CSMC是什么意思C在线翻译读音例句

TheCENTREforEDUCATION

inMATHEMATICSandCOMPUTING

Canadian

Senior

MathematicsContest

Tuesday,November20,2012

(inNorthAmericaandSouthAmerica)

Wednesday,November21,2012

(outsideofNorthAmericaandSouthAmerica)

Time:2hours

c

2012UniversityofWaterloo

Calculatorsarepermitted,providedtheyarenon-programmableandwithoutgraphic

displays.

Donotopenthisbookletuntilinstructedtodoso.

Therearetwopartstothispaper.

PARTA

rtconsistsofsixquestions,eachworth5marks.

heanswerintheappropriateboxintheanswerbooklet.

Forthesequestions,fullmarkswillbegivenforacorrectanswerwhichisplacedinthebox.

Partmarkswillbeawardedonlyifrelevantworkissho冬至谚语顺口溜 wninthespaceprovidedinthe

ans铺组词语 werbooklet.

PARTB

rtconsistsofthreequestions,eachworth10marks.

edsolutionsmustbewrittenintheappropriatelocationintheanswer

equireextrapagesforyour

finishedsolutions,thesepagesinto

towriteyourname,schoolnameandquestionnumberonany

insertedpages.

reawardedforcompleteness,clarity,ctsolution,

poorlypresented,willnotearnfullmarks.

NOTES:

Thequestionsineachpartarearrangedroughlyinorderofincreasingdifficulty.

TheearlyproblemsinPartBarelikelyeasierthanthelaterproblemsinPartA.

Atthecompletionofthecontest,insertyourstudentinformationforminsideyour

answerbooklet.

Donotdiscusstheproblemsorsolutionsfromthiscontestonlineforthenext48hours.

Thename,grade,schoolandlocation,andscorerangeofsometop-scoringstudentswillbe

publishedontheWebsite,tion,thename,grade,school

andlocation,andscoreofsomestudentsmaybesharedwithothermathematicalorganizations

forotherrecognitionopportunities.

CanadianSeniorMathematicsContest

NOTE:readtheinstructionsonthefrontcoverofthisbooklet.

olutionsintheanswerbookletprovided.

pectedthatallcalculationsandanswerswillbeexpressedas

exactnumberssuchas4,2+

√

7少年游之一寸相思演员表 ,etc.,

atorsarepermitted,providedtheyarenon-programmable

andwithoutgraphicdisplays.

eintendedasaidsonly.

PARTA

ForeachquestioninPartA,fullmarkswillbegivenforacorrectanswerwhichisplacedin

rkswillbeawardedonlyifrelevantworkisshownin廉颇蔺相如列传 thespaceprovided

intheanswerbooklet.

ABCDEFhasAB=8,BC=15,and

EF=5,inetheperimeter

ofABCDEF.

A

B

C

D

E

F

15

8

5

rethreedistinctrealnumbersa,bandcthataresolutionsoftheequation

x3−4x=thevalueoftheproductabc?

3x=320320318+319320319+318321319,determinethevalueofx.

ckiseitherblack

40oftheblackpucksandexactly1

7

ofthegoldpucksarecontainedin

inethetotalnumberofgoldhockeypucks.

iagram,squarePQRShasside

length25,Qislocatedat(0,7),andRison

areisrotatedclockwise

aboutRuntilSliesabo月笼沙夜泊秦淮近酒家 vethex-axisonthe

linewithequationx=ethenew

coordinatesofPafterthisrotation?

x

R

Q

P

S

y

x=39

O

lis2tileswide

oingtouseexactly11blacktilesandexactly15white

inethenumberofdistinctwaysoftilingthehallsothatnotwoblack

tilesareadjacent(thatis,shareanedge).

PARTB

ForeachquestioninPar更添波浪向人间 tB,yoursolutionmustbewellorganizedandcontainwords

ofexplanationorjustifireawardedforcompleteness,

clarity,ctsolution,poorlypresented,willnotearnfull

marks.

diagramshowninthisproblem,thenumberonthe

lineconnectingtwocirclesisthesumofthetwonumbers

pleofacompleteddiagramis

showntotheright.

2

5

9

7

314

(a)Whatisthevalueofx?

4

13

10

x

(b)Withjustification,determine

thevalueofy.

y

y

w

3w

48

(c)Withjustification,determine

thevaluesofp,qandr.

p

q

r

13

18

3

ertheequationx2−2y2=1,whichwelabel1.Therearemanypairsof

positiveintegers(x,y)thatsatisfyequation1.

(a)Determineapairofpositiveintegers(x,y)withx≤5thatsatisfiesequation1.

(b)Determineapairofpositiveintegers(u,v)suchthat

(3+2

√

2)2=u+v

√

2

andshowthat(u,v)satisfiesequation1.

(c)Supposethat(a,b)isapairofpositiveintegersthatsatisfiesequation1.

Supposealsothat(c,d)isapairofpositiveintegerssuchthat

(a+b

√

2)(3+2

√

2)=c+d

√

2

Showthat(c,d)satisfiesequation1.

(d)Determineapairofpositiveintegers(x,y)withy>100thatsatisfiesequation1.

2012CanadianSeniorMathematicsContest(English)

3.(a)Right-angledPQRhas∠PQR=90◦,PQ=6andQR七夕节又称什么 =he

midpointofQRandNisthemidpointofPQ,determinethelengthsofthe

mediansPMandRN.

(b)hatDEFisisosceles.

(c)engthsoftwoofthe

mediansofABCareequaltor,determinethesidelengthsofABC.