自主招生數(shù)學(xué)試題及答案

b2017年自招生數(shù)試題b(值:100分

時(shí)間90鐘一選題本題小題，小分共30分，每題出四選中只有個(gè)項(xiàng)正的1、若對(duì)于任意實(shí)數(shù)a，關(guān)于的程

xaxb

都有實(shí)數(shù)根，則實(shí)數(shù)

的取值范圍是（）Ab≤0B≤

1C≤28

D≤-12、如圖D、E分是△ABC的AB、BC上的點(diǎn)，且DE∥AC已知S=1∶3，則S的值為（）A∶3B．1∶4．1．1∶163、校吳老師組織九(班學(xué)展數(shù)學(xué)活動(dòng)，帶領(lǐng)同學(xué)們測(cè)量學(xué)校附近一電線桿的高(如圖所示電線桿直立于地面上在太陽光的照射下桿影(折線BCD)恰好落在水平地面和斜坡上，在D處測(cè)得電線桿頂端A仰角為30，C處得電線桿頂端A得角為45，斜坡與地成60

角，CD=4m，電線桿的高AB)（）A．(43)m．(44)m．3)m．12m4、如圖，矩形ABCD中AB=8，AD=3點(diǎn)E從D向C每秒個(gè)單的速度運(yùn)動(dòng)，以AE為一邊在AE的右方作正方形AEFG垂直于CD的直線MN也從向D以秒2個(gè)單位的速度運(yùn)動(dòng)，當(dāng)經(jīng)過（）時(shí)，直線MN和正形AEFG開始有公共點(diǎn)。A．

53

B．

12．D．23(第2題)第3題圖第圖5、如圖，在反比例函數(shù)

2x

的圖象上有一動(dòng)點(diǎn)A，連接AO并延交圖象的另一支于點(diǎn)B，在第一象限內(nèi)有一點(diǎn)C，足AC=BC當(dāng)點(diǎn)A運(yùn)動(dòng)，點(diǎn)C始在函數(shù)象上運(yùn)動(dòng)，若tan∠CAB=2，則k的為)A.2B.4C.6D.8

kx

的圖6、如圖，O是邊三角形ABC一點(diǎn)，且，OB=4，OC=5將線段OB繞點(diǎn)B逆時(shí)針旋轉(zhuǎn)60

得到線段O，下列結(jié)論：△AO′B以由△COB點(diǎn)逆時(shí)旋轉(zhuǎn)60

得到；②∠AOB=150；③四邊形

3④S

AOC

。其中正確的是（）A.②③④B.①④C.④①②③

O'O(第5題)第6題圖二填題本題6小，小題，30分）

C7、已知方程組

xyk2xy

，且

y

，則

的取值范圍是。8、一次函數(shù)y

4x與y的圖象之間的距離等于3，則b的是。39、如圖，△ABC中∠ACB=90，BC=6cm，AC=8cm，動(dòng)點(diǎn)P從發(fā)，以2cm/s的速度沿AB移到B，則點(diǎn)P出，△BCP為腰三角形。10、已知關(guān)于的程

2x

解為正數(shù)，則m的取值范圍。11、如圖AC⊥BC于C，與直線ABBC、CA都相切，則O的徑等于。12、如圖，在平面直角坐標(biāo)系中將ABO點(diǎn)B順時(shí)旋轉(zhuǎn)到eq\o\ac(△,A)eq\o\ac(△,)BO的置，使點(diǎn)A的對(duì)應(yīng)點(diǎn)落在線

33

上再eq\o\ac(△,A)eq\o\ac(△,)BO繞A順針旋轉(zhuǎn)到eq\o\ac(△,A)eq\o\ac(△,)的置使點(diǎn)O的對(duì)點(diǎn)O落直線

