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620810-9367600Grady High School2017-2018 COURSE SYLLABUSAP Calculus BCTeacher: Andrew NicholsPhone Number: 404-802-3043Office: E213 Classroom: E210Email: atnichols@Semester: Fall 2017 & Spring 2018Tutorial: Mondays and Wednesdays 3:45 – 4:30 p.m.Textbook: Rogawski’s Calculus for AP* ET 2eTuesdays and Thursday 7:45 – 8:25 a.m.Website: Google Classroom. Use Invite Code v9ref3xTutorial Location: E210Course Description: This course will follow the College Board Advanced Placement Curriculum for Calculus BC beyond what is covered in AB with additional material added at the teacher’s discretion. The purpose of the course is twofold. First, the student will master selected concepts and methods from calculus; the scope will be approximately equivalent to college-level Calculus 2. Second, the student will prepare themselves to pass the AP Calculus BC exam. As a result, the course will seek to balance conceptual understanding, computational skills, and the utilization of technology. Course Requirements: The student will…Be present and on-time for every class.Participate in classroom activities and plete all assignments & projects.Maintain a math notebook that includes notes, hand-outs, classwork, and homework.Sign the AP Course Contract and commit to taking the AP exam. Prerequisites: (1) Successful completion of AP Calculus AB. (2) A score of at least 3 on the AP Calculus AB exam. (3) PreCalculus or an equivalent course in advanced algebra and trigonometry.Course Content Standards: A list of content standards, based on the College Board course description and developed by the teacher, will be used to guide instruction and assessment in the course. The course will also follow the Georgia Program Standards for Gifted and High Ability Learners as outlined by the GA DOE Board Rule 160-4-2-.38 and listed below.Advanced Communication Skills: Learners will engage in diverse and authentic learning experiences which will allow them to develop and apply innovative oral, written, visual, and nonverbal communication skills across disciplines.Advanced Research Skills: Learners will gather, decipher, and deter mine credibility of information from a variety of sources and integrate information through analysis of content.Creative Thinking & Problem Solving: Learners will insightfully evaluate a variety of problems and arrive at innovative conclusions.Higher Order & Critical Thinking Skills: Learners will analytically critique a system or set of complex ideas, utilizing logic and reasoning skills in novel ways, to create and/or modify knowledge.Required Materials: BRING THESE ITEMS TO CLASS EVERY DAYMechanical pencil or pen,Ruler/straight edge,Math notebook, Textbook, and Graphing Calculator: Students will be required to obtain a graphing calculator for use in class and at home. The preferred model is the TI-Npire CAS, but any TI-84 model is acceptable. However, the TI-83 is not acceptable. If you purchase a calculator, be sure to select a TI-Nspire CAS model. A limited number of calculators will be assigned for long-term lease ($25/year) to students who are unable to obtain their own. Course Outline: All section references refer to the primary text for the course: Rogawski’s Calculus for AP*, Early Transcendentals, 2nd ed., W.H. Freeman: New York.Note: Items marked with an asterisk (*) are topics not required for the AP Calculus BC exam and may be omitted for time at the teacher’s discretion. Enduring UnderstandingsChapter 7: Techniques of Integration 6 weeks (August/September)SectionsLearning Objectives & Grading StandardsI. Antidifferentiation is the inverse process of differentiation.II. The definite integral of a function over an interval is the limit of a Riemann sum over that interval and can be calculated using a variety of strategies.III. The Fundamental Theorem of Calculus, which has two distinct formulations, connects differentiation and integration.7.1 Integration by Parts7.1 Find the antiderivative of the product of functions using the method of integration by parts.7.1b Evaluate definite integrals using the method of integration by parts.7.2 Trigonometric Integrals*7.2 Evaluate integrals involving powers of trigonometric functions.*7.3 Trigonometric Substitution*Evaluate integrals of algebraic functions using trigonometric identities.*7.4 Hyperbolic Integrals*Evaluate integrals of algebraic functions using hyperbolic antiderivative.*7.5 The Method of Partial Fractions7.5 Find the antiderivative of a certain rational functions using the method of partial fraction decomposition.7.6 Improper Integrals7.6a Evaluate (or determine the divergence of) improper integrals with infinite limits of integration.7.6b Evaluate (or determine the divergence of) improper integrals for integrals with infinite discontinuities.7.7 Probability & Integration*Apply integration to solve probability problems using PDF and CDF functions.