AMC12B试题及解答Word文档下载推荐.docx
- 文档编号:22721627
- 上传时间:2023-02-05
- 格式:DOCX
- 页数:28
- 大小:118.50KB
AMC12B试题及解答Word文档下载推荐.docx
《AMC12B试题及解答Word文档下载推荐.docx》由会员分享,可在线阅读,更多相关《AMC12B试题及解答Word文档下载推荐.docx(28页珍藏版)》请在冰豆网上搜索。
dragonfly
Sincetheharmonicmeanis
Jtimestheirproductdividedbytheirsum,wegettheequation
2x1x2016
1+2016
whichisthen
4032
(A)2
2017
whichisfinallyclosestto
Problem3
LetX-—2016.WhatisthevalueofIM—力I一I刎—兽?
Firstofall,letspluginallofthe©
sintotheequation.
||-2016|一(-2016)1一|-20161-(-2016)
Thenwesimplifytoget
|2016+20161-20161^2016
whichsimplifiesinto
2016+2016
(D)4032
andfinallyweget
Problem4
Theratioofthemeasuresoftwoacuteanglesis5:
1,andthecomplement
ofoneofthesetwoanglesistwiceaslargeasthecomplementoftheother.Whatisthesumofthedegreemeasuresofthetwoangles?
(A)75(B)90(C)135(D)150(E)270
Wesetupequationstofindeachangle.Thelargeranglewillbe
representedasxandthelargeranglewillwerepresentedas/indegrees.
Thisimpliesthat
4x=5y
and
2x(90—j:
)=90—y
(C)135
sincethelargertheoriginalangle,thesmallerthecomplement.
Wethenfindthat「一.£
and彳—沉丄,andtheirsumis
Problem5
TheWarof1S12startedwithadeclarationofwaronThursday,
June1812.Thepeacetreatytoendthewarwassigned019dayslater,
onDecember24,1814.Onwhatdayoftheweekwasthetreatysigned?
Tofindwhatdayoftheweekitisin919days,wehavetodivide919by7toseetheremainder,andthenaddtheremaindertothecurrentday.Weget
919
that7hasaremainderof2,soweincreasethecurrentdayby2to
(B)SatiLrday
get———I
Problem6
AllthreeverticesofAAJ3Clieontheparaboladefinedby9=T,withAattheoriginandBCparalleltothe工-axis.Theareaofthetriangle
is64.WhatisthelengthofDC?
(A)4(B)6(C)8(D)10(E)16
Albert471
Plottingpoints门and:
onthegraphshowsthattheyareat(—上、止)and■,r”),whichisisosceles.Bysettingupthetrianglearea
Makingx=4,andthelength
(c)s
64=—*2t*rr2=G4formulayouget:
2ofDCissotheansweris
Problem7
Joshwritesthenumbers1’2,3,・•・、99,100.Hemarksout1,skipsthenextnumber
(2),marksout3,andcontinuesskippingandmarkingoutthenextnumbertotheendofthelist.Thenhegoesbacktothestartofhislist,
marksoutthefirstremainingnumber⑵,skipsthenextnumber⑴,marks
out6,skips8,marksout10,andsoontotheend.Joshcontinuesinthis
(D)64
manneruntilonlyonenumberremains.Whatisthatnumber?
(A)13(B)32(C)56(D)64
ByAlbert471
Followingthepattern,youarecrossingout...
(E)96
Time1:
Everynon-multipleof
Time2:
4
Time3:
8
Followingthispattern,youareleftwitheverymultipleofG4whichis
only
Problem8
Athinpieceofwoodofuniformdensityintheshapeofanequilateral
trianglewithsidelength3inchesweighs12ounces.Asecondpieceofthesametypeofwood,withthesamethickness,alsointheshapeofanequilateraltriangle,hassidelengthof5inches.Whichofthefollowingis
closesttotheweight,inounces,ofthesecondpiece?
(A)14,0(B)1G.0(C)20.0(D)33.3(E)55.6
Wecansolvethisproblembyusingsimilartriangles,sincetwoequilateral
trianglesarealwayssimilar.Wecanthenuse
100
;
whichisclosest
Anotherapproachtothisproblem,verysimilartothepreviousonebutperhapsexplainedmorethoroughly,istouseproportions.First,sincethe
thicknessanddensityarethesame,wecansetupaproportionbasedontheprinciplethatV,thusdV=m.
However,sincedensityandthicknessarethesame
25
"
and^4ocb3(recognizingthattheareaofanequilateraltriangleiswecansaythatm<
x涉.
5
Then,byincreasingsbyafactorof3,s2isincreasedbyafactorof
(D)333
TH—12#■—
thus9or
Problem9
Carldecidedtofenceinhisrectangulargarden.Hebought20fenceposts,
placedoneoneachofthefourcorners,andspacedouttherestevenlyalongtheedgesofthegarden,leavingexactly4yardsbetween
neighboringposts.Thelongersideofhisgarden,includingthecorners,hastwiceasmanypostsastheshorterside,includingthecorners.Whatisthearea,insquareyards,ofCarl'
sgarden?
