succulents 多肉植物图片介绍英文学习资料

succulents多肉植物图片介绍英文新概念英语2册动词词组及固定搭配练习题(全)新概念英语2册动词词组及固定搭配练习题(全)

/.新概念英语2册动词词组及固定搭配练习题(全)动词词组1Hedidnotknowhowtofight,butheknockedtheboxer_______.(L6)2Thisflowerpotisbroken,Whoknockedit__________?3Iknocked_____earlyyesterdayandwenttoafootballmatch.4Heusuallyknocks_______at6o'clock,buttodayhe'sworkinglate.5Listen!Someoneisknocking________thewindow!6Manyathleteshaveentered________theOlympicGamesthisyear.(L8)7Jansenset________anewworldrecordforthe400metres.(L12)8CaptainAlisonwillset_________ateighto'clock.9TomandIset_____earlyinthemorning.10Willthepersonwhotookmyrulerpleasegiveit_________tome?(L18)11Whenmychildrengrewup,Igavealltheirtoys________.12I'vegiven_______allmyoldfurniture.13Whendowehavetogive______ourcompositions?14Wewerelosingthebattlebutwedidnotgive_____.15Igave______smokinglastyearbutIhavejuststartedagain.16Mrs.Bowerstoldherchildrentoputtheirtoys_______andgotobed.(L27)17Youcanstayheretonight.Wecanputyou______inthespareroom.18I'mnotreadyyet.Ihaven'tputmyshoes_______.19'Openyourexercisebooksandput_____thefollowing,'theteachersaid.20Fatherisputting_____thefirehelitinthegarden.21Whentheyhaveput______thatnewbuilding,itwillspoiltheview.22Ihaveput_____mytriptoJapanuntilnextmonth.23Iamgettingadivorce.Ican'tput______himanylonger.24Icalled_____youfivetimesyesterday.Wereyouout?(L34)25It'stoolatetogotothepictures.Whydon'twecallthewholething______?26Wecalled_______tohimbuthecouldnothearus.271called______thepostofficeonmywaytowork.28Weshallbeholdingapartytomorrow.Iamlooking________itverymuch.(L37)29Look_____!Younearlyknockedthatjugover!30Theysayheisveryfamous.Ishalllookhim____in'Who'sWho'.31MyfriendIngridlivesinStockholm.Whydon'tyoulookher_____whenyou'rethere?32Examinationswillbeheldnextweek.I'mnotlooking_____them.33Havetheyput_____thatforestfire?(L48)34Haven'tyoulearnthowtolook______awordinthedictionary?35Itriedtocallher____butherphonewasoutoforder.36Pick_____allthosetoysandputthem_____.37Ifyoucan'tfindaroomatthehotel,Icanputyou_____.38Look____!Thatbusnearlyhityou!39I'IIpay_____themoneyIborrowedassoonasIcan.40Ican'tput_______thosechildrenanylonger.41He'ssofaraheadofyou,you'llnevercatch_______him.42Weshallhavetodraw______anewplan.(L64)43WhenIrecognizedwhohewasIdrew_______inhorror.44Thecardrew_______outsidethecinema.45Theteacheracceptedtheboy'sapologyandlethim______.(L65)46Hewasgoingtolendmeapoliceman'suniformsothatIcoulddress____fortheparty,butheletme________.47Abigcardrew____outsideourhouse.(L72)48Youcan'trelyonhim.Heissuretoletyou_____.49Don'tletthechildren____ofthegarden.50Weshallhavetodraw_____anewagreement.51Hewasgoingtopunishtheboy,buthelethim______.52Hehasnevergot_____hiswife'sdeath.(L74)53Howdidthethiefmanagetoget____thehouse?54Didyouget_____yourdrivingtest?55Thelidisstuck.Ican'tgetit______.56Hegets______verywell_____allhisnewcolleagues.57Pleasestoptalkingandget_____yourwork,'shesaid.58Ithinkhekept_____________themeetingonpurpose.(L78)59Keep______thefloor.Ihavejustfinishedscrubbingit.60Hehasjustbegunadiary.Iwonderhowlonghewillkeepit______.61Hekept_____makingthesamemistake.62WekeepTim_____oftheroombecauseBettyhasmeasles.63Mostpeoplespendtheirlivestryingtokeep___________theirneighbours.64Threechildrenwerekept______afterschoolforbeingnoisyinclass.65Whowilltake_whenthepresentdirectorleaves?(L79)66Assoonashegotintothelifthetookhishat____.67Youshouldn'tbetaken_____bystorieslikethat.68Lastyearhetook____Russian;nowhe'staking____Chinese.69Noneofmychildrentakes____me.70Thenewrocketwilltake_____fromCapeCanaveral.71'Pleasetake_____thisletterforme,Pamela,'themanagersaid.72Hetakespeople______sowellheoughttogoonthestage.73Whatalotofdirtyplates!Whoisgoingtowash______?(L82)74Don'twearthathat.Peoplewilllaugh_____you.75Thebridgewaswashed_____bytheriver.76Iran_____anoldfriendofmineinarestaurantyesterday.(L88)77Whiledrivingtoworkyesterday,Iran_____petrolandhadtowalktoagarage.78Thiscarwillhavetobeservicedassoonasithasbeenrun______.79She'sbeentakentohospital.Shewasrun_____byacar.80Iran____him,butIcouldnotcatchhim.81Ilostmylecturenotesandhadtomake____anewset.(L91)82lcan'tmake____whatyou'vewritten.83Whenitgotdarkwemade_____home.84Mydaughteroftenmakes_____storiesofherown.85Howcanyoumake____allthoselessonsyoumissed?