* 7.8 Numerical Integration7.8a Approximate the value of a definite integral using left, right, and midpoint rectangular approximations given graphical, numerical, or analytic information about the function given either uniform or non-uniform partitions.7.8b Approximate the value of a definite integral using a trapezoidal approximation given graphical, numerical, or analytic information about the function given either uniform or non-uniform partitions.Enduring UnderstandingsChapters 6 & 8: Applications of Integration3 weeks (September/October)SectionsLearning Objectives & Grading StandardsThe definite integral of a function over an interval is a mathematical tool with many interpretations and applications involving accumulation.6.2 Setting up integrals 6.2a Compute the volume of a solid with a known cross section using an integral. (Review)6.2b Calculate the average value of a function using a definite integral. (Review)6.2b Calculate the density of a solid using an integral.*6.3 & 6.4 Rotational Volumes6.3 Use the disk and washer methods to calculate the volume of a solid.6.4 Use the method of cylindrical shells to calculate the volume of a solid.6.5 Work & Energy*6.5 Solve problems from physics involving work and energy using integration.* 8.1 Arc Length & Surface Area8.1 Find the length of a planar curve described by a function y=f(x).8.2 Fluid Pressure and Force*8.2 Solve problems from physics involving fluid pressure and force using integration.*8.3 Center of Mass*8.3 Calculate the center of mass of a regular solid using integration.*8.4 Taylor Polynomials8.4a Given a function f, construct the nth degree Taylor polynomial centered at x=a and use it to approximate the value of f near x=a8.4b Find the general terms for a Taylor polynomial.8.4c Use the Lagrange Error Bound to determine the error when using the nth degree Taylor polynomial to approximate the value of f.Enduring UnderstandingChapter 9: Differential Equations 3 Weeks (October)SectionsLearning Objectives & Grading StandardsAntidifferentiation is an underlying concept involved in solving separable differential equations. Solving separable differential equations involves determining a function or relation given its rate of change.9.1 Solving Diff. EqnsReview the related objectives from AB.9.2 Models involving y'=k(y-b) *9.2 Use the model y'=k(y-b) to solve problems in various applications.*9.3 Graphical & Numerical Methods9.3a Construct and interpret slope fields for first-order differential equations.9.3b Use Euler’s Method to approximate a solution, or a point a solution curve, for a first-order differential equation.9.4 The Logistic Equation9.4 Use the model for logistic growth that arises from the statement “The rate of change of a quantity is jointly proportional to the size of the quantity and the difference between the quantity and the carrying capacity.” That is, dydt=ky(a-y).9.5 First Order Linear Equations*9.5 Solve first order linear differential equations.*Enduring UnderstandingLimits & Proofs* 2 weeks (November)SectionLearning Objectives & Grading StandardsThe language of mathematics is a tool for clear, concise communication that can be used to investigate complex concepts and write elegant proofs. Appendix A: The Language of Mathematics*Read, write, and interpret formal mathematical language and logical statements.*2.8 Formal Defn. of a Limit*Write proofs involving the epsilon-delta definition of a limit.*10.1 Infinite Sequences*Determine whether an infinite sequence converges or diverges. If it converges, find its limit.*Appendix C: Induction and the Binomial Theorem*Use the process of mathematical induction to prove various statements including the power rule and the binomial theorem.*Chapter 10: Infinite Sequences & Series 6 Weeks (December/January)Enduring UnderstandingsSectionLearning Objectives & Grading StandardsI. The sum of an infinite number of real numbers may converge.II. A function can be represented by an associated power series over the interval of convergence for the power series.10.2 Summing an Infinite Series10.2a Explain the concept of convergence for infinite series in terms of partial sums.10.2b Determine whether a Geometric Series converges and find its sum if it does.10.2c Use the nth-Term Test to determine when a sequence diverges: recognize that a convergent series must have a general term that tends to zero, but not all series whose general term tends to zero are convergent. Be able to provide examples and counterexamples. In particular, discuss the divergence of the Harmonic Series.10.3 Convergence of Series with Positive Terms10.3a Use the Integral Test to determine whether a series converges or diverges.10.3b