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2021美国”大联盟”(MathLvaguel国际It季数学挑战活
动2021MathLeagueInternationalSummerChallenge
Grade5,IndividualQuestions&Solutions
QuestionI:
Sarahisu、ingpopsicleslicksu>buildsonicgridsforhercilyplanningpayed.Sheneeds4
popsiclestickstomakea1by1grid.and12stickstomakea2by2gridasshownbelow.Ilow
manyMicksdocssheneedt>makea10by20grid?
Answer;430
Solution:
Analyzethe2by2grid.TocreateitSarahused3rowsof2stickseachand3columnsof2sticks
each.Similartoit.therewouldbe11rowsandthereshouldbe20sticksineachrow.So.there
are20x11-220sticks(placedhorizontally).
Thereuouldalsobe21columnsandthereshouldbe10sticksineach.Therefore.
thereare21x)0=21()sticksplacedvertically.
Total=220*210=430popsicleslicks
Question2:
Theside、ofthelargerectangleare20mand16m.figurebelow,notdrawnioscale.Allsix
shadedrectanglesareidemical.XMuiistlietotalareaofalltheshadedregions,insquaieineiers?
1
Answer:192
Solulion:
Findthedimensionof(heMnallrectangle.Hielength:16■?2=8m.Theuidth:2(>-X-8=4ni
Thetotalaivaofalltheshadedregions:6x8x4>=192m\
Question3:
Iftwoside?*ofasquarefielducreincreasedbyfivefeet,asseeninthediagrambelow,not
lrauntolheareaoflhefield^ouldincreaseby245squarefeci.Findi))rareaoflhe
originalsquare.
0
Answer:484
Solution:
Theareavftlwshadedsquare1$5*5=25,figurebeluw.Theareaofeachvfthetwo"new"
rectanglesis(245一25)+2=110.Tliustliclengthofthe'new''rectangle,ottlicsidelengthof
theoriginalsquare,is110-?5=22.Sotheareaoflheorigiiulsquareis22*22=4^4.
口
Question4:
Duringpractice,Dana'ssixarrowslandonthetargetshown.Eacharrowisinsideon
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