答案：1-5outoveroff（下班）offat6-10forupoutoffback11-15awayawayininup16-20awayupondownout21-25upoffupwithonoff26-30out,at,forwardto,out,up31-35up,forwardto,out，up，up36-40up…away，up，out，back，upwith41-45upwith,up,back,upoff46-50up…down,up,down,out,up51-55off,over,into,through,off56-60on…with,onwith,awayfrom,off,up61-65on,out,upwith,in,over66-70off,in,up…up,after,off71-75down,off,up,at,away76-80into,outof,in,over,after81-85out,out,for,up,upfor固定搭配1Iwithdrewalotofmoney_______thebankyesterday.(L22)2Irefusetocomment_________hiswork.3Thewaiter'stipisincluded__________thebill.4Hecongratulatedme______havinggotengaged.5Thiswarmcoatwillprotectyou________thecold.6Didanythingemerge______yourdiscussion?7Idreamt________youlastnight.8Youcanneverrely___himtobepunctual.9Nothingwillpreventhim________succeeding.10Areyouinterested_______music?11IsupposeIcancount____youforhelp_______thismatter?12Beware_____thedog.13Hepersisted_____askingquestions.14Iinsist________yourtellingmethetruth.15Ittookmealongtimetogetrid___him.16Doyoumeantosayyouhaveneverheard____Beethoven?17Iseparatedthem______eachotherbecausetheywerefighting.18Theycanonlycurehim_____hisillnessiftheyoperate____him.19Youcandepend______me.20Ihaven'taccusedhim_____anything,butIsuspecthim____havingtakenit.21Whatevermadeyouthink_______suchathing?22Weexpectagreatdeal____you,Smith.23MyhandssmeIl_____soap.24Theydiffer_______eachothersomuch.25Heinvestedalotofmoney______shipping.26Thefilmwasbased_____anovelbyDickens.27Don'tlean___thatshelf!You'llregretit.28Sheoftensuffers_______colds.29Wehaveembarked_______anewscheme.30Ibelieve______takingmytime.31Joneswasdismissed________thefirm.32Theybeganbyexperimenting______rats.33Pleaseconcentrate______whatyouaredoing.34Shepridesherself_______hercleanhouse.35Theclimberfailed_______hisattempttoreachthesummit.36Manypeopleescaped______prisonsduringthelastfiveyears.37Wemusteconomize_____fuel.38He'sneverdoneanywork.Helives______hismother.39Hewasemployed______afactorybeforehejoinedthearmy.40Andwhatdoesthishorribledrinkconsist_______.41Ishallcertainlyact________youradvice.42Don'twrite_____thedesk!43Youshouldnotboast_______oursuccess.44Youmustencouragehim_____hisefforts.45Heshouldbeinstructed______hisduties.46Twoorthreepeoplewereinvolved______theaccident.47Childrenshouldbeprohibited_____smoking.48lcanassureyou_____mysupport.49Doyouapprove____hunting?50Idespair_____everteachinghimanything!51Hasthisplayeverbeenperformed______thestage?52Iwarnedhim_____thedanger,buthewouldn'tlistentome.53Howmuchhaveyouborrowed_______mealready?54Hedelights_______annoyingme.55Idon'tagree______you.(L46)56Shepreferred___wait____him.57Wehavebeencorresponding_____eachotherforyears.58Howdoyouaccount______this?59Doyouobject______mysmoking?60I'msurprised_______you!61Youmustreply_____hisletter.62Hehassomeimportantbusinesstoattend_______.63Doyoumeantosayyouexchangedthatlovelycar_____this?64Hasitoccurred____youthatshemusthavearrived_____LondonAirportbynow?65Iwasshocked______hisindifference!66Youmustcomply_____therulesofthegame.67PoorMary!Shehassomuchtocope_______.68Pleasedon'tmentionit_____myhusband,butIpaid￡50_____thishat.69Shewasquiteunprepared_______thenews.70Don'tblameme______theaccident!71I'mdisgusted_____yourbehavior!72YouforgottothankAuntJane_____herpresent.73ltisrudetostare____people.74I'mnotsatisfied_____yourwork.75Hisdebtnowamounts______$100!76Mixthecontentsofthispacket_____alittlewater.77Iknocked_____thedoor.78Whomdoesthisbookbelong_______?79Ireasoned_____him,buthewouldnotlisten_______me.80She'saccustomed_______livingincomfort.She'llneverpart____herpreciouspossessions.81Atwhattimewillyoucall_____me?82ThespySurrenderedhimself_____theenemyandwascondemned_____death.83I'velooked_____iteverywhere,butlcan'tfindit.84I'llsee______thecookingtonight.85Imustapologize_____keepingyouwaiting.86Theclassfailedtorespond_______theteacher'snewmethods.87Heturned_____meforhelp,evenafterIhadquarreled._____him..88LikeMicawber,Ihope______somethingbetter.89Pleaseapply____thesecretaryforinformation.90Therewasanoteattached______theparcel.91Justguess_____thepriceofthiscarpet.92Howlonghaveyoubeenworking______thisexercise?93Theconcertbegan_____apiecebyanunknowncomposer.94Howmuchdidtheychargeyou________that?95Georgeisjealous______hisyoungersister.