Interpreting Scatter Plots · Interpreting Scatter Plots WARM UP Describe the following scatter...

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Distance from the Basket Number of Baskets Age of House House Price ($) MPM1D – Unit 4: Linear RelationshipsLesson 1 Date:___________ Learning goal: how to create and interpret scatter plots. Interpreting Scatter Plots WARM UP Describe the following scatter plots: Tibia Length (cm) Leg Length (cm)

Transcript of Interpreting Scatter Plots · Interpreting Scatter Plots WARM UP Describe the following scatter...

  • Distance from the Basket

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    Age of House

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    MPM1D–Unit4:LinearRelationships–Lesson1 Date:___________Learninggoal:howtocreateandinterpretscatterplots.

    InterpretingScatterPlotsWARMUP

    Describethefollowingscatterplots:

    Tibia Length (cm)

    Leg Length (cm)

  • ScatterPlotReviewAscatterplotisagraphthatshowsthe_________________________between________variables.Thepointsinascatterplotoftenshowapattern,or_____________________________.Example1:Juliegatheredinformationaboutherageandheightfromthemarkingsonthewallinherhouse.

    Age(years) 1 2 3 4 5 6 7

    Height(cm) 70 82 93 98 106 118 135

    a) Labeltheverticalaxis.b) Describetherelationshipbetweenthe

    variables.c) Describethetrendofthedatapoints.

    INDEPENDENTANDDEPENDENTVARIABLES

    Theindependentvariableislocatedonthe___________axis.Theindependentvariableislocated_________________________inthetableofvalues.Thisvariabledoesnotdependontheothervariable

    Independentvariable:______________________________Thedependentvariableislocatedonthe____________axis.Thedependentvariableislocated___________inthetableofvalues.Thisvariabledependsontheothervariable.

    Dependentvariable:___________________________________

  • Example2:Determinetheindependentvariableandthedependentvariableandthencreateascatterplotforeachsituation.a) Outdoorairtemperatureandamountoficecreamsoldatagrocerystore.IndependentVariable:_________________________DependentVariable:__________________________

    b) NumberofstudentscrossingAdlerStreetandthetimeofday.

    c) Thedayofthemonthyouwerebornandthelastdigitofyourphonenumber.

    d) Aperson’sageandtheiraverageyearlyincome.

    Example3:Comparethefollowingtwoscatterplots,thefirstoneiscorrect,thesecondoneisnot.Listtherequirementwhencreatingascatterplot. Justin’sWalk

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  • Example4:Thefollowingtablecomparesthenumberofhoursthatastudentspentstudying,andtheirtestscore.a) Whatdoesonesquarerepresentonthex-axis?b) Whatdoesonesquarerepresentonthey-axis?c) Createascatterplotofthedata:

    d) Whatisthedependentvariable?Howdoyouknow?Whatistheindependentvariable?Howdoyou

    know? e) Circlethepointonthegraphthatdoesnotseemtofollowthetrend.Thisiscalledanoutlier.Givea

    possibleexplanationforthispoint.f) Therearethreepointswithanx-valueof7.Howisthispossible?g) Isiteasiertoseetherelationshipinthetableofvaluesorinthegraph?Explain.h) Describestherelationshipshownbythedata.

    StudyHours TestScore3 805 902 756 807 901 506 152 657 851 407 100

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  • Assignment4.1:InterpretingScatterPlots1. Supposeyouweretosurveyyourclassmatestoseeifthereisarelationshipbetweenmathmarksandthe

    numberofhoursspentwatchingTV.a) Whatcolumnheadingwouldyouuseinatableofvaluesdesignedtoorganizethedatafromyour

    survey?b) Whichvariablewouldyouchooseastheindependentvariable?Explainc) Howwouldyouinterprettheorderedpair(2,65)ifitweretoappearonascatterplotofyourdata?

