExploration of Geometric Sequence and Proof of Summation Formula for finite and infinite seriesApplications of Geometric seriesHarmonic seriesTelescoping SeriesNth test for divergenceIntegral Test is studied as the area of rectangles and the relationship to improper integrals and the p-seriesDirect comparison and limit comparison tests for convergenceAlternating Series testAlternating Series Remainder and Error BoundThe Ratio and Root TestTaylor polynomials and approximations, using the graphical representation as a introductionMaclaurin series and the general Taylor series centered at x = a. Power Series and the radius and interval of convergenceTaylor and Maclaurin Series for sin x, cos x, and 1/(1-x)Manipulation of series to form a new series from a known oneTechniques for this manipulation include multiplying constants and or variables, integration and differentiation of series Functions defined by power seriesTaylor’s Theorem along with LaGrange Error BoundUnit 5 - Plane Curves, Parametric Equations and Polar Curves (15 Days)Plane curves and parametric equationsDerivatives of parametric equations including velocity and accelerationVectors to represent motion along a curveDerivatives of vector valued functions and applications including velocity vector, acceleration vector, speed, and distance traveledPolar coordinates and polar graphsDifferentiation of polar curves Area and arc length of polar curvesUnit 6 - Differential Equations (15 Days)Solving separable differential equations for general and particular solutionsUse slope fields to determine particular solutions to differential equationsUnderstanding the calculus used to create the logistic curve and how to solve logistical equations with applications in logistical growth functionsNumerical solution to differential equations using Euler’s MethodAP Exam Final – Full AP Exam2 Free Response Calculator4 Free Response Non-CalculatorMultiple Choice Non-CalculatorMultiple Choice Calculator ................
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