(L70)96Sheiswell-qualified______languagesandveryefficient______herwork.97Wearefortunate______havingsufficientsuppliesoffuel______thewinter.98Contrary______myexpectations,there’rewasnoneedtobeuneasy________theresultsofthematch.99Iamnotfamiliar________hisnovelsandnotverykeen________readingthem.100Iknowheisslow______understanding,butyouhavetobepatient_____him.101Itisobvious_______everyonethatheisnotresponsible______thismistake.102Ithinkhe'squitehonest________hisintentions.103Heisnotonlyindifferent_____otherpeople;heisoftenextremelyrude____themaswell.104I'mnotveryfond________dancing.105Childrenremaindependent_______theirparentsforalongtime.106Ishouldbegrateful____anyadviceyoucangive.107Heisnotdifferent_____anyoneelse.108Hemaybequick_____understanding,buthe'snotcapable_____rememberinganything.109Heisintent______passingtheexamination,butI'mdoubtful_______hischances.110Hesayshe'ssorry_____whathedid,sodon'tgetangry______him.111I'veneverbeengood_______arithmetic.112Thatboyisfarahead______everyoneelseintheclass.113Eventhoughhewasoftencruel_____hisdog,itremainedfaithful______him.114Yourconclusionsarenotconsistent_____thefacts.115Thisdiarywillproveuseful______you.116I'mnotsure____theexactdate,butIthinkhearrivedherein1993.117Hewasfoundguilty_____greatmanycrimes.118Youshouldnotbesosensitive_____criticism.119Thispassportisvalid______allcountries.120Manypeopledonotapprove____bloodsports.(L94)121Hewasfoundguilty_____murderandcondemned_____death.122Hasiteveroccurred____youthatthosetwinsarequitedifferent______eachotherinmanyways?123Iconsultedmylawyer_____thematterandIshallact____hisadvice.124Itisimpossibletopreventthem____quarrelling____eachother.125Heisresponding____treatmentandwillsoonbecured___hisillness.126Eventhoughheisthirty-five,helives____hismotherandiscompletelydependent___her.127Itriedtoreason___him,buthewasveryrude____me.128Iamgrateful____youforbeingsopatient______him.129Hemightbegood____hisjob,butyoucan'trely_____him.130Iamthinking_____looking_______anewjob.131lfyouinterfere_____otherpeople'saffairs,youwillregretit.132Doyoubelieve____allthatnonsense?133Itshouldbeobvious___youthatifyoupersist____botheringhim,hewillgetangry____you.134Youdemandtoomuch______him;heisnotreallyequal_____thetask.135Don'tbesosure____yourself!136Hehasprovided______everyemergency.137lwasafraid______mentioningit_____him.138Don'tblamehim____this;Iamresponsible_____whathashappened.139Heissokeen_____learning,youshouldencouragehim____hisefforts.140Beware_____peoplewhoappeartobeenthusiastic____yoursuccess.141Iappealed______himforhelp.142Iamsorry_____havingaskedhim.Iwasshocked____hisrefusal.143Areyouinterested-_____opera?144Areyouaware____thedifficultiesthatlieahead____you?145He'sentitled_____apension,buthewon'tdream____retiringyet.146Whoisgoingtopay____thedamage?147Thiscarisinferior_____theoneIboughtlastyear.148I'mafraidIcan'tcomment_____yourworkjustyet.149Shemayprideherself_____herabilities,butshe'snotcapable_____bringingupchildren.150Weareaccustomed_______badweather.151Howcanyouagree_____suchanideawhenyouareignorant______thebasicfacts?152Heconfessed_____methathehadjustbeenconverted______somestrangereligion.153Shewantedtoborrowtherecord_______mebutshewasshy____asking.154Ifyoufail____thisattempt,don'tcount______meforhelp.155Hislieswouldnottake__anybodybutafool.(L96)156Theexplorersreturnedbecausetheyhadrun____food.157Heisverygoodatmaking_____storiesforchildren.158Ittookhimalongtimetoget______hisillness.159Mrs.Jonestoldherdaughtertokeep____thestove.160Duringthestorm,theshipmade-_____thenearestharbor.161Hasthiscarbeenrun_____yet?162Thebirdaccidentallyflewintotheroomandcouldn'tget_____.163Hespokesoquickly,Ididn'thavetimetotake____whathesaid.164Thoughweallran_______thethief,wecouldnotcatchhim.165Ihadn'tseenhimforyearsandIaccidentallyran______himinthestreetthismorning.166Ronaldwilltake_______thefamilybusinessnowthathisfatherhasdied.167Canyoumake______theaddressonthisenvelope?168I'vetaken________paintinginmysparetime.答案：1-5fromoninonfrom6-10fromofonfromin11-15on…inofinonof16-20offromof…ononof…of21-25ofof/fromoffromin26-30ononfromonin31-35fromonononin36-40fromononinof41-45ononofinin46-50infromofofof51-54on,of,from,in,with55-60to…for,with,for,to,at61-65to,to,for,to…at,at66-70with,with,to…for,for,for71-75with,for,at,with,to76-80with,at,to,with…to,to…with,81-85for,to…to,for,to,for86-90to,to…with,for,to,to91-95at,at,with,for,of96-100in…at,in…for,to…about,with…on,at…with101-105to…for,in,to…to,of,on106-110for,from,at…of,on…about/of,for…with111-115at,of,to…to,with,to,116-120of,of,to,for,of121-125of…to,to…from,on…on,from…with,to…of126-130with…on,with…to,to…with,at…on,of…for131-135in/with,in,to…in…with,of…to,of,136-140for,of…to,for…for,on…in,of…about141-145to,for/about…at/by,in,of…of,to…of146-150for,to,on,on…of,to151-155to/with…of,to…to,from…of,in…on,in156-160outof,up,over,awayfrom,for161-165in,out,down,after,into166-168over,out,up

