2021-2022学年海南省海口某中学高一(下)期末数学试卷(附答案详解)

2021-2022学年海南省海口某中学高一(下)期末数学试卷(附答案详解)

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页数:23页

时间:2023-04-15

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13ᦑ=4F2+DF2-24FDF-COSN4'FD,4'F=FD=HI04஺=3,24E=A'C,A'D1BC,ᦑ4c2=y/A'D2+DC2=3JFAN=CN=3,KA'NC3ῪL2☢ᨬᜧMA'N-NC=£ᦑ஺.ᦑ⌱MACD.ᵫ*+┵A-MNCBḄᨬᜧᓽᨬᜧᓽPᑨR4⌱⚗GBN_L#☢4NC,ᑣBN1A'N,TUVWᓽPᑨRB⌱⚗ᵫ,☢ḄXYᓽPᑨRC⌱⚗ᵫ☢☢ḄXYZ0A'D=3,[\ZU44WC3ῪL2ᓽPᑨR0⌱⚗.]⚪_⌕ὃb☢Ḅcᐵe⚪,☢ᚖḄᑨXghijklḄmn3)opq73⚪.12.ூsᫀ௃BCDூI᪆௃IMwq4,xy=0,ᑣf(y)+/(-y)=0ᑣ/(%)᜻}ᦪx=1,=o,ᑣ/(1)+/(1)=0,ᓽ/'(1)=0,ᦑ/(%)Xᓫ⌴}ᦪ⌱y⚗A┯%wqB6f(x)=cos%,2/(x)/(y)=/(%+y)+/(%-y),9f(0)=1,/(%)Ꮤ}ᦪ9ᨬᜧ1,⌱⚗3wqC,6/(%)=cosx,2/(x)/(y)=/(%+y)+f(x-y),9f()=ᑣ/©)=¥⌱⚗cwqD,ᵫq/(l)=I6/()=cos(^x),2/(x)f(y)=/(x+y)+/(x-y),9/'(100)=cos[?=cos3=-g,⌱⚗஺.ᦑ⌱MBCD.wq4,xx=1,y=0P0/(I)=0,[\ᑨR⌱⚗A┯%wqBC,6/(x)=cosxᓽPᑨRwq஺6/஺)=cos©x)ᓽPᑨR.]⚪ὃbj}ᦪᐸᵨὃbZIklI⚪ḄᐵᱯḄ}ᦪ[\ᓄ¡¢I⚪ᦔ᳛pq7᫏⚪.13.ூsᫀ௃¦§x€R,"¨—ax—3a>0(—12,0)ூI᪆௃IMª⚪pM”ᙠx6R,"/3aW0”ᱯ¬ª⚪,ᡠ®ª⚪PḄᔲXM¦§xeR,"M-ax-3a>0°14⚓ᐳ23⚓

14ᵫPᎷª⚪ᑣµP¶ª⚪ᡠ®/=a2-4x(—3a)<0,I0—120(-12,0).᪷Äᱯ¬ª⚪ḄᔲXᐰ¬ª⚪ᓽPᑏUª⚪PḄᔲXpᎷª⚪ᑣp¶ª⚪È\P0Usᫀ.]⚪ὃbª⚪ḄᔲXpqÉẠ⚪.14.ூsᫀ௃1500ூI᪆௃ூᑖ᪆௃]⚪_⌕ὃbÍXᳮஹL27Ḅ1ᐵÐpq7᫏⚪.KABC7ᵫᩩÕᑭᵨL27Ḅ1ᐵÐZ0ACᙠKlMC7ᑭᵨÍXᳮHCAMØᙠRt/kAMN7᪷ÄMN=4M-sin4MAN,ßZ0àá.ூIs௃IMᙠKABC7•••Z.BAC=45°,/.ABC=90஺,BC=1000,AC==IOOOA/2,Sin45°åᙠ44MC7,4MAe=75°,/.MCA=60°,/.AMC=45°,ᵫÍXᳮP0*-=éêsin600sin450I04M=1000V3.ᡠ®ᙠRtAAMN7MNAM-sin^MAN=1000V3xsin600=1500.ᦑsᫀ1500.15.ூsᫀ௃217rூI᪆௃IMí⚪§P)î☢S4B1ð☢lBCD*+┵S—4BCDḄᨬᜧ.òᳫ=஺ôõR,ö24BCD÷KS48᜜úᙊḄᙊ=ᑖü஺µ஺2

