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Accelerated Integrated Precalculus May 3, 2010 Dr. Brian Wynne, Math Dept. Chair Mrs. Sharon Bean, Math Teacher

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H. Precalculus vs. AIP FUNCTIONS Characteristics of functions domain, range, symmetry, zeros, asymptotes, boundedness, periodicity, points of discontinuity, intervals over which a function increases/decreases, relative extremaCharacteristics of functions domain, range, symmetry, zeros, asymptotes, boundedness, periodicity, points of discontinuity, intervals over which a function increases/decreases, relative extrema Operations with functions composing two or more functions, finding a functions inverse, defining a function parametricallyOperations with functions composing two or more functions, finding a functions inverse, defining a function parametrically Families of functions polynomial, rational, exponential, logarithmic, trigonometricFamilies of functions polynomial, rational, exponential, logarithmic, trigonometricFUNCTIONS Characteristics of functions domain, range, symmetry, zeros, asymptotes, boundedness, periodicity, points of discontinuity, intervals over which a function increases/decreases, relative extremaCharacteristics of functions domain, range, symmetry, zeros, asymptotes, boundedness, periodicity, points of discontinuity, intervals over which a function increases/decreases, relative extrema Operations with functions composing two or more functions, finding the inverse of rational functionsOperations with functions composing two or more functions, finding the inverse of rational functions Families of functions rational, trigonometricFamilies of functions rational, trigonometric

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H. Precalculus vs. AIP EQUATIONS/INEQUALITIES Solving polynomial equations/inequalities over the field of complex numbersSolving polynomial equations/inequalities over the field of complex numbers Solving rational equations/inequalitiesSolving rational equations/inequalities Solving exponential/logarithmic equations/inequalitiesSolving exponential/logarithmic equations/inequalities Solving trigonometric equationsSolving trigonometric equationsEQUATIONS/INEQUALITIES Solving rational equations/inequalitiesSolving rational equations/inequalities Solving trigonometric equationsSolving trigonometric equations

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H. Precalculus vs. AIP TRIGONOMETRY Converting angles between degree measure and radian measureConverting angles between degree measure and radian measure Sketching angles in standard position and identifying co- terminal and reference anglesSketching angles in standard position and identifying co- terminal and reference angles Defining trigonometric functions as circular functions as well as the ratio of the sides of right trianglesDefining trigonometric functions as circular functions as well as the ratio of the sides of right triangles Evaluates and graphs trigonometric functions as well as inverse trigonometric functionsEvaluates and graphs trigonometric functions as well as inverse trigonometric functions Verifies trigonometric identitiesVerifies trigonometric identities Law of Sines/Law of CosinesLaw of Sines/Law of CosinesTRIGONOMETRY Converting angles between degree measure and radian measureConverting angles between degree measure and radian measure Sketching angles in standard position and identifying co- terminal and reference anglesSketching angles in standard position and identifying co- terminal and reference angles Defining trigonometric functions as circular functions as well as the ratio of the sides of right trianglesDefining trigonometric functions as circular functions as well as the ratio of the sides of right triangles Evaluates and graphs trigonometric functions as well as inverse trigonometric functionsEvaluates and graphs trigonometric functions as well as inverse trigonometric functions Verifies trigonometric identitiesVerifies trigonometric identities Law of Sines/Law of CosinesLaw of Sines/Law of Cosines

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H. Precalculus vs. AIP VECTORS/POLAR COORDINATES Graphing vectors in a plane, performing vector operations, and applying vectors to solve contextual problemsGraphing vectors in a plane, performing vector operations, and applying vectors to solve contextual problems Using DeMoivres Theorem to re-express complex numbers in polar form and perform operationsUsing DeMoivres Theorem to re-express complex numbers in polar form and perform operations Converting between polar and rectangular coordinatesConverting between polar and rectangular coordinates Graphing and analyzing polar equationsGraphing and analyzing polar equations VECTORS/POLAR COORDINATES Graphing vectors in a plane, performing vector operations, and applying vectors to solve contextual problemsGraphing vectors in a plane, performing vector operations, and applying vectors to solve contextual problems Using DeMoivres Theorem to re-express complex numbers in polar form and perform operationsUsing DeMoivres Theorem to re-express complex numbers in polar form and perform operations Converting between polar and rectangular coordinatesConverting between polar and rectangular coordinates Graphing and analyzing polar equationsGraphing and analyzing polar equations

