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Pre-AP CalculusCourse SyllabusInstructor: Mr. SweigardCourse Overview:The Reynolds School District’s Pre-AP Calculus course prepares students for the AP Calculus and other college-level mathematics courses. The course focuses on the skills students will need to be successful at Calculus. Calculus skills will be introduced at the end of this course.Grading:Your homework, quizzes, notes, AP practice problems, and class participation are 40% of your grade. Tests are 50% of your grade. Citizenship will be 10% of your grade.Grading uses this scale:92-100 = A84-91 = B72-83 = C60-71 = DBelow 60 = FCitizenship:Every student is to be ready to learn: Bring book, pencil, calculator, and notebook to class every day unless told otherwise. Participate in all class activities. The highest standard of conduct and integrity is required at all times. Disruption of instruction cannot be tolerated.Course Topics/Tentative Outline:Review of Algebra and Geometry: (Approximately 10 days)Unit 1: Exponential and Logarithmic Functions (Approximately 10 days)Exponential and Logarithmic Functions and Their GraphsLogarithmic Functions and their GraphsProperties of LogarithmsExponential and Logarithmic Equations and ModelsUnit 2: Trigonometry and Analytic Trigonometry (Approximately 35 Days)Angles and MeasuresRight Triangle TrigonometryTrigonometric Functions of Any AngleGraphs of Trigonometric FunctionsInverse Trigonometric FunctionsUsing Fundamental IdentitiesVerifying Trigonometric IdentitiesSolving Trigonometric EquationsSum and Difference FormulasMultiple-Angle and Product-to-Sum FormulasLaw of Sines and CosinesTrigonometric Form of a Complex NumberUnit 3: Algebra Skills Needed for Calculus (Approximately 40 Days)Piecewise FunctionsAsymptotes of FunctionsZeros of FunctionsComplex FractionsSign ChartsComposition of FunctionsSolving Rational EquationsUnit 4: Limits and Continuity (Approximately 15 Days)What is a Limit?Limits of PolynomialsLimits of Trigonometric FunctionsThe Definition of ContinuityTypes of DiscontinuitiesUnit 5: Definition of the Derivative and Basic Differentiation (Approximately 30 Days)Deriving the FormulaThe Slope of a CurveThe Secant and the TangentDifferentiabilityNotationThe Power RuleHigher Order DerivativesThe Product RuleThe Quotient RuleThe Chain RuleDerivatives of Trig FunctionsUnit 6: Implicit Differentiation and Basic Applications of the Derivative (Approximately 30 Days)How to Do ItSecond DerivativesEquations of Tangent Lines and Normal LinesThe Mean Value Theorem for DerivativesRolle’s Theorem ................
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