成果p9 ssat数学level2学生版introduction

CHAPTER--­ SSAT 概 必要 新变 成绩 CHAPTER--­ FundamentalMath NumberConceptsand DividingDecimals小数除 Exponents指 Square More 代 SolvingSimple Practice Manipulatingan Manipulatinginequalities(解不等式 Solvingpercentquestionswith Geometry几 Similar ThePythagoreantheorem勾股定 Circles Word Keywordsandphrasestotranslate CHAPTER--­ SSATPractice SSATPracticeTest SSATPracticeTest SSATPracticeTest ISSATINTRODUCTION概述SSAT，全称SecondarySchoolAdmissionTest，中文名称为中学入学考试，适用于、及阅读理解能力，考生的逻辑思维和发展潜力。由AdmissionTestBoard命题。针对不level，8-115-73-4必要性但：受短这样一来，私立中学无疑成为中学生留学的首选。而绝大多数的私立学校要求留学（短期交换生除外）必须参加SSAT测试。所以，要想就读私立中学就必须参加SSAT考试。并且只有顺利通过考试，才能进入著名私立中学就读，为日后进入著名大学迈出坚实分类特点SSAT考试分为三个级别：ElementaryLevel（3-4），MiddleLevel（5-7）和UpperLevel（8-11年级）。考UpperLevel的学生占绝大多数。SSAT授课老师，900-1800，中级分数区间为1320-2130，高级分数区间为1500-2400。就高年级来说，即使整张卷子完全不写也会有1500分，所以一般来说需要考到2000分以上才具有竞争力。另外一方面，每次考试还会给出单项的百分比成绩（percente），这个成绩是将考生这项的成绩和去年你同一级的成进对所出在申出更强指示veba（词汇）的百分比是90%，也就是说这个考生的成绩比过去三年内90%的考生成绩都要好。这孩子来说是一个非常高的分数。SSAT考试共分为四个部分：词汇、阅读、数学和写作。前三个部分为计分项目，写作部分送时ElementaryNumberofTimeAllottedtoEachSection(SectionBreakSection1Middle1 NumberofQuestions 1BreakSection(SectionBreakSectionSection(SectionOfthe167 ludingthewritingsample,only150questionsareUpper1 NumberofQuestions 1BreakSection(SectionBreakSectionSection(SectionOfthe167itemsludingthewritingsample,only150questionsare从上表可以看出，这个考试时间短，题目多，对于初中生来说难度还是比较大的。另外中3000左右，而SSAT低年级的词汇要求已达到7000，而高年级的词汇要求为9000甚至可新变化SSAT考试于2012年10月进行了新的SSAT考试加入的基础层次测试。主要用于小学4-5年级学生的入学。未前的lowerlevel用于5-7年级的入学测试，lowerlevel已经变成了middlelevel。增加了“标准组”分类。尽管SSAT评分策略并未改变，但是，它改进了对于分数的理解拿成绩单CHAPTER--­FundamentalMathDividingDecimals小数除法Todivide,movethedecimalpointinbothnumbersthesa mberofspacestotherightuntilyouareworkingonlywithintegers.12.5÷Nowmovebothdecimalsovertwocesandsolvethe1250÷25=Andyou’redone!RememberthatyoudonotputthedecimalsbackintotheExponents指数Exponentsarejustanotherwaytoindicatemultiplication．Forinstance,32simplymeansmultiplythreebyitself twotimes,socomplicated．Forexample：

32=33=9．Evenhigherexponentsaren’t25=2222ThequestionsontheSSATdon’tgenerallyuseexponentshigherthanfourorfive,sothisistobeascomplicatedasitTheruleforexponentsissimple：Whenindoubt,writeitout!Don’ttrytofigureouttwotimestwotimestwotimestwotimestwoinyourhead(justlookathowsillyitlookswrittendownusingwords!)．Instead,writeitasamathproblemandjustworkthroughitonestepatatime．WhatwouldyoufyouwereaskedtosolvethisQ3Q2Let’slookatthisonecarefully．togetherandyou’ve

meansQQQandQ2meansQQ．Put(QQQ)(QQ)HowmanyQ’sisthat?Countthem．Five!TheanswerisQ5．Becarefulwhenmultiplyingexponentslikethisthatyoudon’tgetconfusedandmultiplytheactualexponents,whichwouldgiveyouQ2．Ifyouareeverunsure,don’tspendasecondworrying;justwriteouttheexponentandcountthenumberofthingsyouaremultiplying．4Asquarerootisjusttheoppositeofsquaringanumber．22=22or4,sothesquarerootof4is2．Youwillseesquarerootswrittenthiswayonatest:41.23

