AP Calculus

AP Calculus 2Month Content Skills AssessmentP.6 Exponential andLogarithmic Functions Develop and use properties of exponentialfunctions.(1 day) Understand the definition of the number e. Understand the definition of the naturallogarithmic function. Develop and use properties of the naturalLimits and Their Properties1.2 Finding Limits Graphicallyand Numerically(3 days)1.3 Evaluating LimitsAnalytically(1 day)1.4 Continuity and One-Sided Limits(2 days)1.5 Infinite Limits(2 days)logarithmic function.Understand that the tangent line problemis basic to calculus.Understand that the area problem is basicto calculus.Estimate a limit using a numerical orgraphical approach.Learn about the different ways that a limitcan fail to exist.Evaluate a limit using the properties oflimits.Evaluate a limit using dividing out andrationalizing techniques.Evaluate a limit using the SqueezeTheorem.Determine continuity at a point andcontinuity on an open interval.Determine one-sided limits and continuityon a closed interval.Use properties of continuity.Understand and use the IntermediateValue Theorem.Determine infinite limits from the left andright.Find and sketch the vertical asymptotes ofthe graph of a function. Teacher-made tests/quizzesconsisting of questions from booktest bank Teacher-made worksheets Questions during class In-class discussions Appropriate homework assignmentwith follow-up discussionsCurriculum Map Revision 2007

AP Calculus 4Month Content Skills Assessment2.5 Implicit Differentiation(2 days) Distinguish between functions written inimplicit form and explicit form. Find the derivative of a function written inimplicit form using the Chain Rule andimplicit differentiation. Find derivatives of functions usinglogarithmic differentiation.2.6 Derivatives of Inverse Find the derivative of an inverse function.Functions(2 days) Differentiate an inverse trigonometricfunction.2.7 Related Rates Find a related rate.(4 days) Use related rates to solve real-lifeproblems.Applications of Understand the definition of extrema of aDifferentiationfunction on an interval. Understand the definition of relative3.1 Extrema on an Interval extrema on an open interval.(1 day) Find extrema on a closed interval.November3.2 Rolle’s Theorem and theMean Value Theorem(1 day)3.3 Increasing andDecreasing Functions andthe First Derivative Test(1 day)3.4 Concavity and theSecond Derivative Test(1 day)Understand and use Rolle’s Theorem andthe Mean Value Theorem.Determine intervals on which a function isincreasing or decreasing.Apply the First Derivative Test to findrelative extrema of a function.Determine the intervals on which afunction is concave up or concave down.Find any points of inflection of the graph ofa function.Apply the Second Derivative Test to findrelative extrema of a function. Teacher-made tests/quizzesconsisting of questions from booktest bank Teacher-made worksheets Questions during class In-class discussions Appropriate homework assignmentwith follow-up discussionsCurriculum Map Revision 2007

AP Calculus 5Month Content Skills Assessment3.5 Limits at Infinity(1 day) Determine finite and infinite limits atinfinity. Determine the horizontal asymptotes, ifany, of the graph of a function.3.6 A Summary of CurveSketching Analyze and sketch the graph of afunction.(2 days)3.7 Optimization Solve applied minimum and maximum(5 days)3.8 Differentials(1 day)problems.Understand the concept of a tangent lineapproximation.Compare the value of the differential, dy,with the actual change in y, Δy.Find the differential of a function usingdifferentiation formulas.Curriculum Map Revision 2007

