2018高中一年级数学竞赛试题参考答案解析和评分标准

完美WORD完美WORD格式资料专业整理分享专业整理分享-12017B．05月1436C．28：30－11：00A={-2,-1,0,1,2}A-BCDABACADA-BCDA-BCDAB=AC=ADA-BCD（第2题图）A-BCDV=-a36xy=2x-3y x(-4,-3)u(0,+8)(0,2)u(4,+8)(—8,-4)u(-3,0)D(-8,0)u(2,4)xy=2x-3y2xx(x(x+4)<0x+3x<-4 -3<x<02x2x+ <0x+3(-8,-4)u(-3,0)m±an〃mm±amHan1Pn〃an〃Pa1PmHP nHPC3a〃PD4ABCD—ABCD11BD面ABCDAC11BDADEFAC11（第4题图）EF〃面ABCD1111面BCCB11ABCD-ABCD1111AD〃面BCCB11ABCD1111ABCDBCEF〃面BCCB11AD〃面ABCD1111f(x)=(x2+2x)(x2+mx+n)x f(-3+x)=f(-3-x)-16B-14C-12-10f(-6Aff(x)(A) 0f(-4)=f(-2)=024(36-6m+n)=08(16-4m+n)=0m=10n=24m=10n=24f(x)=(x2+2x)(x2+10x+24)=x(x+2)(x+4)(x+6)=(x2+6x)(x2+6x+8)f(x)=(x+6x2)+8x+x[=)对2邛 9上 8式,)9f(x)=(x+3)4-10(x+3)2+9=1(x+3)2-52-16f(-3+x)=(x2-5)2-16 f(-3-x)=(x2-5)2-16(x+32)-5=0x=-3±/ f(x)-16bceR a2cbc2c=1((a—1)(b—1)(c—1)=abcabc—ab—bc—ca+a+b+c—1=abcab+ab+bc+ca=x—1c2=(acbc)c2—(ax2—x2—2(x—abc(ac1*1bc=0acbcc=1abcbccca=0ab+(a+b)(1—a—b)=0a2a2+b2+ab—a—b=0b2+(a—1)b+a2—a=0△二(a—1)2—4(a2—a)>03a2—22—6L1,0]366L1,0]36=10g(xcm) a>0a[-1,0]f(—1)=log(f(—1)=log(—1+m)=—1af(0)*log(0cm)*0a[-1,f(—1)*log(—1cm)*0af(0)*log(0cm)*—1a[-1,0]0]P—ABCPA=PC=P—ABCPA=PC=BA=BC=5AC=6PB=4PA面ABC2735ACOOPOBPA=PCBABCAC=6AC±OPAC±OBOP=OB=4AC1面POB面ABC1面POBPB=4 △POBPH1OBHPH1面ABC PH=2^/3/PAHPA面ABCPH2\：3sin0=sin/PAH== （第8题图）（第8题图）A(-9（第8题图）（第8题图）A(-9,12) B(-16,-12)O(0，0)OBAD/OAB(-6，-22x4-=316t+t=6OBAO0B9tADAO32x4-=316t+t=6OBAO0B9tADAO3y=—x4/OABAB96-2t4 30025D(4t，3t)AB—4<t<0（-6，-91。 f(%)f(2兀)=2f(%)f(%)f(%)

f(冗)=1R2；1<%V211<f(%)<2L-2,8-2]f(%)