    2. Thescatterplotshowsthesalesofbottlewatera

    refreshmentboothatthefarmer’smarketfordifferentdaysduringthesummer.

    a) WhatinformationdoespointArepresent?b) WhatinformationdoespointBrepresent?c) Whatdoesthescatterplotshowaboutthe

    relationshipbetweenthevariables?3. Asurveyof200studentsfindsoutthatstudentsneed

    lesssleepastheygetolder.a) Identifytheindependentvariableandthe

    dependentvariable.b) Sketchascatterplotofthissituation.

    4. Considerthegraphshownonright.Whichrelationshipismostlikelytobe

    representedbythisgraph?Explainyourchoice

    a) heightvs.weightb) payvs.numberofhoursworkedc) gasremainingvs.distancetravelledd) volumeofwaterinabucketvs.itsmass

    5. Thetablebelowshowstheheightofsomegrade9boysandtheirfathers.

    a) Identifytheindependentvariableandthedependentvariable.b) Constructascatterplotforthedata.c) Doesthescatterplotsuggestarelationshipbetweenaboy’sheightandhisfather’sheight?Explain.

  • MPM1D–Unit4:LinearRelationships–Lesson2 Date:___________Learninggoal:howtodrawalineofbestfit,interpolate,andextrapolate.

    LinesofBestFitandMakingPredictionsWARMUPThegraphbelowrepresentstherelationshipbetweenearningsandtimeworked.

    a) Whichpointrepresentsthepersonwhoworkedtheleastamountofhours?

    b) Whichpointrepresentsthepersonwhoearnedthemostamountofmoney?

    c) Whichpointrepresentsthepersonwhohasthehighestrateofpay?

    a)Howmanyhourswheredrivenwhen40passengerswereaboardthebus?b)Howmanypassengerswereaboardthebusafter10hourswheredriven?c)Howmanypassengerswereaboardthebusafter6hourswheredriven?Isthisanswertorealistic?Whyorwhynot?

    d)Canyoudeterminehowmanypassengerswereaboardthebusafter26hourswheredriven?Whyorwhynot?

  • MAKINGPREDICTIONSFROMDATAAskateboarderstartsfromvariouspointsalongasteeprampandpracticescoastingtothebottom.Thistableliststheskateboarder’sinitialheightabovethebottomoftherampandhisspeedatthebottomoftheramp.

    a)Identifytheindependentvariableandthedependentvariable.Explainyourreasoning.

    b)Makeascatterplotofthedata.

  • c)Describetherelationshipbetweenthevariables.

    d)Identifyanyoutliers.Whatmightcauseanoutlierinthedata?

    e)Drawastraightlinethatpassesclosetothedatapoints.

    Howmanydatapointslieonyourline?

    Aboveyourline?

    Belowyourline?

    f)Compareyourlinewithtwootherstudents’lines.Areallthreelinesthesame?Whyorwhynot?g)Usingthelinethatyoudrew;predictthespeedoftheskateboarderataninitialheightof1m.h)Willtherestofthestudentsgetthesameanswertoquestiong)asyoudo?Explain.LINEOFBESTFIT

    Thelineofbestfitofascatterplotisthelinethatisdrawnonthegraphsothatthedistancefromthelinetoallofthepointsisminimized.Tobeabletomakepredictions,weneedtomodelthedatawithalineofbestfit.

    SuccessCriteriaforDrawingaLineofBestFit1. Thelinemustfollowthe_____________________.2. Thelineshould__________throughasmanypointsaspossible.3. Thereshouldbe__________________________________ofpointsaboveandbelowtheline.4. Thelineshouldpassthroughpointsallalongtheline,notjustattheends.5.Thelinemustbedrawnwitha_________________________.

  • Example1:Drawalineofbestfitforthescatterplotbelow.

    InterpolateWhenyouinterpolate,youaremakingaprediction__________thedata.Thesepredictionsareusuallyfairly_________.ExtrapolateWhenyouextrapolate,youaremakingaprediction_____________thedata.Itoftenrequiresyouto____________theline.Thesepredictionsareless______________.MAKINGPREDICTIONSUseyourlineofbestfittoestimatethefollowing:

    Question Answer MethodofPrediction

    Astudent’smarkiftheystudiedfor4hours.

