北京市海淀区2020届高三上学期期末考试数学试题-Word版含答案

海淀区高三年级第一学期期末练习数学4共4AIðB是1,2,3,4,5,6A1,3,5B2,3,4）已知集合U，，U1,3,5}1,3}1,5}1,3,5,6}））））y24x(0,1)）(1,0)））(10)）(0,)(1)(1)2x2y2yxyx）））y2x）y2xa,bÎRa1111()()<）a>b2）<）sinasinb）ab2ab133(x)3x）-5x5）5-10）10）a,b,cabc||||||1abc0ab11233））））--222==m，In“m∥n“∥的,,IABC点D在，7.ScosBAD）cosCADsinBADsinCADBDCD2）2）ABD2）2SACD-1-x(x)()xW/m2ffx.11012）倍）倍）倍）倍681012(M)点N=f.如NMaD1Ca11ABCD-ABCD1111A1ABCD为b面为gPCC1，1CQ=f1[f(P)]Q=f[f(P)]，.PC112gbbgDC12PQ[,AB)；222PQ；Pb1PQ^PQ.P12共655a2aa，an2571+iz=|z|ix2y2(0,3)1(a0).A,BCa23a(x)xfax(x)Asin(x)f-2-xx022f(x)000221(1)ff()则f，2yy1：x4（m.422CC1(,)PxyxC|1|1或ym.2.）当mCm.61()2x3xxf.2(x)ff()m]1.mVAC和VABCVBC2，ACCV，，△ABVA,VB.MNMN；ACABVC；BCMN.4-3-）04.4））））TwTwTwTwT注：每个小区分钟社区生活圈”指数，其中11223344w,w,w,w,,,TTTT12341234.））））C22ξξ.A3x22y22:1(ab0)．C2abCP，AP和OOlCQAQ4,MN.xAPQ()e(ax1)(a0).fx2f()(0,f(0))yf(x)f(x)1.-4-x,x,L,xA2n1(2)Annx,2n1122n1k为m(1,2,,21).将mLn,m,L,mAkk122n12n1:1,2,3,3,3m,m,mAA51235i(n1)][j(n1)]0ijLn,且xLxx122n1ij||与||mmxxijij1||An2n1xxijij2n1-5-海淀区高三年级第一学期期末练习参考答案数学:4分.123456789DDBACAABCB65.022(1,16)；2①m；0261cos2x312(x)sin2xf2231sin2xcos2x22πsin(2x).6ππ22kπ,2kπ(kZ)sinxy，2πππ22x2kπ,2kπ(kZ)令，62ππ6kπ,π(Z)kk得xf.3ππ6π,π(Z).(x)kkk3x[0,m]，πππ2x[,2m].666-6-πsin(2x)6[0,m]f(x)，x，ππ2m.62πm.6πm.6ππ(kZ)(x)xf6f()m]1，πm.6πm.6△VABNMN.zMN//AB.VABCMNMNCMN，，ABCMNM.NACCV△VAC,所以VCAC.AxC因为平面VACABCVACIBABCACVC平面VAC，，Hy所以VCABC.ABABC，ABVC.做，CHCVCABC，CH所以VCCHABC，.xyz以C.C-7-11则C(0,0,0)V(0,0,2)BM(1,0,1)N(,，.，，，2211VB(1,1,2)CM(1,0,1)CN(,,1).，，22CMN(,,)，xyznCM0,CN0.n则nxz0,即11xyz0.221则y1，z1,令x1).n直线VBCMN，nVB|n||VB|sin|cos,VB223.223所以直线VBCMN.A0.70.20.70.20.50.320.50.280.58T，0.580.60AB0.90.20.60.20.70.320.60.280.692T，，0.6920.60BC0.10.20.30.20.20.320.10.280.172T0.1720.60CA0.70.20.70.20.50.320.50.280.58T0.580.60AB0.90.20.60.20.70.320.60.28T0.60.20.60.20.60.320.60.280.6.BCT0.10.20.30.20.20.320.10.28-8-0.60.20