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H. Precalculus vs. AIP DATA ANALYSIS/ PROBABILITY Using combinations, permutations, and the Fundamental Principle of Counting to count eventsUsing combinations, permutations, and the Fundamental Principle of Counting to count events Applying the Binomial Theorem to expand binomial expressionsApplying the Binomial Theorem to expand binomial expressions Defining sample spaces, outcomes, and eventsDefining sample spaces, outcomes, and events Computing the probability of an eventincluding independent, dependent, and conditionalComputing the probability of an eventincluding independent, dependent, and conditional Analyzing data using mean, median, mode, standard deviation, and varianceAnalyzing data using mean, median, mode, standard deviation, and variance DATA ANALYSIS/ PROBABILITY Applying the Central Limit Theorem to calculate confidence intervals for a populationApplying the Central Limit Theorem to calculate confidence intervals for a population Determining the margin or error for a specified level of confidenceDetermining the margin or error for a specified level of confidence Using confidence intervals and margins of error to make inferences from data about a populationUsing confidence intervals and margins of error to make inferences from data about a population

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SEQUENCES/SERIES Determining terms of arithmetic/geometric sequencesDetermining terms of arithmetic/geometric sequences Using sigma notationUsing sigma notation Finding partial sums of arithmetic/geometric seriesFinding partial sums of arithmetic/geometric series Proving the truth of a statement using mathematical inductionProving the truth of a statement using mathematical inductionSEQUENCES/SERIES Determining terms of arithmetic/geometric sequencesDetermining terms of arithmetic/geometric sequences Using sigma notationUsing sigma notation Finding partial sums of arithmetic/geometric seriesFinding partial sums of arithmetic/geometric series Proving the truth of a statement using mathematical inductionProving the truth of a statement using mathematical induction H. Precalculus vs. AIP

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MATRICES Performing operations with matricesPerforming operations with matrices Solving 2 x 2 and 3 x 3 systems of equations using matricesSolving 2 x 2 and 3 x 3 systems of equations using matrices Finding the inverse of a square matrixif it existsFinding the inverse of a square matrixif it exists Using matrices to de- compose a rational expression into partial fractionsUsing matrices to de- compose a rational expression into partial fractionsMATRICES Nothing included in AIP Curriculum

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H. Precalculus vs. AIP CONIC SECTIONS Identifying whether an equation represents a circle, a parabola, an ellipse, or a hyperbolaIdentifying whether an equation represents a circle, a parabola, an ellipse, or a hyperbola Writing an equation for and graphing standard conic sectionsWriting an equation for and graphing standard conic sections CONIC SECTIONS Nothing included in AIP Curriculum

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Student Expectations: 1.Do homework every night – not just before test or at end of semester so you can get credit. 2.Take notes during class. 3.Exhibit good work ethic – no slacking off! 4.Come in for extra help when needed.

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Teacher Expectations: 1.Have optional prerequisite skills packet on- line that can be done this summer 2.Hold before school help sessions 2 days each week (after school sessions will be held when needed) 3.Post calendar for periods of 1 or 2 weeks on- line 4.Hold study sessions in preparation for the new GHSGT

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Assessments: 1.Higher level thinking questions will be included 2.Will have one or more assessments during each chapter 3.Will prepare students to take NEW GHSGT 4.No more PLATO for recovery of low or failing test grades or averages

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Placement for School Year AP Calculus AB or AP Calculus BC and/or AP Statistics or New Discrete Math Placement will be determined by students work ethic and grades. If a student does not exhibit a good work ethic along with good grades, he or she will not be recommended for the AP Calculus BC class.

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Contact Information: Dr. Brian Wynne Sharon Bean

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