单纯的课本内容，并不能满足学生的需要，通过补充，达到内容的完善教育之通病是教用脑的人不用手，不教用手的人用脑，所以一无所能。教育革命的对策是手脑联盟，结果是手与脑的力量都可以大到不可思议。

柱坐标和球坐标系下拉普拉斯算符表达式的简单推导柱坐标和球坐标系下拉普拉斯算符表达式的简单推导柱坐标和球坐标系下拉普拉斯算符表达式的简单推导柱坐标和球坐标系下拉普拉斯算符表达式的简单推导[摘要]：本文采用多元微积分，利用球坐标与柱坐标、柱坐标与直角坐标变量转换的相同关系，以拉普拉斯算符为例，简化了在柱坐标和球坐标系下拉普拉斯算符表达式的推导。本文提出了此法在柱坐标和球坐标系下梯度、旋度、散度算符表达式的推导中的适用性，适合广大非数学专业本科生学习与掌握。[关键词]：拉普拉斯算符；球坐标；柱坐标；多元微积分[中图分类号]：O13[文献标识码]：A[文章编号]:1672-1452(2015)**-****-041引言在材料科学基础、近代物理、量子力学等课程的内容中，菲克第二定律和薛定谔方程中的拉普拉斯算符在柱坐标系和球坐标系中的表达式十分重要。在近代物理的课本[1]和材料科学基础的课本[2]上，提到了拉普拉斯算符在柱坐标和球坐标系下的表达式，但没有给出具体的推导过程。在电动力学课本[3]中,这方面的内容是通过引入“正交曲线坐标系”得出关于拉普拉斯算符的一般结论，再推导出球坐标和柱坐标下的表达式。但是利用正交曲线坐标系的一般结论进行推导比较抽象，对于非数学专业的同学来说，理解一般性的结论需要较高的数学水平。现有的文献[4][5]中，有采用多元复合函数微商法则完成推导的，虽然此法在对学生的微积分要求较低，但是所给出的证明计算繁琐，无助于学生直接理解公式的正确性和自主完成推导。本文给出了用多元微积分导出拉普拉斯算符在柱面坐标系和球面坐标系中表达式的简单方法。此法仅要求学生掌握基本的多元微积分知识，计算过程简洁美观，便于广大的非数学系专业的学生掌握和理解。建议在近代物理、量子力学、材料科学基础等课程教材和教学中应用。2柱坐标和球坐标下拉普拉斯算符的推导2.1柱坐标系下的拉普拉斯算符表达式的推导首先，直角坐标系的分量与柱坐标系的分量有如下的转换关系： （1） （2） （3） （4）（1）式两端分别对x和y求偏导，得 （5） （6）（2）两端对x求偏导，并将（5）式代入，得