33

上，依次進(jìn)行下去…，若點(diǎn)A的坐標(biāo)(0,1)點(diǎn)的坐標(biāo)是(

,1)，則點(diǎn)A的坐標(biāo)是。AOB

C(第9題)第11題)第12題)三解題本題3小，分40分）13、(本題共12分如，在△ABC中，，以AB一點(diǎn)O為圓，長半徑的圓與BC相切點(diǎn)D，分別交AC、AB點(diǎn)、F(1)若AC=6，AB=10，求⊙O的徑；

(2)連接OE，若四形是平行四邊形，試判斷四邊形OFDE的形狀，并說明理由。CEDA

F14、(本題共14分(1)已：△ABC是腰三角形，其底邊是BC，D在段上，是直線BC上一，且∠DEC=∠DCE若A=60(圖)，求證EB=AD；(2)若將1)中的“點(diǎn)D在段AB”改為“點(diǎn)在段AB延長線上”，其它條件不變?nèi)纰冢?1)的結(jié)論是否成，并說明理由；(3)若將1)中的“若∠”為“若A=90”，其它條件不變，則的是多少？AD(直接寫出結(jié)論，不要求寫解答)15、(本題共14分在面直角標(biāo)系中，拋物線-x+3(a≠0)交x軸A、B兩點(diǎn)，交y軸于點(diǎn)C，且對(duì)稱軸為直線x=-2(1)求該拋物線的解析式及頂點(diǎn)D的標(biāo)；(2)若點(diǎn)P(0,t)是y軸的一個(gè)點(diǎn)，請(qǐng)進(jìn)行如下探究：探究一：如圖，設(shè)△PAD的面為S令W=t?S，當(dāng)＜t時(shí)，W是有最大值？如果有，求出的最值和此時(shí)t的；如果沒有，說明理由；探究二：如圖，是否存在以P、D為頂?shù)娜切闻ceq\o\ac(△,Rt)AOC相似如果存在，求點(diǎn)P的標(biāo)；如果不存在，請(qǐng)說明由。

2017年自主生學(xué)試題考案一選題本題小題，小分共30分，每題出四選中只有個(gè)項(xiàng)正的12、D3、A、A、D6、B二填題本題6小，小題，30分）7、＜＜18、-4或；、22.5或；10、且≠-4；11、212636。三解題本題3小，分40分）13、解）接OD，設(shè)⊙O的徑為，∵BC切⊙點(diǎn)D，⊥BC∵∠C=90°，∥AC，eq\o\ac(△,∽)eq\o\ac(△,，)ABC∴

，即，得r=，∴⊙O的半徑為；（2）四邊形OFDE是形，∵四邊形BDEF是行四邊形，∠DEF=∠B，∵∠DEF=∠DOB，∴∠B=∠DOB∵∠ODB=90°，∴∠DOB+∠B=90°∴∠DOB=60°，∵DE∥AB，∴∠ODE=60°，∵OD=OE，∴△ODE是邊三角，，∵OD=OF∴DE=OF，∴四邊形OFDE是行四邊形，∵OE=OF∴平行四邊形OFDE是菱。14、(1)證明：作DF∥BC交AC于F，如圖所示則∠ADF=∠ABC，∠ACB，∠FDC=，∵△ABC是腰三角,∠A=60，∴△ABC是邊三角形，∴∠ABC=∠ACB=60∴∠DBE=120,∠ADF==∠A∴△ADF是邊三角,，∴AD=DF∵∠DCE，∴∠FDC=∠DEC，ED=CD，在△和△中由∠DEC=∠FDC∠DBE=∠DFC=120，ED=CD，∴eq\o\ac(△,≌)DBEeq\o\ac(△,，)CFD(AAS)∴EB=DF，∴EB=AD；成；理由如下：作DF∥BC交AC的延線于F，圖2示：同1)得：AD=DF，∠FDC=∠ECD∠FDC=∠DEC，ED=CD，又∵∠DBE=∠DFC=60，∴在△和△中由DEC=∠FDC，∠DBE=∠DFC，∴eq\o\ac(△,≌)DBE，∴EB=AD；

(3)

