module 3 – geometry and measurement
TRANSCRIPT
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SECTION B – Module 3 – continued
Module 3 – Geometry and measurement
Question 1 (2marks)Agolfballissphericalinshapeandhasaradiusof21.4mm,asshowninthediagrambelow.
r = 21.4 mm
Assumethatthesurfaceofthegolfballissmooth.
a. Whatisthesurfaceareaofthegolfballshown? Roundyouranswertothenearestsquaremillimetre. 1mark
b. Golfballsaresoldinarectangularboxthatcontainsfiveidenticalgolfballs,asshowninthediagrambelow.
r = 21.4 mm
Whatistheminimumlength,inmillimetres,ofthebox? 1mark
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SECTION B – Module 3 – continuedTURN OVER
Question 2 (2marks)SalenapractisesgolfatadrivingrangebyhittinggolfballsfrompointT.ThefirstballthatSalenahitstravelsdirectlynorth,landingatpointA.ThesecondballthatSalenahitstravels50monabearingof030°,landingatpointB.Thediagrambelowshowsthepositionsofthetwoballsaftertheyhavelanded.
A
T
Bnorth
50 m
30°
a. Howfarapart,inmetres,arethetwogolfballs? 1mark
b. Afenceispositionedattheendofthedrivingrange. Thefenceis16.8mhighandis200mfromthepointT.
T200 m
16.8 mfence
WhatistheangleofelevationfromTtothetopofthefence? Roundyouranswertothenearestdegree. 1mark
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SECTION B – Module 3 – continued
Question 3 (2marks)AgolftournamentisplayedinStAndrews,Scotland,atlocation56°N,3°W.
a. AssumethattheradiusofEarthis6400km.
FindtheshortestgreatcircledistancetotheequatorfromStAndrews. Roundyouranswertothenearestkilometre. 1mark
b. ThetournamentbeginsonThursdayat6.32aminStAndrews,Scotland. ManypeopleinMelbournewillwatchthetournamentliveontelevision. AssumethatthetimedifferencebetweenMelbourne(38°S,145°E)andStAndrews(56°N,3°W)is
10hours.
OnwhatdayandatwhattimewillthetournamentbegininMelbourne? 1mark
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SECTION B – Module 3 – continuedTURN OVER
Question 4 (3marks)Duringagameofgolf,Salenahitsaballtwice,fromP to QandthenfromQ to R.Thepathoftheballaftereachhitisshowninthediagrambelow.
P
Q
R130°
50° 54°80 m 100 m
north
AfterSalena’sfirsthit,theballtravelled80monabearingof130°frompointPtopointQ.AfterSalena’ssecondhit,theballtravelled100monabearingof054°frompointQtopointR.
a. AnotherballishitandtravelsdirectlyfromP to R.
Usethecosineruletofindthedistancetravelledbythisball. Roundyouranswertothenearestmetre. 2marks
b. WhatisthebearingofRfromP? Roundyouranswertothenearestdegree. 1mark
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SECTION B – Module 3 – Question 5 – continued
Question 5 (3marks)Agolfcoursehasasprinklersystemthatwatersthegrassintheshapeofasector,asshowninthediagrambelow.
100°S
d
AsprinklerispositionedatpointSandcanturnthroughanangleof100°.Theshadedareaonthediagramshowstheareaofgrassthatiswateredbythesprinkler.
a. If147.5m2ofgrassiswatered,whatisthemaximumdistance,dmetres,thatthewaterreaches fromS?
Roundyouranswertothenearestmetre. 1mark
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End of Module 3 – SECTION B – continuedTURN OVER
b. Anothersprinklercanwateralargerareaofgrass. Thissprinklerwillwaterasectionofgrassasshowninthediagrambelow.
M
N
L
100°
area watered by sprinkler
4.5 m12 m
Thesectionofgrassthatiswateredis4.5mwideatallpoints. Watercanreachamaximumof12mfromthesprinkleratL.