    Astudent’smarkiftheydidnotstudy.

    Howlongastudentstudiedforiftheyreceived60outof100.

    Howlongastudentstudiedforiftheyreceived100outof100.

    Linesofbestfitareusefulwhenwewanttopredictwhatweexpecttohappen.

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    Thinkaboutit:Doyouincludeanoutlierpointinyouconsiderationwhencreatingalineofbestfit?Recall:Wealwaysidentifyanyoutliersbycirclingthepointonthescatterplot.

    Youareinterpolatingwhenthevalueyouarefindingissomewherebetweenthefirstpointandthelastpoint.

    Youareextrapolatingwhenthevalueyouarefindingisbeforethefirstpointorafterthelastpoint.Thismeansyoumayneedtoextendtheline.

  • Example2:Maliarecordsthenumberoficecreamconesshesellseachdayandthemaximumdailytemperature,asshownonthegraph.Accordingtothisgraph,approximatelyhowmanyicecreamconeswillMaliasellonadaywhenthemaximumtemperatureis36°?Justifyyouranswer.Example3:Dechenhasacandy-makingbusiness.Thegraphshowsthetotalnumberofcandieshisbusinesshasproducedbytheendofeachdayforthefirstfourdays.Ifthistrendcontinues,whichofthefollowingpointsrepresentsadaywithmorecandiesproducedthanexpected?

    a) (5,500)b) (9,850)c) (10,1300)d) (14,1400)

  • Example4:Plotthedataonthescatterplotbelow,choosingappropriatescalesandlabels.

    Note:Thesymbol_______isusedtosignala“break”intheaxiswhenthescaledoesnotstartatzerotoavoid

    alargeemptyspaceinonecornerofthegraph.a) Drawalineofbestfit.Describethetrendinthedata.b) Predicttheearningsofa29yearold.Whichmethodofpredictiondidyouuse?c) Predicttheearningsofan80yearold.Whichmethodofpredictiondidyouuse?Isthisaccurate?d)Explainwhythedataforagesover65donotfollowthetrendinthedata.

    Age Earnings($)

    25 22000

    30 26500

    35 29500

    37 29000

    38 30000

    40 32000

    41 35000

    45 36000

    55 41000

    60 41000

    62 42500

    65 43000

    70 37000

    75 37500

  • Assignment4.2:LinesofBestFitandMakingPredictions1. Studythescatterplotbelow,thenanswerthefollowingquestions.

    a) Ifyouwereasked,whatwastheherringpopulationwhen4fishermenfished?”Whatwouldbeyouranswer?

    b) Butwhatifyouwereasked,“Whatwastheherringpopulationwhen12fishermenfished?”What

    wouldbeyouranswer?

    c) Couldyougiveananswerifasked,“Whatwastheherringpopulationwhen7fishermenfished?”Ifso,whatwouldbeyouranswer?

    d) DrawtheLineofBestFittorepresentthecorrelationofthedatainthegraphabove.

    e) NowuseyourLineofBestFittotheherringpopulationwith...

    i)4fishermen ii)12fishermen iii)7fishermen iv)18fishermen v)Nofishermen

    f) Statewhichtypeofpredictionyouusedinquestione).

    g) Howdotheherringpopulationpredictionswith4fishermen,7fishermenand12fishermendifferfromthepredictionswith18and0fishermen?

  • 2. Defineinterpolation.3. Defineextrapolation.4. GraphthedataanddrawtheLineofBestFit.Describetherelationships.

    Forgrapha)

    i. Determinetheheightat6years.Isitinterpolationorextrapolation?ii. ii)Determinetheageforaperson75cm.Isitinterpolationorextrapolation?

    Forgraphb)

    i. Determinethespeedat45min.Isitinterpolationorextrapolation?ii. Determinethetimeat80km/h.Isitinterpolationorextrapolation?

    Forgraphc)

    i. Determinethemarkifapersonstudiedfor6hours.Isitinterpolationorextrapolation?ii. Determinenumberofhoursrequiredtoobtain95%.Isitinterpolationorextrapolation?

