Precalculus Planned Course, Mifflin County School District ...

Mifflin County School DistrictPlanned InstructionTitle of Planned Instruction: Precalculus (Honors)Subject Area: Mathematics Grade Level: Grades 11-12Prerequisites: Honors Geometry or GeometryCourse Description:This course continues the development of solving equations and graphingfunctions started in earlier courses. The focus will include polynomial,rational, trigonometric, exponential, logarithmic functions and theirinverses. Some proofs and many situations that require higher orderthinking skills will be employed in this course.Required Time:180 daysMajor Text(s) and Resources: Advanced Mathematical Concepts: Precalculus with Applications,Copyright 1999 by GlencoeNames of District Subject Area Curriculum Writing Committee:Sonya D. Curry,Susan L. Hass,Allen C. Muir,Indian Valley High SchoolIndian Valley High SchoolLewistown High SchoolDate of Board Approval: July 24, 2003

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUSMajor Topics• Systems of equations and inequalities• Nature of graphs• Polynomial and rational functions• Trigonometric functions• Graphs and inverses of trigonometricfunctions• Trigonometric identities and equations• Vectors and parametric equations• Polar coordinates and complex numbers• Exponential and logarithmic functions• Sequences and seriesCourse Objectives and Performance IndicatorsStrand: 2.1Standard: Numbers, Number Systems and Number RelationshipsCourse: PrecalculusCourse Objectives Performance Indicators Assessment Options2.1.11A Use operations. • Add, subtract, multiply,and divide functions.• Find composition offunctions.• Find inverse functions.• Add, subtract, multiply,and find the magnitude ofvectors algebraically.• Find the inner and crossproducts of two vectors.• Add and subtract vectors inthree-dimensional space.• Find the magnitude ofvectors in threedimensionalspace.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse1

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUSStrand: 2.2Standard: Computation and EstimationCourse: Precalculus2.2.11ACourse Objectives Performance Indicators Assessment OptionsDevelop and usecomputation concepts,operations and procedureswith real numbers inproblem-solving situations.• Perform calculationsinvolving polynomial,rational, trigonometric,exponential/logarithmicand any other previouslylearned functions or theirinverses.• Give exact answers toproblems involvingtrigonometric functions ofspecial angles.• Evaluate inversetrigonometric functionswith and without acalculator or by drawing adiagram.• Evaluate expressionsinvolving logarithms withand without a calculator.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse2.2.11BUse estimation to solveproblems for which an exactanswer is not needed.• Estimate answers toproblems that contain anyof the functions studied inthis course withoutreferences (no calculatorsor notes).• Use a calculator to findestimated answers toproblems that involve anyof the functions studied inthis course.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse2

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUS2.2.11CCourse Objectives Performance Indicators Assessment OptionsConstruct and applymathematical models toestimate values of relatedquantities.• Estimate values of relatedquantities by constructing andapplying mathematicalmodels including:a) polynomial functionsb) rational functionsc) trigonometric functionsd) exponential/logarithmicfunctionse) arithmetic/geometric/othersequences or seriesf) other curves of best fit.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse2.2.11DDescribe and explain theamount of error that mayexist in a computationusing estimates.• Identify and explain theamount of error that may existin a computation usingestimates when a real lifeanswer is also known.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse2.2.11ERecognize that the degreeof precision needed incalculating a numberdepends on how theresults will be used andthe instruments used togenerate the measure.• Compare and contrast thesolution(s) of an equationsolved by graphing (hand andgraphing calculator) therelated function and solvedusing other techniques.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse3

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUS2.2.11FCourse Objectives Performance Indicators Assessment OptionsDemonstrate skills forusing scientific andgraphing calculators.• Using a calculator:a) graph the functionsstudied in this courseb) evaluate expressionsinvolving the sixtrigonometric functions(both degree and radianmeasures) and theirinversesc) evaluate expressionsinvolving logarithms andanti logarithmsd) solve problems involvingsequences and seriese) find regression equations(exponential, power, andquadratic)f) solve problems involvingvarious functions.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponseStrand: 2.3Standard: Measurement and EstimationCourse: Precalculus2.3.11ACourse Objectives Performance Indicators Assessment OptionsSelect and use appropriate • Select and use appropriate • Observationunits in measurementunits in all measurement • Evaluate writtensituations.situations.work• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse4