Whatistheareaofgrassthatthissprinklerwillwater? Roundyouranswertothenearestsquaremetre. 2marks
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SECTION B – Module 3 – continued
Module 3 – Geometry and measurement
Question 1 (3marks)MikiisplanningagapyearinJapan.Shewillstoresomeofherbelongingsinasmallstorageboxwhilesheisaway.Thissmallstorageboxisintheshapeofarectangularprism.Thediagrambelowshowsthatthedimensionsofthesmallstorageboxare40cm×19cm×32cm.
lid
19 cm40 cm
32 cm
Thelidofthesmallstorageboxislabelledonthediagramabove.
a. i. Whatisthesurfaceareaofthelid,insquarecentimetres? 1mark
ii. Whatisthetotaloutsidesurfaceareaofthisstoragebox,includingthelidandbase,insquarecentimetres? 1mark
b. Mikihasalargestorageboxthatisalsoarectangularprism. Thelargestorageboxandthesmallstorageboxaresimilarinshape. Thevolumeofthelargestorageboxiseighttimesthevolumeofthesmallstoragebox. Thelengthofthesmallstorageboxis40cm.
Whatisthelengthofthelargestoragebox,incentimetres? 1mark
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SECTION B – Module 3 – continuedTURN OVER
CONTINUES OVER PAGE
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SECTION B – Module 3 – Question 2 – continued
Question 2 (5marks)MikiwilltravelfromMelbourne(38°S,145°E)toTokyo(36°N,140°E)onWednesday,20December.TheflightwillleaveMelbourneat11.20am,andwilltake10hoursand40minutestoreachTokyo.ThetimedifferencebetweenMelbourneandTokyoistwohoursatthattimeofyear.
a. OnwhatdayandatwhattimewillMikiarriveinTokyo? 1mark
MikiwilltravelbytrainfromTokyotoNemuroandshewillstayinahostelwhenshearrives.Thehostelislocated186mnorthand50mwestoftheNemurorailwaystation.
b. i. WhatdistancewillMikihavetowalkifsheweretowalkinastraightlinefromtheNemurorailwaystationtothehostel?
Roundyouranswertothenearestmetre. 1mark
ii. Whatisthethree-figurebearingofthehostelfromtheNemurorailwaystation? Roundyouranswertothenearestdegree. 1mark
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SECTION B – Module 3 – continuedTURN OVER
ThecityofNemuroislocated43°N,145°E.AssumethattheradiusofEarthis6400km.
c. ThesmallcircleofEarthatlatitude43°Nisshowninthediagrambelow.
latitude = 43° N
6400 km equator
WhatistheradiusofthesmallcircleofEarthatlatitude43°N? Roundyouranswertothenearestkilometre. 1mark
d. FindtheshortestgreatcircledistancebetweenMelbourne(38°S,145°E)andNemuro (43°N,145°E).
Roundyouranswertothenearestkilometre. 1mark
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SECTION B – Module 3 – Question 3 – continued
Question 3 (4marks)Thehostelbuildingsarearrangedaroundagrassedarea.Thegrassedareaisshownshadedinthediagrambelow.
θ
65 m
65 m
50 m
Thegrassedareaismadeupofasquareoverlappingacircle.Thesquarehassidelengthsof65m.Thecirclehasaradiusof50m.Anangle,θ,isalsoshownonthediagram.
a. Usethecosineruletoshowthattheangleθ,correcttothenearestdegree,isequalto81°. 1mark
b. Whatistheperimeter,inmetres,oftheentiregrassedarea? Roundyouranswertothenearestmetre. 1mark
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End of Module 3 – SECTION B – continuedTURN OVER
c. Thehostel’smanagementisplanningtobuildapathwayfrompointAtopointB,asshownonthediagrambelow.
65 m
65 mpathway
BA
50 m
θ
Calculatethelength,inmetres,oftheplannedpathway. Roundyouranswertothenearestmetre. 2marks