2021年全国高考甲卷数学（理）试题（解析）

《2021年全国高考甲卷数学（理）试题（解析）》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

2021ᐰὃᵬᔁᦪᳮ⚪1.ᔠM={x[03]3C.{x|4?@'ABᙢ;ᡝDEFᦈᐭIJK᪵M%'N;ᡝDEFᦈᐭḄM%ᦪ᦮ᳮR᪷S⚣᳛ᑖVWXY'Z☢\]-0^_Ḅ`abA.Bᙢ;ᡝDEFᦈᐭcd4.5eᐗḄ;ᡝg᳛hi6%B.Bᙢ;ᡝDEFᦈᐭ0cd10.5eᐗḄ;ᡝg᳛hi10%

1C.hiBᙢ;ᡝDEFᦈᐭḄlᙳn0op6.5eᐗD.hiBᙢᨵuvwḄ;ᡝ'ᐸDEFᦈᐭyd4.5eᐗ{8.5eᐗ}~ூᫀ௃Cூ᪆௃ூᑖ᪆௃᪷WXYḄWiᑁḄ⚣᳛'ᓽᑨABD,ᔜḄ-~n⊤Ḅ⚣᳛'ᯠ/ᓽRᑮ᪵"ḄlᙳᦪḄhin'`lᙳnḄhin'iᓽᑨC.ூ௃⚣᳛WXY-Ḅ1,ᡠᔜḄWXYḄ,d⚣᳛.᪵"⚣᳛WXY-Ḅ⚣᳛ᓽḄg᳛Ḅhin.Bᙢ;ᡝDEFᦈᐭcd4.5eᐗḄ;ᡝḄg᳛hin0.02+0.04=().06=6%,ᦑA^_Bᙢ;ᡝDEFᦈᐭ0cd10.5eᐗḄ;ᡝg᳛hin0.04+0.02x3=0.10=1()%,ᦑB^_Bᙢ;ᡝDEFᦈᐭyd4.5eᐗ{8.5eᐗ}~Ḅg£hin0.10+0.14+0.20x2=0.64=64%>50%,ᦑD^_Bᙢ;ᡝDEFᦈᐭḄlᙳnḄhin3x0.02+4x0.04+5x0.10+6x0.14+7x0.20+8x0.20+9x0.10+10x0.10+11x0.04+12x0.02+13x0.02+14x0.02=7.68(7JTC)>op6.5eᐗ'ᦑC┯©.ªw'«¬\]-0^_Ḅ`C.ᦑ⌱C.ூ!௃"⚪ὃ%ᑭᵨ᪵"⚣᳛WXYhi⚣᳛lᙳn'()Ạ⚪'᪵"Ḅ⚣᳛Ḅ⚣᳛Ḅhin'᪵"ḄlᙳnḄhin`ᔜḄ-~nᐸ⚣᳛ᯠ/ᡠRn'ḄlᙳnḄhin.¯ᔜḄ⚣᳛d°X.3.²³(l—i)2z=3+2i,ᑣ2=()3333A.-1—iB.-Id—iC.----FiD.----i2222ூᫀ௃B