2.243.334.437．497．49 9．9．9MoreMultiplyingandDividingExponentswiththeSameYoucanmultiplyanddivideexponentswiththesamebasewithouthavingtoexpandoutandcalculatethevalueofeachexponent．Thebottomnumber,theoneyouaremultiplying,iscalledthebase．(However,notethattomultiply2352youmustcalculatethevalueofeachexponentseparayandthenmultiplytheresults．)Tomultiply,addtheTodivide,subtractthe2825Totakeanexponenttoanotherpower,multiplythe(23)31.35332.72773.53544．152315205．413446．10101067.(53)68.(812)39.(95)510.(22)14 代数AnIfyou’reaLowerLevel,ElementaryLevel,orMiddleLevelstudentyoumaynotyethavemultiply,anddivide,youcansolvegebraicequation．LowerLevelstudentsonlyneedtounderstandthesectionbelowtitled“SolvingSimpleEquations．”MiddleLevelISEEstudentsshouldcompleteallofthe“SolvingSimpleEquations”drillsandasmuchoftheUpperLevelmaterialaspossible．UpperLevelstudentsneedtogothroughtheentireAlgebrasectioncarefullytomakesuretheycansolveeachofthequestiontypes．SolvingSimpleAlgebraicequationsinvolvethesamebasicoperationsthatwe’vedealtwiththroughoutthischapter,butinsteadofusingonlynumbers,theseequationsuseacombinationofnumbersandletters.Theselettersarecalledvariables(变量).Tosolvesimplealgebraicequationsyouneedto lyabouttheequation.Let’stry2+x=WhatdoesxWellwhatnumberplus2givesyou7?Ifyousaid5,youwererightand2y=WhatdoesyNowyouneedtoaskwhatmultipliedby2givesyou16. Ifyousaid8,thenyouarerightandIf35−x=23,thenxIfy+12=27,thenyIfz−7=21,thenzIf5x=25,thenxIf18÷x=6,thenxIf3x=33,thenxIf65÷y=13,thenyIf14=17−z,thenzManipulatinganTosolveanequation,yourgoalistoisolatethevariable,meaningthatyouwanttogetthevariableononesideoftheequationandeverythingelseontheotherside.Tosolveanequation,followthesetwoStep1:Moveelementsaroundusingadditionandsubtraction.Getvariablesononesideandnumbersontheotherside.Step2:Dividebothsidesoftheequationbythecoefficient(系数)，thenumbereverythingbytheIf8=11−x,thenxIf5x−20=10,thenxIfm+5=3m−3,thenmIf0.2x+2=3.6,thenxIf3x+y=21,thenx+yIf100−5y=65,thenyManipulatinginequalities(解不等式Manipulatinganinequalityisjustlikemanipulatinganequationthathasanequalsign,exceptforonerule:ifyoumultiplyordividebyanegativenumber(负数),fliptheinequalitysign.Let’stryan−3x<Dividebothsidesby--­3andthenfliptheinequalityx>PracticeSolvefor4x>13−x>15x−20x<12+2x>24−7<−14−SolvingpercentquestionswithWheneveryouseewordsfromthefollowingtable,justtranslatethemintomathlanguageandgotoworkontheequation!PercentMath%orOutof100(!Times(asinYourfavoriteIs,are,were,was,For24is60percentof24 Practice30iswhatpercentofWhatis12%ofWhatis25%of10%of75%of20%ofwhatnumberis16%ofwhatnumberis25%of!Whatpercentisequal !30iswhatpercentofWhatis11%ofWhatpercentof24isequalto60%ofwhatpercentof500isequaltoGeometry几何Similar 相似三角形Similartrianglesaretrianglesthathavethesameanglesbutsidesofdifferentlengths.Theratioofanytwocorrespondingsideswillbethesameastheratioofanyothertwocorrespondingsides.Forexample,atrianglewithsides3,4,and5issimilartoatrianglewithsidesof6,8,and10,becausetheratioofthecorrespondingsides(6:12or7:14or9:18)allreducesto1:2.63 ThePythagoreantheorem勾股定理Fortriangles,𝑎!+𝑏!=𝑐!wherea,b,andcarethelengthsofthetriangle’abAlwaysrememberthatcrepresentsthehypotenuse,thelongestsideofthetriangle,whichisalwaysoppositetherightangle.CirclesOAnylinedrawnfromtheorigin(thecenterofthecircle)toitsedgeiscalledaAnylhatpassesthroughtheoriginiscalledthediameter.Thediameteristwotimesthelengthoftheradius.Areaand 𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒:𝐶=𝜋𝑑=𝐴𝑟𝑒𝑎:𝐴=Practice1WhatisthelengthofsideB3 42WhatisthelengthofsideF6 3WhatisthecircumferenceoftheabovecircleWhatisthearea?4Whatistheareaofacirclewithradius4?5Whatistheareaofacirclewithdiameter8?6whatistheradiusofacirclewitharea9π？7Whatisthediameterofacirclewitharea8WhatisthecircumferenceofacirclewithareaWord 文字描述的理解Manyarithmeticandalgebraproblemsarewritteninparagraphformwithmanywords.Thehardpartisusuallynotthearithmeticorthealgebra;thehardpranslatingthewordsintomath.Solet’sfocusontranslating. KeywordsandphrasestotranslateSpecificwordsandphrasesshowuprepeatedlyinwordproblems.Youshouldbefamiliarwithalloftheonesbelow.WhatWhatyoureadin What nAnd,morethan,thesumof, LessLessthan,the ween,takeaway Of,theproductof,asmuch GoesGoesinto,dividedby,the Is,are,was,were,theresultwillbe,has,have, What,whatnumber,acertainWhat,whatnumber,acertain Variable(x,y,Halfofa TwiceasmuchTwiceasmuchas,twiceasold HowmanyHowmanytimes DividethetwoProportionsshowrelationshipsbetweentwosetsofinformation.Forexample,ifyouwantedtomakesyouhadarecipeforadozensbutwantedtomaketwodozens,youwouldhavetodoublealloftheingredients.That’saproportion.Here’showwe’dlookatitinequationform.!!"#$!"!!"#$%

