【统计(tngj)】1Theresasparentshaveagreedtobuyherticketstoseeherfavoritebandifshespendsanaverageof10hoursperweekhelpingaroundthehousefor6weeks.Forthefirst5weeksshehelpsaroundthehousefor8,11,7,12and10hours.Howmanyhoursmustsheworksduringthefinalweektoearnthetickets?A9B10C11D12E132024/7/301第2页/共30页第1页/共30页第一页，共31页。【统计(tngj)】7Theaverageageof5peopleinaroomis30years.An18-year-oldpersonleavestheroom.Whatistheaverageageofthefourremainingpeople?A25B26C29D33E362024/7/302第3页/共30页第2页/共30页第二页，共31页。【统计(tngj)】6Antonettegets70%ona10-problemtest,80%ona20-problemtestand90%ona30-problemtest.Ifthethreetestsarecombinedintoone60-problemtest,whichpercentisclosesttoheroverallscore？A40B77C80D83 E872024/7/303第4页/共30页第3页/共30页第三页，共31页。【统计(tngj)】17Amixtureof30litersofapaintis25%redtint,30%yellowtintand45%water.Fivelitersofyellowtintareaddedtotheoriginalmixture.Whatisthepercentofyellowtintinthenewmixture?A25B35C40D45E502024/7/304第5页/共30页第4页/共30页第四页，共31页。【统计(tngj)】2Theresultsofthesurveyaredisplayedinthebargraph.Whatistheratioofthenumberofstudentswhopreferredspaghettitothenumberofstudentswhopreferredmanicotti?2024/7/305第6页/共30页第5页/共30页第五页，共31页。【比例(bl)】20Beforedistrictplay,theUnicornshadwon45%oftheirbasketballgames.Duringdistrictplay,theywonsixmoregamesandlosttwo,tofinishtheseasonhavingwonhalftheirgames.HowmanygamesdidtheUnicornsplayinall?A48B50C52D54E642024/7/306第7页/共30页第6页/共30页第六页，共31页。代数(dish)运算(ynsun)（sum,remainder,ratio,product,positive,negative）函数（function,mapping,domain,range）2024/7/307第8页/共30页第7页/共30页第七页，共31页。【代数(dish)】5Chandlerwantstobuya$500mountainbike.Forhisbirthday,hisgrandparentssendhim$50,hisauntsendshim$35andhiscousingiveshim$15.Heearns$16perweekforhispaperroute.Hewilluseallofhisbirthdaymoneyandallofthemoneyheearnsfromhispaperroute.Inhowmanyweekswillhebeabletobuythemountainbike.A24B25C26D27E282024/7/308第9页/共30页第8页/共30页第八页，共31页。【代数(dish)】15Leta,bandcbenumberswith0abc.whichofthefollowingisimpossible?Aa+cbBabcCa+bcDacbE(b/c)=a2024/7/309第10页/共30页第9页/共30页第九页，共31页。【代数(dish)】19Picktwoconsecutivepositiveintegerswhosesumislessthan100.Squarebothofthoseintegersandthenfindthedifferenceofthesquares.Whichofthefollowingcouldbethedifference?A2B64C79D96E1312024/7/3010第11页/共30页第10页/共30页第十页，共31页。【代数(dish)】21Theaveragecostofalong-distancecallintheUSAin1985was41centsperminute,andtheaveragecostofalongdistancecallintheUSAin2005was7centsperminute.Findtheapproximatepercentdecreaseinthecostperminuteofalong-distancecall?A7B17C34D41E802024/7/3011第12页/共30页第11页/共30页第十一页，共31页。【几何(jh)】周长（perimeter）面积（area）平面图形（triangle,circle,square,quadrilateral,trapezoid,hexagon,isosceles/equilateraltriangle,）立体图形（cone,pyramid,cylinder,cube）线段(xindun)关系（perpendicular,parallel）固定周长，求面积最大最小值固定面积，求周长最大最小值2024/7/3012第13页/共30页第12页/共30页第十二页，共31页。【几何(jh)】14ThebaseofisoscelesABCis24anditsareais60.Whatisthelengthofoneofthecongruentsides?A5B8C13D14E18等腰三角形性质：底边中线、高、顶角(dnjio)角平分线，三线合一勾股定理：2024/7/3013第14页/共30页第13页/共30页第十三页，共31页。【几何(jh)】22Alemmingsitsatacornerofasquarewithsidelength10meters.Thelemmingruns6.2metersalongadiagonaltowardtheoppositecorner.Itstops,makesa90degreerightturnandruns2moremeters.Ascientistmeasurestheshortestdistancebetweenthelemmingandeachsideofthesquare.Whatistheaverageofthesefourdistancesinmeters?A2B4.5C5D6.2E72024/7/3014第15页/共30页第14页/共30页第十四页，共31页。