Math 3 Honors Portfolio ASSIGNMENT IncomingFreshmenMath3Honorsstudents,TheattachedquestionscoverthecontentassociatedwiththetwoStatisticsunitsoftheMath1courseandafewadditionalAlgebratopics.Theyrepresenttheknowledge,skill,andconceptualunderstandingsthatMath3studentswillneedinordertobesuccessful.NotesoutliningthetopicsofthesummerassignmentcanbefoundontheLakesmathdepartmentwebpage,underMathResourcesonthelefthandmargin.Theyshouldbecarefullyreadandreviewedfirst,aswellasusedasaresourcewhilecompletingtheassignmentproblems.Thenotesdocumentisalargefile,sopleasebepatientwithloadtime.http://www.chsd117.org/index.php/lakes/mathThedirecturltothenotesis:http://www.chsd117.org/assets/attachments/l06012015_Math_3_Honors_Portfolio_reduced.pdfPleasecompleteallassignmentproblemstothebestofyourability.Math3HonorsPortfolioAssignmentsareduetoMrs.VikkiEcker,MathDepartmentLeaderatLakesCommunityHighSchoolbyJuly1,2016.Theymaybedroppedoffbetween7:30amand12:00pmatthefrontofficeofthehighschoolsormailed.FeedbackonsummerassignmentpacketswillbeprovidedbyAugust1st,2016.Thankyouforyourhardwork!We’relookingforwardtoanexcellentfouryears!

Mrs.VikkiEcker Mr.ScottLeverentz1600EagleWay 1600EagleWayLakeVilla,IL60046 LakeVilla,IL60046

victoria.ecker@chsd117.org scott.leverentz@chsd117.org847)395-9393 (847)395-9335

Lastupdated:May27,2016

Name:________________________________

CategoricalvsQuantitativeData1. Classifyeachofthefollowingascategoricalorquantitative:

a) typeofcar ________________________________

b) gasprices ________________________________

c) breedofdog ________________________________

d) distancetravelledtoschool ___________________________________

2. Thepiechartbelowdescribesthesurveyresultsshowingthefavoriteflowerofagroupofpeople.

a) Whatistheleastpopularflower?

b) Howmanypeopleweresurveyed?

c) Whatpercentofthepeoplesurveyedchosea

flowerotherthanarose?

3. AtoneparticularVirginiahighschool,themathdepartmentconsistsof20teachers.Their

agesareasfollows:

54586043353247283342

65734427323528254833 a) Constructadotplot:

b) Completethechartandcreateahistogram:4. Thestemplotbelowshowsstudentheartratesafterdoingoneminuteofjumpingjacks.

a) Howmanystudentshadheartratesabove100beatsperminute?

b) Howmanystudents’heartratesweremeasured?c) Whatisthemostcommonheartraterecorded?

QuantitativeData–Center&Spread5. NumberofgamesWayneGretzkyplayedeachseasonofhiscareer: 79,80,80,80,74,80,80,79,64,78,73,78,74,45,81,48,80,82,82,70 Mean:___________________ Median:____________________ Range:__________________ IQR:_______________________ Createaboxplot:

QuantitativeData–Shape&Outliers

Describetheshapeofeachdistributionbelowandcircleanyoutliersontheimages.6. 7.8. 9.10. 11.

ChoosinganAppropriateModel

12. Theweights(inpounds)ofthedefensiveplayersofahighschoolfootballteamaregiveninthetable:

173 145 205 192 197 227 156 240 172 185208 185 190 167 212 228 190 184 195

a) Isthedatasymmetric,skewedright,orskewedleft?Explain.

b) Basedonyouranswerinparta),whatmeasuresofcenterandspreadwouldbeappropriatetoreport?

c) Calculatetheappropriatemeasuresofcenterandspreadforthedata.

