2018年全國(guó)初中數(shù)學(xué)競(jìng)賽試題及答案

2018年全國(guó)初中數(shù)學(xué)競(jìng)賽試題及答案年4月1：：56，D0xy）xy6123409562個(gè)8234種）a、、cx2bc0，a2b2c22a0，2b012解）03c0a0b02，2，2(abc)(t2t1)0tt10a3bc233，Aa2b2c2abcabc3＝333＝abcOOOLnFKEmH）DCBOOF，F(xiàn)作H，EHOO6x5xyy2(xy)，x3023）1366１5633(xDxCyx，D．A(a,3a),C(2ab,b)Cy即D(2ab,0)D(26,0)a3,b63，x==PP是．OACQAG=n．7BBCGαβEa．12a322(1)1a330f(1)1a330fxf(2)42(a3)30,f11a,或a3232111na．a(chǎn)112n23aaa(n1)an(n1)n(n1)1解3及3得3312n12n1111111111()(a13n1n3n2n2n4yx3x4P．已知拋物線C：y：2212CABQCAB812A61∥y4xxx2或g=-3x-4Px3x4y22=-x-3x+4OAB）x5(22)(66)410AB22，ybaa4，2pQyQy2BQy(aa4)(aa2a28＝y(tǒng)＝22pQ。1a，xx2b21abx(ab)0x,xx2，212xab0,xx(ab)0x0,x0，由x知12121212x）x12x(ab)2(ab)0(ab)2(ab)，，x22122()2(11)4即abab2()b或11abab(ab)2(ab)b2xx122xxab112xxxx2x，則12xx1ab1212222xx11x1111ab(ab)02()20即ab4)15ab把x121(2ab52a112a15a1a3b1,或或則b15,b11,b3,３xabx1312由x得122或12abx()0ab1,2。xxx221DEADCFBCF的．ADPDBCPC）；．PG，180180PCEPCFEDAADPDBCPCFCB）APDBPCAPBDPCPABPDCPAPDPAPBPDPCPBPCm，nm(m2)n(n？k(kmnm(mk)n(n，？m(m2)n(n(m1)nn122nn1(n1)n2n1nn222m，nm(m2)n(n當(dāng)m(mn(nm3mn(n1)0，294n(n1)8(2n1)l2（lm2(2n1)8,[l(2nl(2n1)]8即l22４l(2n1)8l(2n1)4,或，l(2n1)1l(2n1)2,0m，nm(mk)n(n。n543ktt的正整數(shù))m(mk)n(ntmnn2(1)0當(dāng)km2t4n(n1)(4t1)(2n1)l2（l設(shè)222即l2(2n1)24t2[l(2nl(2n1)]4t1)12(21)41lt2tt2222tllnt2mtt令2(2n1)1122ltn2tt的正整數(shù)m(mk)n(nm(2tmn(n1)0k2(2t1)4n(n1)4t(t1)(2n1)l設(shè)222（l即l2(2n1)24t(t1)[l(2nl(2n1)]2t(t1)212lttl(2n1)tt1)令(1)tt，l(2n1)2n12(2tl(2ttt1tt22mn2223mnm(mk)n(n，；kmtt2當(dāng)k當(dāng)ktt的正整數(shù))m(mk)n(n；t1n2tt2mn2t1(t的正整數(shù))m(mk)n(n。tt212５l(2n1)8l(2n1)4,或，l(2n1)1l(2n1)2,0m，nm(mk)n(n。n543ktt的正整數(shù))m(mk)n(ntmnn2(1)0當(dāng)km2t4n(n1)(4t1)(2n1)l2（l設(shè)222即l2(2n1)24t2[l(2nl(2n1)]4t1)12(21)41lt2tt2222tllnt2mtt令2(2n1)1122ltn2tt的正整數(shù)m(mk)n(nm(2tmn(n1)0k2(2t1)4n(n1)4t(t1)(2n1)l設(shè)222（l即l2(2n1)24t(t1)[l(2nl(2n1)]2t(t1)212lttl(2n1)tt1)令(1)tt，l(2n1)2n12(2tl(2ttt1tt22mn2223mnm(mk)n(n，；kmtt2當(dāng)k當(dāng)ktt的正整數(shù))m(mk)n(n；t1n2tt2mn2t1(t的正整數(shù))m(mk)n(n。tt212５l(2n1)8l(2n1)4,或，l(2n1)1l(2n1)2,0m，nm(mk)n(n。n543ktt的正整數(shù))m(mk)n(ntmnn2(1)0當(dāng)km2t4n(n1)(4t1)(2n1)l2（l設(shè)222即l2(2n1)24t2[l(2nl(2n1)]4t1)12(21)41lt2tt2222tllnt2mtt令2(2n1)1122ltn2tt的正整數(shù)m(mk)n(nm(2tmn(n1)0k2(2t1)4n(n1)4t(t1)(2n1)l設(shè)222（l即l2(2n1)24t(t1)[l(2nl(2n1)]2t(t1)212lttl(2n1)tt1)