2ூ᪆௃ூᑖ᪆௃ᵫ²³Rz=^—᪷½ᦪ◀¿¿ᑣ'ᓽ/.-2iூ௃(1-Z)2Z=-2ZZ=3+2Z,3+2Z(3+2z)-z-2+3z,3.z=---------=------------=-----------=-l+-z.-2i-2i-i22ᦑ⌱:B.4.☘ÂFÃÄ`ÅÆÇÈᐵ¯ḄÊ⚪'ÃÄ?@ËÌÃÄ⊤ÍÎ.ÏÐᵨÑᑖÒÓ¿°ᦪÒÓ¿ÒÓÃÄᦪ'ÑᑖÒÓ¿ḄᦪÔ°ᦪÒÓ⊤ḄᦪVḄÕÖL=5+lgV.׳9ØÙÃÄḄÑᑖÒÓ¿Ḅᦪ4.9,ᑣᐸÃÄḄ°ᦪÒÓ¿Ḅᦪ()(ÚÛ1.259)A.1.5B.1.2C.0.8D.0.6ூᫀ௃Cூ᪆௃ᑖ᪆௃᪷ᐵÜ'ÝL=4.9Þ'/¬IgV,ßᵨᢣᦪ⊤áV,ᓽ/.ூ௃ᵫL=5+lgV,ÝL=4.9Þ'lgV=-0.1,__Liiᑣv=i(r°â=io|஺=“-----«o.8.æ1.259ᦑ⌱C.5.²³ᱏ'è`éêëCḄìíᯖ'PCwu'ï5=60஺,ðñ=3|ò|,ᑣCḄóô᳛()A.@B.
C.D.V1322ூᫀ௃Aூ᪆௃ூᑖ᪆௃᪷éêëḄõᩩ÷'⊤á¬|P4|,|øù'\ᔠúûᳮRᫀ.ூ௃|üὡ|=3|þᵨ,ᵫéêëḄRðᵨu|üñ=2|þÿ=2a,ᡠ|Pᕜ=a,|Pὡ|=3a/ὡ=60஺,ᵫᳮ4c2=9/+a2_2x3aa-cos60°

3᦮ᳮ4c2=7/,ᡠe2=0=N,ᓽe=Ea242ᦑ⌱"Aூ%&௃ᐵ)%&"*+,Ḅ./ᐭ1%2ᑭᵨᳮ5627Ḅ89ᐵ:/;<Ḅᐵ).6.ᙠ@ABCDE2F⚔%AḄHᩩJḄE%ᑖLE,F,G.MBCDNOHJ┵A-EFGT2ᡠU☢DḄHWXE2BWX᝞XᡠZ2ᑣ\]Ḅ^WX/_`BWXூ<᪆௃ூᑖ᪆௃᪷c⚪ef⚪gᡠhḄBWXijklmDḄnoX2pᔠnoXrsᑨu.ூv<௃ᵫ⚪efBWXlmDḄnoX2᝞XᡠZ,7.8wᦪᑡz4{Ḅ|wq,~஻⚗S“2ᵬ"4>0,"z"{/⌴ᦪᑡ2ᑣ_`

4A.ᵬ/Ḅᐙᑖᩩ/⌕ᩩB.ᵬ/Ḅ⌕ᩩ/ᐙᑖᩩC.ᵬ/Ḅᐙ⌕ᩩD.ᵬ/Ḅᐙᑖᩩ/Ḅ⌕ᩩூᫀ௃Bூ<᪆௃ூᑖ᪆௃4>02Fᵬ/ḄᐙᑖᩩzS,,{/⌴ᦪᑡ2ᨵ஺“>0ᡂ6ᓽ᜛>0ᡂ62ᑣᵬ/Ḅ⌕ᩩ2ᓽ⌱kᫀ.ூv<௃ᵫ⚪2ᦪᑡ8,…2¥¦4>0,/z*{/⌴ᦪᑡ2ᡠᵬ/Ḅᐙᑖᩩ.¨zS,,{/⌴ᦪᑡ2ᑣᨵ>0ᡂ62¨4>0ᡂ62ᑣ©kª@B@«Ḅ¬2/®¯Ḅ2ᑣ“>0ᡂ62ᡠᵬ/Ḅ⌕ᩩ.ᦑ⌱"B.ூ%&௃ᙠᡂ6Ḅ¬°2ᡃ²F2/ᙠᡂ6Ḅ¬°2ᡃ²³⌕h´ᐸ¶F·.8.2020¸12ᨴ8»2E¼½¾¿ὶᔠ|ÁÂÃᨽÅÆᨬÈÉ·8848.86_ᓫË"m`,HÍÉ·Î9Ï/ÂÆÉ·Î9CÏÐ@.᝞X/HÍÉ·Î9ÏḄ@AZeX2ªᨵA,B,CH%2ÑA,B,CᙠÒ@ÓÔ☢ÕḄᢗ×A,B',C¥¦NAC8=45°,NA'8'C=60°.ᵫC%ÎB%ḄÛÍ15°,BB'ÜCCḄÝ100ᵫB%ÎA%ḄÛÍ45஺2ᑣA,CÞ%ᑮÓÔ☢AB'CḄÉàÝAA-CCá_73®1.732`_`