（7）同理可知， （8）假设所研究的函数为由于z关于x，y是独立的变量，故 （9）同理 （10）利用公式（5）（7）（9），对f求x的二次偏导 （11）类似地，计算f关于y的二阶偏导数。计算过程与上面相同，将x换为y，换为，换为即可。于是（12）结合（11）（12）式，合并同类项后可以得到（13）式 （13）最后，拉普拉斯算子的柱坐标可表示如下 （14-a）或者 （14-b）2.2球坐标系下的拉普拉斯算子的推导上述柱坐标系下拉普拉斯算符表达式的推导方法较为常用，运算量不大，也是大多数理工类本科生可以独立完成的。采用多元复合函数微商法则进行证明的现有文献中，推导路径是从直角坐标公式分别推导出柱坐标和球坐标系下的算符表达式。但是从直角坐标系出发推导球坐标系下的拉普拉斯算符表达式较为繁琐，运算量过大，不利于学生理解整个证明过程，许多同学难以完成。本文采取从（14）式出发，利用与的关系式和与的关系式（1）（2）（3）（4）间的相似性，给出利用柱坐标系下的拉普拉斯算符的表达式导出球坐标系下拉普拉斯算符表达式的方法。此法亦适用于旋度、梯度、散度算符在球坐标系下表达式的推导。球坐标系下的变量和柱坐标系下的变量间的关系如下： （15） （16） （17） （18）对比（14）（15）（16）（17）式与（1）（2）（3）（4）式，可以发现球坐标系和柱坐标系的变量关系与柱坐标系和直角坐标系的变量关系相同。于是在利用（13）式推导球坐标系的拉普拉斯算符表达式时，可以将上一节的推导过程中得到的公式套用过来。将（10）（13）式中的分别换为可得， （19） （20）将（19）（20）式代入（14-a）式，并注意到，有最后整理得， （21）（21）式即为球坐标系下的拉普拉斯算子。3结论本文利用多元微积分，从直角坐标系出发导出柱坐标系下的拉普拉斯算符表达式，利用球坐标系变量与柱坐标系变量的关系式与柱坐标系变量与直角坐标系变量的关系式相同的特点，从柱坐标系的算符表达式出发导出球坐标系下的算符表达式，证明简洁易懂。此外，此法在证明梯度、旋度、散度算符的柱坐标和球坐标的表达式时同样能简化计算，适合理工类本科生学习和掌握。[参考文献][1]Beiser,A.Conceptsofmodernphysics[M].NewYork:McGraw-HillEducation,2003.[2]潘金生，田民波，仝健民.材料科学基础[M].北京：清华大学出版社，2011.[3]郭硕鸿，电动力学[M].北京：高等教育出版社，2008.[4]江俊勤.柱面坐标系和球面坐标系中的拉普拉斯算符[J].广东教育学院学报,2003，2：32-34.[5]姚久民，石凤良.球坐标系中拉普拉斯算符表达式的推导[J].唐山师范学院学报,2005，5：67-71.AConciseDerivationoftheExpressionsofLaplacianOperatorinCylindricalandSphericalCoordinateSystemsZhangJinyuSchoolofMaterialScienceandEngineering,TsinghuaUniversity，Beijing100084,China;Abstract:Inthispaper,theexpressionsofLaplacianoperatorincylindricalandsphericalcoordinatesystemarederivedbyusingtheknowledgeofmultivariablecalculus.TherelationshipbetweenvariablesinsphericalcoordinatesystemandthoseinsphericalcoordinatesystemissimilartothatbetweenvariablesincylindricalcoordinatesystemandthoseinCartesiancoordinate,whichsimplifiesthederivationgreatly.Itisproposedthatthismethodcanalsopredigestthederivationoftheexpressionsofthecurl,gradient,divergenceoperatorinthetwocurvilinearcoordinatesystemsmentionedabove.Insum,thismethodissuitableforundergraduatesofengineeringtograsp.Itissuggestedthatthismethodcouldbeinvolvedintherelativetextbooksandteachingprocesses.Keywords:Laplacianoperator;sphericalcoordinatesystem;cylindricalcoordinatesystem;multivariablecalculus

