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AP Calculus AB Syllabus 2020-2021Contact info: bmilam@ 210-945-1100Curricular RequirementsThe course is structured around the enduring understandings withinBig Idea 1: Change Big Idea 2: LimitsBig Idea 3: Analysis of FunctionsThe course provides opportunities for students to Reason with definitions and theoremsConnect concepts and processesImplement algebraic/computational processesEngage with graphical, numerical, analytical, and verbal representations and demonstrate connections among themBuild notational fluencyCommunicate mathematical ideas in words, both orally and in writingCourse OverviewThis is a college-level calculus course designed to meet the Advanced Placement curricular requirements for Calculus AB (equivalent to a one-semester college course). The major topics of this course are limits, derivatives, integrals, and the Fundamental Theorem of Calculus. We will investigate and analyze course topics using equations, graphs, tables, and words, with a particular emphasis on a conceptual understanding of calculus. Applications, in particular to solid geometry and physics, will be studied were appropriate.Course OutlineUnit 1—Limits and ContinuityDefinition of a limit and Limit notationEstimating Limit Values from Graphs and TablesDetermining limits using Algebraic Properties and Algebraic manipulationSelecting procedures for determining limitsDetermining limits using the Squeeze TheoremConnecting multiple representations of limitsExploring types of discontinuitiesDefining continuity at a pointConfirming continuity over an intervalRemoving discontinuitiesConnecting infinite limits and vertical asymptotesConnecting limits at infinity and horizontal AsymptotesWorking with the Intermediate Value Theorem (IVT)Unit 2—Definition and Fundamental PropertiesDefining average and instantaneous rates of change at a pointDefining the derivative of a function and using derivative notationEstimating derivatives of a function at a pointConnecting differentiability and continuityApplying the power ruleDerivative rules: Constant, sum, difference, and constant multipleDerivatives of cos x, sin x, ex, and ln xThe product ruleThe quotient ruleFinding the derivatives of tangent, cotangent, secant, and/or cosecant functionsUnit 3—Differentiation: Composite, Implicit, and Inverse FunctionsChain ruleImplicit differentiationDifferentiating inverse functionsDifferentiating inverse trig functionsSelecting procedures for calculating derivativesCalculating higher-order derivativesUnit 4—Contextual Applications of DifferentiationInterpreting the meaning of the derivative in ContextStraight-Line Motion: Connecting position, velocity, and accelerationRates of change in applied contexts other than MotionIntroduction to related ratesSolve related rates problemsApproximating values of a function using local linearity and linearizationUsing L’Hospital’s rule for determining limits of indeterminate formsUnit 5—Analytical Applications of DifferentiationUsing the Mean Value Theorem (MVT)Extreme Value Theorem (EVT), Global vs Local extrema, and critical pointsDetermining intervals on which a function is increasing or decreasingUsing the first derivative test to determine relative extremaUsing the candidates test to determine absolute extremaDetermining concavity of functions over their domainsUsing the second derivative test to determine extremaSketching graphs of functions and their derivativesConnecting a function, its first and its second derivativesIntroduction to optimization problemsSolving optimization problemsExploring behaviors of implicit relationsUnit 6—Integration and Accumulation of ChangeExploring accumulations of changeApproximating areas with Reimann sumsReimann sums, summation notation, and definite integral notationThe Fundamental Theorem of Calculus and accumulation functionsInterpreting the behavior of accumulationFunctions involving areaApplying properties of definite integralsThe Fundamental Theorem of Calculus and definite integralsFinding antiderivatives and indefinite integrals: basic rules and notationIntegrating using substitutionIntegrating functions using long division and completing the squareSelecting techniques for antidifferentiationUnit 7—Differential EquationsModeling situations with differential equationsVerifying solutions for differential equationsSketching slope fieldsReasoning using slope fieldsFinding general solutions using separation of variablesFinding particular solutions using initial conditions and separation of variablesExponential models with differential equationsUnit 8—Applications of IntegrationFinding the average value of a function on an intervalConnecting position, velocity, and acceleration of functions using integralsUsing accumulation functions and definite integrals in applied contextsFinding the area between curves expressed as functions of xFinding the area between curves expressed as functions of yFinding the area between curves that intersect at more than two pointsVolumes with cross sections: Squares, rectangles, triangles, and semicirclesVolume with disc method: revolving around the x- or y-axis, or other axesVolume with washer method: revolving around the x- or y-axis, or other axesTechnology RequirementYou will need a handheld graphing calculator every day. TI-Nspires will be used in class. Information regarding borrowing a calculator from the school will be made available as soon as possible. Assignments, notes, and messages will be posted in Canvas for student access. Electronic access to AP Classroom, Khan Academy, and Delta Math will also be necessary.Because we are now a 1-to-1 technology campus, please bring your devise to class each day. If internet access outside the classroom is an issue, please let me know so other arrangements can be made.Tutoring hours: 8:00 – 8:30 and 4:30 – 5:15 Days to be determinedSupplies: Journal for notetaking Notebook paper for assignments Graphing calculator or graphing appTextbook/ResoucesFinney Ross L., Franklin D. Demana, Bert K Waits, and Daniel Kennedy. Calculus: Graphical, Numerical, Algebraic, 3rd ed. Boston: Pearson, 2006NMSI—National Math Science InitiativeKhan AcademyDeltaMathAP ClassroomAP ReviewReview for the AP test is ongoing throughout the year. Past multiple choice and free response problems are regularly used for in class practice. Problems sets centered on particular themes and written in AP style are used for assignments and assessments. Saturday study sessions will be offered in the Spring for additional test preparation. Three to four weeks prior to the AP Calculus AB test date, a variety of activities will be used in class to review for the test, ranging from individual work and presentations, group work and presentations, circuit reviews, flash card practice, and AP style practice assessments. AP Calculus AB test date: Tuesday, May 4, 2021Grading Policy40% Test/major projects60% Daily/Homework—quizzes will count as two homework grades10% Semester examsLate assignments will be accepted 3 days from the assignment due date or at the end of the nine weeks, whichever is sooner. When an assignment is submitted after the due date, a maximum penalty of ten points per day will be deducted from the grade. In the case of extenuating circumstances, it is the parent/guardian and/or student’s responsibility to inform the teacher and/or appropriate administrator so that an exception to the rule may be considered. When absent, it is the student’s responsibility to check Canvas for the missed assignment and will be given one day to make up work for each day they are absent.RetestingStudents will be provided an opportunity to improve test scores through test corrections. Half the deducted points will be returned for each completed correction.Classroom Rules Face-to-FaceOnlineRespect is to be a part of all your personal interactions.Be on time. Excessive tardies will result in disciplinary actions.Give yourself and others a legitimate chance to learn.Students must follow the dress code described in the Student Handbook.If you are absent, YOU are responsible for getting your missing work.Respect others in the class. Be kind, considerate, and MUTE yourself when you are not talking.Be on time. Log on a few minutes BEFORE class.Be prepared. Find a quiet place to work. Check your surroundings. Make sure your computer is charged and your CAMERA is ON, with both your first and last name displayed.Dress appropriately and remain in camera view.Look up when speaking and speak clearly. Avoid side conversations. Stay on topic!Consequences in accordance with the Student Handbook,Verbal/non-verbal warningParent call/conferenceOffice referralAdministrative actionContacting information –-You may contact me via email at bmilam@ (preferred), using Canvas, or by calling the school at 210-945-1100. Feel free to contact me whenever you have questions or concerns about your academic progress. In addition, make sure the school has updated, correct information to contact you via email, if possible. I will send regular updates of what is happening in the classroom (i.e. test dates, upcoming progress reports, etc.). ................
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