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUS2.4.11CCourse Objectives Performance Indicators Assessment OptionsDetermine the validity ofan argument.• Determine the validity ofan argument (possiblechoices include law ofsines, law of cosines, andtrigonometric identitiesand area of triangles).• Given a proof’s steps andreasons, determine if thesteps and reasons arevalid.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse2.4.11EDemonstrate mathematicalsolutions to problems.• Demonstratemathematical solutions toproblems that involveapplications of thecontent studied in thiscourse.• Solve problems by usinglinear programmingprocedures.• Solve problems involvingsimple harmonic motion.• Solve problems related tothe motion of a projectile,its trajectory, and range.• Solve problems usingvectors and right triangletrigonometry.• Solve linear velocity andangular velocityproblems.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse6

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUSStrand: 2.5Standard: Mathematical Problem Solving and CommunicationCourse: Precalculus2.5.11ACourse Objectives Performance Indicators Assessment OptionsSelect and use appropriate • Select, use, and display all • Observationmathematical concepts and of the mathematical• Evaluate writtentechniques from differentprocedures that areworkareas of mathematics andnecessary to the solution of • Performanceapply them to solving nonroutineand multi-stepachieve the correct answer. • Tests, quizzesa problem situation andassessmentsproblems.• Problem solvingjournal/activity• Evaluate oralresponse2.5.11BUse symbols, mathematicalterminology, standardnotation, mathematicalrules, graphing and othertypes of mathematicalrepresentations tocommunicate observations,predictions, concepts,procedures, generalizations,ideas and results.• Communicate all of themathematical proceduresconcepts, conclusions, etc.necessary to the solution ofa problem situation usingcorrect and appropriatemathematicalrepresentations.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse2.5.11CPresent mathematicalprocedures and resultsclearly, systematically,succinctly and correctly.• Present all of theprocedures important to thesolution of a problem inways that areunderstandable.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse7

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUS2.5.11DCourse Objectives Performance Indicators Assessment OptionsConclude a solution process • Explain how a problem • Observationwith a summary of resultswas solved and why the • Evaluate writtenand evaluate the degree tochosen procedures wereworkwhich the results obtained used.• Performancerepresent an acceptableassessmentsresponse to the initial• Tests, quizzesproblem and why the• Problem solvingreasoning is valid.journal/activity• Evaluate oralresponseStrand: 2.6Standard: Statistics and Data AnalysisCourse: Precalculus2.6.11CCourse Objectives Performance Indicators Assessment OptionsDetermine the regressionequation of best fit (e.g.quadratic, exponential,periodic, and logarithmic).• Determine the regressionequation of best fit for aproblem situation and useit to make predictionsabout the situation.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse2.6.11DMake predictions usinginterpolation, extrapolation,regression and estimationusing technology to verifythem.• Make predictions usinginterpolation,extrapolation, regressionand estimation for any ofthe functions studied inthis course and use agraphing calculator toverify them.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse8

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUS2.6.11ICourse Objectives Performance Indicators Assessment OptionsDescribe the normal curveand use its properties toanswer questions about setsof data that are assumed tobe normally distributed.• Approximate the graph ofa normal curve using aversion of the graph of thenatural number and usethe graph to answerquestions about thesituation.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponseStrand: 2.8Standard: Algebra and FunctionsCourse: Precalculus2.8.11ACourse Objectives Performance Indicators Assessment OptionsAnalyze a given set of datafor the existence of apattern and represent thepattern algebraically andgraphically.• Analyze a given set of datafor the existence of apattern of any of thefunctions studied in thiscourse and represent thepattern algebraically andgraphically.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse2.8.11BGive examples of patternsthat occur in data fromother disciplines.• Give examples of any ofthe functions studied in thiscourse that occur in realworldsituations.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse9