Determine whether a p-Series converges.10.3c Use the Direct Comparison Test to determine the convergence or divergence of certain series.10.3c Use the Limit Comparison Test to determine the convergence or divergence of certain series when the Direct Comparison Test is inconclusive.10.4 Absolute & Conditional Convergence10.4a Classify series as absolutely convergent, conditionally convergent, or divergent.10.4b Use absolute convergence to determine convergence of series with positive and negative terms.10.4c Use the Alternating Series Test to determine the convergence of series whose terms alternate in sign.10.4d Estimate the error when using the nth partial sum to approximate the sum of an alternating series.Chapter 10: Infinite Sequences & Series – Continued 6 Weeks (December/January)Enduring UnderstandingsSectionLearning Objectives & Grading StandardsI. The sum of an infinite number of real numbers may converge.II. A function can be represented by an associated power series over the interval of convergence for the power series.10.5 The Ratio & Root Tests10.5 Use the Ratio Test to determine the convergence of series whose general term has factors that are power, exponential, or factorial functions.10.6 Power Series10.6a Use the Ratio Test to determine the radius and interval of convergence for a power series and recognize that the radius, but possibly not the endpoints, are unchanged by differentiation and integration.10.6b Construct a power series representation for a function from a known power series using (i) substitution, (ii) differentiation, or (iii) antidifferentiation. 10.7 Taylor Series10.7a Generalize Taylor polynomials as partial sums for Taylor series and recognize that if a function has a power series representation, then it must be its Taylor series.10.7b Construct a Taylor series from a function f and determine for which values of x does the Taylor series converges to f.10.7c Use well-know Maclaurin Series (11-x, sinx, cosx, ex, etc.) to construct Taylor series for other functions via (i) multiplication, (ii) substitution, (iii) differentiation, and (iv) integration.10.7d Evaluate definite integrals by transforming the integrand into a Taylor Series. 10.7e Use the Alternating Series Error Bound to determine the error when using the nth degree Taylor polynomial to approximate the value of f (when possible).Chapter 11: Parametric Functions, Polar Functions, and & Vectors 7 Weeks (February/March)Enduring UnderstandingsTextbook AlignmentLearning Objectives & Grading StandardsThe methods of differential and integral calculus can be extended to multiple representations and coordinate systems including parametric, polar, and vector forms.11.1 Parametric Equations11.1a Model planar curves using parametric equations or a vector-valued function.11.1b Find the slope and write the equation of a line tangent to a planar curve described by parametric equations or vector-valued function. 11.2 Arc Length & Speed11.2a Find the length of a planar curve described by parametric equations or vector valued function.11.2b Find the speed a particle moving along a planar curve described by parametric equations or vector valued function.11.3 Polar CoordinatesReview the polar coordinate system.11.4 Area, Arc Length, & Slope in Polar Coordinates11.4a Find the area enclosed by polar curves.11.4b Find dy/dx and d2ydx2 for a planar curve described by a polar equation.11.4c Find the slope and write the equation of a line tangent to a planar curve described by a polar equation.11.5 Vectors in the PlaneReview the basics of planar vectors.11.6 Dot Product*Calculate the dot product of two vectors and use it in various applications.*11.7 Calculus of Vector-Valued Functions11.7a Differentiate and integrate vector valued functions.11.7b Represent motion along a planar curve using parametric or vector-valued functions and solve problems involving position, distance traveled, velocity, speed, and acceleration using differentiation and integration.Review for AP Exam: 4 weeksPost AP Exam Topics: 3 weeksEvaluation and Grading: This course will employ Standards Based Grading (SBG). In SBG, a grade is a measure of what a student understands about a specific standard. SBG gives students formative control over their own progress (and grade) through opportunities for reassessment. SBG grades do not measure whether a student is obedient and do not a measure how much effort the student puts into homework. For each chapter or section there will be a short list of objectives. In-class assessments will be used to measure each student’s mastery of the standards. You will never receive a grade for “Quiz 3” or “Chapter 5 Quiz.” When an assessment is graded you will received a grade for each standard assessed. Students are required to complete all homework/classwork