5A.346B.373C.446D.473ூᫀ௃Bூ<᪆௃ூᑖ᪆௃Fâãä,2åæçᡠ;9èᓄᑮ@AHÍêE2ëäBᳮ2;©3'2rìᑮᫀ.F஺íF8íBD_LA4'2ᦑA4'-CC'=A4'-('-)=A4'-î'+100=AD+100,ᵫ⚪2᧕çñADB8ῪnÍHÍê2ᡠAO=DB.ᡠA4CC'=DB+100=A'3'+1(X).NBCH=15°,ᡠ=tanl50ᙠñA'8'CE,ᵫBᳮ:A®_C'B'_100_100sin45°ߟsin75°.tan15°cos15°.sin15°2,V6-V2ìsin15஺=sin(45°-30°)=sin45°cos300-cos45°sin300=-~~—2100x4xvᡠA®2=100(6+1)=273A/6-V2ᡠj'—CC'=4B'+100a373.ᦑ⌱"B.ூ%&௃õ⚪ᐵ)%ᙠö᝞mB÷åA4'-CC'ḄøàFíãä,ḄCùèᓄA'B'+100.(ஹ-cosa9.¨ae|0,ú|,tan2a=~——2ᑣtana=()I2J2-sina

6üV5D.ýu.----3ூᫀ௃Aூ<᪆௃ூᑖ᪆௃ᵫþÿ
tan2஺==ᓾᔠsina=,ᑭᵨcos2al-2sin~a4ᦪḄᐵᓽ.ூ#௃tan2a=-----------2-sina%sinla2sinacos஺cosa/.tan2a=--------=------------——=----------,cos2al-2sin-a2-sina'%(ஹ%2sina1…—1vG0,—,*.cosawO,/.--------T—=------,sina=+,I2jl-2sin2a2-sina4r-—y/i5sinaVl_5cosa-5/1-sin-a-------/.tana---------=------•4cosa15ᦑ⌱.A.ூ/0௃ᐵ1/0.⚪ὃ4ᦪḄᓄ67⚪⚪Ḅᐵ18ᑭᵨ*9
ᓄ6:sina.10.;4<1=2<0>?᣸ᡂ+Bᑣ2<0DEFḄᭆ᳛I'J12-24A.-B.-C.-D.+3535ூKᫀ௃Cூ᪆௃ூᑖ᪆௃OᵨPQ4<1RS5<ᑖ2<0EF=2<0DEFTB.ூ#௃;4<1=2<0>?᣸ᡂ+BᑭᵨPQ4<1RS5

7ூKᫀ௃Aூ᪆௃ூᑖ᪆௃ᵫ⚪AA8cIlῪno:pqড஺᜜tᙊḄ]^ᑣ஺ᑮw☢4BCḄ{|T}de.ூ#௃•••AC1.BC,AC=8C=1,.•.pABCIlῪno=JᑣAABC᜜tᙊḄ]^IᳫḄ]^I1,20ᑮw☢ABCḄ{|Id,gr-pl_1_11..x/2_V2cZᓃJAt>r~-S•d=-x—x1X1X--=-C/-/1OC3A/IOC322]2ᦑ⌱.A.ூ/0௃ᐵ1/0.⚪ὃ4ᳫᑁ¥¦d7⚪⚪Ḅᐵ18§¨ᑭᵨ©☢ᙊ]^ஹᳫ]^ஹᳫªᑮ©☢{|Ḅ«¬ᐵ.12.ᦪ/'xJḄIR,஻+1JI᜻ᦪ/'x+2JIᏔᦪxe[l,4£f#x%^ax2+b.U/''JJ+/'3J=6,ᑣ'J9375A.--B.---C.+D.-4242ூKᫀ௃Dூ᪆௃ூᑖ᪆௃±²/'%+1J8᜻ᦪ=/'%+2J8ᏔᦪᩩµZᔣÉ:ᦪ᪆/'xJ=—2^+2,T}ᑭᵨᡈᕜ¹ឋ»ᓽᑮKᫀ.ூ#௃¼I/'X+1J8᜻ᦪᡠZ/'+x+lJ=-/'X+1Jজ;¼I஻x+2J8ᏔᦪᡠZ“x+2J=/'—x+2Jঝ.Á=1,ᵫজ:/'0J=—/'2J=—'4"+Äᵫঝ:஻3J=¼I/'0J+/'3J=6,ᡠZ+'4a+Z?J+a+Z?=6=a=-2,