AD

=2；由如下：作DF∥BC交AC于F，如圖所：同1)得：eq\o\ac(△,，)∴EB=DF∵△ABC是腰直角三角,DF，∴△ADF是腰直角三角形，EB∴DF=AD∴=2，∴=2.ADAD15、解：）拋物線

的對(duì)稱軸為直線

，∴∴

，∴；

，∴

，（2）探究一：當(dāng)∵拋物線交y軸于點(diǎn)C，∴當(dāng)時(shí)，作

時(shí)，W有大值，交x軸A、B兩點(diǎn)，，∴軸于M，則

，

，∵∵

，∴

，，∴探究二：存在，分三種情況：

∴當(dāng)

時(shí)，W有最值，，①當(dāng)

時(shí)，作

軸于E，則

，∴∴∴

，∵∴∴∴

軸，

軸，∴，

，，，此時(shí)

，又因?yàn)?/p>

，∴

，∴

，∴，

∴當(dāng)

時(shí)，存在點(diǎn)P，，此時(shí)P點(diǎn)坐標(biāo)為0，2）；②當(dāng)∴∴

與

時(shí)，則，∴，∵，∴，不相似，此時(shí)點(diǎn)P不在；

，③當(dāng)

時(shí)，以AD為徑作，則

的半徑，心O到軸的距離，∵

，∴

與y軸相離，不存在點(diǎn)P，

，∴綜上所述，只存在一點(diǎn)

使

與

相似。

IndependentRecruitmentEnglishExam90minutesStudent’s

School’sName注：有題案須在題上寫試上效SectionI

UseofLanguage語言用(TotalMarksForofthemtherearechoicesA,C,D.Youthechoiceeachquestioninthesheet.1.Itisnolongera_______thepoorchildreninthisdistrictgothatB.whetherC.D.because2.AsurveyoutondeathofthosewhobyresultsB.whichtheresultsofitD.theofwhich3.Therules,butitactedresponsibly.B.C.D.4.Manywereorganizedclear______remainedtheWorldCenter.B.thatC.whatD.5.trainarriveinNewYorkateighto'clocktonight.planeIwouldliketakefrom______bywouldB.willleftC.leftD.had6.Thecouldhardlyfind_____hisinofthetheory.tobasedonB.tobaseC.whichtobaseD.ontobase7.—Willgotheparty?—OfIwillif______.havinginvitedB.C.IwasD.Iwillinvited8.—Therewerefivepeopleincarbuttheymanagedtotakeme—acomfortablejourney.A.can’tbeB.shouldn’tbeC.mustn’tbeenD.couldn’thavebeen9.—couldwalkedtostation;itwassonear.—Yes.AatA.wasn’tB.hadn’tbeenC.wouldn’tbeD.won’tbe10.—Amanansweredphone.Iitwasherhusband.—husband.Hehasbeenforages.

A.mustn’tbeB.mustn’thavebeenC.couldn’tD.couldn’thavebeen11.It_____quiteafew_____accusedwasinnocentsetwas;sinceB.thatC.willD.12.Thespeakersaidhetalk_____audience.anyB.whichtopicC.whichevertopicD.theit13.Under_____tochildrenB.childrenallowedC.childrenwillallowD.willallow14.Modernandtechnology_____communicationbetweenfarapart.convenientB.itC.madeitforD.itconvenient15.IheardthatyoureallyhadtimeatJohn'sbirthdayparty,didn'tIdidn'tC.youD.will16.Thegreatuseofeducationnotsomuchtoteachyou_____toteachyouartoflearning.B.thatD.but17.matterfrequentlytheofalwaysaofpeople.performingB.performedC.toD.performed18._____theirrealsituations,theygotrelieffromthegovernment.ConsideringB.ConsideredHavingD.considered19._____knowntruth,orshewouldtoldus.B.shouldn'tC.can'tD.20._____ofwaterValleyabutitisbyLackingB.lackC.ofD.21.—Yourperformancewasvery—IcoulddonebetterifI_____morehavehadB.D.will22.—Whatdidyou—IseemedknockatB.toC.tohearD.23.—Iopenthewindow?—Yes,please.Iwishit.