15ö24BCD᜜úᙊôõᑣ஺/I#☢4BCD,஺஺þJ•☢S4B.ASAB4BCDḄᙳ3,4BḄE,ᡠ001=0E=1SE=0]B=q=2ᵫ!"#ᳮ%R2=0B2=001+ᶭ=(+)2+(-)2=?ᡠᳫ஺Ḅ⊤☢2S=4TIR2—217r.ᦑ6ᫀ8217r.᪷:⚪<=>?☢SABIB☢CBCD,ᯠEFᔠHᵫB☢᜜JᙊLMஹᳫOᑮB☢ḄQRᳫḄLMST!"#ᳮ=%.U⚪V⌕ὃYᳫZ[☢\ḄᑗJ^⚪_`abcdCḄefg>h_ijg⚪.16.ூ6ᫀ௃জঝটூq᪆௃q8sᦪy=WḄHcᐵjxyz=x|}_a,0~sᦪy=2y=log2%ḄHcZsᦪy=ḄHcḄḄᙶ᪗_X—1᧕>a=log20,0=2a.0=ᔠ=1+_(a-1)05-1)=1,ᓽa/?=a+஺_জ_ঝᙳa+/?=a+-j=a-l+-L+224,++a-1=_ᓽa=2gᡂ_ᔆa-1a-1a-1"2)=a-22=-2¥°_a#2,£¤g¥ᡂ_ᡠa+/?>4,ঞ¥¨16⚓_ᐳ23⚓

16.«/'(|)=3—25=3—¯>0_f(2)——22=—2<0,|/1(|)=:º2>-2,ᡠট.ᦑ⌱8জঝট.sᦪ'=WḄHcᐵjxy¼=½|}_¾_0~sᦪy=2½y=log2%ḄHcZsᦪy=¿ḄHcḄḄᙶ᪗_ᑣᨵa=log20_0=2%0==1+,xJÂᑨÄজঝᑭᵨÇU¥g¤ᑨÄঞᵫÈÉᙠ#ᳮ_=%|hßàᡂáḄᙳᑖ71,(3)ãᗩᝄḄæçᑖᦪ¥èjéᑖ_ê80,90),ê90,100ë|ÕḄ⚣᳛ᑖîU0.15,0.1,ᡠ(90-x)X0.015=0.1,q%x=gb83.3.ᦑãᗩᝄḄæçᑖᦪ¥èj83.3ᑖ.ூq᪆௃(1)ᵫ⚣᳛ñgj1%òaḄÐ(2)ᵫ⚣᳛ᑖóxHᦪ:ÎÏᙳᦪᓽ=(3)ãᗩᝄḄæçᑖᦪ¥èjôᑖ_ᵫ(90-%)x0.015=0.1%òé.U⚪ὃY⚣᳛ᑖóxH_ijÇẠ⚪.18.ூ6ᫀ௃q8(I)ᵫ⚪<_=%/(%)=2sin(Dxcosa)x+2V3sin2a)x—V3=sin2a)x—V3cos2a>x=2sin(2a)x—½•••sᦪḄᨬúᕜüᐔ_.•.þ=?r,qñ%3=1.23ᵫ=%sᦪḄq᪆¤f(x)=2sin(2%-=).

17G2kn—<2%—<2kn+R,ZCTT-^-g(%)=0"si/i2x=—i,42%=2kn+3ᡈ2%=2kn+—(kGZ)266X=kn+FᡈX=kᐔ+G(kez).Hy=g(x)ᙠ[0,J2KLMᨵ10/OP"ᑣbḄᨬTUV47r+ூ᪆௃\⚪ὃ_`aᦪḄឋcdeOP"Ḽgὃ_hijaklஹnoaklpqr"stu᫏⚪.(I)᪷yijaklznoaklᓄ|/(X)=2s)(23%8,ᑭᵨᕜkl3=1,ᦪ᪆lV/(X)=2sin(2x-$.1ᵫᦪᓫḄkl"ᐵtXḄplᓽ4ᑮᦪ஻X)Ḅᓫ(II)᪷yᦪ(),-Ḅkl"ᦪg(x)Ḅ᪆lVg(x)=2s2x+1.ᵫg(x)=0=/ot+"ᡈx=ᐔ+G(keZ),ᓽ4bḄᨬTU.19.ூᫀ௃(1)4cBDtP஺"MO,ᵫ¢£ABCDq஺VACḄuP"VPCḄuP"•••MO//PA,vMOu,☢MB஺"PAC,☢MB஺,©18⚓"ᐳ23⚓