13. Matchthescenariowiththedatatable.Explainyourreasoninganddescribetheshapeof

thehistogram.(Youdonotneedtodrawthehistogram,butyoumaywanttographitinyourcalculator!)

a) Dormroomprices($peryear)forasampleof4-yearuniversitiesb) Weeklysalaries($)forasampleofregisterednursesc) Sampleannualsalaries($)ofpublicschoolteachers

46,098 36,259 35,084 38,617 42,690 26,202 47,169 37,109

2445 2940 2399 1960 2421 2940 2657 21531947 2383 2710 2761 2377 2278 2430

774 446 1019 795 908 667 444 960

IntroductiontotheNormalModel

Inanormaldistribution,whatpercentofthevalueslie:14.belowthemean?____________ 15.abovethemean?____________16.withinonestandarddeviationofthemean?____________17.withintwostandarddeviationsofthemean?____________18.withinthreestandarddeviationsofthemean?____________19. 2000freshmenatIllinoisStateUniversitytookabiologytest.Thescoresweredistributed

normallywithameanof70andastandarddeviationof5.FillintheNormalcurveusingtheEmpiricalRule.

a)Whatpercentageofscoresarebetweenscores65and75?

b)Whatpercentageofscoresarebetweenscores60and70?c)Whatpercentageofscoresarebetweenscores60and85?

d)Whatpercentageofscoresislessthanascoreof55?e)Whatpercentageofscoresisgreaterthanascoreof80?

20. TheNormalcurveshowstheheightsof16-yearoldgirls. a)Whatisthemeanheight? b)Whatisthestandarddeviation?

c) Whatvaluesshouldbelabeledat3standarddeviationsfromthemean?

d) Whatpercentageofheightsfallbetween59inchesand71inches?

AnalyzingNormalData

21.HerearethescoresforarecenttestinStatistics.

90 90 95 100 80 80 75 80 7095 100 100 100 75 80 90 90 9070 80 85 90 90 85 60 70

a) Calculate:

Mean=_________ StandardDeviation=_________

b) SketchaNormalcurveusingtheEmpiricalRule.

c) 68%ofthedatafallbetweenwhichtwovalues?

d) Wouldyouconsiderascoreof50%tobeunusual?Explainusingstatisticalconcepts.22.AnautomobiletirebrandhasalifeexpectancythatisNormallydistributed,withameanof30,000milesandastandarddeviationof2500miles.

a) SketchaNormalcurveusingtheEmpiricalRule.

b)Thelifespansoffourtiresselectedatrandomare35,150miles,24,750miles,30,000miles,and33,000miles.DescribethelocationofeachofthesevalueswithrespecttotheNormalcurve.

23.Themileage(inthousands)forarentalcarcompany’sfleetislisted

a) Calculate:Mean=_________ StandardDeviation=_________

b)SketchaNormalcurveusingtheEmpiricalRule.

c)Nameavaluethatwouldbeconsideredunusual.Explainusingstatisticalconcepts.

AmINormal?ReadthefollowingscenariosanddecideiftheywouldbelikelytofollowaNormalmodel.Explainyourreasoning.24. Homeprices($)25. Weightsofinfants(lbs)26. NumberofhoursspentstudyingforyourMath1test27. Numberofcitiesapersonhaslivedin28. HeightsofallfreshmenboysatLakes

6 14 3 7 11 138 5 10 9 12 10

29. Thefollowingdatashowsthemagnitudesofthelast22earthquakesinonecityinCalifornia:

5.2 5.4 5.6 5.6 5.8 5.9 6.0 6.1 6.1 6.1 6.36.3 6.3 6.7 6.7 6.7 6.7 6.9 7.0 7.1 7.2 7.2

a) Drawahistogramtodisplaythedata.

b) IsitreasonabletosaythatthemagnitudeoftheearthquakesisNormallydistributed?Explain.