一些数学的体积和表面积计算公式一些数学的体积和表面积计算公式

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一些数学的体积和表面积计算公式一些数学的体积和表面积计算公式长方形的周长=（长+宽）×2

正方形的周长=边长×4

长方形的面积=长×宽

正方形的面积=边长×边长

三角形的面积=底×高÷2

平行四边形的面积=底×高

梯形的面积=（上底+下底）×高÷2

直径=半径×2半径=直径÷2

圆的周长=圆周率×直径=圆周率×半径×2

圆的面积=圆周率×半径×半径

长方体的表面积=（长×宽+长×高＋宽×高）×2

长方体的体积=长×宽×高

正方体的表面积=棱长×棱长×6

正方体的体积=棱长×棱长×棱长

圆柱的侧面积=底面圆的周长×高

圆柱的表面积=上下底面面积+侧面积

圆柱的体积=底面积×高

圆锥的体积=底面积×高÷3

长方体（正方体、圆柱体）的体积=底面积×高

平面图形

名称符号周长C和面积S正方形a—边长C＝4aS＝a2

长方形a和b－边长C＝2(a+b)S＝ab

三角形a,b,c－三边长h－a边上的高s－周长的一半

A,B,C－内角其中s＝(a+b+c)/2S=ah/2=ab/2·sinC=[s(s-a)(s-b)(s-c)]1/2=a2sinBsinC/(2sinA)

四边形d,D－对角线长

α－对角线夹角S＝dD/2·sinα

平行四边形a,b－边长h－a边的高

α－两边夹角S＝ah＝absinα

菱形a－边长α－夹角D－长对角线长

d－短对角线长S＝Dd/2＝a2sinα

梯形a和b－上、下底长

h－高m－中位线长S＝(a+b)h/2＝mh

圆r－半径d－直径C＝πd＝2πr

S＝πr2＝πd2/4

扇形r—扇形半径a—圆心角度数

C＝2r＋2πr×(a/360)

S＝πr2×(a/360)