18PA஻,☢MBD;(2)•.•,☢ABC஺z`a£4DPᡠᙠ,☢®ᚖ°",☢4BCDn,☢ADP=A஺"Q4஺ḄuP"•••PQA.AD,PQu,☢4DP,PQJL,☢ABCD,ᵫ⚪᧕qPQ=2V3,²☢³P-4BC஺Ḅ³´=Fx4x4x273=—:33(3)µᙠPN,¶NV4BuP·"D☢PQBD☢PNC,•••¸¹£ºBCD¢£"QVADḄuP";BQ1NC.ᵫ(2)q"PQ1,☢4BCZ),NCu,☢4BCD,PQ1NC,;BQCPQ=Q,PQ,BQu,☢PQB,NC",☢PQB,vNCu,☢PCN,i,☢PCN1,☢PQB.ூ᪆௃\⚪ὃ_°»z,☢,¼Ḅ"ὃ_¸½┵³´Ḅ¿À"ὃ_,☢z,☢ᚖ°Ḅ"stu᫏⚪.(1)AC8஺tP0,M஺"ᵫ¢£4BCDq஺V4cḄuP"ᵫMVPCḄuP,qM0஻PA,ᵫÁÂPA஻,☢MB஺(2)ᑭᵨ½┵Ḅ³´kl"4ÃÄ.(3)µᙠPN,¶NV48uP·",☢PQ8,☢PNC.ᵫ¸¹£ABCD¢£"Q9ADḄuP"qBQ1NC,ᵫÁÂ,☢PCN,☢PQB.b_c20.ூᫀ௃(1)ᵫÅᳮq,2R,sinZJlBCsxnLACBb=2Rsinz.ABC,c=2RsinZ-ACB,••b2—ac,:.b•2RsinVABC=a•2RsinZ.ACB,^bsinZ-ABC=asinC,••BDsinZ.ABC=asinC.•BD=b(2)ᵫপqBD=b,-AD=2DC,

19DC=”,8஺2+Ë-482_b2+©b)2_c2_13b2-Î2ᙠÈABDu,ᵫÉÅᳮq,cosZ.BDA=22BDAD~2b-b—12bÏ+Ð8T_᮱+(Ò2.210ᡝ9a2ᙠ4CBDu,ᵫÉÅᳮq"COSZ.BDC=-6^2-2BDCD2b-b3vZ.BDA+Z.BDC=7T,•cosZ-BDA+cosVBDC=0,13d2-9c2.10b2-9a2Ùnnᓽ---K----1------K-=0"12b26b211᮱=3c2+6a2,,:b2=ac,•3c2—llac+6a2=0,•c=3aᡈc=|a"ᙠÈABCu"ᵫÉÅᳮq"cos4aBe=M+'f2=a-c,2aclacWc=3a·"cosZ.ABC=7>1(Ú)¶c=|a·,cosZ-ABC=~Û2ᡠÜ"cosÝ4BC=Wூ᪆௃\⚪Þ⌕ὃ_ÅᳮàÉÅᳮ"áâᜧ.(1)ᑭᵨÅᳮ¿(2)⌕Áäᑮ◚MᩩçNBD4à480c⊡"éᑡplᐵë¿.21.ூᫀ௃(I)&E,᝞(ᡠí"îV=&C,PE½ACḄuP"ᡠd&E1AC,ï,☢AACC11,☢ABC,&Eu,☢/“1",☢4⍗"1n,☢ABC=AC,ᡠd&EJ_,☢4BC,ï4cu,☢ºBC,ᡠd&E1AC,dEPVᙶ᪗óP",☢ABCᑁõPEöACḄᚖ»Vx÷"ECஹEkᡠᙠ°»ᑖùVyஹz÷"úû᝞(ᡠíḄü°aᙶ᪗ëE-xyz,©20⚓"ᐳ23⚓