DecemberAP Calculus 6Month Content Skills AssessmentSlope Fields Draw a slope field from a differential Teacher-made tests/quizzesequation.consisting of questions from book(2 days) Use a slope field to draw the graphs oftest bankseveral solutions to a differential equation. Teacher-made worksheets Given the graph of a function, sketch its Questions during classderivative, and vice-versa. In-class discussions Appropriate homework assignmentwith follow-up discussionsIntegration4.1 Antiderivatives andIndefinite Integration(3 days)4.2 Area(2 days)4.3 Riemann Sums andDefinite Integrals(2 days)4.4 The FundamentalTheorem of Calculus(5 days)Write the general solution of a differentialequation.Use indefinite integral notation forantiderivatives.Use basic integration rules to findantiderivatives.Find a particular solution of a differentialequation.Use sigma notation to write and evaluate asum.Understand the concept of area.Approximate the area of a plane region.Find the area of a plane region usinglimits.Understand the definition of a RiemannSumEvaluate a definite integral using limits.Evaluate a definite integral usingproperties of definite integrals.Evaluate a definite integral using theFundamental Theorem of Calculus.Understand and use the Mean ValueTheorem for integrals.Find the average value of a function over aclosed interval.Understand and use the SecondFundamental Theorem of Calculus. Worksheet packet Teacher-made tests/quizzesconsisting of questions from booktest bank Teacher-made worksheets Questions during class In-class discussions Appropriate homework assignmentwith follow-up discussionsCurriculum Map Revision 2007

AP Calculus 7Month Content Skills Assessment4.5 Integration by Use pattern recognition to evaluate anSubstitutionindefinite integral.(6 days) Use a change of variables to find anindefinite or definite integral. Use the General Power Rule forIntegration to evaluate an indefiniteintegral. Use a change of variables to evaluate adefinite integral. Evaluate a definite integral involving aneven or odd function.MIDTERM EXAM Review of previous skills Midterm ExamJanuaryFebruary4.6 Numerical Integration(1 day)4.7 The Natural LogarithmicFunction(2 days)4.8 Inverse TrigonometricFunctions: Integration(2 days)Differential Equations5.1 Differential Equations:Growth and Decay(1 day)Approximate a definite integral using theTrapezoidal Rule.Approximate a definite integral using theSimpson’s Rule.Use the Log Rule for Integration tointegrate a rational function.Integrate trigonometric functions.Integrate functions whose antiderivativesinvolve inverse trigonometric functions.Use the method of completing the squareto integrate a function.Review the basic integration formulasinvolving elementary functions.Use separation of variables to solve asimple differential equation.Use exponential functions to model growthand decay in applied problems.Curriculum Map Revision 2007

MarchAP Calculus 8Month Content Skills Assessment5.2 Differential Equations:Separation of Variables Use initial conditions to find particularsolutions of differential equations.(3 days) Use a slope field to sketch solutions of adifferential equation. Solve differential equations by separationof variables. Use a differential equation to model andsolve an applied problem.Applications of Integration Find the area of a region between twocurves using integration.6.1 Area of a Region Find the area of a region betweenBetween Two Curvesintersecting curves using integration.(2 days) Describe integration as an accumulationprocess.6.2 Volume: The DiskMethod(6 days)Find the volume of a solid of revolutionusing the disk method.Find the volume of a solid of revolutionusing the washer method.Find the volume of a solid with knowncross sections. Teacher-made tests/quizzesconsisting of questions from booktest bank Teacher-made worksheets Questions during class In-class discussions Appropriate homework assignmentwith follow-up discussionsCurriculum Map Revision 2007

AP Calculus 9Month Content Skills AssessmentReview for AP Exam Students will review using old AP exams Collect and grade practice exams.and a test-preparation review book. Students will become familiar with theformat of the AP Exam.AP Exam Students will take the AP Exam. AP Exam resultsAprilMayJuneIndividual ResearchProjectsStudents will choose a calculus topic notcovered in class, and will prepare an oralpresentation and written report. (Topicsmay include Hyperbolic Functions, ErrorAnalysis, the Shell Method, Arc Length,Surfaces of Revolution, etc.)Presentations of Projects Students will give oral presentations andsubmit their written report.Teacher will monitor students’progress as needed.Students will be assessed based ona rubric evaluating both the oral andwritten components of the project.Curriculum Map Revision 2007