=!!"#$!"!!"#$%

=!!"#$!"!!"#$%Wheneveraquestiongivesyouonesetofdateandpartofanotherset,itwillaskyouforthemissingpartofthesecondsetofthedate.Tofindthemissinginformation,setuptheinformationinafractionliketheoneshownabove.Becarefultoputthesameinformationinthesamece.Inourexample,wehaveflourontopandsonthebottom.Makesurebothfractionshavetheflouroverthes.Oncewehaveourfractionsetup,wecanseetherelationshipisbetweenthetwoelements(inthiscase,flourands).Whateverthatrelationshipis,it’sthesameastherelationshipbetweentheothertwothings.Practice1Thereare30ouncesin1quart128ouncesequalshowmanyquartsHowmanyouncesaretherein7quarts?2、Acartravelsatarateof perhour.Howlongwillittaketotravel 3BettyistwiceasoldasherdaughterFiona.FionaistwiceasoldasherdogRufusIfRufusis11,howoldisBetty?4Aclothingstoresold1250pairsofsocksthisyearLastyearitsold250pairsofsocksyear’ssalesarehowmanytimesgreaterthanlastyear’s5、Thereare500studentsatEisenhowerhighschool.! thetotalstudentsarefreshmen. ofallthefreshmenaregirls.HowmanyfreshmengirlsareCHAPTER--­SSATPracticeSSATPracticeTest25QuestionsFollowingeachprobleminthissection,therearefivesuggestedanswers.Workeachprobleminyourheadorontheblankspaceprovidedattherightofthepage.Thenlookatthefivesuggestedanswersanddecidewhichoneisbest.Note:FiguresthproblemsinthissectionaredrawnasaccurayaspossibleEXCEPTwhenitisstatedinaspecificproblemthatitsfigureisnotdrawntoscale.Eaemberofaclubsoldthesa mberofraffletickets.Iftheclubsoldatotalof120tickets,whichofthefollowingCANNOTbethenumberofticketssoldbyeaember?28AccordingtothegraphinFigure1,abouthowmanystudentsareartMAJORSOF900FigureSeanarriveshome14minutesbeforemidnight,andhissistergetshome25minuteslater.WhendoesSean'ssis rrivehome?11minutesbefore11minutesafter14minutesafter25minutesafter39minutesafterWhichofthefollowingisclosestto0.52×!of!!of!!of!!of!!of!Questions5--­6refertothegraphinFigureSUMMER=50$Brian:Andy:FigureBrian'ssummersavingsaregreaterthanJames'ssummersavingsbyhowmany34TheamountofmoneysavedbyAndyishowmanytimestheamountofmoneysavedby346Howmanystudentsareinaclassif30percentoftheclassisequalto30ItcannotbedeterminedfromtheinformationEachofthefollowingislessthan2!