youopenB.yourC.youwillopenD.willopen24.—Iturnon—No.I’drathernot_____tonight.B.toC.D.forwatching25.—Tommustbe—Yes,hemoreinoneIdoahasbeenearnedB.C.D.hasSectionII.ReadingComprehension閱讀理解

(TotalMarkspassagescarefullyandchoicesA,CD.Passage1ThefrighteningriseincrimesofthroughoutthecountryhastoTheybuygunsprotecttheirhomescarrywiththemforpersonaltravelling.ofthetoooftentragedy.AsIfoundinmyreading,ahandguntheAmericanhomeThehomehandgunismorelikelytokillinjurefamilymembersfriendsanyonewhoin,andis90percentofbreaktakewhennoishome,thehandgunfordefenseisverystolen.tosomestatistics,fromcitizens.gunsthenenterthecriminalareinThus,citizenswhogunshelpingtoarmthecriminalclass.aYorkCityofficerrecentlyouttowhoaskedifhebuyahandgunprotecthome,itisthehomeownerwhogettingshotkilled,oftentherobberbysayingsomethinglike“Stop!”or“whatdothinkyoud”Possibly,thethiefturnsandfires.Instreettheuseofhandgunisveryrisky,withthegunandhavingitusedagainsthim.ThehandgunownerseldomgetschancetohisgunthemomentiswiththeInfact,tryingtotokeepsomeoneofftheofquiteabitForthecitizen,usingahandgunisseldomforoninhome,waytofromahandgunwouldbetohaveitalwaysatready,perhapsinhandreadytofireeveryisknocktheThatis

ideaofcivilized26.dopeoplewanttotowanttogunstotheirB.Becausewithgunstheirsport.C.BecausethenumberofcrimesofviolenceisstillD.Becauseintenttootherswithgunsincrimes.27.thannot,thehandgunbringstheownerisB.C.luckD.happiness28.ItcanbeunderstoodfromthehomedomoregoodthanordinaryB.homehandgunsmorethangoodordinaryC.stolenhandgunsusuallyawayinsteadofbeingD.arelongerneededinacivilizedsociety29.Ifacitizenuseahandgunprotectinstreetcrime,hewillbesafesoundB.killtheC.hislifeD.attacker30.TheismainlyhowcriminalsgethandgunsfromthecitizensB.isthegunisnotessentialforC.howthehandgunagainstordinaryD.whynotcivilizedsocietyPassage2RobertofofaNobelin1972.Theyhumanhassides,andhasdifferentworktoleftofbraincontrolslanguagenumber;itanalysesreasons.Therightimagination;itunderstandingofoursenseofItisthesideofbrainwhichartistsaretheyusesidesoftheirbrain.Itwell-knownthatEinstein,agreatart,playing

hisscientificfromhisimaginationratherfromanalysis,reasonandsaidthatwordswerenotinHegotideasbyhisHeusedleftsideoftoandreasonthenhetoexplaininschoolstoleftofouranalysisreasonaregiveninourschoolsdaydreaming.However,weareencouragedhopwhenwehaveperfectlylegs!Thenwhydon’twegivetovisualInallofusneedbothsidesofourWeneeduseourtoofsolutionstoproblemsandenjoyexperiences.AndwetobetobeabletoanalyzeandinordertoonIttruethatsomepeoplefindittosideofbrainratherthebutallofususebothsidesandofusbenefitallpowerswewell-knownphilosopher,thatknowledgebymakingtheunconscious.31.Accordingtocomposermusicbyofhisbrain.therightB.leftsideC.bothsidesD.side32.AlbertEinstein’sexampleusedtosupporttheideathat.allscientificbasedB.peopledonothingbutC.twoofbrainD.goodimaginingwhatmayhappen33.Itimpliedthethatregulareducation.shouldbebecauseitsidesofbrain.B.itveryhavedaydreamsC.claimsthatanalysisareofnoD.failstotherightsideofbrain34.WhatNietzschesaytothehave?wenotconscious.