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUS2.8.11CCourse Objectives Performance Indicators Assessment OptionsUse patterns, sequences andseries to solve routine andnon-routine problems.• Use patterns, sequencesand series to solve routineand non-routine problemsinvolving any of thefunctions studied in thiscourse.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse2.8.11DFormulate expressions,equations, inequalities,systems of equations,systems of inequalities andmatrices to model routineand non-routine problemsituations.• Formulate expressions,equations, inequalities,systems of equations,systems of inequalities andmatrices to model routineand non-routine problemsituations.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse2.8.11D1Select and use a strategy tosolve a non-linear equationor inequality, explain thesolution and check thesolution for accuracy.• Solve quadratic equations.• Solve rational equationsand inequalities.• Solve radical equations andinequalities.• Solve trigonometricequations.• Solve exponential orlogarithmic equations.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse10

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUS2.8.11ECourse Objectives Performance Indicators Assessment OptionsUse equations to represent • Use equations to represent • Observationcurves and functions (e.g.curves and functions• Evaluate writtencircles, ellipses, parabolas, studied in this course.workhyperbolas, polynomial• Performancefunctions, rationalassessmentsfunctions, trigonometric• Tests, quizzesfunctions, exponential and• Problem solvinglogarithmic functions).journal/activity• Evaluate oralresponse2.8.11GCreate, analyze and explainsystems of equations,systems of inequalities andmatrices.• Create systems of equations(including non-linearsystems), inequalities, andmatrices.• Find solutions to systems ofequations (including nonlinearsystems),inequalities, and matrices.• Explain how a solution wasfound for a system.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse2.8.11HSelect and use anappropriate strategy to solvesystems of equations andinequalities.• Determine an appropriatestrategy to solve a systemof equations andinequalities and then solvethe system.• Use linear programmingprocedures to solveproblems.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse11

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUS2.8.11JCourse Objectives Performance Indicators Assessment OptionsDemonstrate theconnections betweenalgebraic equations andinequalities and thegeometry of relations in thecoordinate plane.• Given an algebraicequation or inequality,draw the graph on thecoordinate plane.• Determine the algebraicequation or inequality fromits graph on the coordinateplane.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse2.8.11K2.8.11LSelect, justify and apply anappropriate technique tograph a function in twovariables, including slopeintercept,x- and y-intercepts, graphing bytransformations and the useof a graphing calculator.Write the equation of afunction when givenenough information to findits equation.• Select, justify and apply anappropriate technique tograph a function in twovariables, including slopeintercept,x- and y-intercepts, graphing bytransformations and the useof a graphing calculator.Note: All functions studiedin this course should beused.• Write the equation of afunction when givenenough information to findits equation.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse12

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUS2.8.11MCourse Objectives Performance Indicators Assessment OptionsGiven a set of data points, • Given a set of data points, • Observationwrite an equation for a line write an equation for a line • Evaluate writtenof best fit.of best fit.work• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse2.8.11NSolve polynomial, rational,trigonometric, andexponential equations bothsymbolically andgraphically.• Solve polynomial, rational,trigonometric, andexponential equations bothsymbolically andgraphically.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse2.8.11ODetermine the domain andrange of a relation, given agraph or set of ordered pairsand possible asymptotes forthe function.• Determine the domain andrange of all the relationsand functions studied inthis course, given a graphor set of ordered pairs.• Determine horizontal,vertical, and slantasymptotes.• Find possible holes ingraphs of rationalfunctions.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse13

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUS2.8.11Q2.8.11RCourse Objectives Performance Indicators Assessment OptionsRepresent functionalrelationships in tables,charts and graphs.Create and interpretfunctional models.• Represent all functionalrelationships studied in thiscourse in tables, charts andgraphs.• Find inverses for all studiedrelations and graph them.• Determine roots ofpolynomial equations tohelp graph.• Apply the FundamentalTheorem of Algebra to helpgraph.• Use the discriminant todescribe the roots ofquadratic equations.• Create and interpretfunctional models for thevarious functions studied inthis course.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse2.8.11SAnalyze properties andrelationships of functions(e.g., linear, polynomial,rational, trigonometric,exponential, logarithmic)• Use transformations to“parent” functions todetermine properties andrelationships of functions.• Identify graphs of thefollowing:a) simple polynomialfunctionsb) absolute value functionsc) step functionsd) rational functionse) trigonometric functionsf) exponential andlogarithmic functionsg) inverses for relations andfunctions.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse14