8Áx=0,ᵫজ.==0ᡠZ/(%)=_2/+2.ÍÎ+.ÏᐭÑ.ᡠZ/ÍÎ*.Ïᕜ¹ឋᐭÑᵫÒ<ÓÔឋᦪ/(x)Ḅᕜ¹7=4.ᦑ⌱.D.ூ/0௃ᙠÖᦪឋ×Ø7⚪Ḅ£᎛ᡃÛ±ÜZÝÞ+ß*à»:ᐸᕜ¹ឋT}âᑮ6ãäåḄᦔç.*ஹè⚪.⚪ᐳ4ê⚪ëê⚪5ᑖᐳ20ᑖ.2T—I13.ìíy=------ᙠ/(T-3)ᜐḄᑗíðñIx+2ூKᫀ௃5x-y+2=0ூ᪆௃ூᑖ᪆௃ᐜóô/ᙠìíaõöᐭᑗíðñ
ᓽ.ூ#௃ᵫ⚪=—1£÷=+3,ᦑ/ᙠìía.,2(x+2)-(2x-l)5õ.y=-H—M—=7~#ᡠZVL-=5(x+2)(x+2)ᦑᑗíðñI5x—y+2=0.ᦑKᫀI.5x-y+2=0.14.ᔣøa=(3),B=(1,0),C=Q+Z:B.U£_1ᑣû=

9……10ூKᫀ௃-"—3ூ᪆௃ூᑖ᪆௃ᑭᵨᔣøḄᙶ᪗þåQᑣᔣøÿḄᙶ᪗ᑭᵨᔣḄᦪḄூ௃.2=3,1
,5=1,0,5=5+■=3+1
,_1_♦=33+k
+lxl=0,ᦇᦑ!ᫀ#----.3ூ&'௃(⚪ὃ+,☢ᔣḄᙶ᪗./,☢ᔣᚖ1Ḅᩩ345Ạ⚪ᑭᵨ,☢ᔣ»=8X
0=W9
ᚖ1Ḅᐙᑖ<⌕ᩩ3>ᐸᦪ᳝ᐭ2+%%0.15.DE£,HIᙊC#ᘤ+5=1LMᯖ&,P,QCOᐵQᙶ᪗R&STḄL&U=|6VᑣXYZPF"Ḅ☢.ூ!ᫀ௃8ூ᪆௃ூᑖ᪆௃᪷]DE^PὡH`ab|`"=᪷,1e61=஻ᑭᵨghiᳮkᔠm+”=8,op஻XYZPFQF☢qQnrn,ᓽ^.,2ூ௃sP,Q஺OᐵQᙶ᪗R&STḄL&UIPQR66IᡠvXYZwZb|PF|=m,\PF\=n,^lm+n=S,m2+n2=48,t2ᡠv64=m+n
2=m2+2mn+n'=48+2mn,x=8,ᓽXYZPὡ஺y☢qQ8.ᦑ!ᫀ#8.16.Ezᦪ/x
=2cos0x+0
Ḅ{ᑖ|}᝞|ᡠᑣᩩ3/X—/1-41]//13]]>0Ḅᨬ᦮ᦪ'.

10ூ᪆௃7ᐔ4ᐔூᑖ᪆௃ᐜ᪷]|ozᦪḄ᪆o(-?),/(,)Ḅᯠq^ᨬ᦮ᦪᡈᦪ^.313717T3712TLூ௃ᵫ|^E7=*—¢=£ᓽ7=¤=¥ᡠv஺=2§41234coTT7777ᵫ¨&©^2x—+0=—,ᓽ°=§326ᡠv/(X)=2cos(2x/s/(²)=2(#05(-'^)=1,/(g)=2cos(¶)=0§7ᐔ4ᐔᡠvᵫ(/(/(—y))(/(%)-/(y))>0^/(x)>1ᡈ/(X)<0§sº1)=2(#05(2_2)<2856_5]=1,ᡠv¾©#kᔠ|Z^Eᨬ᦮ᦪ¿À/(x)