ONEVARIABLESTATS:SELFEVALUATION(MockTest)

1. Accordingtothepiechart,whichcoloristhemostpopular?

A. BlueB. GreenC. RedD. Yellow

2. Whichofthefollowingisnotanappropriatewaytorepresentcategoricaldata?A. BarchartB. HistogramC. PiechartD. Segmentedbarchart

3. Whichofthefollowingwouldbeclassifiedasquantitative?

A. FavoritefoodB. FavoritestoreC. CarbrandD. Noneoftheabove

4. Aphysicalfitnessassociationisincludingthemileruninitshighschoolfitnesstest.Thetimeforthiseventforhighschoolboysisknowntofollowanormaldistributionwithameanof460secondsandastandarddeviationof50seconds.Betweenwhattimesdoweexpectapproximately95%oftheboystorunthemile?A.between360and560secondsB.between410and510secondsC.between310and610secondsD.between0and800seconds

5. Thefollowinghistogramwouldbedescribedas:

A.NormalB.SymmetricC.SkewedLeftD.SkewedRight

6. Theweightsof14ofMrs.Smith’shomemadecandies,ingrams,areshown.

0.78 1.48 0.78 1.62 0.60 0.74 1.041.48 1.53 0.94 0.78 1.42 1.29 0.76

a) Describetheshapeofthedistribution.(Hint:Youmaywanttographitinyour

calculatorfirst!)

b) Arethereanyoutliers?Ifso,whichone?

c) Whatmeasuresofcenterandspreadwouldbeappropriateforthisdataset?Explain.

d) Calculatethecenterandspreadofthedataset.

7. AtIowaState,GPA’sareroughlysymmetricandunimodalwithameanof2.6andstandarddeviationof0.5.a) SketchandlabelaNormalcurve.

b) WhatpercentofstudentshaveGPA’sbetween2.1and3.1?

c) WhatGPAwouldbeconsideredunusuallylow?Explainusingstatisticalconcepts.

8. Thetestscoresof26studentsarelisted.

a. Constructaboxplot,labelingthe5numbersummary

b. Constructastemplot

Two-WayTablesApublicopinionsurveyexploredtherelationshipbetweenageandsupportforincreasingtheminimumwage.Theresultsarefoundinthefollowingtwo-wayfrequencytable.

For Against NoOpinion TOTAL

Ages21-40 25 20 5 50

Ages41-60 30 30 15 75

Over60 50 20 5 75

TOTAL 105 70 25 2001. Inthe41to60agegroup,whatpercentagesupportsincreasingtheminimumwage?

2. Outofthepeoplethathavenoopinion,whatpercentageisover60yearsold?3. Whatpercentageofpeopleisforincreasingminimumwage?4. Howmanypeopleover60areagainstincreasingtheminimumwage?5. Forages21-60howmanywerenotagainstincreasingtheminimumwage?

6. Whatpercentofpeopleover60areagainstorhavenoopinion?

32 55 57 57 59 63 65 6668 69 70 71 74 74 75 7778 79 81 82 83 86 89 9295 99

Thetablerepresentsasurveyofwhat50peopledidwiththeirleisuretime.7. Convertthefrequencytableintoarelativefrequencytable.8. Whatpercentageofthosesurveyedareinvolvedinleisureactivitiesthatrequirephysical

exercise?9. Whatpercentofthosesurveyeddance?Whatpercentageofmendance?10. Whatpercentofmoviewatchersaremen?11. Whatpercentofmenandwomenplaysportsofthosesurveyed?12. Whatpercentofwomenplaysportsordance? 13. Ofthosethatdanceorplaysports,whatpercentaremen?14. Whatpercentofmenwatchmovies?15. Ifyouwanttoopenanexercisegymwouldyouadvertisemoretomenorwomenorboth

equally?Explainusingstatisticalconcepts.

Dance Sports Movies TOTALWomen 16 6 8 30Men 2 10 8 20TOTAL 18 16 16 50

Dance Sports Movies TOTALWomen 16 6 8 30Men 2 10 8 20TOTAL 18 16 16 50

Dance Sports Movies TOTALWomen 16 6 8 30Men 2 10 8 20TOTAL 18 16 16 50

Dance Sports Movies TOTALWomen 16 6 8 30Men 2 10 8 20TOTAL 18 16 16 50

ScatterPlotsUsethefollowingtabletoanswerquestions16-21.16. Graphlatitudevs.temperature 17. Graphlatitudevs.elevation

18. Describethegraph. 19. Describethegraph.

20.Doyoubelievethereisarelationshipbetweenlatitudeandtemperature?21.Predicttheelevationifthelatitudeis40degrees.