  • MPM1D–Unit4:LinearRelationships–Lesson3 Date:___________Learninggoal:howtoidentifypositivevs.negativecorrelationandthestrengthofcorrelation.

    CorrelationofDataWARMUPStudythegraphbelow

    a)Whatistheindependentvariable?b)Whatdoesthesymbolonthex-axisrepresent?

    c)DescribewhatthepointWrepresents?d)Whichpointrepresentsagirlwhoseshoesizeissmallerthanexpectedforagirlofherheight?d)DescribewhattheYrepresents.

    Iseachlineofbestfitagoodmodelforthedata?Whyorwhynot?a) b)c)

  • Whatiscorrelation?TYPESOFCORRELATION

    Ascatterplotshowsa____________correlationwhenthepatternrisesuptotheright.Thismeansthatthetwoquantitiesincreasetogether.

    Ascatterplotshowsa____________correlationwhenthepatternfallsdowntotheright.Thismeansthatasonequantityincreasestheotherdecreases.

    Ascatterplotshows_____________correlationwhennopatternappears.Hint:Ifthepointsareroughlyenclosedbyacircle,thenthereisnocorrelation.

    STRONGvs.WEAK• Ifthepointsnearlyformaline,thenthecorrelationis

    ___________________.

    • Ifthepointsaredispersedmorewidely,butstillformaroughline,

    thenthecorrelationis_______________________.

    Example1:Writetwokeywordstodescribeeachrelation,thendrawalineofbestfit.

    Hint:Tovisualizethis,enclosetheplottedpointsinanoval.Iftheovalisthin,thenthecorrelationisstrong.Iftheovalisfat,thenthecorrelationisweak.

  • LINEARORNON-LINEAR

    Ifthepointsformarelativelystraightlineonascatterplot,wesaythatthereisa_______________

    relationship.

    A_________________________ofbestfitcanbeusedtomodelalinearrelationship.

    Ifthepointsdonotformarelativelystraightlineonascatterplot,butatrendisstillevident,wesaythatthere

    isa_______________relationship.

    Example2:Writetwokeywordstodescribeeachrelation,thendrawalineorcurveofbestfit.

    Example2:Wouldyouexpectapositivecorrelation,anegativecorrelation,ornoassociationbetweenthetwodatasets?Wherepossible,identifytheindependentanddependentvariable,thensketchascatterplotthatdescribestherelationship.

    a)Theamountoffreetimeyouhaveandthenumberofclassesyoutakeb)Thesalesofsnowshovelsandtheamountofsnowfallc)Lengthofababyatbirthandthemonthinwhichthebabywasbornd)Amountofgasremaininginacaranddistancetravelledbythatcar.e)Markonatestandhairlength

  • Example3:Thelocalicecreamshopkeepstrackofhowmuchicecreamtheysellversusthetemperatureonthatday,herearetheirfiguresfor12days.

    a) Identifythe: IndependentVariable- DependentVariable-

    b) Createascatterplotofthedata.

    c) IsthisrelationshipLinearorNon–linear?Explain!

    d) Describethecorrelation.

    e) Ifthetemperatureis20°C,howmuchsalesfromicecreamdidtheshopget?Isthisanexampleofinterpolationorextrapolation?Explainhowyouknow.

    f) Iftheicecreamshopmade$350insales,whatisthetemperature?Isthisanexampleofinterpolationorextrapolation?Explainhowyouknow.