20Xᵫ⚪ýq/ABC=90°,NB4C=30°,AA=41c=AC,EஹFᑖ4Cஹ௃Ḅt4⍗=AC=AC=4,ᑣ4E=EC=BE=2,AB-ACcos30°-2A/3>&E=rV42-22=2V3.ᡠ%Bᑮx(Ḅ)*+BEsin30஺=1,Bᑮy(Ḅ)*+ABsin30஺=6ᑣ4(0,-2,0),C(0,2,0),%(0,0,2®B(V3,l,0).B7ἕ3,29)F◀|,29)ᡠ%<=(=|,2ᡃ)BC=(-73,1,0).@+A-BC=yx(-V3)+|x1+2A/3x0=0ᡠ%EF1BC.(n)CDEFEF☢&BCᡠᡂI+஺ᵫ(I)LM=(-75,1,0)O=(0,2,-29)£F=(y,|,2V3).ᡠ%IMI=j(y)2+(j)2+(2V3)2=715-F☢4BCḄRᔣTU=Q,y,z),ᑣXYZ[9\]0,^ᑣᐗ=(],a),(41஺[n=y—V3z=0ᡠ%IᐗI=J12+(c)2+12=aFF.n=yXl+|xV3+2V3xl=4V3.ᡠ%sin"Icos\=ᑴ=ឫI=?k஺e[0,90஺],ᡠ%cos஺=Jl-(1)2=IᦑCDEFEF☢&BCᡠᡂIḄpqr+|.stuᵫsIuvF☢A&CḄRᔣT+w=s1,0,0u,Z☢IZ-4C—BḄF☢I+"ᵫzv0+┦I,@+cos9=|cosswᐗ||=}==?

21kW+┦Iᡠ%sing=yjl-cos2(p=ᓩᦑZ☢I-&C-BḄqr+.ூ᪆௃⚪ὃCDEF☢ᡠᡂIḄᔣTRஹF☢EF☢ᡠᡂIḄᔣTRஹDDᚖCḄᔣT⊤ஹ☢☢ᚖCḄឋஹᵫ[YIᦪrᐸYIᦪr,᫏⚪.(I)&E,&E1AC,ᑭᵨ☢☢ᚖCḄឋᳮ&E1F☢4BC,%E+ᙶ᪗¢F☢BCᑁ¤E¥ACḄᚖD+x(ECஹEaᡠᙠCDᑖ+yஹz(§¨᝞zᡠḄª«CIᙶ᪗¬E-z.ᑖ᮱¯°Ḅᙶ᪗±¤MBC=OᓽaLEF1BC.(U)F☢4BCḄRᔣTᐗᑭᵨᔣTRCDE³EF☢418cᡠᡂIḄqrᵫ´IYIᦪµᐵ¬ᐸpqr.(t)F☢7L41cḄRᔣTᑭᵨᔣTRZ☢IḄpqrᵫ´IYIᦪµᐵ¬ᐸqr.22.ூ·ᫀ௃](1)a=5¹/(%)=-*2+5%-4>0Ḅº¹=(1,4),ᦪy=93)=ln^■ln(ex)=(Inx—3)(2nx+1)=ln2x—2lnx—3,%E(1,4)¹,^t=Inx,ᑣy=t2—2t—3tE(0,2Zn2),f^,yḄr¼+½[4,[3).ফ¿(X)_r(%)+g(x)+l/(K)-g(%)l_1(%)/(%)25(x)iÀJ[z[JO)1.¹g(x)>0,¿(%)>g(x)>0,^¿஺)ᙠ(L+8)ÅÆÃ.ঞ0<%<1¹g(x)<0,g(x)ᙠ(0,1)ÅÆÿ(%)ᙠ(0,1)ÅḄÃᦪ/(%)ᙠ(0,1)ÅḄÃᦪv/(0)=-i(a-l)2<0,/(l)=a-l-i(a-l)2<0,A=2a-1.(i)2a-1<0,ᓽQVᡈÉᦪf(x)ÆÃᓽ¿(%)ᙠ(0,1)ÅÆÃ.Ê2஺-1=0,ᓽ஺=Ëᦪf(%)ḄÃ+Ìᓽ¿Êᙠ(0,1)ÅᨵÃÎ22⚓ᐳ23⚓

22(Ñ2a-l>0,ᓽl>a>:¹Ó)=ᓤ>0,ᦪf(x)ᙠ(0,1)ÅᨵÕÃᓽᦪ¿஺)ᙠ(0,1)ÅᨵÕÃ.ÖÅᡠ×a<Ù¹/i(x)ᨵ1Ãa=Ú¹,h(x)ᨵ2Ã.l>a>¹¿஺)ᨵ3Ã.ூ᪆௃পa=5¹/(X)=-/+5%[4>0ḄºM=(1,4),ᦪᦪÜ=஺Ý)(ex))=ln2x—2lnx—3,ÞW(1,4)¹,^C=)n=,ᑣÜ=ß[2t—3,tE(0,2Zn2)ᵫàáyḄr¼Úফᡃপ=âãäåæçJ9(^ᵫàᑭᵨᑖèéêëìá=ᦪḄÃᦪ.⚪ὃᦪrஹᦪḄr¼ḄRὃᦪḄÃᦪḄéêὃᦪឋíµẠvïὃðñáὃᑖèéêE᦮ᔠëì᫏⚪.

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