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUS2.8.11TCourse Objectives Performance Indicators Assessment OptionsAnalyze and categorizefunctions by theircharacteristics.• Given a graph of a function,identify it using algebraicequations to describe thefunction.• Given an algebraic equationfor a function, determinethe type of function theequation represents.• Identify an odd functionand an even function.• Determine continuity ordiscontinuity of functions.• Identify the end behavior ofgraphs.• Find the factors ofpolynomials using theremainder and factortheorems.• Identify all possible rationalroots of a polynomialequation by using therational root theorem.• Determine the number ofpositive and negative realzeros a polynomial functionhas.• Approximate the real zerosof a polynomial function.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse15

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUSStrand: 2.9Standard: GeometryCourse: Precalculus2.9.11ECourse Objectives Performance Indicators Assessment OptionsSolve problems involvinginscribed andcircumscribed polygons.• Find the apothem of aregular polygon.• Solve problems involvinginscribed andcircumscribed polygons.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse2.9.11FUse the properties ofangles, arcs, chords,tangents and secants tosolve problems involvingcircles.• Use the unit circle todefine a radian.• Find the length of an arc,given the measure of thecentral angle.• Find the area of a sector.• Use the unit circle todefine the sixtrigonometric functions.• Find the area of a circularsegment.• Use circles and theirproperties andcharacteristics to solveproblems.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse16

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUS2.9.11GCourse Objectives Performance Indicators Assessment OptionsSolve problems usinganalytic geometry.• Prove geometric theoremsinvolving parallel andperpendicular linesanalytically.• Solve problems usinganalytic geometry.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse2.9.11HConstruct a geometricfigure and its image usingvarious transformations.• Use the parent graph of afunction to construct thegraph of a new function byapplying knowledge ofvarious transformations.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse2.9.11IModel situationsgeometrically to formulateand solve problems.• Model situationsgeometrically to formulateand solve problems.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse17

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUS2.9.11JCourse Objectives Performance Indicators Assessment OptionsAnalyze figures in terms ofthe kinds of symmetriesthey have.• Identify symmetricalgraphs.• Use symmetry to completea graph.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponseStrand: 2.10Standard: TrigonometryCourse: Precalculus2.10.11A1Course Objectives Performance Indicators Assessment OptionsUse graphing calculators todisplay periodic andcircular functions; describeproperties of the graphs.• Graph periodic andcircular functions.• Determine the amplitude,period, phase shift, andthe vertical shift for allcircular and periodicfunctions.• Graph inverses oftrigonometric functionsusing principal values.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse2.10.11A2Graph periodic and circularfunctions by hand; describeproperties of the graphs.• Graph periodic andcircular functions.• Determine the amplitude,period, phase shift, andthe vertical shift for allcircular and periodicfunctions.• Graph inverses oftrigonometric functionsusing principal values.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse18

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUS2.10.11B2.10.11B1Course Objectives Performance Indicators Assessment OptionsIdentify, create and solvepractical problemsinvolving triangles usingthe trigonometricfunctions, the PythagoreanTheorem and the Law ofSines/Cosines.Analyze, evaluate, andidentify characteristics ofangles with respect totrigonometric concepts.• Identify, create and solvepractical problemsinvolving right trianglesusing the trigonometricfunctions and thePythagorean Theorem.• Determine whether atriangle has zero, one, ortwo solutions.• Identify, create and solvepractical problemsinvolving triangles usingLaw of Sines or Law ofCosines.• Find the area of trianglesusing various formulas.• Find angles that arecoterminal with a givenangle.• Find the reference anglefor a given sum.• Find the values of the sixtrigonometric functionsof an angle in standardposition given a point onits terminal side.• Find numerical values oftrigonometric functions.• Use sum and differenceidentities for sine,cosine, and tangent.• Use the double- and halfangleidentities for thesine, cosine, and tangentfunctions.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse19

