北京市西城区抽样测试Sampling test in Beijing Xicheng District in.docx

北京市西城区抽样测试Sampling test in Beijing Xicheng District in.docx

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北京市西城区抽样测试SamplingtestinBeijingXichengDistrictin

北京市西城区2004年抽样测试（SamplingtestinBeijing,XichengDistrictin2004）

SamplingtestinBeijing,XichengDistrictin2004

Mathematicstestpaperforseniorthree（WenKe）

Twothousandandfourpointfive

Theschool_____________________________classname______________

Referenceformula:

Theproductofsumanddifferentiationoftrigonometricfunctions

Theareaofthesideistruncatedconefrustumandformula

Amongthem,Csaidonthebottomsurfaceoftheperimeter,lorofbendinglongbus

Volumeformulaofspheres

Achoice:

thebigquestions,8items,eachitemof5points,atotalof40points.Foreachquestiontherearefouroptions,oneisinlinewiththerequirementsofthesubject.

Thetwolineis（1.）hyperbolicequation

A.B.C.D.

Thesufficientandnecessaryconditionfortheestablishmentof2.inequality（2x-1）（1-|x|）<0is（）

A.x>1,orB.x>1,or

C.D.x<-1,or

3.thefixedpointA（0,1）pointBmovesontheliney=x.WhenthelinesegmentABisatitsminimum,thecoordinatesofthepointBare（）

A.B.

C.D.

4.knownalpha,betarepresentsflat,m,nmeansstraightline.Thefollowingpropositioniscorrect（）

IftheA./alphabeta,m//n.

B.ifanalpha,beta,m,NGroup

IftheC.m//alpha,n//beta,MgroupofN,isanalphabeta

D.mifanalpha,betam//n,nt,thenthealpha/beta

5.theinversefunctionofafunctionis（）

A.,X（1,3）

B.,X（1,3）

C.,X（1,3]

D.,X（1,3]

6.incomplexplane,thecomplexnumberofvectorsis2+i,thecomplexnumbercorrespondingtovectoris-1-3i,andthecomplexnumbercorrespondingtovectoris（）

A.1-2IB.-1+2IC.3+4ID.-3-4i

7.setA={1,2,3,4,5},a,B,A,saidthefocusisontheellipticequationsontheYaxis（a）

A.5,B.10,C.20,D.25

8.ofthepopulationproblemisoneofChina'sbiggestsocialproblems,theestimatednumberofpopulationanddevelopmenttrendisourfoundationtodevelopaseriesofrelatedpolicies.Theannualpopulationstatistics,canChinafollowsfrom1974to1999populationdata:

Particularyear

Onethousandninehundredandseventy-four

Onethousandninehundredandseventy-nine

Onethousandninehundredandeighty-four

Onethousandninehundredandeighty-nine

Onethousandninehundredandninety-four

Onethousandninehundredandninety-nine

Population

Ninepointzeroeight

Ninepointsevenfive

Tenpointthreefive

Elevenpointzeroseven

Elevenpointsevenseven

Twelvepointfivezero

（unit:

100million）

ItcanbeestimatedthatthenumberofpeopleinChinain2004is（）

A.13.02billionB.13.22billion,C.13.42billionD.13.66million

Two,fillinthetitle:

6items,eachitemof5points,atotalof30points.Writetheanswersinthetitleontheline.

9.ifthefunctionisanoddfunction,f（x）=_________.

The10.functionin[0,1]andthemaximumvalueandtheminimumvalueis3,thenthevalueofais_________.

Aminimumof11.functionis__________.

Themidpointofthe12.lineLcircularsectionABisthechord,thenlinearlequationsfor_________________;|AB|=___________.

13.lettheedgesofthecubeoflengtha,withitssixfacesofthecenterfortheverticesofthepolyhedronvolumeis_________.

Asshowninfigure14.,anumberofNrowsncolumnssquare.SymbolislocatedintheIforthejcolumnknownpositive.Eachlineofthenumberofarithmeticprogression,eachcolumnthenumberofgeometricseries,andthecolumnnumberisequaltotheratioofQ..Then,if,q=___________;.

Three,answerquestions:

thistopic6items,atotalof80points.Theanswershouldbetowritethetext,theprooforthecalculationsteps.

15.（12pointsoutofthequestion）

Letx,R,f（x）functionisknown.TheminimumpositiveperiodforPI,and.

（I）findthesumofthesumofomega;

（II）findingthemonotonicallyincreasingintervalofF（x）

16.（14pointsoutofthequestion）

AsshowninFig.three,theEisthemidpointoftheAC

（I）verification:

;

（II）proof:

;

（III）if,forthesizeofthedihedralangle.

17.（12pointsoutofthequestion）

Acommodityinthelast30daysofeachpieceofthesalesprice（yuan）Pandt（daytime）thefunctionsatisfiesapproximately.TheCommoditydailysalesofQ（）andt（timeofday）thefunctionapproximationsatisfiesQ=-t+40（t=1~30）.Themaximumvalueforthegoodsonsaletheamountof,

Andpointoutthatthemaximumamountofdailysalesisthefirst30daysoftheday

18.（14pointsoutofthequestion）

Setthefunctionf（x）=0,

（I）provethatf（x）isanincreasingfunctionon（-）;

（II）solvinginequalityf（x）>1.