assignments. Assignments will be given daily, but may not be graded formally. Classwork/homework assignments are practice. Students who fail to practice will likely fail quizzes and exams leading to lower grades or failure in the course.Your grade will be based on the percentage of points accumulated out of a total number of possible points in the following categories. The categories will be weighted according to the percentages indicated in parentheses; each assignment/standard within a category is of equal weight. Course ComponentsWeightsGrading Scale100-90A89-80B79-70C69-0FNot EvaluatedNEContent Standards: formative assessments such as quizzes, tasks, and projects.50%Reading Checks, Problem Sets and other classwork/homework20%Cumulative Exams: summative assessments such as end of unit, mid-semester, and final exams.30%TOTAL100%Campus Portal for Parents and Guardians: to view class schedules, attendance records & grades. To activate your account, visit the school to receive your login information.Reassessments: After a quiz, you will always have an opportunity for reassessment on the standards/objectives covered on that quiz. If you score lower than 70% on a standard, you are required to attend tutorial to address that standard. After tutorial you may elect to take a reassessment for that standard.Mandatory reassessment for all students will often be built into future assessments. No standard is ever “once & done.”Your grade in IC for a standard will always reflect your most recent performance on that standard, not an average, and not a maximum. If your performance drops upon reassessment, your grade for that standard will drop accordingly. Don’t blow a reassessment opportunity by being unprepared!Students are allowed a maximum of one elective reassessment per day. Students who procrastinate until the end of the grading period will not be allowed to abuse the reassessment policy. Students should use Infinite Campus to keep track of their standards-based grades.Cumulative exams are not covered under this policy; the grade you receive on a cumulative exam will be final. Reassessments must be completed and presented to Mr. Nichols or Ms. Hunter in tutorial. Reassessment DeadlinesSeptember 22 for assignments from August 1-September 21December 8 for assignments from September 22-December 7March 2 for assignments from January 8th through March 1May 11 for assignments after March 2nd through May 10thGrady High School School-wide Grade GuidelinesMASTERY LEARNING: With mastery learning, a unit of material is taught, and student understanding is evaluated before students are able to move on to the next unit. Students who have not shown mastery for a particular unit will receive feedback and support in reaching mastery. They may be given practice exercises, study guides, group work or complementary resources to help them improve and achieve mastery. Students who demonstrate mastery of the content for a particular unit are given enrichment exercises like special projects, tasks or academic games to further or broaden their knowledge of the material.LATE ASSIGNMENTS: ?It is important that students are responsible and meet established due dates for assignments. A late assignment is defined as work submitted after the teacher collected the assignment.??All missing/not turned in assignments will be recorded in Infinite Campus with an "M-Missing" designation.MISSING ASSIGNMENTS (late assignments or unexcused absences): Students with late assignments or unexcused absences will be expected to submit missed work within two weeks of the end of the grading periods. ?The deadlines for missing assignments are as follows:September 22 for assignments from August 1-September 21December 8 for assignments from September 22-December 7March 2 for assignments from January 8th through March 1May 11 for assignments after March 2nd through May 10thAs noted above, all missing/not turned in assignments will be recorded in Infinite Campus with an "M-Missing" designation. Late?assignments?will be assessed a 20% penalty.MAKE-UP ASSIGNMENTS (Excused Absences): Students with an excused absence will be expected to submit missed work on or before the third class meeting after the absence. Pre-announced assignments are due upon return to school. After the third class meeting, the 20% late penalty will apply.REASSESSMENT OPPORTUNITIES IN AP CLASSES: Reassessment opportunities are available for all students on FORMATIVE assessments only. ?There will be only one reassessment opportunity on assessments. ?This reassessment will be a newly generated teacher assessment and the reassessment score will replace the original score. ?Reassessment can occur during the class period, tutorials, and/or lunch-and-learn sessions (at the teacher’s discretion).Important Notes for AP Calculus StudentsThe