弓形l－弧长b－弦长h－矢高r－半径

α－圆心角的度数S＝r2/2·(πα/180-sinα)

＝r2arccos[(r-h)/r]-(r-h)(2rh-h2)1/2

＝παr2/360-b/2·[r2-(b/2)2]1/2＝r(l-b)/2+bh/2

≈2bh/3

圆环R－外圆半径r－内圆半径D－外圆直径d－内圆直径S＝π(R2-r2)＝π(D2-d2)/4

椭圆D－长轴d－短轴S＝πDd/4

立方图形

名称符号面积S和体积V

正方体a－边长S＝6a2V＝a3

长方体a－长b－宽c－高S＝2(ab+ac+bc)V＝abc

棱柱S－底面积h－高V＝Sh

棱锥S－底面积h－高V＝Sh/3

棱台S1和S2－上、下底面积

h－高V＝h[S1+S2+(S1S2)1/2]/3

拟柱体S1－上底面积S2－下底面积S0－中截面积h－高V＝h(S1+S2+4S0)/6

圆柱r－底半径h－高C—底面周长S底—底面积S侧—侧面积S表—表面积C＝2πr

S底＝πr2S侧＝ChS表＝Ch+2S底

V＝S底h＝πr2h

空心圆柱R－外圆半径r－内圆半径h－高V＝πh(R2-r2)

直圆锥r－底半径h－高V＝πr2h/3

圆台r－上底半径R－下底半径h－高V＝πh(R2＋Rr＋r2)/3

球r－半径d－直径V＝4/3πr3＝πd2/6

球缺h－球缺高r－球半径a－球缺底半径V＝πh(3a2+h2)/6＝πh2(3r-h)/3

a2＝h(2r-h)

球台r1和r2－球台上、下底半径h－高V＝πh[3(r12＋r22)+h2]/6

圆环体R－环体半径D－环体直径r－环体截面半径d－环体截面直径V＝2π2Rr2＝π2Dd2/4

桶状体D－桶腹直径d－桶底直径h－桶高V＝πh(2D2＋d2)/12(母线是圆弧形,圆心是桶的中心)

V＝πh(2D2＋Dd＋3d2/4)/15(母线是抛物线形)