【几何(jh)】8IntrapezoidABCD,ADisperpendiculartoDC,AD=AB=3,andDC=6.InadditionEisonDC,andBEisparalleltoAD.FindtheareaofBEC.A3B4.5C6D9E182024/7/3015ADECB第16页/共30页第15页/共30页第十五页，共31页。【几何(jh)】4Ms.Osborneaskseachstudentinherclasstodrawarectanglewithintegersidelengthsandaperimeterof50units.Allofherstudentscalculatetheareaoftherectangletheydraw.Whatisthedifferencebetweenthelargestandsmallestpossibleareasoftherectangles?A76B120C128D132E1362024/7/3016第17页/共30页第16页/共30页第十六页，共31页。【几何】4二次函数(hnsh)极值设长为x，则宽为25-x面积(minj)=x(25-x)=X越接近值越大，越远离值越小2024/7/3017第18页/共30页第17页/共30页第十七页，共31页。【几何(jh)】12Aunithexagramiscomposedofaregularhexagonofsidelength1andits6equilateraltriangularextensions,asshowninthediagram.Whatistheratiooftheareaoftheextensionstotheareaoftheoriginalhexagon?A1:1B6:5C3:2D2:1E3:12024/7/3018第19页/共30页第18页/共30页第十八页，共31页。【数形结合(jih)】16AmandaReckonwithdrawsfivecircleswithradii1,2,3,4and5.Thenforeachcirclesheplotsthepoint(C,A),whereCisitscircumferenceandAisitsarea.Whichofthefollowingcouldbehergraph?2024/7/3019第20页/共30页第19页/共30页第十九页，共31页。【几何(jh)】23Whatistheareaoftheshadedpinwheelshowninthe5*5grid?A4B6C8D10E122024/7/3020第21页/共30页第20页/共30页第二十页，共31页。【几何(jh)】13Thefollowingnetisgiven:whichoneofthefollowingcubescannotbefoldedfromthisnet?2024/7/3021第22页/共30页第21页/共30页第二十一页，共31页。【数论(shln)】约数与倍数（multiple,divisor,commondivisor/factor）数列（array,series,consecutive,integer,wholenumber,positive,negative）数字(shz)（digit,remainder-差/余数）2024/7/3022第23页/共30页第22页/共30页第二十二页，共31页。【数论(shln)】3Whatisthesumoftwosmallestprimefactorsof250?A2B5C7D10E122024/7/3023第24页/共30页第23页/共30页第二十三页，共31页。【数论(shln)】18Theproductofthetwo99-digitnumbers303,030,303,030,303and505,050,505,050,505hasthousandsdigitAandunitdigitB.WhatisthesumofAandB?A2B64C79D96E131只用计算( jsun)到千位2024/7/3024第25页/共30页第24页/共30页第二十四页，共31页。【数论(shln)】练习3Youdivideapositivewholenumberby1995,andyougetaremainderof75.Whatistheremainderifyoudividetheoriginalnumberby57?设整数(zhngsh)为NN=1995k+75(k是正整数(zhngsh)N=(35*57)k+57+18=(35k+1)*57+182024/7/3025第26页/共30页第25页/共30页第二十五页，共31页。【数论(shln)】9Ifthecoinsareequallydividedamongsixpeople,fourcoinsareleftover.Ifthecoinsareequallydividedamongfivepeople,threecoinsareleftover.Iftheboxholdsthesmallestnumberofcoinsthatmeetsthesetwoconditions,howmanycoinsareleftwhenequallydividedamongsevenpeople?A0B1C2D3E52024/7/3026第27页/共30页第26页/共30页第二十六页，共31页。【数论(shln)】9设有N个硬币(yngb)N=6m+4N4(mod6)N=5n+3N3(mod5)找一个数是5的倍数，且除以6余125找一个数是6的倍数，且除以5余16N=4*25+6*3-5,6k=118-30k最小的正整数为282024/7/3027第28页/共30页第27页/共30页第二十七页，共31页。【数论(shln)】9扩展一个(y)数，被3除余1，被4除余2，被5除余4，这个数最小是几？找一个(y)数是4和5的公倍数，且除以3余140找一个(y)数是3和5的公倍数，且除以4余145找一个(y)数是3和4的公倍数，且除以5余136N=1*40+2*45+4*36-3,4,5k=274-120k最小值为342024/7/3028第29页/共30页第28页/共30页第二十八页，共31页。【数论(shln)】练习4SupposenandDarepositiveintegersand0D9.Determinenif循环小数(xnhunxiosh)化分数设A=0.9D59D59D5（1）则1000A=9D5.9D59D59D5 （2）（2）-（1）得：999A=9D5,A=解得D=2，n=7502024/7/3029第30页/共30页第29页/共30页第二十九页，共31页。2024/7/3030感谢您的观赏(gunshng)！第30页/共30页第三十页，共31页。内容(nirng)总结【统计】1。设长为x，则宽为25-x。找一个数是5的倍数(bish)，且除以6余125。找一个数是6的倍数(bish)，且除以5余16。找一个数是3和4的公倍数(bish)，且除以5余136。解得D=2， n=750。感谢您的观赏第三十一页，共31页。