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUS2.10.11CCourse Objectives Performance Indicators Assessment OptionsDevelop and applytrigonometric concepts tovectors and parametricequations.• Find equal, opposite, andparallel vectors.• Add and subtract vectorsgeometrically.• Find ordered pairs thatrepresent vectors.• Determine whether twovectors are perpendicular.• Write vector andparametric equations oflines.• Graph parametricequations.• Model the motion of aprojectile usingparametric equations.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse20

Strand: 2.11Standard: Concepts of CalculusCourse: PrecalculusMIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUS2.11.11A2.11.11BCourse Objectives Performance Indicators Assessment OptionsDetermine maximum andminimum values of afunction over a specifiedinterval by usingderivative concepts.Interpret maximum andminimum values inproblem situations.• Determine the derivativeof a polynomial functionusing the limit form.• Find the derivative of apolynomial functionusing the power rule andother properties.• Find the slope and theequation of a line tangentto the graph of a functionat a given point.• Find the critical points ofthe graph of a polynomialfunction and determine ifeach is a minimum,maximum, or point ofinflection.• Use the maximum andminimum values of aperiodic function to helpgraph it.• Solve problem situationsthat involve maximum orminimum valueinterpretations.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse21

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUS2.11.11CCourse Objectives Performance Indicators Assessment OptionsGraph and interpretexponential andlogarithmic functionsincluding rates ofgrowth/decay.• Use properties ofexponents to simplifyexpressions.• Evaluate and simplifyexpressions containingrational exponents.• Evaluate expressionswith irrational exponents.• Graph exponential andlogarithmic functions andinequalities with andwithout a graphingcalculator.• Graph the exponentialfunction that contains thenatural number as a base.• Use the natural logarithmwhen the natural numberis involved in theproblem.• Solve equationsinvolving logarithmswithout the use of acalculator by applyingthe properties oflogarithms.• Find common logarithmsand antilogarithms ofnumbers.• Solve exponential andlogarithmic equationsand inequalities.• Solve equations usingnatural logarithms.• Find answers togrowth/decay problemsituations.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse22

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUS2.11.11DCourse Objectives Performance Indicators Assessment OptionsWork with series andsequence problems whichinclude determining sumsof finite sequences ofnumbers and infinitegeometric series.• Find the nth term andarithmetic means of anarithmetic sequence.• Find the sum of n termsof an arithmetic series.• Find the nth term andgeometric means of ageometric sequence.• Find the sum of n termsof a geometric series.• Find the sum of aninfinite geometric series.• Use sigma notation.• Use the binomialtheorem to expandbinomials.• Evaluate an exponentialfunction with the naturalnumber as the base byusing the exponentialseries.• Use Euler’s formula towrite the exponentialform of a complexnumber.• Evaluate the logarithmsof negative numbers.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse23

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUSStrand: NoneStandard: Polar Coordinates and Complex NumbersCourse: PrecalculusCourse Objectives Performance Indicators Assessment Options12.11A Develop and apply polarcoordinate and complexnumber concepts.• Graph polar coordinatesand simple polarequations.• Graph polar equations.• Convert between polarcoordinates andrectangular coordinates.• Write the polar form of alinear equation.• Graph the polar form of alinear equation.• Add, subtract, multiply,and divide complexnumbers in rectangularform.• Change complexnumbers between polarform and rectangularform.• Find the product andquotient of complexnumbers in polar form.• Find powers and roots ofcomplex numbers inpolar form usingDeMoivre’s theorem.• Observation• Evaluate writtenwork• Performanceassessments• Tests, quizzes• Problem solvingjournal/activity• Evaluate oralresponse24

MIFFLIN COUNTY SCHOOL DISTRICTPRECALCULUSDistrict Recommended Instructional Approach For the CourseTo Drive Teacher’s Instructional Activities• Whole group instruction• Small group instruction• Projects• Class discussion• Peer evaluation• Teacher and peer conferencing• Oral presentations• Individual instruction• Research• Dramatization• Role playing• Independent reading• Read aloud• Directed reading-thinking activities• Modeling process• Games• Self-reflection• Self-evaluation• Independent study• Guest speaker• Guest reading• Writing activities• Thematic units• Notebooks• Study Guides• Computer technology25