AP Calculus BC Mr. Peterson Room H110 wpeterson@fcusd.org 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: Website: URL: http://apcentral.collegeboard.com 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 http://www.larsoncalculus.com/ to access math tutors for additional help and work out solutions to all odd-numbered exercise through Calc Chat. PowerSchool (www.fcusd.org/vdlhs) Your teacher s contact information is available on the Vista del Lago website. The math department website as well as math teacher websites are updated on a regular basis and are an excellent source of information for parents/guardians and students. 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
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%= A 80-89%= B 70-79%= C 60-69%= D Below 60%= F 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 pencil All 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 paper The final solution is clearly stated Answers 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 class Assessments: 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. There will be no Unit Test-Retakes Most 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 Exam: Students will take a comprehensive final exam at the end of the semester (including materials from Calculus AB). Free Response Calculator Free Response Non-Calculator Multiple Choice Calculator Multiple Choice Non-Calculator Extra 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 website Citizenship: 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. AP Exam: Tuesday, May 9 For more information on AP Exam fees and fee reductions visit: http://professionals.collegeboard.com/testing/ap/about/fees Tardy Policy: Vista tardy policy will be enforced in my classroom refer to hand book for details Make-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. Electronic Devices Cell phones may not be out during class time, unless your instructor has asked you to use your phone for the learning activity. Students should always get permission from their instructor before using a cell phone or other personal electronic device All electronic devices (cell phones, smart watches, laptops, etc.) are prohibited when tests are out. This includes when tests are being given as well as when tests are being reviewed or corrected. When tests are out, all electronic devices will be placed in backpacks/purses. Students will not be able to access their electronic devices until the end of the testing session or test review (when all students have turned in their tests). If a student chooses to have any electronic devices out during a testing session or test review, it is considered academic dishonesty and the student will be held accountable with the consequences for academic dishonesty (see section above). 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: o Keep hands, feet, and objects to yourself BE RESPONSIBLE: o Be on time in your seat when the bell rings o Be prepared to learn by bringing materials, and participate, o No gum or food, except water o Sharpen your pencils before the bell rings o Do not cheat BE RESPECTFUL: o Be a good listener - Avoid interrupting when other people are talking o Use appropriate language o Do not distract other students from learning o Follow directions o Do not leave your desk without asking permission, even to throw away trash or sharpen your pencil o Working on other subjects is permitted only if you have finished your math assignment
AP Calculus BC Syllabus 2016/2017 I have read the rules and expectation sheet for Mr. Peterson 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. Peterson (wpeterson@fcusd.org). 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 I 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. Date Name of Student (Print) Signature of Student Date Please fill in the following contact information: Phone number: Parent Email: Student Email: Preferred school to home communication method: (circle one) phone / email Do 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 Understanding It 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 Calculators Graphing 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 Outline Block Schedule 90 minutes per day for 89 days = 1 year on traditional schedule Unit 1 - Calculus AB Review: Limits and Differentiation - 10 Days Limits Rates of Change Tangents, velocities, and other rates of change Limits at a Point One sided limits, two sided limits, limits that do not exist Tangents and Velocity - two points to find tangent (secant line), instantaneous velocity and average velocity. 1 x Limits at Infinity Asymptotes, infinite limits at infinity, lim 0, lim e 0, limits x r x x algebraically and graphically Calculating Limits using Limit Laws Limit Laws to find algebraically, direct substitution, greatest integer function, Squeeze Theorem, estimating limits from graphs or tables of data Precise Definition of Limits - - proofs and definition of limits Continuity Definition of continuity, graphical representation of continuity, continuity in terms of limits, jump discontinuity, removable discontinuity, infinite discontinuity, The Intermediate Value Theorem. Differentiation f a h f a Definition of Derivative as a Limit lim h0 h f x f c Definition of Differentiable If f ' x lim, then the function is xc x c differentiable at point c, functions that are continuous but not differentiable, dy Derivative Notation f ',, f ' x and derivatives with respect to different variables dx Rules for Differentiation Power rule, product rule, quotient rule, chain rule Higher Derivatives 1 st, 2 nd, 3 rd, and n th derivatives of functions, correlation using position, velocity, acceleration, and jerk Derivative of Trig Functions Derivatives of sine, cosine, tangent, cosecant, secant and cotangent
Implicit Differentiation Differentiating with respect to x when y and x are present in the function Separable Differentiable Functions solving equations using separable differentiable functions, specifically, exponential growth and y =ky Related Rates Differentiating functions with respect to time, applications of related rates Slope 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 conditions Related rates project (see student activity 1) Extreme Value Theorem First Derivative Test Absolute and Local Extrema Second Derivative Test Determine concavity and points of inflection Mean Value Theorem Rolle s Theorem and Mean Value Theorem and applications Curve 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, extrema Newton s Method of Approximation - Using Newton s iterative process to find an approximation of a root both graphically and algebraically Optimization Problems Finding max and min to maximize or minimize Unit 2 - Review of Integration Techniques (13 Days) Area between two curves Volume Volume of known cross sections The Integral as Net Change Fundamental Theorem of Calculus Arc length Surface Area Applications to particle motion Applications in Physics, including the integral as Work, Total Fluid Force, and Centroid Unit 3 Advanced Integration (13 Days) Integration by Parts Trigonometric Integrals Trigonometric Substitution Integration by Partial Fractions L Hopitals Rule and its application Improper Integrals and their convergence or divergence, including the use of L Hopital s Rule Application of new techniques in context of finding area, centroid, volume, including applications to motion on a line. Unit 4 Sequences and Series (23 Days) Sequences
Convergence 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 sums Exploration of Geometric Sequence and Proof of Summation Formula for finite and infinite series Applications of Geometric series Harmonic series Telescoping Series Nth test for divergence Integral Test is studied as the area of rectangles and the relationship to improper integrals and the p-series Direct comparison and limit comparison tests for convergence Alternating Series test Alternating Series Remainder and Error Bound The Ratio and Root Test Taylor polynomials and approximations, using the graphical representation as a introduction Maclaurin series and the general Taylor series centered at x = a. Power Series and the radius and interval of convergence Taylor and Maclaurin Series for sin x, cos x, and 1/(1-x) Manipulation of series to form a new series from a known one Techniques for this manipulation include multiplying constants and or variables, integration and differentiation of series Functions defined by power series Taylor s Theorem along with LaGrange Error Bound Unit 5 - Plane Curves, Parametric Equations and Polar Curves (15 Days) Plane curves and parametric equations Derivatives of parametric equations including velocity and acceleration Vectors to represent motion along a curve Derivatives of vector valued functions and applications including velocity vector, acceleration vector, speed, and distance traveled Polar coordinates and polar graphs Differentiation of polar curves Area and arc length of polar curves Unit 6 - Differential Equations (15 Days) Solving separable differential equations for general and particular solutions Use slope fields to determine particular solutions to differential equations Understanding the calculus used to create the logistic curve and how to solve logistical equations with applications in logistical growth functions Numerical solution to differential equations using Euler s Method
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