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
[email protected] [email protected])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
