Photoswithquestions文档格式.docx
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Photoswithquestions文档格式.docx
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ron.lancaster@utoronto.ca
Anglesinapolygon
Photograph1
Location:
Toronto,Ontario
Question1
FindanexampleofeachofthefollowinginPhotograph1
(i)ananglelessthan
.
(ii)ananglemorethan
(iii)arightangle.
(iv)anexteriorangle.
Parallellines
Photograph2
Yellowknife,NWT
Question2
(a)IdentifyatleastfivedifferentsetsofparallellinesinPhotograph2.
(b)Whatmeasurementswouldyoumaketodeterminehowmuchpaintwouldbeneededtopaintthefront,backandtwosidesofthehouse?
(c)Whatmeasurementswouldyoumaketodeterminetheslopeoftheroofofthehouse?
(d)Thedesignofthishouseiscertainlyveryunusual.Doyoulikeit?
Drawadiagramofwhatyouthinkitwouldlooklikeinside.
2-Dshapesand3-Dsolids
Photograph3
RockHill,SouthCarolina
Question3
Identifyatleastsix2-Dshapesand3-DsolidsinPhotograph3.
Integers
Photographs4&
5
Montreal,Quebec
Question4
(a)IfyouareonthefloorshowninPhotograph4andyougodownonefloor,wherewillyoube?
(b)Wouldyouneedtogoupordowntogofromfloor-3tofloor-7?
Question5
Writeastoryaboutbeingintheelevatorrelatedtoeachofthefollowing.
(i)
(ii)
(iii)
(iv)
Photograph4
Photograph5
Powers
Photograph6
SuntecCityshoppingmall,Singapore
Question6
(a)FindanexampleofanexponentinPhotograph6.
(b)Useexponentstorenamethestore.
(c)AnumberofnamesofstoresinNorthAmericacouldberenamedusingexponents.ExamplesthatcometomindareMEXXandmmmuffins.Renamethesestoresusingexponents.Whatotherstorescouldberenamedinasimilarfashion?
Ratios
Photograph7
Provincetown,CapeCod,Massachusetts
Question7
(a)ForeachlocationshownonthesigninPhotograph7,findtheratioofthedistanceinkilometres(Km)tothedistanceinmiles(Mi).Arethethreeratiosthesame?
Shouldtheybethesame?
(b)Supposeafourthlocationis8kilometresfromthesign.Howfaristhisinmiles?
Unitrates
Photograph8
Chicago,Illinois
Question8
(a)Whatisthepriceof1gallonofgas?
(b)Howmanygallonsofgasdidthispersonpurchase?
(c)Whatcalculationwoulddoyoudotocheckthatthepriceisright.Doitandverifythatthe$11iscorrect.
(d)Howmanygallonsofgaswouldapersongetfor$16?
Solvingequations
Photograph9
St.Catharines,Ontario
Question9
(a)NameseveraldifferentpossibleoccupationsforthepersonwhoownsthecarwiththelicenceplateshowninPhotograph9.
(b)Createseveraldifferentequationsusingthevariablexforwhichasolutionis
Relationshipsandequations
Photograph10
NewYork(Manhattan),NewYork
Question10
(a)Letnbethenumberofshotsandletgbethenumberofgramsofespresso(seePhotograph10).Whichisthecorrectequationforgintermsofn?
(b)Letsbethesizeofthecoffee(inounces)andletnbethenumberofshotsaddedtoacoffee.Writeanequationforsintermsofn.
Scatterplots,lineofbestfit,firstdifferences
Photograph11
Question11
LetxandyrepresenttheshoesizesforwomeninCanadaandEuroperespectively(seePhotograph11).
(a)EnterthedatashowninPhotograph11intoaT-table.Findthefirstdifferencesanddecideifthedataappearstobelinear.
(b)Makeascatterplotofyversusx.
(c)Findthelineofbestfitforthedata.UsetheequationofthelineofbestfittopredicttheEuropeanwomen'
sshoesizeforaCanadianwomen'
sshoesizeof12.
Constantrateofchange
Photograph12
Atlanta,Georgia
Question12
Usearulertomeasuretheradius(representedbyr)ofeachoftheeightcirclesthatappearonthegrateshowninPhotograph12.
(a)RecordyourmeasurementsinTable1.Woulditbecorrecttosaythatthisisanexampleofconstantgrowth?
(b)Usetheformula
tocalculatethecircumferenceofeachcircle.Isthisanotherexampleofconstantgrowth?
Table1
radius
circumference
circle1
circle2
circle3
circle4
circle5
circle6
circle7
circle8
DirectVariation
Photograph13
Taipei101,Taipei,Taiwan
Question13
ForaperiodoftimeTaipei101wasthetallestbuildingintheworld.Theelevatorsinthebuilding(seePhotograph13)arethefastestintheworld.
(a)Istherelationshipbetweenthedistancetheelevatorhastraveledup(inmetres)andthetime(measuredinminutes)anexampleofdirectvariation?
(b)Howfarupwouldtheelevatortravelin30seconds?
(c)Theheightofthebuildingatthe90thflooris386metres.Startingfromthegroundfloor,howlongwouldittheelevatortogettothisfloor?
PythagoreanTheorem
Photograph14
PetronasTowers,KualaLumpur,Malaysia
Question14
ThePetronasTowersarethetallesttwintowerbuildingsintheworld.Thebuildingsandthebridge(seePhotograph14)thatconnectsthemwereusedforseveralscenesinthe1999movieEntrapmentstarringSeanConneryandCatherineZeta-Jones.
Thelengthofthebridgeis58.44metresandthelengthofeachofthetwosupportsis51.5metres.UsethePythagoreanTheoremtodeterminehowhighthebridgeisabovethepointwhereeachsupportisattachedtothebuilding.
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