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1、ModelTestforCambridgeInternationalSchoolSolvethefollowingquestionscomprehensive】y1. Threeunitcirclesarearrangedsothateachtouchestheothertwo.Findtheradiiofthetwocircleswhichtouchallthree.2. Findallrealnumbersxsuchthatx+1=lx+31-lx-IL3. (1)Givenx=(1+l/n)n,y=(1+l/n)n+i,showthatxy=yx.(2)Showthat12-22+32-
2、42+.+(-1)n+g=(-1)n+1(1+2+.+n).4. Allcoefficientsofthepolynomialp(x)arenon-negativeandnoneexceedp(0).Ifp(x)hasdegreen,showthatthecoefficientofxn+1inp(x)2isatmostp(1)2/2.5. Whatisthemaximumpossiblevalueforthesumoftheabsolutevaluesofthedifferencesbetweeneachpairofnnon-negativerealnumberswhichdonotexcee
3、d1?6. ABisadiameterofacircle.XisapointonthecircleotherthanthemidpointofthearcAB.BXmeetsthetangentatAatP,andAXmeetsthetangentatBatQ.ShowthatthelinePQ,thetangentatXandthelineABareconcurrent.第#页申乍”7. Fourpointsonacircledivideitintofourarcs.Thefourmidpointsformaquadrilateral.Showthatitsdiagonalsareperpe
4、ndicular.8. Findthesmallestpositiveintegerbforwhich7+7b+7b2isafourthpower.9. Showthattherearenopositiveintegersm,nsuchthat4m(m+l)=n(n+l).10. ABCDisaconvexquadrilateralwitharea1.ThelinesAD,BCmeetatX.ThemidpointsofthediagonalsACandBDareYandZ.FindtheareaofthetriangleXYZ.11. Asquarehastensdigit7.Whatistheunitsdigit?12. Findallorderedtriples(x,y,z)ofrealnumberswhichsatisfythefollowingsystemofequations:xy=z-x-yxz=y-x-zyz=x-y-z第#页