    IceCreamSalesvsTemperature

    Temperature°C

    IceCreamSales

    14.2° $215

    16.4° $325

    11.9° $185

    15.2° $332

    18.5° $406

    22.1° $522

    19.4° $412

    25.1° $614

    23.4° $544

    18.1° $421

    22.6° $445

    17.2° $408

  • Assignment4.3:CorrelationofData1. ThemanagerofaPetroCanadaservicestationinCollingwoodandBrampton,Ontariochangesthepriceof

    unleadedgasolineandrecordstheamountofgassoldperhourateachprice.Theresultsareshowninthetablebelow:

    CollingwoodPrice(c/L) 100.2 98.4 96.3 94.5 95 95.9 99.2 102.3Amountsold(L/h) 293 242 264 272 292 289 271 241BramptonPrice(c/L) 100.2 98.4 96.3 94.5 95 95.9 99.2 102.3Amountsold(L/h) 202 227 250 286 278 272 212 183

    a)Foreachtown,i.Makeascatterplotofthedata.Drawalineofbestfitifpossible.ii.Describethetrendandcorrelationinthedata.iii.Doesthepriceofgasaffecthowmuchispurchased?

    b)HowdoestheBramptondatacomparetotheCollingwooddata?Givereasonsforthedifferences.

    2. Wouldyouexpectapositivecorrelation,anegativecorrelation,ornoassociationbetweenthetwodata

    sets?Wherepossible,identifytheindependentanddependentvariable.a) Kilometersdrivenonthehighwayversustheamountofgasleftinthetank.b) Temperatureoutsideversusthenumberofpeopleatthebeach.c) Timespentreadingversusthenumberofpagesleftinthebook.d) Timespentexercisingversusweight.e) Bodytemperatureversusthelengthofhair.f) Ageversusheight.g) Ageversusthenumberofteethinyourmouth.

    3. Bacteriacangrowveryquickly;hereisatabletoshowhowfastthiscanhappen.

    time(inmins) 1 3 5 7 9 11#ofbacteria 5 25 125 250 425 700

    a) IdentifytheindependentVariableanddependentvariable.b) Createascatterplotofthedata.c) IsthisrelationshipLinearorNon–linear?Explain!d) Describethecorrelation.e) Howmanybacteriaarethereafter10minutes?Whattechniquedidyouuse?f) Howlongdoesittakefortheretobe500bacteria?Whattechniquedidyouuse?

  • MPM1D–Unit4:Relationships–Lesson4 Date:___________Learninggoal:howtointerpretandcreatedistancetimegraphs.

    DistanceTimeGraphs

    WARMUP

    1. Studentstarts1mawayfromtheCBRandwalksawayataconstantspeed(slowly).

    2. Studentstarts3mawayfromtheCBRandwalkstowardsataconstantspeed(slowly).

    REFLECT

    a)Howarethegraphsdifferent?Howaretheyalike?

    b)Howdoesthestartingpositionshowuponthegraph?

  • 3. Studentstarts5mawayfromtheCBRandthenwalksveryquicklytowardsit.

    REFLECT

    a)Howisthespeedofthewalkershownonthegraph?

    b)Howdowecalculateaperson’sspeed? 4. StudentincreasesspeedwhilewalkingtowardstheCBR™.

  • 5. StudentdecreasesspeedwhilewalkingawayfromtheCBR™.

    6. Studentwalksawayfromranger,at2metresstopsfor5seconds,thenreturnsatthesamepace.

    a)Whathappensonthegraphifapersonisnotmoving?

    b)Doesitmatterwhichdirectionthepersonisfacing?

    c)Whatletterofthealphabetcouldyoucreateonadistancetimegraph?Howdoyouknow?

  • Distancevs.TimeGraphsSummary

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  • Example:Describeeachofthefollowinggraphs:Besuretomentiondirection,distance,time,andspeed.Graph 1stsection 2ndsection 3rdsection

  • Assignment4.4:DistanceTimeGraphs1.JulieandOsawereexperimentingwithaCBRandmadethesegraphs.Describetheirmotionsusingwordslikeaway,towards,stopped.Youmayalsoincludewordslikefastandslowifapplicable.

    2.ThefollowinggraphrepresentstherelationshipbetweenKenny’sdistancefromhomeonabikerideandtime.Describethe3segmentsofKenny’sride.