11ᨬ᦮ᦪ2.ᦑ!ᫀ#2.ூ&'௃ᐵÍ&'#᪷]|zᦪḄ᪆>(⚪ḄᐵÍ᪷]ᕜÏ᪷]ᱯÑ&஺.ஹ!⚪#ᐳ70ᑖ.!¿ᑏoÕÖ×ØஹØÙÚᡈÛ/ÜÝÞ1721⚪<ὃ⚪,ßMà⚪ὃáâ<ãä!.Þ22ஹ23⚪⌱ὃ⚪ὃá᪷]⌕ä!.-<ὃ⚪#ᐳ60ᑖ.17.ᵬஹLçèéáêëìêíêíᢥïᑖðíñðíòóLçèéêíḄïᑖôᵨLçèéᔜáê2003êíêíḄïö÷øù᝞ú⊤#ðíðíᔠùᵬèé15050200èé12080200ᔠù2701304001ᵬèéஹèéáêḄêíüðíḄ⚣᳛ᑖô>ÿ
2ᔲᨵ99%ḄᵬḄḄᨵ?n(ad-bc)2(«+b)(c+d)(a+c)(b+d)P(K2>k)0.0500.0100.001k3.8416.63510.828ூᫀ௃175%#60%#2.ூ'᪆௃ூᑖ᪆௃*⚪ὃ-⚣᳛01234ឋ6789:Ạ⚪8᪷=>?@A1BᓽDூE'௃1ᵬFḄGḄHIḄ⚣᳛J=75%,120FḄGḄHIḄ⚣᳛■—=60%.200

12c,400(150x80—120x50)2400ফK2=—~----------^-=7>10>6.635,270x130x200x20039ᦑᨵ99%ḄᵬḄḄᨵ.18.Z[ᦪᑡ^4_Ḅᔜ⚗ᙳcᦪ8dS“^4_Ḅg஻⚗28ij☢জঝঞG⌱pqrsᩩu8vwx᜜Hrᡂ4.জᦪᑡ^4_{|ᦪᑡ}ঝᦪᑡ^~_{|ᦪᑡ#ঞ0=34.}⌱Ḅᔠᑖ'8ᑣᢥHr'1ᑖ.ூᫀ௃ᫀ'᪆ூ'᪆௃ூᑖ᪆௃⌱জঝsᩩuvwঞ8D?8ᔠ,S”Ḅᐵ?4,ᑭᵨ^%_{|ᦪᑡDv%=3஻]#⌱জঞsᩩuvwঝ8᪷=|ᦪᑡḄ2@A⊤?8ᔠ|ᦪᑡDv#⌱ঝঞsᩩuvwজ8?E=ᔠ4,S”Ḅᐵ?w8᪷=4=3D஺8ᯠDv^{|ᦪᑡ.ூE'௃⌱জঝsᩩuvwঞ}=an+b(a>0),ᑣS”=(an+by,J஻=18q=S[=(஻+/?¤#J஻N28a=S-S„_=^an+by-(an-tz+Z?)--a(2an-a+2b^#nn(^®J°{|ᦪᑡ8ᡠ²(a+b1=a(2a—a+2´)8'µ஺=0#ᡠ²ᡠ²“2=3%.⌱জঞsᩩuvwঝ}஺=3®,^4_{|ᦪᑡ8ᡠ²@1=஺2=2q,ᡠ²+=ᓽ=•7,