reassessment policy above does not allow for reassessment on summative exams such as end-of-chapter, unit, or semester exams. Students are limited to one reassessment attempt per standard. This makes it vitally important that students are well-prepared for reassessment before they make their one attempt.Students are restricted to one standard reassessment per day.Reassessment must be completed in tutorialDEFICIENCY REPORTS: Parents and guardians are informed when students are making unsatisfactory progress in classes. Poor performance will be reported to parents and guardians as soon as problems are evident. Deficiency reports with plans for remediation will be provided for all students making unsatisfactory progress, and parent-guardians conferences must be scheduled. Unsatisfactory grades should never come as a surprise to parents, guardians, or students. Also, see Board Policy Administrative Regulation IHA-R(1) under “Students in danger of not meeting academic expectations” for further information. Teachers will:Contact parents/guardians early in the semester if academic, attendance, or behavioral difficulties are apparent.Notify the counselor, Student Support Team (SST)/Response To Intervention(RTI) Chair, and/or an Assistant Principal of serious problems that are affecting classroom performance.Set up parent conferences as necessary.ATHLETIC ELIGIBILITY: Students wanting to participate in athletic programs governed by the GHSA and extracurricular activities must meet eligibility requirements to participate. The Athletic Director (and the Extracurricular Activities sponsors) will collaborate with teachers to monitor and to identify students in danger of failing courses. A master list of students participating in extracurricular activities and athletics under the auspices of the GHSA will be available to all staff.Classroom Positive Behavior ExpectationsThe student will…1.Be present and on time for every class, every day.2.Be respectful of yourself, all peers, all adults, the school community, and the environment. Individually we are different, together we are Grady3.Be responsible for your putting forth your best effort in your work, for your materials, in your actions, and your interactions with the school community. Always report unsafe situations to an adults. 4.Be on task, be a good listener, a good thinker, and never give up. Follow the teacher directions and all school policies.5.Be a peaceful, productive, problem solver. Be polite and well-mannered. Think before you act and avoid confrontation. Fighting is never acceptable. Seek help from a trusted adult when you need help with a problem/situation with a peer or adult.6.Dispose of food and drink (H2O ok) before entering the classroom.7.Keep all phones and personal electronic devices turned off and out of sight.*8.Observe the dress code at all times.Primary Consequences may include a verbal warning, change seat in classroom, afterschool detention, parent phone call/email, or parent-teacher conference.Secondary Consequences may include referral to the Discipline Office for In School Suspension, Saturday Detention, or Out-of-School Suspension.*BYOT Policy: Students may keep their phone turned on in class to use for instructional purposes IF and ONLY IF they abide by the following guidelines:The phone is silenced and vibration mode is turned off.The phone is in the student’s bag when not being used for an approved purpose.The phone is used for non-instructional purposes only by permission of the teacher.If these guidelines are not followed, the device will be confiscated, turned into the Discipline Office, and held until claimed by a parent.Academic Integrity Policy: While it is expected that students will discuss homework and classwork assignments, a student should never submit another person’s work or ideas as their own. Quizzes, tests, and exams are always individual assignments and are never collaborative. If a student submits another’s work or ideas as their own, at minimum, a grade of “0” will be assigned, his/her parents will be contacted, and/or detention(s) will be assigned. To remove the “0,” the assignment must be completed in tutorial under the teacher’s supervision. Any suspicion of academic dishonesty will be reported to the Discipline Office and consequences may include, but are not limited to:Notation placed on the student’s permanent discipline record which is shared with colleges and universities upon request.Parent contact or conference, Immediate removal from the AP course, Retraction of letters of recommendation to colleges and universities in severe cases, In-school or out-of-school suspension.Support and Incentives from NMSI – National Math & Science InitiativeGrady High School has partnered with NMSI to provide additional support and incentives for students