Pearcy, Paul
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- MacArthur High School
- AP Calculus
Welcome to On Ramps College Algebra
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Here is the page for AP Calculus students. Students enrolled in AP courses will have the opportunity to earn credit for high school while being exposed to the rigors of a college level course. AP students have the opportunity to earn credit for college by taking and passing the AP exam for the course. AP Calculus requires thourough understanding of several of the major topics that are covered in Algebra classes. However, this course goes deeper into the content than previous classes did and (most significantly) strictly limits the use of a graphing calculator. AB and BC Calculus are very similar in their scope, however, BC covers content (mostly related to Precalculus) that AB students will not be exposed to.
College Board’s Advanced Placement® Program (AP®) enables willing and academically prepared students to pursue college-level studies—with the opportunity to earn college credit, advanced placement, or both—while still in high school. Through AP courses in 38 subjects, each culminating in a challenging exam, students learn to think critically, construct solid arguments, and see many sides of an issue—skills that prepare them for college and beyond. Taking AP courses demonstrates to college admission officers that students have sought the most challenging curriculum available to them, and research indicates that students who score a 3 or higher on an AP Exam typically experience greater academic success in college and are more likely to earn a college degree than non-AP students. Each AP teacher’s syllabus is evaluated and approved by faculty from some of the nation’s leading colleges and universities, and AP Exams are developed and scored by college faculty and experienced AP teachers. Most four-year colleges and universities in the United States grant credit, advanced placement, or both on the basis of successful AP Exam scores—more than 3,300 institutions worldwide annually receive AP scores.Enrolling Students:Equity and Access College Board strongly encourages educators to make equitable access a guiding principle for their AP programs by giving all willing and academically prepared students the opportunity to participate in AP. We encourage the elimination of barriers that restrict access to AP for students from ethnic, racial, and socioeconomic groups that have been traditionally underserved. College Board also believes that all students should have access to academically challenging coursework before they enroll in AP classes, which can prepare them for AP success. It is only through a commitment to equitable preparation and access that true equity and excellence can be achieved.Topics Covered in AP Calculus:Limits & ContinuityInstantaneous Rates of ChangeUnderstanding Limits Graphically & NumericallyProperties of limitsFinding Limits AnalyticallyLimits of Transcendental FunctionsLimits & ContinuityInfinite Limits & Limits at InfinityIntermediate Value TheoremDifferentiation & Basic Derivative RulesRates of Change & Tangent LinesTangent Lines and the DerivativeUnderstanding the DerivativeDifferentiability & ContinuityBasic Derivative RulesThe Product & Quotient RulesVelocity and Other Rates of ChangeDerivatives of Composite, Implicit and Inverse FunctionsThe Chain RuleSymbolic DifferentiationImplicit DifferentiationInverse DerivativesDerivatives of Inverse Trig FunctionsContextual Applications of DerivativesInterpretations of the DerivativeStraight Line MotionOther Rates of ChangeRelated RatesLinear ApproximationsL'Hopital's RuleAnalytical Applications of DifferentiationMean Value TheoremExtrema on an IntervalFirst & Second Derivative TestCurve SketchingOptimizationIntegrationRiemann SumsSummation NotationAccumulation FunctionsProperties of Definite IntegralsAntiderivatives and Indefinite IntegralsFundamental Theorem of CalculusU-SubstitutionIntegration of Transcendental FunctionsIntegration by Parts - BC ONLYPartial Fractions - BC ONLYImproper Integrals - BC ONLYDifferential EquationsSlope FieldsSeparation of VariablesGrowth & DecayEuler's Method - BC ONLYLogistic Growth - BC ONLYApplications of IntegrationAverage Value for IntegralsParticle MotionAccumulation Functions in ContextArea Between CurvesVolumes by Cross SectionVolumes by Disk & Washer MethodVolumes of Curves Around Other AxesArc Length of a Plane Curve - BC ONLYParametrics, Polars & Vectors - ALL BC ONLYParametric EquationsVector Valued FunctionsVelocity & Acceleration of Vector FunctionsPolar Coordinates & GraphsArea & Arc Length in Polar CoordinatesInfinite Series & Sequences - ALL BC ONLYSeries & ConvergenceIntegral Test & P-SeriesComparison of SeriesAlternating SeriesRatio & Root TestsTaylor & Maclaurin PolynomialsLagrange Error BoundPower SeriesTaylor & Maclaurin Series