13■H·=¸”+1H¹஻=ᔣ,ᡠ²^ஹᵨ_{|ᦪᑡ.⌱ঝঞsᩩuvwজ}=an+b#a>0,ᑣS“=a஻+b2,J஻=18q=S[=a+b¤#J஻¼28q?=S஻-S஻_]=Q஻+b2Q+b~=a#2an-a+2b%#4=34,ᡠ²a3a+᝞=3a+஻,'µ1=0ᡈஹ=—-#J஺=084=/84,=/2஻_1,J“¼28q--=24ÁÂ|ᦪᑡḄ8Ã^4_|ᦪᑡ#Jᓃ=HÅ•8Js~=an+h=an--a,=HÆ<0ᔠ⚪È8ÉÊ.3ஹ3Y3ËÌD[^4_|ᦪᑡ.ூÍÎ௃ÏÐ⚪Ñᙠ'⚪GÓÔ8'ḄᐵÕ{ᱞᱞᢕØÙ[ᩩu8ᔠÚᐵ@A8⌲ÜÝÞ8|ᦪᑡḄvwßàáᵨâᡈὅ|G⚗â.19.Ù[äåæçABC—A4aG8ë☢᯿ᱏ8cîï8AB=BC^2,E,FᑖAC2CGḄG3,஺æ4ᵨÌḄÍ.BF±1vw}BF5DE72Jᱏ஺òó8☢B4GC☢஺ôõᡠᡂḄö☢÷Ḅcøóᨬú?ூᫀ௃1'᪆#2BD=-,2

14ூ'᪆௃ூᑖ᪆௃ßûÙ[ᩩu8üåᩩýÚᚖäḄäÿ
ᔠ〉Ḅᙶ᪗ᔣᚖ☢Ḅ☢Ḅᨬᜧ!"#$%&ᫀ.ூ*+௃-./01ABC-A4G2/01ᡠ#.4☢ABC,ᡠ#-.BFᡠ#66A68BB[CBF=B,ᡠ#9_1☢8஺஺ᵪ.ᡠ#499ᚖ.#8.ᙶ᪗:;ᑖ=#ᡠᙠ.x,y,z?
ᙶ᪗᝞A.ᡠ#3(0,0,0),A(2,0,0),0(020),4(0,0,2),A(2,0,2),G(0,2,2),E(l,l,0),F(0,2,l).ᵫ⚪F஺(a,0,2)(0«a42).(1)-.G=(0,2,1),H=(1-a,1-2),ᡠ#G.H=0x(l-a)+2xl+lx(-2)=0,ᡠ#BE_LDE.(2)F☢OEEḄJᔣ.£=(x,y,z),-.L=(M1,1,1),H=(l_a,l,_2),in-EF=0[-x+y+z=0ᡠ#NMOapt,ஹ..nffi-DE=0[(l-«)x+y-2z=0Rz=2—஺ᑣT=U3V+a,2-a

15-.☢8CG4ḄJᔣ.G=U2,0,0_,F☢8CC4`☢DEFḄ☢Ḅ☢.஺,ᑣ1=d=63tM|/n|-|BA|2xV2a2-2«+14>/2«2-2a+14127r஺=Ms2a2-2a+4tᨬu.M22ூ;v௃w⚪ὃyᔣḄzᐵ|}~᪷⚪F஺U஺,0,2_U0VaW2_,ᙠᨬᜧᑮᨬu2ᐵM.20.ᱥCḄ⚔;.ᙶ᪗:;஺ᯖ;ᙠx?/x=lCP,஺9;OP_LOQ.;ᵨU2,0_,`/zᑗ.U1_C,OMḄL¡U2_FA4,42cḄ/£;4444ᙳ`zᑗ.ᑨ¦&A`Ḅ¨©ᐵ,ª«ᳮᵫ.ூ&ᫀ௃U1_ᱥCy2=x,0ML¡.Ux—2_2+y2=i°U2_zᑗᳮᵫ±+᪆ூ+᪆௃ூᑖ᪆௃U1_᪷ᱥ`x=lz"³ᱥ´µᔣ¶F᪗·L¡¸ᑭᵨº»ឋFP,Qᙶ᪗ᵫOP_LOQ,ᓽ"P°ᵫᙊM`x=lzᑗ¿Àᓽ"³ÁÂ;U2_ᐜὃ⇋A4Æ᳛ÈÉᙠ᪷º»ឋᓽ"³Á°ÊAA2A|A34A3Æ᳛Éᙠᵫ44,4/;ᙠᱥËA4A4,44Æ᳛ᑖ=ᵨÌᙶ᪗⊤θᵫ44,44`ᙊMzᑗ³%+r%..`ḄᐵᨬÐM;ᑮ44ḄÑÒᓽ"³ÁÂ.ூ*+௃U1_Ó⚪FᱥCy2=2pxUÕo_,pUi,_o_,QUi,—yo_