to succeed in AP math, science, and ELA courses. The goal of this partnership is to increase the number of students taking and scoring 3 or above on AP exams at Grady. NMSI supports instruction by providing teacher training and resources. NMSI supports students by providing Saturday review sessions, paying half the cost to take the exam for all students, and paying a $100 stipend to students who score a 3 or above per AP exam!? Attending Saturday Study sessions is an extremely important part of the NMSI program and will significantly help students prepare for and succeed on AP exams.??All students enrolled in NMSI AP courses are strongly encouraged to attend these sessions.? ?Research shows that students who succeed on AP exams are?3 times more likely?to graduate from college in 4 years with a diploma or certificate than students who do not succeed on AP exams.? Additionally, the college remediation rate among students who take AP exams is significantly lower than among students who do not take?AP exams.?For each Saturday session a student attend, the teacher will drop their lowest quiz or homework grade. There will be three?Saturdays (11/11, 2/3, 4/28) throughout the 2017-18 school year during which time NMSI expert teachers from across the United States will lead Study Sessions for Grady High?School and?North Atlanta High School AP students. Collaborating with Grady and North Atlanta teachers, the expert teachers will work with students on specific course topics, which will prepare them for the AP (insert?subject area) exam in May.? All sessions are provided at no cost to students and families. ?All Saturday sessions will take place at Grady High School.To the Parents/Guardians of my most promising student: First, let me say that I am looking forward to this school year and the mathematics your child and I will be exploring together. To get the school year off to a good start, there are a few things I need you to do for your son or daughter:Visit the course website, submit student/parent contact information, and download the syllabus: classroom., log in using username = yourAPSid@, password = lunch ID, and the invite code v9ref3x.On this site, parents and students can access the course syllabus and information about daily assignments, projects, and exams.Click on Student & Parent Contact Information Submission. It is imperative that every student/parent complete this process.Download and read over the syllabus with your child and sign below to show you have done so. You can find the complete syllabus for your course on the course website by clicking on the name of your course on the left hand side of the page.Please stress the importance of homework and set up a system for doing homework at home nightly. Homework will be assigned two to three times every week.Provide a TI-84 or TI-Nspire CAS graphing calculator for your son/daughter. The calculator will be used daily in class, will be vital for homework completion, and is required on the AP exam. If you are unable to provide a calculator please write a note to request that I loan your student a calculator.Parent-Student-Teacher Contract475297525209500I, ___________________________________, have read and understand the course syllabus for AP Calculus.print student’s nameI commit toFulfill the requirements of the course as outlined in the syllabus, Diligently prepare for the AP exam throughout the year, Commit to taking the AP exam in May,Maintain an unweighted* grade of at least “C,” andMaintain a high level of academic integrity. I understand that if I fail to fulfill any of these commitments, I may be dropped from the course and the AP course will not appear on my transcript. Furthermore, I understand that I must earn an unweighted* grade of 71 or higher in the first semester to be allowed to continue into the second semester of the course. *Unweighted grade refers to your grade before the 10 AP bonus points are added.___________________________________________ ____________student’s signature DateI, the parent/guardian, have read the course syllabus for AP Calculus, discussed its contents with my son/daughter, and submitted accurate contact information on the course website. _________________________________________________________________ __________________parent’s signature DateI, Andrew Nichols, pledge to uphold my responsibility as a teacher by providing a rich learning environment for all my students. I pledge to follow all the guidelines and policies set forth by this syllabus, by Grady High School, and by the APS Board of Education. I will make every effort to keep parents informed of their student’s progress in my class. ___________________________________________ ____________teacher’s signature Date ................
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