[-1,d2[1,2]f(2兀)=2 f(%)[0,1][0,1]f(2)=1f(2-2>f贝=)1f(8-2兀)=f(2k-8)=f(2兀)=21<2—2<8-22<211[2-2,8-2k]11f(%)=f(%) f(%)=f(f(%))f2017(3)二322019-332324-33

f(3)=—

2 1333

f(3)=-= 1 5 23-333f(3)=—=——3 29 25-3122%yf(3)=

n%>0y>0z>0 %2+5y2+z=11=%2+5y2+z2=(%2+4y2)+(y2+z2)>4盯+2yz=2(2%y+yz)1+yz<-2y=z%=—j=y=z=—j=10 .1013、14、15、16题每题1617题147813．(1f(x)=ax2+(3一a)x+c-1<x<1if(x)i<6f(x)p(-1p(-1，1)611<c<662 4(xi,y)B(x2，y2)xx x<x<3 AB12 121 1 , , 1 11 |f(0)1=1c|<6|f(1)|=3+c<6f(0)=-1 f(x) [-1,11 f(0)6f(x) x=0 1-a=0a=133f(f(x)=—x2-TOC\o"1-5"\h\z3 61 1 11x-1k=—PB3yx-1k=—PB32 1k=♦6_'31 6，6—x,-1PAx-(-1) x+1 311PA±PBPAPBxx3dPAPBxx3d1212(x-1)(x-1)=-912xx12x-1=-91x-1=12x<32ABx<x12H-1=-3Ix-1=32x=-8，x=2

12A(-8，127Ix1-1=-1Ix-1=927B(2，一)6AB12x+6y—31=016PB14lx+y—10=0PC(x—4)2+(y—2)2=4 PAPBB1l P /APB=120° P2AB0P1 P/APB/APB=120°ZAPC=60°CA=2CA±PAPC=4C(4，2)4+2—10I L LdPC=4C(4，2)4+2—10I L Ld= =2也 PC>2gv24L>2J2<3P2 P(x,y)l00PA=PB=(；(x—4)2+(y—2)2—4% 0 0/x0—4)2+(y°一2)2—4AB (x—x)2+(y—y)2=(x—4)2+(y—2)2—40 00 0x2+y2—2xx—2yy+8x+4y—16=00 00ABC (x—4)2+(y—2)2=4x2+y2—8x—4y+16=0(x—4)x+(y—2)y—4x—2y+16=00 0 00AB(x—4)x+(y—2)y—4x—2y+16=00 0 00ABO —4x—2y+16=000x+y—10=0x=—2y=1200 0 0P (—2,12)1216H△ABC MAH（第15H△ABC MAH（第15题图）（第15题图）15 △ABC CF±ABFGCMCG±GB/MFG=/GCF/MCA=/HAGBF±FCBG±GCBCGF/AFG=ZBCG 4MAHMF=MAMHZAFM=ZFAMAHBCNH△ABCAN±BCZBAN=ZFCBZAFM=ZBANZFCZMFG=ZAFG—ZAFMZGCF=ZBCG—ZFCBZMFG=ZGCF 81 ZMFG=ZGCFZFMG=ZCMF△MFG^MCF竺=MGC 12MCMFMF二MAMA_MGMC：一~MAZCMA_ZAMG△MCA^^MAG16ZMCA_ZMAG=ZHC1616f(x) (-8,0)U(0,+8)f(f(x)=](1(2a-1<a<0 S(a)f(x)2x-2 ,0x< 2,、 ，/、g(x)=f(x)-a|x—5|-1,x>2g(x)S(a) g(x)】(1)如图，（第16题图）a=2 a=-2 y=a y=f(x)a=2 a=-2 g(x)a=2 a=-2f(x)-1<a<0 g(x) 66个零点6个零点+x=-1022x-2-a=0x1x+x=10x56 3

x，x，x，x2345-2-x+2-a=0S(a)=-10-log隹+)loga(2+aa力二log12-1e(3，1)S(a)e-log,30)2(-log3,0)16-1<a<0 (-log3,0)16171eS，901eS901ISIS—<x1，x，x，L

23，xn<x<x<L

23<x=901

n23X-x in-1eN*-akX-x 1n-1X-xx-1—k n-1n-1n-1eN*2<k<n(n-D|(xk-1)-xk-1二(x-1)-(x-1)2<k<n2<k<nk-1(n