19.（14pointsoutofthequestion）

Knownfixed-pointA（-2,-4）,overpointAasatiltangleof45degreeslinearlparabolicparabola（P>o）atB,Ctwopoints,and|AB|,|BC|,|AC|intogeometricseries

（I）parabolicequation;

（II）whetherthereisapointDintheparabolaof（I）,sothat|DB|=|DC|isestablished?

Ifitexists,findthecoordinatesofthepointD;ifnot,explainthereason

20.（14pointsoutofthequestion）

Theknownpositivesequenceand,（0

.

（I）proof:

Yes,whatever;

（II）findingthegeneraltermformulaofaseries;

Third,mathematics（liberalarts）referenceanswersandscoringstandards

Achoice:

thebigquestions,8items,eachitemof5points,atotalof40points.

1.C,2.B,3.C,4.D,5.A,6.D,7.B,8.B

Two,fillinthetitle:

6items,eachitemof5points,atotalof30points.

9.2x+3（5points）10.2（5points）11.-2（5points）

12.（firstempty2points,secondempty3points）

13.（5points）

14.;（firstempty2points,secondempty3points）

Three,answerquestions:

thistopic6items,atotalof80points,theothersolution,pleasecopythistothepoint.

15.（12pointsoutofthequestion）

Solution:

dreamsofF（x）theminimumpositiveperiodforpi*...........................3...

Stardreams

Dreams,star..............................5...

Sorghum..........................................8...

（II）solution:

obtainedby（I）,

Whenl,

Immediately,f（x）monotonicallyincreases

*f（x）monotonicallyincreasingintervalis...........................12...

16.（14pointsoutofthequestion）

（I）thatis:

dreamsarethreeprism,

L

L

DreamsisaregulartriangleDeltaABC,EisthemidpointofAC,

L

So,...............................................................4...

（II）prove:

even

Dreamsisthreeprism,

Risarectangle,Disthemidpoint.

EACisthemidpointofdreams,

L"DE.dreams,

L"plane.....................................................................8...

（III）solution:

forG,evenCG.

Knowfrom（I）plane,

*.....................................................................9...

HenceFGisCGintheplaneoftheprojection.

Accordingtotheoremthree.*,

L/CGFisplanedihedralangle.......................................11...

AB=a,dreams

IntheRtDelta

IntheRtDelta

Indreams,*.

Thesizeofthedihedralangleis45degreesw..................................14...

17.（12pointsoutofthequestion）

Solution:

thedailysalesamountisyyuan,andy=P=Q:

...2points

L

Thatis,......6

When............8

Whenmonotonicallydecreasing,

Rt=25,.............................................10...

Star.

Themaximumamountofthegoodssolddryfor1125yuan,andnearly30daysinthetwenty-fifthdayofthebiggestsales....12...

18.（14pointsoutofthequestion）

（I）prove:

takeit,and,

...3

Dreams,.........5...

Dreams,star.

Thatis,dry.

So,theincreasingfunctionofR......................8...

（II）solution:

[1]solutionofdreams,

*.....................11...

Solutionstoinequalities

（1）areobtained,,

Solutionstoinequalities

（2）areobtained,

0

Hencetheoriginalinequalitysolutionsetfor.......................................14...

[solution2]functionf（x）definitiondomainfor:

...8points

Solvingequationf（x）=1isobtained

（I）byF（x）isanincreasingfunctionofthestarf（x）>1,.

TheoriginalStardreams,inequalitysolutionsetfor......................13...

19.（14pointsoutofthequestion）

（I）solution:

thelinearlequationisy=x-2,andissubstitutedbyit,

Sortout...For.......2

P>0dreams,*.

Set.

*............................4...

|AB||BC|,|AC|dreams,equiratiosequences,

Star.

L,

Organizeas...

Willbereplacedbytheformula,thesolutionp=1.

Hencetheparabolicequation..................................7...

（II）solution:

supposethatthereisapointontheparabolathatmakes|DB|+|DC|,

RememberthelineBCatthemidpointof

Then....10minutes

Whenp=1,theformbecomes

So,.

Acupuncturepointshouldmeet............................12...

Getit

Thereislittleordry（8,-4）,theestablishmentof|DB|=|DC|...........................14...

20.（14pointsoutofthequestion）

（I）proving:

provingbymathematicalinduction:

Whenn=1,thepropositionisestablished;......2

Assumethatwhenn=k,thepropositionisestablished,i.e.,whenn=k+1,

.

Lwhenn=k+1,thepropositionisalsotrue.

Synthesisone,twoknow,pairofHengholdswater......7!

（II）solution:

dreams,

*............................11...

Peryleneseriesistoleranceof1arithmeticprogression,thefirstitemis.

*..................................14...

[Note:

（I）,（II）twoquestions,independentpoints.]

NorthhighschoolschoolIwishyousuccessinthecollegeentranceexamination