B.decisions.C.weawareofthingsus.D.35.Theauthor’sattitudetowardusingtwosidesoftheisB.C.notlogicalD.Passage3"Cultureconsistsofallsharedof(Robertson,1981).Thisthingscities,schools,butalsonon-materialascustoms,patterns,toofofaofapeople".isapartofcultureplaysaveryimportantroleinsocialconsiderittheofculturewouldnotbeOnotherlanguageshapedbyItcultureintherepresentationapeople,anditcompriseshistoricalculturalbackgrounds.displayspeople'sapproachtolifeandoflivingWenotgointobetweenlanguageandculture.WhatneedsbeisthattwothatofrequiresoftheSocialtellusthatdifferfromoneanotherthatcultureunique.Asculturesdiverse,languagesarediverse.Itnaturalthatwithdifferenceinculturesdifferencesinlanguages,difficultiesoftenincommunicatingbetweenofisnoteasy.aforeignlanguagethanmerelymasteringpronunciation,grammar,idioms.Italsolearningtonativespeakersofthattheinwhichtheirlanguagereflectscustoms,andbehaviorsoftheirsociety.Itlearningto"languageofthemind".inisfrom36.towhatisNOTpartofnon-materialLegalB.C.Religion.D.Tools.37.ThesecondparagraphistheisbysocialscientistsB.betweenlanguageandcultureC.thecultureonD.hasculture

38.Ifwanttoaforeignwell,mustgraspwords,B.masterasC.knowthewayoflanguageD.thecountry'sfirst39.ThebetweenculturethatB.C.areconnectedwithD.languageofculture40."LanguageofthethethingsthatB.methodaC.themannerinD.culturebyallofPassage4Dannyhisdiplomabelowcablicense.After17ofintheinAmerica,couldn'tveryevenlocate(化器)inhiscar.Dannyanaofwritingpapers,fillingforms.HecanFreudfromaviewpointhecanfromaFreudianviewpoint.Inshort,Dannyanheatoproveofveryusetoisnothingnew.CollegeshavebeenturningunskilledforUntilfivemostofunskilledtookdegreesinsociology,philosophy,science,AmericanmiddleworkinbusinessbutifnotwentwhichisthethingtheyknewanythingOncethere,theytaughtgenerationtheskillstaketeststhecycledown.Teacherstoodays,applicationsdown,aremakingliberal-artsgraduatesarefacedwithachoice:agraduateschoolortaxicab.Dannychosetaxicabbecausetheonlyskillhepossessed.to"RealWorldhasbeenbeatenandat.Buthehasalsopracticalskills:gethisfixed;howtothecompanyoutafewaweek;hiscarburetorhefix

41.Whatdidstudyatcollege?B.Psychology.C.Sociology.D.Philosophy.42.ThereasonwhyDannybeataxicabdriverafterhefromcollegeis________.hetoexperienceinsocietyB.hedidn'thowtorepairataxicab,sowantedtotheskillC.taxidriverscanearnmoremiddleworkersD.hehadotherskillsbutdrivingtohimself43.WhichthefollowingisgraduateswentongraduateschoolsinB.workersC.SeveraldegreeaplaceinAmericanmiddleD.AcollegeinAmericanowadays.44.Whattheword"ticket"inlastparagraphLabeltogivingdetailsofitssize,etc.B.AofC.ofanoffensetrafficD.Apieceofthatgivestheholderacertainof45.Whattheimply?CollegeoutofnowadaysB.It'shardfornewgraduatesfromintofindjobintheU.S.A.C.Thepracticalatall.D.Onefromsocietyfromeducation.SectionIII.

填詞10%)Afterreadingpassagesfillinthepassagesandgrammaticallycorrect.Fortheblankswithagivenword,fillinblankwithproperfo