2020-2021学年辽宁省沈阳市郊联体高一上学期期末考试数学试题(解析版)

2020数学考试时间：120分钟试卷总分：150分注意事项：本试卷由第Ⅰ卷和第Ⅱ卷组成.第Ⅰ卷为选择题，一律答在答题卡上；第Ⅱ卷为非选择题，按要求答在答题纸的相应位置上.第Ⅰ卷（选择题60分）85）1,2b6,k//a，abk（3370%30%82））()0，g(x)logxfxxax）a12(x)x1f）x0,122,e3,430.1b3，log0.2a，c）2abcbcacbacab8为575%）22256256行2.511）（lg20.3010lg30.477，）4.5104.5104.5107秒秒秒秒4540,5050,6060,7070,8080,9090,100，，，，，）270,80分分）ab,a,b若a//bb//ca//c，a，b，ca//bab若a若a5,71b6，ab(x)4xaf）x2(x)a，fa，f(x)0,1(x)a，f在,1(x)5axfABCPBCBP2PCM、NPAMmAB，ANnACm0，n0）12mn2n3m912mnn2m、nm，第Ⅱ卷（非选择题）4538yx,00,x0f(x)()2fxx2()0xxfx，y则x21812log3lg(21)lg1427100221(0)x2xx(x)()afxfx，x，x，x3logx(x0)1241216xxxxa，xxxxx31234412246共.AB.ABP(AB)P(A)P(B)0.80.71.5.1x28m22102，Cxxm.Ax，Bxx242mB，Cp：xAq：使p是qm.AB；xYY.4Y6201Y66221如图，在OABPAB，是OB.Q38310,0A1,3,03O，，BNQtOP.t与OPOMAQMx(x)3xfaR.a933ax0f(x)01,27()fx.9Mx,yy(x)logxaa0g(x)f2N3x,2yyf(x)yg(x)yf(x).xf(x)1；50,1a()，fxxF(x)f(x)g(x)，x0,1a1当F(x).2020－1,2b6,k，12；a//kab70%，10070%70；ABCDD0yxx0ylogxx与，aaAxx00a1yxx0a中1ylogB中C中D中a，中0a1中ayxx0中0a1，logyxxxxaax0yxy0a1，log00a1中a中D；a20,(x)xf(x)f在x1ln220f2ln310，xfx0f；.000(0.9)1、331，，ca03log0.2log10，22bac658，，875%675%A22.5102xx，xlg2，lgx12lg211256lg2lgx258lg21265.658即，9101010lglg2x，2所以10x4.510B70,80A40,600.005100.015100.220000.2400B70,8040,70CDbabaA//bb//c，aca//bab，a，b，ca，B0bCD.f(x)4xa，x2fxf(x)fx()xR..Afx0a2时0xB.7fxy0x0x,1C.(x)故f在0x0yx0xf(x)5,1aD.1323BCBP2PC、P，1212mABANnAC，1若AMMPN，mnmn123mn12Amn11212m2n12m2n3，nmm2n(m2n)552，，3mn3nm32m2nn1m2nBmnm11212mn12mnnm223mn(mn)3nm321，3mn332mnC112mn23m，nM为ABC为AN2D,22,x2x2或、323xx888yy5xy13.22()0fxxf(x)0当x当0x2f(x)0xf(x)02x0()0xf(x)0当fx2()0xf(x)0当xfx2x2或.xx2181、2log3lg(2lg1427100219213.4421(0)x2xx(x)flogx(x0)12ya(x)axxxx，，，f(x)f1234f01f12，aaxxlogxlogx，1xx22，1212349logxlogxlogxx0xx1，34故故34341616xxx2x.xxx41224434a1logx412a2当logxx，24x44416162,4x2,42xx4x42y2xy故又在4x44x44y224.2()0.8P(B)0.7，A，BPAB，P(AB)P()P(B)0.80.70.56；，ABABABABPABABPABPABPAPBPAPB0.20.70.80.30.38.A，B.ABABAB，ABAB，ABPABABABPABPABPABPAPBPAPBPAPB0.20.70.80.30.80.70.94.记C1PAB1PAPB10.20.30.94PC.2mxm210xx，430mx222解得1x3{|13}Bxx.101x28Ax22223又A23Axx，xx4x1x3AB.x(m1)x(m1)0x2mxm10，22Bx|m1xm，∴m1xm1pq由是BA12m∴，m131m2，xm2m2xm2，Cx|m2xm∴，pq由是CA22m∴，m230m1.Y6Y.6件产品中，指标Y在1A，10.6,11.0在3B，B，B2C，C，12312从62,B，,B，,B，,C，,C，B,B，B,B，B,C，B,C，B,B，123121213111223B,C，B,C，B,C，B,C，C,C，2122313212,B，,B，,B，B,B，B,B，B,C，B,C，B,B，B,C，B,C，12312131112232122B,C，B,C，31321124P.5x13sx6x133sx6xx，.分111,3，B,0是QA，OB23341,0ON,1NQOQON1,1OQ，，33112.且NQ221，3121，3332OMtOPtOA132tttOP又OMOBOAOB①3331，1由是Q，OB21即②212tt341t23，.3212tt2t2ttOPtOAOBOAOBOAOQOM，333333tt341tA，M，Q2.33a0f(x)logxlogx2，33由f(x)0得()loglog2fxxx，330logx2log1logxlog919x，f3333(x)0的解集为x1x.x(x)3x3xx9）faa9333333logxalogx233x(ax2a2.331u2,3，ulogxx,27令931(x)x,27f在92,3(u)u(a2)u2aug2在a2(a2)22a2u2,3gu)ux.2242a3a4x2在g(u)g(3)a3；gu2,3min2a23a4623a3a2gu2,,3在2132a(a2)2gu)g；242a26ax2gu2,3在g(u)g(2)84a.min4fxa3；()aa224a6()当fx；46()84afx.当axa0xa02ax2a，log(xa)1ax2所求不等式的解集为a,2a.13xa，2ylog3xa()(x)fgx2220,1()，fxx10,1()()())0xfxgxxaxa222aa03xa0a0由xx，，得x，30,1(xa)(3xa)22223axa2a在2300,1axa即xx20a2a0a1，12a3aa02a0,1.10,1()g(x)fxa，13x1(x)f(x)g(x)g(x)f(x)logF，2212x143x11(x2(0,1)令t，x，(x2t3x113x1(1,4)x令，32213141489424.t991x3193F(x)3.28222152a(a2)2gu)g；242a26ax2gu2,3在g(u)g(2)84a.min4fxa3；()aa224a6()当fx；46()84afx.当axa0xa02ax2a，log(xa)1ax2所求不等式的解集为a,2a.13xa，2ylog3xa()(x)fgx2220,1()，fxx10,1()()())0xfxgxxaxa222aa03xa0a0由xx，，得x，3