AnalyzingScatterplots22. ThescatterplotshowsthepopulationofCaliforniafrom1997to2002.Whatkindof

correlationdoesthereappeartobe?

Inversecorrelation

Nocorrelation

Negativecorrelation

PositivecorrelationExplain:

23. Whatkindofcorrelationdoesthestatementdescribe?

"Asthenumberofworkersincreases,thenumberofdaysrequiredtocompleteajobdecreases(assumeeachpersonworksatsamerate.)"

Stronglypositivecorrelation

Positivecorrelation

Negativecorrelation

NocorrelationExplain:

24. Pointsthatcannotbeapproximatedbyalinehave

negativecorrelation

positivecorrelation

eitherpositiveornegativecorrelation

nocorrelationExplain:

25. Thedatatableshowstheagesofcoupleswhentheyweremarried.a) Drawascatterplotforhusband’sagevs.wife’sage.Checkthegraphwithyourgraphing

calculator.

b) Describethegraph–besuretocommentondirection,form,andstrength.c) Isthereacorrelationbetweenhusband’sageandwife’sage?Explainusingstatistical

concepts.

BasicsofLinearRegression

26. Thefollowingtableshowswaterdepthvs.temperatureintheAtlanticOcean.

a)Describethedirection,form,andstrength.b)Isalinearmodelappropriate?Explain.c)Calculatethelinearregressionequation.d)Useyourequationtopredictthetemperatureatadepthof175meters.

27. Thefollowingtableshowshomeworkgradesvs.testgradesforaclass.

a)Describethedirection,form,andstrength.b)Isalinearmodelappropriate?Explain.c)Calculatethelinearregressionequation.d)Useyourequationtopredictthetestgradeforapersonwhosehomeworkgradeisa60%.

ImportantAspectsofLinearRegression28. ThedatashowsthepercentoftheadultpopulationoftheU.S.thatgotmarriedbeforethe

ageof25inseveralyears,beginningwith1971.

#ofyearssince1971 0 5 9 13 18 22 26 29Percent 42.4 37.4 37.1 34.1 32.1 28.8 25.7 25.5

a) Drawascatterplot. b) Describethedirection,form,and

strengthofthescatterplot.

c) Calculatethelineofbestfit.

d) Interprettheslopeincontext.

e) Interpretthey-interceptincontext. f) Interpretther2valueincontext. g) Interpretthervalueincontext.h) Isalinearmodelappropriateforthisdata?ExplainusingALLofyourstatistical

knowledge!

TWOVARIABLESTATISTICS:SELFEVALUATION(MockTest)MultipleChoice.Showyourworkandcircleyourfinalanswer.1. Agroupoffriendsrecordedthetimeittooktoride

theirbikesaroundthepark.Thescatterplotshowstheirresultswiththelineofbestfit.Basedonthelineofbestfit,whatistheapproximatetimeitshouldtakethecomplete9laps?

a.4 b.5 c.6 d.72. Whichofthefollowingsituationscouldbedisplayedasascatterplot? a.Thefavoritebreakfastcerealsof10friends. b.Thetimeittakes10studentstoswimamile. c.Theheightandshoesizeof10students d.Thecostoflunchfor10students3. Theregressionequationforthepredictedcostofalargepizzaisgivenby 50.75.1 += xy⌢ ,where𝑦

isthepredictedcostofthepizzaandxisthenumberoftoppings.Whatdoesthesloperepresent? a.numberoftoppings b.costperslice c.costofeachtopping d.costofthepizzawithnotoppings

4. Thetableshowstherelationshipbetweencaloriesandfatgramscontainedinordersoffriedchickenfromvariousrestaurants.Assumingthedatacanbedescribedbyalinearmodel,howmanyfatgramswouldtheequationforthelineofbestfitpredictfora275-calorieorderoffriedchicken?