(A)256(B)336(C)384(D)448(E)512
Tostart,usealgebratodeterminethenumberofpostsoneachside.Youhave(thelongsidescountfor2becausetherearetwiceasmany)Gx=20+4(eachcornerisdoublecountedsoyoumustadd4)
Makingtheshorterendhave1,andthelongerend
have8.((8一1)7"
((4-1)木1)=28.12=336.Therefore,the
(B)336
answeris
Problem10
AquadrilateralhasverticesP(a、b),and人一"
),
whereaandbareintegerswithd>
b>
0.TheareaofPQRSis16.What
is«
+b?
Bydistaneeformulawehave'
'
■1'
■'
1'
■1■'
I■?
■■
SImplifyingweget—^)(a+b)=8.ThusU+ftanda—bhavetobea
■-andremainintegersis
factorof8.Theonlywayforthemtobefactorsof
if:
I;
:
and:
丄Sotheansweris
Solutionbyl_Dont_Do_Math
Solution2
Solutionbye_power_pi_times_i
BytheShoelaceTheorem,theareaofthequadrilateralis2ti2—2b'
soa2—b2—8.Sineeaand&
areintegers,u=3andb=1,
a+b=(A)4I
so.
Problem11
Howmanysquareswhosesidesareparalleltotheaxesandwhoseverticeshavecoordinatesthatareintegerslieentirelywithintheregionboundedbytheline站=齐工,theline~_0.1andtheline龙=5.1?
(A)30(B)41(C)45(D)50(E)57
(Note:
diagramisneeded)
Ifwedrawapictureshowingthetriangle,weseethatitwouldbeeasiertocountthesquaresverticallyandnothorizontally.Theupperbound
is1Gsquares(卩=5」木汗),andthelimitforthe工-valueis5squares.First
wecountthe1*1squares.Inthebackrow,thereare12squareswithlength1becausey=4床ugeneratessquaresfrom@,0)to(蠶仆),andcontinuingonwehave9,6,and3for©
valuesfor1,2,and3intheequationV—兀卫.Sothereare12+9+6+3=30squareswithlengthIinthefigure.For_一’squares,eachsquaretakesup_unleftand2unup.Squarescanalsooverlap.For2*2squares,thebackrow
stretchesfrom(N°
〉to('
*'
兀),sothereare8squareswithlength2ina2by0box.Repeatingtheprocess,thenextrowstretchesfrom(2,0)
to(2,2打)
sothereare5squares.Continuingandaddingupin
theend,thereare
&
”■:
乞一、:
:
squareswithlength-inthefigure.
Squareswithlength3inthebackrowstartatandendat(2*277),so
thereare4suchsquaresinthebackrow.Asthefrontrowstarts
at(10andendsat(1"
)thereare
I1squareswithlength■■.As
squareswithlengthJwouldnotfitinthetriangle,theanswer
is;
I丨whichis
D)5()
Problem12
Allthenumbers1,N3,4,5,6,7*&
0arewrittenina3x3arrayofsquares,
onenumberineachsquare,insuchawaythatiftwonumbersare
consecutivethentheyoccupysquaresthatshareanedge.Thenumbersinthefourcornersaddupto18.Whatisthenumberinthecenter?
(A)5(B)6(C)7(D)8(E)9
SolutionbyMlux:
Drawa3x3matrix.Noticethatnoadjacentnumbers
couldbeinthecornerssincetwoconsecutivenumbersmustsharean
edge.Nowfind4nonconsecutivenumbersthataddupto18.
Trying1+3+5+9—18works.Placeeachoddnumberinthecornerin
aclockwiseorder.Thenfillinthespaces.Therehastobea2inbetween
the1and3.Thereisa4between3and5.Thefinalgridshouldsimilartothis.
1,2.3
8,7A
9.6,5
(C)7
isinthemiddle.
Ifwecolorthesquarelikeachessboard,sincethenumbersaltrenatebetweenevenandodd,andtherearefiveoddnumbersandfourevennumbers,theoddnumbersmustbeinthecorners/center,whiletheevennumbersmustbeontheedges.Sincetheoddnumbersaddupto25,andthenumbersinthecornersaddupto18,thenumberinthecentermustbe25-18=7
Problem13
AliceandBoblive10milesapart.OnedayAlicelooksduenorthfromherhouseandseesanairplane.AtthesametimeBoblooksduewestfromhishouseandseesthesameairplane.Theangleofelevationoftheairplaneis30nfromAlice'
spositionand60^fromBob'
sposition.Whichofthefollowingisclosesttotheairplane'
saltitude,inmiles?
(A)3.5(B)4(C)4*5(D)5(E)5.5
Let'
ssetthealtitude=z,distaneefromAlicetoairplane'
sgroundposition(pointrightbelowairplane)二yanddistaneefromBobtoairplane'
sground
position=x
FromAlice'
spointofview,
y.cos30品
cos
tan(0)=-GO=S1D男=亞工二㊁
FromBob'
T.CUSGO.So,VO
'
、'
l■'
=about5.5.
Weknowthat*+/=丄°
°
Solvingtheequation(byplugginginxandy),wegetz=
So,answeris
solutionbysudeepnarala
Non-trigsolutionbye_power_pi_times_i
SetthedistaneefromAlice'
sandBob'
spositiontothepointdirectlybelowtheairplanetobexand甘,respectively.FromthePythagorean
3or.Solvingthe
Theorem,◎?
+『=100.Asbothare30—60—90triangles,thealtitudeoftheairplanecanbeexpressedas
eq
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- AMC12B 试题 解答