2021-2022学年广东省广州市三校联考高一（下）期末数学试卷（附答案详解）

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2021-2022
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15y(3+i)(2+i)_S+5i_ÑZ2¡(2-i)(2+i)-5-1+t.D=Ò+f#ᡠKᔣvÓÊḄÔᦪ.Z1+Z2=(1+2i)+(1+i)=2+3L(2)Í⚪"#0P=M=஺2#72)#ᑣAPOQḄ☢ws=T|x/2-Ý.1#ᵫ(1)y#ÓÊḄÔᦪ.2+3i,ᓽᨵD=(2,3),ßÊḄÔᦪ.l+2i,ᓽᨵß=(L2),ᡠKáABCḄ☢w.:x|lx3-2x2|=1ூ᪆௃(1)ᑭᵨᐳãÔᦪḄ"äÂÔᦪ◀?nᑖç!ÀZiZ2,lèéÔᦪᔣvḄᐵë!¿.(2)ᵫ(1)!Àì#ᐗḄᙶ᪗#lᑭᵨ»yËÈmn¿.:⚪q⌕ὃ<=ÔᦪḄᑣ?nÂÔᦪðñ"äḄÊᵨ#@
Ạ⚪.18.ூᫀ௃প•••ÎôõḄ⚣᳛.1-(0.020+0.025+0.030+0.035+0.050)x5=0.200.ΡõḄ⚣᳛.0.025x5=0.125,ÎõḄ⚣᳛.0.035x5=0.175,ÎôõḄ⚣᳛.0.200.•••DôõḄ⚣᳛øù.0.125+0.175+0.200=0.500.••ú300ûüqýᑖḄ{«ᦪ.85,þᦪ.ÿ=87.5.(2)ᵫ⚣᳛ᑖᑖᙠ90,95)Ḅᦪᑖᙠ95,100ḄᦪḄ!3#2.%ᵨᑖ'(᪵*(+5ᑖᙠ90,95)Ḅᨵ3ᑖᙠ95,100ᨵ2.-./ᑖᙠ90,95)Ḅ3ᑖ0!4,A,432ᑖᙠ95,100Ḅ2ᑖ0!3,B.224567Ḅ᪵89:!#A,A
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122312232ঝ<5=>⌱2ḄᡠᨵABCDᨵᐳ10F.ᐸ=⌱+Ḅ2=HIᨵ1Ḅᑖᙠ95,100ḄCDᨵ#{A,B},{AB},{A,B},(AB
,{J%}ᐳ7F.122I1223I2ᦑ42=HIᨵ1Ḅᑖᙠ95,100Ḅᭆ᳛!P=Q.ூS᪆௃(1)ᵫ⚣᳛ᑖḄឋWᡠᨵXYZḄ☢\]^!1,AS_஻Ḅᵫ=aᦪḄbcdᑮ⚣᳛]^!0.5Ḅfgᦪhi!ᨬkXYZḄ=f.(2)✌ᐜ᪷op5ᑖqḄᦪ]%ᵨᑖ'(᪵Ḅ*_ᑮr5ᑖq(+Ḅᦪ᪷osᐺᭆuḄᭆ᳛ivwxySᓽA.8⚪|⌕ὃ⚣᳛ᑖẠ⚪.

1619.ூᫀ௃S#(1):BC஻☢PAD,BCu☢ABCD,☢PADn☢ABCD=AD,ᡠ.BC஻AD.(2)#!☢PAD1☢4BCD,☢PADn[SABCD=AD,BAA.AD,ᡠB4_L☢PAD,+!BAu☢PAB,ᡠ☢P4B☢P4D.(3)N!A஺=fMN஻☢PAB.#+AOḄ=fMCN,EN,E,NᑖM=PD,AZ)Ḅ=fᡠEN஻/M,EN<5tTffiPAB,PAc5FffiPAB,ᡠEN஻☢PAB,§!BC=14D,BC//AD,ᡠ¨©Z4BCN!ª¨©ZᡠCN஻4B,CNPAB,ABu☢ᡠCN஻☢PAB,CNCNE,ᡠ☢CNE஻☢PAB,§!MNu☢CNE,ᡠMN஻☢P4B.«¬AD®ᙠfN,NOMN஻P☢PAB.ூS᪆௃(1)ᵫ«☢ªḄឋWbᳮᓽA.(2)ᵫ☢☢ᚖḄឋWbᳮ_B4☢PAD,§!B4u☢PAB,ᡠ☢P4B1☢PAD.(3)+AOḄ=fN,CN,EN,ᵫ«☢ªḄᑨbbᳮEN஻☢PAB,CN஻☢PAB,ᡠ☢CNE஻☢PA8,²ᵫ☢☢ªḄឋWbᳮA_MN஻☢P4B.8⚪ὃ«☢Ḅa³ᐵµ¶·«☢ªḄᑨ¸^ឋWḄ¹ᵨẠ⚪.20.ூᫀ௃S#(1)ᙠºABC=»A,B,CḄ¼©ᑖ0!a,b,c,!siMB+sin2c=(sinA+6sinBsinC)sinA,ᡠ᮱+c2=a2+6bcs

