2020-2021學年高三上學期六校聯(lián)考(一)數(shù)學試卷及答案

.ABU，CAB）U）acbcababcd，acbd若若若11abbbc2aab若24ababb（aaa3b）n7n7759842，，mnmn；mnmnmnmnmn當，Ma,b|ab12,aN,bN**）個個個abc個abCAB，，，）cosBcosAa5aR272若xa（）xx233.Ay1x22y4x）1711722532PFF，F(xiàn)P1212172eFee2）2221e1633645503.）i13iz3i.z10102zzi1，z,yx2y21.z0.z，zzzz212112z1i6月16月16月2）813211335722AB2ABCDABCD，，111111AABBCC2）11173CCAA11163,02xxx(x)f）(xx0ff2f4fxxii6xyfxb在96ii1fx1111,3k3..三、填空題：本大題共45135.1b6，4ab與a，abaPX0~N1,2X2PXaBAD，AC11ABCDAAa2ABCD11111與BC17fxfxx0fx,436.AxA.fx2f1xRf(x)f0f333fxfx,.331SanSanN*.4nnnnan(n2)a14TnTbbn.nn(nnnnPABCD中，//ADABCDABCDBC，，EPA2，AP3ABBC2，4.，PC//.7PCD.fxx,fe4eyxe.fxxfxtx11.t332x2y22Pa2b1ab0PP，P0,3C：，，23124C.Clymm0Cx：yMN，MONl.ABA、B兩種餐盒的配餐比例為3:15.5BBBABnnN*ABA餐XX.CCACABUUDc0acbcabA當70ab0cd，acbd當若B11ab11Cab00ab或a0babc2ac2bbc2abD若2c2c2Aaa4aa4aa47ba，a27n377774bbb8∴bb7n597Bab12ab，ab12,bN*，，a，bab12a,bNa，4，*，，，，，，，，，，DabasinAab，sinAsinBbsinBcosBcosAsinAcosBsin2Asin2BA或2A2B，BABAB或∴sinBcosA2∴ABCDa5arxCx5raCxr0,1,2,3,4,5103r，.2r1r2rrx5x5令10r7r1，37aC1155axA7Aa3bAA',bxy4'M,xy4，22a3b4a422A'PBb0b11a3PA'PA'A'A'到x2y21OA'1171CFFFPc2a2a，12122FPFPaFPFPaFPcaFPca，，，12112211122e2ac4aac2a2ca，21122c2a2ca12e12242caacca4ac2eac2222422∴∵22，22e21ca2cac2a2222ac2a2eacc2222222，c2acac2ae212227113i3i由Az3i(3ii)zixy2i1,yx(y2)1，由z22y21則x22Babizabi2zz(abi)(abi)ab0Cz22112z1iD-1(86255714322016040217160121158867937)15614在6月16月123766136月16月1，共41，，4133月522ABC22；△SAB與，1111232AA4SO233A則SA，11SASCAC4B錯AA與CC1；1(22SSS8441267SC22側OO13BO1OB2OBBBOO1，OBB111111rOB216則D7x3fx3fxfx在故在329fxfxx0x在A24ff22f2f4yfx又Byfxb在yfxb6y與在63x23xxxix，xx，x32ii112493396x，xxx2229C222256ii113kyy1，3xx0x3kx10，kx1yx與22令03240k或k1k5，當k1x1k5x1k1.kx1yfx與k1.y在7fx1ykx1yfx與331k1D.1k∴或323；3223ba42416cos,ab14aaba，1223cosa,b0a,ba,b.a與b232.3PX~N1,2，X2，PX0PX2PX01PX01.AC，AB1//ACACBAC與BC1AC.11111aBAD，AA，2a171CB(2a)a5a2aaaAB22，a2a2.211(a)(5a)(5a)15222cosACB.2a5a101AC與BC1.11.3；2fxxfxx0，,fxfx43,,，432233422）223212fx4.700k6kZ，f.36.261A1A1，f336612()fxxA.262fxxR()fx1，fx3332kZk，.32261A1A1A2.f33661(x)xf.261x13x,x,,，3326632622fxfxx3；當x33fx3.-11114aSaSSaaS，444n1n1n1n1nnnn1aaan1a，n∴a2n1nn111n1aa，a1令4811181aa12n1111n1n2∴a.8222n2n7(n2)ab，nn(nn2111n∴b，n(n1)2n22n2(n1)2nn1nTbbbb∴n123n1111111111112122222232232422n2(n1)2122334nn11111114，212(n1)24(n1)2n21n114∴T.nAC交.FABCDAD2BC，AF:CFAD:BC2:1AFCF，∴在PAC2，AFCF，EF//PC∴又∴.，PC，PC//.A、、為xyzzBCDEP，，，，.2,0,2BD2,4,0PC2,2,3PD0,4,3，BE，，，x,y,znx,y,z設m和PCD1112220240xymm，2y1z211x得，2x2z00111m1102230xyznn3,3,4，3x3z4222y得，4y3z00222n22mn,n，36mn6PCD.7fxf'xnxmn，，f'em2n4m2，fe4een1fx2xxx；fxtx11）2xxxtx11，2xxlnx1xt，x12xxlnx1，令g(x)(x1)，xtgxx1minx2xx，g'x而，(x21x1h'x1hxx2xx10，xxhx1,在h310h42ln40，，又xhx0x02lnx，000gx1,xxxhx0g'x0，當當在00gxx,xx,hx0g'x0，在002xxx212xxx1(x)gxx，1gt000000110xx000x1，07xx1又，00ttP，PP，1243Pa4.Pb3221x2y21.C43x2y214k3xkmx4m12043.222ykxm64km44k34m120，22224k3.m22mkk0MNm，，，11mm2OMONm∴S，22k2k△MON4k3，∵m∴S224k31324k.2k2k△123k04k23∵，k33，234k23，kkS2k4k3∵m∴m222，0mm.6633x6y或x6.ly2271B5B414~則B，314523CPB35.44512）Xn.131331n1P(X0)，P(X1)P(Xn1)，44416443nP(Xn).4X012131432n4444444X313131313423n1nE(X)123(n1)n①444444443431313131323n1nn1E(X)12(n2)(n1)n②4444444441313131313123n1nE(X)，44444444444343n1433333323n1nn∴E(X)31.3444444413n即X33.47xx1又，00ttP，PP，1243Pa4.Pb3221x2y21.C43x2y214k3xkmx4m12043.222ykxm64km44k34m120，22224k3.m22mkk0MNm，，，11mm2OMONm∴S，22k2k△MON4k3，∵m∴S224k31324k.2k2k△123k04k23∵，k33，234k23，kkS2k4k3∵m∴m222，0mm.6633x6y或x6.ly2271B5B414~則B，314523CPB35.44512）Xn.131331n1P(X0)，P(X1)P(Xn1)，44416443nP(Xn).4X012131432n4444444X313131313