冠词练习题冠词练习题

/冠词练习题冠词专项复习?题组训练一单项选择?(??)1.?Last?night?I?sawUFO?flying?in?the?sky?and?took?pictures?of?it.???A.?a???????????B.?an???????????C.?the?????????D.?不填?(??)2.?Tim?had?tried?twice,?and?his?father?asks?him?to?have??third?try.?A.?the????????????B.??a??????C.?another???????D.?/?(??)3.?Many?students?in?our?school?can?play?________?guitar.?A.?the??????B.?a?????C.?不填?(??)4.?Liu?Changchun?is?_________?first?Chinese?to?join?the?Olympics.?A.?a?????????B.?an???????C.?the????????D.?不填?(??)5.?I?think?it's?_________?useful?advice,?so?I?will?always?remember?it.?A.?a???????????B.?an?????????C.?the?????????D.?/?(??)6.?—Will?you?get?there?by?_______?train??—No,?I'll?take?_______?taxi.??A.?/;?a???????B.?a;?the???????C.?/;?/??????D.?the;?a?(??)7.?I?read?_____?story.?It?is?_____?interesting?story.?A.?a;?an???B.?a;?a???C.?the;?the???D.?/;?an?(??)8.?We?always?have?_____?rice?for?______?lunch.?A.?/;?/???B.?the;?/???C.?/;?a????D.?/;?the?(??)9.?______?train?is?faster?than?_______?bus.?A.?A;?a???B.?The;?/????C.?A;?the????D.?/;?the?(??)10.?January?is?______?first?month?of?the?year.?A.?a?????B.?/???C.?the????D.?/?(??)11.?Einstein?won?______?Nobel?Prize?in?Physics?in?1921.?A.?a???B.?an???C.?the???D.?/?(??)12.?I?like?music,?but?I?don't?like?______?music?of?that?TV?play.?A.?a???B.?an??C.?the???D.?/?(??)13.?______?girl?over?there?is?______?English?teacher.?A.?The;?an????B.?A;?/???C.?The;?/????D.?A;?a?(??)14.?We?often?have?sports?after?class,?and?I?like?to?play?_____?basketball.?A.?a???B.?an????C.?the???D.?/?(??)15.?More?college?graduates?would?like?to?work?in?____?west?part?of?our?country?___?next?year.?A.?the;?the???B.?/;?/???C.?/;?the???D.?the;?/?(??)16.?We?work?five?days?________?week.?A.?a???B.?an???C.?the?????D.?/?(??)17.?There's?_______?“u”?and?_______?“s”?in?______?word?“use”.?A.?an;a;?the????B.?a;?an;?/???C.?a;?a;?a,??????D.?a;?an;?the?(??)18.?That's?______?useful?book.?I?have?read?it?already.A.?the??B.?an??C.?a????D.?/?(??)19.?______?Whites?have?moved?to?a?new?house.?A.?A?????B.?An?????C.?The????D.?/?(??)20.?Avatar?is?such?_______?wonderful?science?fiction?movie?that?I?want?to?see?it?_____?second?time.?A.?a;?a????B.?a;?the???C.?/;?the????D.?/;?a题组训练二单项选择?(??)1.?I?got?the?news?on?______?radio.?A.?/?????????B.?a??????????C.?an????????D.?the?(??)2.?—Who?is?_____?man?in?a?black?hat??It's?Jim?Brown.?We?often?play?_____?basketball?together?in?our?free?time.?A.?an;?a??B.?a;?/??C.?the;?a??D.?the;?/?(??)3.?______?exciting?news!?We're?never?had?_______?long?vacation?before.???A.?What;?such?a???B.?What?an;?such?a?????C.?How;?such?a??????D.?What;?so?a?(??)4.?What?_______?interesting?game!?Let?me?have?______?try,?OK??A.?an;?a??????????B.?a;?an??????C.?/;?a??????????D.?an;?/?(??)5.?—What?do?you?think?of?the?cartoon?????—Oh,?it?is?really?____?fantastic?one.????A.?a???B.?an????C.?the?????D.?/?(??)6.?________?sad?news?it?is!?We?must?try?our?best?to?help?them?out?of?trouble.????A.?What?an????????B.?What????????C.?How?an????????D.?How?(??)7.?—What?can?I?do?for?you????—I?want?______?MP?4?player?for?my?daughter.???A.?a????????????B.?an?????????????C.?the??????????D.不填?(??)8.—I?hear?there’ll?be?_______?talk?on?teenager?problems?next?Monday.????—Do?you?mean?________?talk?our?teacher?asked?us?to?listen?to?????A.?a;?the?????B.?a;?a??????C.?the;?the??????????D.?the;?a?(??)9.?—What?was?Marc?doing?when?his?mother?got?home?yesterday????—He?was?playing?______?guitar.???A.?the????B.?a?????C.?an??????D.?/?(??)10.?Look,?Simon,?______?Walkman?that?I?bought?last?year?isn't?working?properly.???A.?a????????????B.?an???????????C.?the??????????D.?不填?(??)11.?—Did?you?see?________?dog?just?now?????—Is?it?______?black?dog??????A.?the;?a???B.?a;?a????????C.?the;?不填?(??)12.?He?is?______?kind?man.?He?often?gives?money?to?charity.????A.?a????B.?an??C.?the???D.?/?(??)13.?—Do?you?know?________?woman?in?pink?over?there????—Yes.?She?is?_______?office?worker?of?Lijing?Hotel.???A.?a;?an???B.?the;?the??????C.?a;?the???D.?the;?an?(??)14.?Don't?talk?to?Tom?like?that.?He?is?only?_______?eleven-year-old?boy.???A.?a?????B.?an???C.?the????D.?不填?(??)15.?—Why?did?you?laugh?just?now??Ted?wanted?to?tell?us?________?very?funny?story,?but?he?forgot?_________?end?himself.?A.?/;?the?????????B.?a;?an????????C.?a;?the?????????D.?the;?the题组训练三（与中考链接）?一、单项选择?【中考预测】?(??)1.?There?is?________?“s”?in?the?word?“six”?and?______?“s”?is?the?first?letter?of?the?word.?A.?a;?the??????B.?a;?an????????C.?an;?the?????D.?a;?a?(??)2.?—Is?it?_______?English?dictionary??—Yes,?and?it?is?______?us