.60.20.60.320.60.280.6.CC113010个小区中，共有优质小区1041001046.C126PPP；C2310CC81416；C210C262.4C210则2011382P15151824012315155.a2,c3,a2c2a2b2(0).ababx2Cy1.24Q(x,y)(x,y)P，0000-9-x2y1220（x且y024000y(x2)QAy0x202y2y4N(4,)令xy.00x20x20y2yy(x2)M(4,).0PA0x2x2004设B为x与x11SS|OA||yy||AB||yy|22PQMN112y2y|2y|||0022x2x2000112|y|2|y|||00x02x2042|y|2|y|||.x400204y4xS，y0,2020012Sy|2|y|=2|y|4.|y|00y2000y14.SS0APQf(x)e(ax21)，ax2x(0)1，f(0)=1，fly=x+.0<a?11ax21ax(1)1，02ax2a()e(ax21)01且x1afxax2x(x)Rff在(x)R在.-10-1ax22104(1)0aa，a>,xxx.记x1212xx212则1xx12axx0.12()fx()，fx随x(x,)x1122+0-0+f(x)↗↘↗(x)f(x).f2[x(x)f在2f(x)<f1.2(x)1.fm(33)(23)1;1m2;2m3.3A5|mm|=|xx|.ijiji(n1)][j(n1)]01i,jL,nm(xxLx)(xxLxx)i2n12nn2n1n1i-11-xxLx)(xxLx)x2n12nn2n1n1i=(xxLx)(xxLx)xmj2n12nn2n1n1jmxxm.ijij|mm|=|xx|.ijij当i,jnnL,2n○2○1m(xxLxx)(xxLx)i2n12nn1inn11xxLx)(xxLx)x2n12nn1nn11im=(xxLx)(xxLx)xj2n12nn1nn11jmxxm.ijji|mm|=|xx|.ijij|mm|=|xx|.ijijxLxx，122n1||xxijij2n12(2nxL2x0x2xL22n12nn2n1n12n(xx)(2n2)(xx)Lxx)，2n112n2n2nxxxLxxx，2n112n2n2nxxLx(xxLx)2n12nn2nn11(xLx)(xxLx)m.n12n12n2n1xxn12n1xxLx(xxLx)2n12nn2nn11(xLx)(xxLx)mn22n123n11-12-xx1n1m,mn1，12n1xxLx(xxLx)n1.2n12nn2nn11xxx1n12n1A2n1xxLx(xxLx)n.2n12nn2nn112kn，q0(2n2k)pkq(n1)(pq).p(2n2k)pkq(n1)(pq)=(n1k)p(n1k)q0(n1k)(pq).(2n2k)pkq(n1)(pq).|xx|ijij2n12n(xx)(2n2)(xx)Lxx)2n112n2n2n(nxxLxxxLx)2n12nn2nn11n(n1).1k,当xn1knk|xx|n(n.ijij2n1|xx|n(n.ijij2n1-13-xxLx)(xxLx)x2n12nn2n1n1i=(xxLx)(xxLx)xmj2n12nn2n1n1jmxxm.ijij|mm|=|xx|.ijij当i,jnnL,2n○2○1m(xxLxx)(xxLx)i2n12nn1inn11xxLx)(xxLx)x2n12nn1nn11im=(xxLx)(xxLx)xj2n12nn1nn11jmxxm.ijji|mm|=|xx|.ijij|mm|=|xx|.ijijxLxx，122n1||xxijij2n12(2nxL2x0x2xL22n12nn2n1n12n(xx)(2n2)(xx)Lxx)，2n112n2n2nxxxLxxx，2n112n2n2nxxLx(xxLx)2n12nn2nn11(xLx)(xxLx)m.n12n12n2n1xxn12n1xxLx(xxLx)2n12nn2nn11(xLx)(xxLx)mn22n123n11-12-xx1n1m,mn1，12n1xxLx(xxLx)n1.2n12nn2nn11xxx1n12n1A2n1xxLx(xxLx)n.2n12nn2nn112kn，q0(2n2k)pkq