    Segment Distance Time Direction Speed

    a

    b

    c

    3.Jenleftherhouseanddrovetoschoolinthemorning,asshownintheaccompanyinggraph.Explainwhatishappeningduringeachpartofthegraphbelow

  • 4.ThegraphshowsJorge’sdistancefromhomeashewalkstoschool.Describehiswalkbyfillingintheblanksbelow:

    a) FromAtoB,Jorgewalks______________(towards/away)fromhome.Jorgeiswalkingfor____________min.Hewalks_________m.

    b) FromBtoC,Jorgeisstillwalking

    _____________(towards/away)fromhome.ThesegmentfromBtoCis____________(less/more)steepthanthatfromAtoB.So,Jorge’saveragespeedhasdecreasedandheiswalkingslower.Hewalksfor_______minandtravels_____________m.

    c) FromCtoD,thesegmentishorizontal.
Thismeansthat

    timeispassing,butJorge’sdistance
fromhomestaysthesame.Jorgeis_________________for2min.

    d) FromDtoE,JorgecontinueshiswalktoschoolataboutthesameaveragespeedasfromBtoC.
He

    walksfor_________minandtravels_________m.

    e) IttakesJorge_________mintowalk________mtoschool.5.ThegraphshowsOlivia’sdistancefromhomeasshewalkstothestoreandback.Completethetablebelowbasedonherwalk.

    Section Distance Time Direction Speed

    A-B

    B-C

    C-D

    D-E

    E-F

  • 6.ThefollowingdescribesIvan’sdrivefromWindsortoToronto:

    a)HowmanytimesdidIvanstop? b)Whichstopwasthelongest? c)DuringwhatsectionwasIvantravellingthefastest?Explain howyouknow.

    7.ThreestudentsmadethegraphsbelowusingtheCBRmotionsensor,analyzethegraphsandthenanswer

    thequestions.Student#1 Student#2 Student#3a) Whichstudentneverstopped?Explainhowyouknow.

    b) Whichstudentwalkedtowards,thenstopped?Explainhowyouknow.

    c) Whichstudentreturnedtotheirstartingposition?Explainhowyouknow.

  • 8.Describethemotionofthestudentthatcreatedthisdistancetimegraph.Giveasmuchinformationaspossibleforeachsectionofthegraph.

  • MPM1D–Unit4:Relationships–Lesson5 Date:___________Learninggoal:howtointerpretandanalyzegraphs.

    InterpretingGraphs

    WARMUP

    1)WhatishappeningbetweenpointsAandB?2)WhatishappeningbetweenpointsBandC?3)WhatishappeningbetweenpointsCandD?4)WhatishappeningbetweenpointsDandE?5)WhatishappeningbetweenpointsEandF?6)Tellastorythatdescribeswhatishappeninginthegraph.

  • InterpretingGraphsExample1:Supposetapwater,flowingfromafaucetataconstantrateisusedtofilleachofthesecontainers.Matcheachofthefollowinggraphswiththeappropriatecontainer.Justifyyourchoice.

    Example2:AdrianandJosephdecidedtoraceoneanother.Thegraphshowstheirmotionduringtherace.

    a) Overwhatdistancewastheracerun?Whowon?

    b) Whogotaheadstart?Howmanysecondswastheheadstart?

    c) Whoranfasterduringtherace?

    d) ForhowmanysecondshadAdrianbeenrunningwhenhewasovertakenbyJoseph?

    e) HowfarfromthestartdidJosephovertakeAdrian?

  • Example3:Chrisrunseachdayaspartofhisdailyexercise.Thegraphshowshisdistancefromhomeasherunshisroute.a)WhichsegmentisChristravellingthefastest/slowest? b)Theformulatocalculatespeedisc)Calculatehisrateofchange(speed)foreachsegmentofthegraph.Example4:Thegraphrepresentthedistancebetweenasquirrelandatree,d,inmetres,asafunctionoftime,t,inseconds.Calculatethespeedofeachsectionofthegraph.Showyourwork

  • Assignment4.5:InterpretingGraphs1. Ianandhisfriendsweresittingonadeckandeatingsunflowerseeds.Eachpersonhadabowlwiththe

    sameamountofseeds.Thegraphsbelowallshowtheamountofsunflowerseedsremainingintheperson’sbowloveraperiodoftime.Writesentencesthatdescribewhatmayhavehappenedforeachperson.a) b) c) d)

    2. Indicatewhichgraphmatchesthestatement.Givereasonsforyouranswer.

    a)Abicyclevalve’sdistancefromthegroundasaboyridesataconstantspeed.

    a) b) c) d)

    b)Achildswingsonaswing,asaparentwatchesfromthefrontoftheswing.