16-.■OP±OQ,:.OPOQ=l-yl=l-2p=0,:.2p=l,ᡠ#ᱥ஺ḄL¡.y2=x,MU0,2_,OM`x=lzᑗᡠ#¿À.1ᡠ#ḄL¡.Ux—2×+V=1°U2_F4ØM_4U%2%_43U*3%_Ê44Æ᳛ÈÉᙠᑣ44L¡.X=1ᡈx=3,Ê44L¡.x=i,᪷º»ឋÈÜF4U1,1_,ᑣ4`ᙊ”zᑗḄÞMᩩL¡.y=1,àsá`ᱥâᨵM£;ᓽÈÉᙠä,Èᔠ⚪°Ê44L¡.X=3,᪷º»ឋÈÜFAU3,6_,4U3,—G_,ᑣ4`ᙊMzᑗḄAA3.y—`UX—3_LMy-%_1.1—Ð.IVæMAM—M1-—FM=è•.%MU_%M$*+%J3+%3w=o,4Uo,o_,àsaA&Aᐵx?º»ᡠ#&A`ᙊMzᑗ;Ê4Æ᳛ᙳÉᙠ,111ᑣ,àíM~᝕'M+ñM+%…ó+%1/ஹᡠ#44L¡.y-y=------Ux-᳝_,■æ+%᦮ᳮ³x—Uy+%_Õ+ññ=°øᳮ44ḄL¡.ùMUú+._û+%%=°44ḄL¡.X-U%+/_Õ'+%%=°

17`ᙊMzᑗ,y+iJ᦮ᳮ³U4-1_ü+2yly2+3-y°=0,44`ᙊMzᑗ,øᳮUy°—Dy°+2ñ.+3-Õ°=0ᡠ##%.L¡Uþ-1_/+2yy+3-4=0Ḅ9᪷,Mᑮ44Ḅ|2+314+%஺21+(-ÿ)2M-1L+1|W+L17^2-12+4/+]ᡠ!44"ᙊM$ᑗ&'(44,A4"ᙊM$ᑗ+ᑣ44"ᙊM$ᑗ.ூ/0௃ᐵ3//0145ᱥ'Ḅ7/8᳛:◤ᵨᐸ>ᙶ᪗ᡈBᙶ᪗⊤D+EF⚪Hᓄ:">ᙶ᪗ᡈBᙶ᪗ᨵᐵ2⌕ᐙᑖᑭᵨAA2,A&ḄPQឋ+STU++♦%"MᐵV+W%+%ḄᐵVHᓄᵨM⊤D.x"21.Z[஺>0^a0l,aᦪ/(x)=±-(x>0).ax1fa=2g+hḄᓫjkl;2(ny=/x"y=lᨵ^pᨵ7qr/+h஺Ḅstv.ூwᫀ௃প°,ᔁ'ᓫj⌴};2---,+00'ᓫj⌴2l,eDe,yo.ln2ூ᪆௃ூᑖ᪆௃1haᦪḄaᦪ+ᑭᵨaᦪḄ"aᦪḄᓫjឋḄᐵVᓽᑮaᦪḄᓫjឋ;

18(2)ᑭᵨᢣᦪPᦪḄᑣ+!Eny=/(x)"y=lᨵ^pᨵ7qr/Hᓄ=30ᨵ7qḄᦪ᪷+ᓽny=g(x)"=ᨵ7qr/+ᑭᵨaᦪẆg(x)Ḅxainaᓫjឋ+ᔠg(x)Ḅ+/¡᩽▲tᑖ᪆g(x)Ḅ¤T+¥¦ᑮ00,fx>»g+f\x)<0,In2In2In2.aᦪ/(x)ᙠ(o,À'ᓫj⌴}Á,+8)'ᓫj⌴(2)/(x)=^=loav=xa<=>11110=4111Ä0^^=^^,Åaᦪ8(Æ=^^,aXcixᑣ8'")=ᓃÈ+ºg'(x)=0+x=e,Xᙠ(0+e)ᑁg'(x)>0,g(x)ᓫj⌴}ᙠ(e,+oo)'g'(x)<0,g(x)ᓫj⌴g(xtu=g(e)=+Ìg(l)=0,fxÍÎÏ+8g+g(x)ÍÎÏ0,ᡠ!ny=/(x)"y=1ᨵ^pᨵ7qr/+ᓽn>=g(x)">=ᯅᨵ7qr/Ḅᐙᑖ⌕ᩩÒ0<<(+«ᓽ0