ThesidesandanglesoftrianglesABC,BDE,BCE,andCEFinFigure3areallequal.WhichofthefollowingisthelongestpathfromAtoF?A FigureA-­­C-­­B-­­D--­A-­­B-­­E-­­C--­A-­­B-­­C-­­E--­A-­­C-­­E--­A-­­B-­­D--­WhichofthefollowingisclosesttoIf!ofanumberislessthan12,thenthenumberis!LessthanEqualtoGreaterthanEqualtoGreaterthanInabasketballgame,TeamAscored39points,andTeamBscoredmorepointsthanTeamA.IfTeamBhas5yers,theaveragescoreoftheyersonTeamBmusthavebeenatleasthowmanypoints?1568InthetriangleshowninFigure4,whatisthevalueofaa6Figure4689ItcannotbedeterminedfromtheinformationAmanboughtapieceoflandfor40thousanddollars.Thenhespent2milliondollarsbuildahouseonit.Thecostofthehouseishowmanytimesthecostofthe5If(x-­­y)+2=6andyislessthan3,whichofthefollowingCANNOTbethevalueof01!48InFigure5,thedistancefromAtoDis55,andthedistancefromAtoBisequaltothedistancefromCtoD.IfthedistancefromAtoBistwicethedistancefromBtoC,howfarapartareBandD? FigureAbookiscedonaflattablesurface,asshowninFigure6.Whichofthefollowingbestshowsallofthepointswherethebooktouchesthetable?FigureWhichofthefollowingcanbeexpressedas(J+2)×3whereJisawholeIfa-­­7=3b+4,whatdoesa+5b-­­4b-­­3b+3b+ItcannotbedeterminedfromtheinformationAccordingtoacensusreportforCountryA,21.5outofevery100familiesliveinruralareas.Basedonthisreport,howmanyofthe2millionfamiliesountryAliveinruralareas?Bobisxyearsold,andJerryis7yearsolder.Intermsofx,whatwasthesumoftheirages,inyears,5yearsago?2x+2x+2x--­x--­x--­ Agameshowcontestantansweredexactly20percentofthequestionscorrectly.Ofthefirst15questions,heanswered4correctly.Ifheansweredonlyoneoftheremainingquestionscorrectly,whichofthefollowingmustbetrue?Therewereatotalof20Heanswered10percentoftheremainingquestionsHedidn'tanswer9oftheremainingquestionsIIIIandIIIIandIIII,II,andIfCistheproductofconsecutiveintegersAandB,thenCmustgreaterthanA+anegativeapositiveanevenanoddA20percentdiscountisofferedonallsweatersatStoreS.Ifacottonsweaterisonsale$48.00andawoolsweaterisonsalefor$64.00,whatwasthedifferenceinpriceofthesweatersbeforethediscount?!Theumloadthatarailwaycarcancarryis tonsoffreight.Ifatrainhas!!railwaycars,andeachofthese ofatonlessthanitsumload,how!tonsoffreightisthetra!!!!IFYOUFINISHBEFORETIMEISYOUMAYCHECKYOURWORKONTHISSECTIONONLY.DONOTWORKONANYOTHERSECTIONINTHETEST.SSATPracticeTestTime--30Minutes25QuestionsFollowingeachprobleminthissection,therearefivesuggestedanswers.Workeachprobleminyourheadorontheblankspaceprovidedattherightofthepage.Thenlookatthefivesuggestedanswersanddecidewhichoneisbest.Note:FiguresthproblemsinthissectionaredrawnasaccurayaspossibleEXCEPTwhenitisstatedinaspecificproblemthatitsfigureisnotdrawntoscale.ThecrowninFigure1ismadeupoftoothpicksthateachhavethesamelength.Ifeachtoothpickis2meterslongandeachsideisequalto oothpick,whatistheperimeterofthecrowninmeters?Figure57Disanoddnumberbetween4and11.IfDisalsobetween7and18,whatisthevalueof5789Garyhasacollectionof16differentoperasandhisroommatePaulhasacollectionof18differentoperas.IfPaulandGaryhave4operascommontobothrecordcollections,howmanydifferentoperasdotheyhavweenthem? G=18,thenG 69Amodelsailboatfloatingonthewaterisattachedtoastring1meterlong,asshowninFigure2.Ifthestringistiedtoapostonthedock,whichofthefollowingbestshowstheareaofwateronwhichthesailboatcanfloat?FigureAtaparty,thereareexactly4timesasmanyadultsaschildren.Whichofthefollowingcouldbethetotalnumberofpeopleatthisparty?Usingapairofscissors,whichofthefollowingcanbemadefroma20cmby28cmrectangularsheetofpaperby1straightcut?IIIIIIIandIII,II,andAccordingtothegraphinFigure3,theaveragenumberofstudentstakingtheswimmingclassduringthefourmonthsofMarchthroughJunewasNUMBEROFSTUDENTSTAKINGSWIMMINGFigureQuestions9-­­11refertothefollowingdefinition.Forallrealnumbersnand!nr=n−1−!! Example:53=5−1!

