2005年重庆市初中数学竞赛

93(2x-210-y)=x+y,x=126+45y.y0y5,x126+4=130.,130.15.(1)9.(2)6.ABCx;DEFy;z.,x+y+z=1+2++9=45.9,18,,z+3y+2x=618=108.-x+2y=108-45=63.ABBCCA,2x+y=318=54.,x=15,y=24,z=6.1,2,,924789,,DEF,789,6.,,,.,6.()2005(5,35)1.a|2004-a|+a-2005=a.,a-20042().(A)2003(B)2004(C)2005(D)20062.m,20%(=-).25%,m,().(A)25%(B)20%(C)16%(D)1215%3.1,,,.,2(yL)(t)().4.x0ax2+bx+c=0(a0),M=(2ax0+b)2,N=b2-4ac.MN().(A)MN(B)M=N(C)MN(D)NM2N5.3,,.23©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.().(A)35(B)45(C)56(D)676.OA(2,-2),B.AOB,B().(A)4(B)5(C)6(D)87.x2+mx+n=0,mn1,2,3,4,5,6.,().(A)20(B)19(C)16(D)10(5,35)8.9.2,2,6,22,10,,102:22622102314432252226102,32(2,4),26(3,2).,.10.0.a1a2a31,ai(i=1,2,3)02,T,S.ST=.11.abcdef,bcdefa=12,acdefb=14,abdefc=18,abcefd=2,abcdfe=4,abcdef=8.a+b+c+d+e+f.12.,|x|+|y|3p.p.13.4,RtABC98,DBC,BDDC=25.ADADEF.4514.5,÷ABCD,ACB=30,ABCAC,B÷ABCDE,DE.AC+DEAD.15.(16),66.xcm,ycm,zcm.,:,xy=xz+3,yz=xy+xz-7.,()?16.(16)7,ABCD,EFABAD,EFEH3320069©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(ab).(1)AE=AF=1,EHAC,ab,CHCG?,ab;,.(2)SAHGSCEF,.17.(18)1,2,,200200,k,mn25nm52.k,.1.C.a-20050,,a-2004+a-2005=a.a-20042=2005.2.C.a,x%,m=a20%=a(1+25%)x%.x%=16%.3.B..4.B.x0=-b2a.(2ax0+b)2=b2-4ac.5.D.a,b(ab),p,aa-b,p1.a(a+b)a(a-b)=53.b=14a.a=4,b=1,p1p=(3+4+5)(1+4+4+5)=67.6.D.Bxy3,1,8.7.B.=m2-4n0,m24n.n=1,m=2,3,4,5,6,5;n=2,m=3,4,5,6,4;n=3,m=4,5,6,3;n=4,m=4,5,6,3;n=5,m=5,6,2;n=6,m=5,6,2.19.8.2-7.(3-m)(8+m)=10.9.(20,3).,2,4,6,,200,100.520,196=14.10.011111.a1a2a3000,200,020,002,022,202,220,222.8.S=018888.11.52+1524.6(abcdef)4=1.abcdef=1,a2=2,b2=4,c2=8,d2=12,e2=14,f2=18.a+b+c+d+e+f=2+4+8+12+14+18=52+1524.12.122.32.13.116.DGAB,DHAC,GH.AB=AC=14.BDDC=GDHD=25,DG=4,DH=10.,AD=42+102.SADEF=116.14.3.BAC180E,ABCDE.EC=BC=AD,AE=AB=CD,43©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=30.ACF,CF=ED,ADF30.AC+DEAD=AFAD=3.15.xy=xz+3,,x(y-z)=3.xyz,x=3,y-z=1x=1,y-z=3.(1)x=3,y=z+1,yz=xy+xz-7,(z+1)z=3(z+1)+3z-7,z2-5z+4=0.z1=1,y1=2;z2=4,y2=5.2(xy+xz+yz)=2(32+31+21)=22(cm2),2(xy+xz+yz)=2(35+34+54)=94(cm2)().(2)x=1,y=z+3,yz=xy+xz-7,(z+3)z=z+3+z-7,z2+z+4=0..22cm2.16.(1).AB=a,AD=b,AE=AF=1,,BE=a-1,DF=b-1.EHAC,BHBC=BEAB,b-CHb=a-1a]CH=ba.,CG=ab.ab,CG,abCHCG.(2)BE=m,DF=n,SCEF=ab-(SBCE+SDCF+SAEF)=ab-12[bm+an+(a-m)(b-n)]=12(ab-mn).BH=p,DG=q,SAHG=ab-(SABH+SADG+SCHG)=ab-12[ap+bq+(b-p)(a-q)]=12(ab-pq).BEHDGF.,mp=qn,mn=pq.SAHG=SCEF.17.12002006,2552.:1(1,2)2(3,4,5,6,7)3(8,9,10,,20)4(21,22,23,,52)5(53,54,55,,132)6(133,134,135,,200)k=7,6200,7,,,mn,25nm52.k7.(),,,,,,,,5320069©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.