19p=2V2cos^.lcḄ᩽ᙶ᪗ᓄᙶ᪗2AḄᙶ᪗1,0,MCḄP!/=0$ᑏ&PḄ'(GḄ*ᦪ,ᑨ.C/G0ᔲᨵ3ᐳ.x=3-8+2cos஺=>?,ூEᫀ௃1x-⊈/+I=22PḄ'(GḄ*ᦪ᜛*ᦪ,C/y=2sin஺GJᨵ3ᐳ.ூK᪆௃ூᑖ᪆௃1NOCḄ᩽ᙶ᪗ᓄ02=20஺cos6,Q=pcos6,y=psin஺SᐭUV2Px,y,M8+&cos6,Xsin஺᪷Zᔣ\ᐵ^ᓽU`VPḄ'(CḄ*ᦪ`&aᙊᙊcdefghijkUV.ூlK௃1ᵫNOCḄ᩽ᙶ᪗᜛=2&COS஺UV᜛p=2j^ocos6,r=2s05஺,>=᜛5&஺SᐭUVQ2+y2=2vX,ᓽ—+y2=2,ᓽNOCḄᙶ᪗x—J5y+y2=22Px,y,M8+J^cos6,•••AP=42AM<x-1,y=V2#41+V2cos6-1,0sin6=2+2cos6-&,2sin6,x—1=2+2cos0—\p2x=3—\/2+2cos0ᑣீᓽீy=2sin0~y=2sin஺=x=3—yf2+2cos0ᦑḄ'(&Ḅ*ᦪ஺*ᦪy=2sin6•••NOCḄᙊcJ5,0,fg0,NOGḄᙊc3-&0fg2,ᑣᙊcd3-20•.•3—2ஹᔊ<2-ஹᔊaᙊᑁᦑNOC/GJᨵ3ᐳ.ூ௃ᐵs⚪ὃ*ᦪḄ`KK⚪Ḅᐵ0&MḄ*ᦪᙶ᪗ᑭᵨᔣ\ᐵ^`K.~⌱4-5⌱10ᑖ

2023.ᦪ/(x)=|x-2|,g(x)=|2x+3|-|2x-l|.2/x+a2gx,`aḄ¡¢¤.ூEᫀ௃1¥¦§K᪆2a>—2ூK᪆௃ூᑖ᪆௃1ᑖ¨©ª«¢ᓽU¬&¥¦2᪷Zᦪ¥¦ᦪ®eUV◤y=f#x%ᔣ°±²U!³`Vy=/x+a´µaḄ¢U`...f2-x,x<2ூlK௃1UV/·=1>2=¸.°,¬&¥¦᝞»s[x—2,x>2

213]g(x)=|2x+3|-|2x-l|=<4x+2,F-2y=g(x)(2)f(x+a)=|x+a—2\,᝞¥ᙠ³>Àᙶ᪗^Á¬&஻x),g(x)¥¦y=/(%+«)0y=f(x)±²Å³ÀᓫÇVᑮᑣ⌕Ê/(x+a)Ng(x)◤Ì=/(x)ᔣ°±²ᓽaÌ0,Í)=/(x+a)´µ|g+a—2|=4,KVᡈ>ᑣᦪ®ᔠUV◤ÐÑÌ=/(x)ᔣ°±²?■ÀᓫÇ•.aNg.y/y=g(x)y=f{x+d)

22ூ௃ᐵs⚪ὃª«¢ḄឤᡂÖ×⚪K⚪Ḅᐵ0᪷Zᦪ¥¦ᦪ®ᔠ`K.

23