=4−= Whatisthevalueof42126810.If=4,thenQ8642Ifn≠0andr≠0,whichofthefollowingmustbennIII

IandIIIIandIIII,II,andRobertwantstoleavea15percenttipforadinnerthatcosts$20.95.Whichofthefollowingisclosesttotheamountoftipheshouldleave?Juanstudiedfrom4:00P.M.to6:00P.M.andfinishedone--­thirdofhisassignments.Heistakingabreakandwantstofinishhisby10:30P.M.Ifhenstocontinueworkingatthesamerate,whatisthelatestthathecanreturntohisstudies?6:307:007:308:008:30Mrs.Brownandherzchildreneachate2peaches.What'sthetotalnumberofpeachestheyz+2z+2z+WhichfigurecanbedrawnWITHOUTliftingthepencilorretracing?If0.59isabout𝑁,thenNisclosesttowhichofthe5123Ifthelargestof7consecutiveintegersis25,whatistheaverageofthe7Thepriceofaboxofraisinsreasedfrom$0.93to$1.08.Thereaseinpriceisclosesttowhatpercent?2121remainderSSInthedivisionproblemsshownabove,S-­­Q68Whatistheleastnumberofsquaretileswithside6cmneededtocoverarectangularfloor72cmlongand48cmwide?IttakesCraig5minutestotypenpages.Atthisrate,howmanyminuteswillittakehimtotype20pages?n 4

nnThewidthofarectangularswimmingpoolisonequarterofitslength.Ifthelengthis60meters,whatistheperimeterofthepool?60120150180240Thepriceofadressatadepartmentstoredecreasesby20percenteverymonthitisnotsold.After3months,thecurrentpriceoftheunsolddressisapproximaywhatpercentoftheoriginalprice?Ifpisapositiveintegerandnisanegativeinteger,whichofthefollowingispnnp

p1nItcannotbedeterminedfromtheinformationInayogaschool,!ofthemenand ofthewomenarevegetarians,andtwiceas menaswomenarevegetarians.Ifthereare84peopleintheyogaschool,howmanymenarevegetarians?48IFYOUFINISHBEFORETIMEISYOUMAYCHECKYOURWORKONTHISSECTIONONLY.DONOTWORKONANYOTHERSECTIONINTHETEST.SSATPracticeTestTime-­­-­­30Minutes25QuestionsFollowingeachprobleminthissection,therearefivesuggestedanswers.Workprobleminyourheadorontheblankspaceprovidedattherightofthepage.Thenlookatthefivesuggestedanswersanddecidewhichoneisbest.Note:Figuresthproblemsinthissectionaredrawnasaccura yaspossibleEXCEPTwhenitisstatedinaspecificproblemthatitsfigureisnotdrawntoscale.ThepolygoninFigure1hasaperimeterof30.Ifeachsideofthepolygonhasthesamelength,whatisthelengthofoneside?Figure(A)(B)(C)(D)(E)Mr.Stuartsoldpeppermintcandyto25customersandcaramelcandyto17customers.If4ofthesecustomersboughtbothtypesofcandy,howmanyboughtonlycaramelcandy?Inabagof24balloons,thereisanequalnumberofballoonsofeachcolor.WhichofthefollowingCANNOTbethenumberofdifferentcolorsinthebag?(A)(B)(C)(D)(E)Whichofthefollowingisawholenumberlessthan13andalsoawholenumberbetween11and18?AccordingtothegraphinFigure2,SusanspentabouthowmanyhourswatchingHOWSUSANSPENT12HOURSSoapFigure(A)(B)(C)(D)(E)If!R=16,then! 8Whichofthefollowingisclosestto1of4AccordingtothegraphinFigure3,theaveragesalesofMfrom1983to1987SALESOFM:1983--­FigureQuestions9-­­10refertothefollowingdefinition,Forallrealnumbersuandvuøv=u−(1−!)(Example:3ø2=3−1 =3−!=2 Whichofthefollowingisequalto5ø0 !!!Ifaø3=!!!!

,thena5Twentypercentof64isequalto5percentofwhatDuringthe4fishingtripsthatRichandAndymade,Richcaughtatotalof35fish.IfAndycaught