2021.1海淀區(qū)高三上期末數(shù)學(xué)試題+答案

2021北京海淀高三（上）期末數(shù)學(xué)8共4yx212141214xyy））x））i1i（25xx4）5）5）10）l:x202）l//（）a）1B1（）C2（）D2（）2B4（）CD12（））（）6a1，b（）ab2aba，b01C1（）D2（）））1，“），，n，m，且∥nl，l，l(x)1(x)f則4(x)）f(x)f2ππyf(x)x4ff）annn∈nSa2，Nnnn,n(mn)；SaSmn,n(mn)；a2aamnmna(1,2,3,)TnTnaa1n2①③OO，12aFF1⊙CC.，G·Dandelin122aFF，120⊙C,CMCP122PMPF12）33D43（））6）8共.a}SSSaa}若、、3.nnn12ny2x1F,FM(3,4)2；212;12(x)0()fxaex1f(x)，fRx；a:(x5)(y2)2:(5,22)(,)Ast.PlyaxM224a0lP2l圓Pa；532021；NMANalAP528NMANt④P.4.46ABCABCBCCB1AC平面BCCB,D,EAABB，.11111111AE∥平面BCD11CC平面ABC:若AC1BCAA2BCDAB與.111ABCAcosB和a.3314sinC；7cab；3a1；52bcosA5345669ab年返修臺數(shù)c年返修率=.年生產(chǎn)臺數(shù)33求s,s,s.2222若13smax{s,s}max{s,s}s,s2321221222a..22121[(xx)(xx)(xx)],x,,xs2xx1222n122nn3x2y22:1ab））.已知橢圓W2a2bWxxA，B分別為橢圓WD在橢圓WCD交Q△23.D67x(x)f.x(x)fg(x)f(x)xg(x)1；(x)f(x)x2ax4a1xhx()0a.h2200nn(nA設(shè)nn行1A“n是AA4“；，12R(s)A為s1）As“5”i,j,k5R(i)R(j)R(k)3；2k(kN)nAn*“”k行kk行k2k.k82021北京海淀高三（上）期末數(shù)學(xué)參考答案4））））））））））BADBACDCCA55）））10（）26ABC.1111111D，E，11BE.11.1BCD平面BCD，，11111平面BCD.11BB，，11111，1B11，1C平面ABC，BC平面ABC，，AC平面.19CA，CB，Cxyz1(2,0,0)B(0,2,0)(0,2,2)(0,0,2)D(，C，.A，，B11(CBCD.AB，，111112xz0.1令xn，nAB252210cosn,AB.10|n||AB|10BCD1.AB10173314c,sinCa，3a32sinAsinC.cbaa1，b.0A.2A.37ac，3.ac0C.2103314sinC，cosC1C2.cosBcos((AC))cos(AC)ACAC3331131721421443sinB1cosB2.74337278ba.baba1，a7.733c,sinC,a314a3sinAsinC.c252ABC,bA在0C.2A37ABC,ac3ac0C.2113314sinC，cosC1C2cosBcos((AC))cos(AC)ACAC33311311214214145314sinB1cosB25bA25215.b23sinAsinB253ab57.14.680.75ξ．C16CC223C26CC12C36CC052383838===,ξ12a7，WC2,3431a2b2W，32c3a2b2c2a2{a4b2yW28x2a21164D2,3,2,0,CDQA4,0,B4,0.××△16ξ1232，33△的335P為××12332△ACQ的面積比△BDQ的.23k0ykx3(2)13令由0y33x2Q(2,0)kk.1423343)yy3k(x2)(4)y(1202kkkkk222x2y21164D.234k43kk432yD314k14k22在Dx.y0D3424kACQ121333AQy(24)3(6),2k2kcBDQ121313BQy42y2Dy2k2kDD134k4k32(2)()2k14k2134k4k32(2)()2k14k2△ACQ的面積比BDQ，2333134k4k32(6)(2)()232k2k14k2D.(2,3)在Dx.ABQ(4,0),(4,0).AB△1，43232QOCQ的面積等于BDQ.的面積等于△.14//.Dmnn設(shè)(,)，,0則.n033m422DW.m2n214m2n3D，lnxf(x)x.1lnxf'(x)x2令.xef'(x)0與(x)f'(x)fx)eef'(x)f(x)+0-↗↙(x)e)(e,)f.lnxlnx(x)g(x)x.fxx1x1xx2g'(x)1.x2x2(10,ln0g'(x)0；xxgx2x)10,ln0g'(x)0.x2x(x)））.在15g(x)g1.lnxlnx(x)h(x)x24a1.f22xx10ah2a4a22a2a)0h0；21lnxlnxx1x1.a2xxh(x)xx2ax4a222a1(2a2（x)24a22414aa2(2aa400()0，hx()0.xxhx001.a2a(i,j)Aknnkkai,j)Aij行ka(i,j)Ai1j1i1j1A；A．12a(i,j)1,1，，jA，iR(s)(sR(1)RRRR0．R(1)RRRR．R0RR1．RR(2)+R3R3．R0RR1．RR2R2．RR(2)+RRR2．16，，RRR3．RRRA1行列(2)．nnknnn設(shè)R(t)a(i,j)(,)()0．Riinj1i1(1)()．RRRnn1nRinn1n-1()(1)()()(1)()Ri()()0，RiRnnRinRni1i1i1i1n1n1n()Ri()0Rini1i1A前n1行列(n2k)．n2121行．kkkk2k1221kk設(shè)()Tj(,)()T(j)Ri)0．a(chǎn)ijjki1j1i1T(1)TT(2k)．()為21()(,2k)．TjTjkj①T(k)0T(k)T(k)1．kT(j)kT(k)k．j1②()0()T(k)1．TkTk2kT(j)kT(k)k．jk1k2kT(j)T(j)k．j1jk1A2k1kk行kk．k2k1i1k設(shè)R(i)ai,j)i,2kR(i)T(j)k．j1j1k①(k)1Ri)kR(k)k；i1②(k)0(2k(2k(k)0．17k2k1kkk()Ri()Ri(,)aij()．Rikkki1ik1i1j1i1“”A行行kkkkkn18，，RRR3．RRRA1行列(2)．nnknnn設(shè)R(t)a(i,j)(,)()0．Riinj1i1(1)()．RRRnn1nRinn1n-1()(1)()()(1)()Ri()()0，RiRnnRinRni1i1i1i1n1n1n()Ri()0Rini1i1A前n1行列(n2k)．n2121行．kkkk2k1221kk設(shè)()Tj(,)()T(j)Ri)0．a(chǎn)ijjki1j1i1T(1)TT(2k)．()為21()(,2k)．TjTjkj①T(k)0T(k)T(k)1．kT(j)kT(k)k．j1②()0()T(k)1．TkTk2kT(j)kT(