    3. Liquidispouredatasteadyrateintothebottle

    showninthediagram.Asthebottleisfilled,theheight,h,oftheliquidinthebottlechanges.Which ofthefivegraphsbelowshowsthischange?Giveareasonforyourchoice.

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    Graph A

    Graph C

    Graph B

    Graph D

    Graph E

  • 4. 11o’clock,Micha’smothersendshimtothecornerstoreformilkandtellshimtobebackin30minutes.Examinethegraph.

    a)Whyaresomelinesegmentsonthegraphsteeperthan

    others?b)Calculatetherateofchange(speed)ofeachoftheline

    segments:c) Overwhatinterval(s)oftimeisMichatravellingthe

    fastest?Comparesteepness,notdirection.d) Overwhatinterval(s)oftimeisMichatravellingthe

    slowest?Comparesteepness,notdirection.e) HowlongdidittakeMichatoreachthestore?Howdoyou

    know?f) HowlongdidMichastayatthestore?g) HowlongdidittakeMichatogethomefromthestore?h) HowcanyouusethegraphtotellwhichdirectionMichais

    travelling?i) DidMichamakeithomein30minutes?Howdoyou

    know?5. Thetortoiseandtheharerunaraceagainsteachother.Thedistancetimegraphfortheirraceisshown

    below.ThemotionofthetortoiseisshownbythelineAB.ThemotionofthehareisshownbythelineCDEF.

    a) Overwhatdistancewastheracerun?b) Whatisthespeedofthetortoise?c) Howmanysecondsofaheadstartdidthetortoisehaveoverthehare?d) DescribewhattheharewasdoingbetweenthepointsCandD,DandE,EandF.e) WhatisthespeedoftheharebetweenthepointsCandD,DandE,EandFf) Howlonghasthetortoisebeenmovingwhenitwasovertakenbythefare?g) Whowontheraceandwhy?

  • 6. TheinformationshowninagraphdoesnothavetorepresentdistancefromaCBR.Foreachofthefollowing,choosethedescriptionthatmostcloselymatchesthegraph.

    (a) (i)Theelevatorstartsonthesecondfloor,goesto

    thefifthfloorwhereittakesonpassengersandthengoestotheseventhfloor.

    (b)

    (ii)Sarahtakeshalfanhourtogetdressedinthemorning,hurriestoherfriend’shousesotheycanwalktothebusstoptocatchthebustowork.

    (c) (iii)Astheweathercoolsintheautumn,salesatMatt’sicecreamshophavebeendecreasing.Duringonerainyweekonlytheregularswhoworkinthesamebuildingpurchasedtheirusualsnacks.WhenMattintroducesanewproduct,salesbegintoimprove.

    (d) (iv)Daniel’scompanyassetsdecreaseduringthemonthswhenheispreparinghisnewstorebutimprovedramaticallywhenthestoreopens.Whenacompetitoropensanearbystore,Daniel’sfortunestakeadownturn.

    (e) (v)Sandyhasbeensavingaregularamounteachweek.Whenshejoinsherfamilyonavacationshespendspartofhersavingsbutresumeshersavinghabitwhenshereturns.

    (f)

    (vi)Jeff’sstrengthtrainingprogramcallsforhimtoaddtimetohisworkoutgradually.AfterafewweeksJeffdecidestosuddenlyincreasethetimeheisspendingbutfindshecanmaintainbutnotincreasethenewlevelforseveralweeks.Thenheisabletograduallyincreasetheworkouttimeagain.