a.28 b.27 c.25 d.225. Theequation 3495460 += xy⌢ representsthevalueofaworkofart,𝑦,basedonthenumberof

years,x,since1982.(Forexample,x=1represents1yearsince1982-ortheyear1983.)Whatdoesthenumber3,495represent?

a.Thevalueoftheworkofartin1982. b.Thevalueoftheworkofarttoday. c.Theyearlydecreaseinvalueoftheworkofart. d.Theyearlyincreaseinvalueintheworkofart.Matching.6. Thescatterplotsshownhavethecorrelationcoefficientsofr=-0.9,r=-0.6,

r=0.1,andr=0.6.Matcheachscatterplotwiththecorrectrvalue. r=_______ r=______ r=_______ r=______

ShortAnswer.Showyourworkandcircleyourfinalanswer.7. ApublicopinionsurveyofUSteensexploredtherelationshipbetweengenderandfavorite

televisionshow.Theresultsarefoundinthefollowingtwo-wayfrequencytable.

Grey’sAnatomy

DanceMoms

BigBangTheory Other TOTAL

Female 38 42 125 45 250Male 62 8 75 105 250

TOTAL 100 50 200 150 500a.HowmanyUSteensweresurveyed?b.WhatpercentageofUSteenschoseBigBangTheoryastheirfavoriteshow?

c.HowmanyfemaleschoseDanceMomsastheirfavoriteshow?d.Whatpercentageofmaleschose“Other?”

8.Calcollecteddatabymeasuringthepencilsofhisclassmates.Herecordedthelengthofthepaintedpart

ofeachpencilanditsweight.Hisdataisshowninthegraph.a.Describethedirection,form,andstrength.b.WhymightCal’sdatahaveanoutlier?c.Calcameupwith 4.125.0ˆ += xy forhislineofbestfit.Whatdoesthesloperepresentinthiscontext?d.Whatdoesthey-interceptrepresentinthiscontext?e.IfIhaveapencilwith11.5cmofpaint,usetheequationforthelineofbestfittopredicthowmuchitshouldweigh.

9. Thedatashowsthesalesofacompany(inmillions)foreachyeartheyhavebeeninbusiness.NumberofYearsSince2005 0 1 2 3 4Sales 12 19 29 37 45

a) Drawascatterplot. b) Describethedirection,form,and

strengthofthescatterplot.

c) Calculatethelineofbestfit.

d) Interprettheslopeincontext.

e) Interpretthey-interceptincontext. f) Interpretther2valueincontext. g) Interpretthervalueincontext.h) Isalinearmodelappropriateforthisdata?ExplainusingALLofyourstatisticalknowledge!

ComplexNumbersWritetheexpressionasacomplexnumberinstandardfrom

A.) ( ) ( )4 3 2− + +i i B.)5 2i i( )− + C.) ( )( )7 4 1 2− − +i i D.) 5 31 2+−ii

E.) ( ) ( )2 3 3 7− − −i i F.2 3 2 3i i i− + + −( ) ( )Solvetheequations.A.) x2 16= − B.)2 26 102x + = − C.)3 10 262x + = −

FactoringandSolvingbyFactoring IdentifytheGCFandfactoritoutofthepolynomial.

93 +x xx 84 2 − 7714 2 −+ xx Factorthefollowingtrinomials

28122 −− xx 4822 −− xx 10173 2 +− xx

254 2 −x 16249 2 ++ xx 372 2 ++ xx

205 2 −x xx 183 2 − 3312 2 ++ xx Solvethefollowingquadraticequationsbyfactoring

01832 =−+ xx 1063 2 −=− xx 040132 =++ xx

01282 =+− xx 09188 2 =++ xx 11323 2 =+ xx

CompletingtheSquareSolve the quadratic equations using completing the square A.) 0762 =−+ xx B.) 01522 =−+ xx C.) 01062 =++ xx D.) 262 += xx E.)3x2+4x+2=x2+6x F.)x2–8=6xx! = 6x+ 2