17A,ᡠ2bccosA=6bcsinA,ᡠtanA=I2(2)!a—\/5/10x5x^=|.Ò16⚓ᐳ19⚓

18ூS᪆௃(1)ᑭᵨÕÈbᳮ^ÇÈbᳮ_ᑮ2bccos4=6bcsin4,ᓽAyÖtan4=12(2)ᐜᵫtan4=yÖsin4=ᘊcos4=ᑭᵨÇÈbᳮS_c=1ᡈc=5.ØᐭºÚBCḄ☢\y☢\ᓽA.8⚪ὃÛÕÈbᳮ^ÇÈbᳮḄ¹ᵨ=᫏⚪.21.ூᫀ௃S#প#&CஹBQßᚖ§ᵫàáḄឋW4B஻4â,ABIBC,481AlC,§BCCMiC=C,AB☢&BC,+ABu☢ABC.ᦑ☢4BC_L☢4BC.(2)ᵫ(1)☢&BC_L☢4BC.᝞ᡠäå4æ4஺1BCD,ᑣ4D1☢ABC,èé4ê£)ì&B☢A8CᡠᡂḄ»ᓽ=6.æDEJ.ACE,ᑣ“ï஺!è☢»4-AC-BḄ☢».ᙠRtAABC=ᵫ⚪ð_BC=4.ᙠRt/iAiDB=AB—4,AD=4sin0,BD=4cos0,CD=4—4cos0.Xr^RtiiABC-RtUDEC,ODE=,”.cosZ-Aj^ED=ñ""""tanZ-A^ED=1ᓽó1141DEV33(l-cos6)V3ìsin0+V3cos0=V3,2sin(0+g)=g,ôðᑮ0<0õᦑ0=ö(3)fCᑮ☢&ABB1Ḅ÷øᓽ!fCᑮ☢4ABḄ÷ø.■•AC=AA=5,JLABC=/_ABA=pAB=3,rX:.RtUABC=RtUABA^>§ᵫ^^I-ABC=%-A148AfCᑮ☢4⍗BḄ÷øᓽfᓰᑮ☢ABCḄ÷øᵫ(2)&OJL☢ABC,û=4sin஺=4x?=2¨ìCᑮ☢&4BḄ÷ø!2ü.ூS᪆௃(1)4B஻&BiABLBC,ABLAC,<ýAB1☢&BC,ᵫþB☢rAiBC_L☢4BC.(2)åÿAi஺1BCAD,ᑣ4஺1☢ABC,4᝞஺☢ABCᡠᡂḄᓽ4&8஺=஺.஺_14஺ᑣN4ED☢4C-BḄ☢ᵫ

19.(3)#Cᑮ☢448(Ḅ)*ᓽ#Cᑮ☢Ḅ)*ᵫᓃ,-஺=%-AAB./#Cᑮ☢44BḄ)*ᓽ#1ᑮ☢ABCḄ)*ᵫCᑮ☢44BḄ)*.3⚪ὃ67☢ᚖ9Ḅᑨ;ឋ=ஹ☢☢ᚖ9Ḅᑨ;ឋ=ஹ☢ஹ7☢ஹ#ᑮ☢Ḅ)*ஹ?@AB?CẠ/Eὃ6FGHIJ᫏⚪.22.ூNᫀ௃HQপ/Q)=sin஺XYᦪ”./(J+^)=siᔩ`+x)=sin©+c)/(Q-x)=sin|(^-x)=sin(g—c)•••6+%)"(>%)(%6R)0.•./(X)=singxXYᦪ”.(2)•.•Yᦪf(x)pqf(x)=/■(s+t.•.Yᦪf(x)ḄᕜvT=y,/(J+^)=/(;x)(xER),Vf(x)=&-x)(xeR),(xeRkir+'ᐔ+ᐔ](eZ)f(x)=/(x—kn)=sin(x--kn'),(fcGZ),124222(*e[|/C7T-p|/C7T+^](/ceZ),/(x)=/[^-(X-|/C7T)]=COS(X-|/C7T),cos(x--kn),(j-kn--

20ூH᪆௃(1)ᵫXpq+#C-x)(x6R),/(x)=sin[xX“MYᦪ”»(2)Yᦪ/(%)Ḅᕜv7=¼/(x)=/(^-x)(xe/?),(["ᐔ+£,"ᐔ+22242TT](/C6Z)/(%)=/(X—|/CTT)=sin(x—|kn),(k6Z)»(x6[|/ot-1,|/£ᐔ+g(keZ),f(x)=/[^-(X—|/C7T)]=COS(X-|fc/r),ᵫYᦪᙠ(0,tḄᓫ⌴»(3)Yᦪᙠ[-¾¿ḄᦪÀᔠ.3⚪ὃ6ÂYᦪḄஹឋ=ὃ6ÂYᦪឤ?ÄᣚஹÂYᦪƲ³?Ç⚪ὃ6FGHIJ᫏⚪.