2022年全国高考甲卷数学（文）试题

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9ூᑖ᪆௃᪷H☢%ḄÜÝ&ìḄ\᪀ᱯïᓽN!.ூOC௃᝞Xᡠð.ñòóÛ8=ô/஺=a/4=஺à⚪&ìḄ\᪀ᱯïN(8Q"_☢Z8COᡠᡂ%chNB,DB,8Q"_☢//ö/ᡠᡂ%ᡠsin3(y=Mx=MKᓽb=c,DUDD}}BD=2c=yja2+h2+c2,Cha=>f2c-}A,AB=a,AD=h,AB=6AD!A┯÷B,ø8ù8E_L/14E,᧕(ûJ__☢/qCQ,ᡠ48"_☢/8CQᡠᡂ%/BAE,Ptan/84E=£=জᡠ/A4Ew30°,B┯÷a2C,AC=yja2+b2=Vi;»CBஹ=[b?+c?=JJc,ACCB,C┯÷]D,ý஺"_☢88CCᡠᡂ%ND8CsinND8Q=þ=*=,BஹD2c20

104=2஽45ᔠᙊ789:*;4ᑖ<ᵨ/⊤?4ᑭᵨABCᳮᑖ'~~na~,a\a23k994,4ᑖ<CḄyz⚔|ᑣ40),4(஺0)8⚔|ᡠ8(0,b).ᡠ=(ߟa,—4=(ߟ6)r1,ᫀ.5⚓ᐳ15⚓

11Qᡠ;஻=?/ᐭ+஽2=9,஻=8,9ᦑᙊḄᔁ+=1.ᦑ⌱B.12.Aூ᪆௃ூᑖ᪆௃᪷$ᢣiᓄhᦪᦪḄᓫឋᓽ*=bg910>l,4ᑭᵨR)ᣚ()*+஻7>lgll,bg89>஻?ᯠ¢ᵫᢣᦪᦪḄᓫឋᓽ*F.ூK௃ᵫ9"=10*+¤=1¥10=¦>1Ig91g]]<(lg9©gll)=(R)<1=UglO)2,ᡠª>¬ᓽ¤>lg",ᡠ"=10.-11>10®"-11=0.1g9IglO¯lg81gl0<g8©gl°)=(±2)4²ᡠ³>´g[Jlog9>w.sᡠ6=8"'-9<8'°g"-9=0.µa>0>b.ᦑ⌱A.13.--##-0.754ூ᪆௃ூᑖ᪆௃¶·ᵫᔣpᚖ¶Ḅᙶ᪗⊤?Eᓽ*.ூK௃_3ᵫ⚪½a-h=m+3(in+1)=0,+¤=—.43ᦑ,ᫀ-414.(X-1)2+(^+1)2=5ூ᪆௃ூᑖ᪆௃F|MḄᙶ᪗ᑭᵨ(3,0):(0,1)ᙳᙠE+ᙊ7hᓽ*+ᙊḄ.,ᫀ.6⚓ᐳ15⚓

12ூK௃•.♦|Mᙠ¶2x+y-I=0V|M31-2a),Or|(3,0):(0,ᙳᙠ,...|MᑮG|ḄÅfRÆR,VJ("3y+(1-20)2=È2+(-2É2=Ra2-6a+9+4a2-4a+\=5a2>+஺=1,AM(1,-1),R=7,QMḄ(x-1)2+(j+1?=5.ᦑ,ᫀ(x-l)2+(y+l)2=515.2(ÌÍl0,ft>0),ᡠCḄ×Ø'=±2àa-b'a5ᔠ×ØḄᱯ|Ó◤஺<â2,ᓽ444,aa~*ÌÍᩩ䓶V=2x஺ç(ᐳ|”ᡠe=£=Jl+—Y4V1+4=-J5a\aOre>l,ᡠ1ீ76'ᦑ,ᫀ2(ÌÍl0,ᑭᵨîïCᳮ⊤?F£¢5ᔠR)ᓽ*+.AB-ூK௃,ᫀ.7⚓ᐳ15⚓

138=280=2">0,ᑣᙠAABDUAB2BD2+AD2-2BD-ADcosNADB=஻/+4+2mᙠò/CO41,AC2=CD2+AD2-2CD-ADcosZADC=4m2+4-4m/C?4÷2+4-454ø/+4+2ᑗú-12ø1+íú312ᡠ4᮱m2+4+2mm2+4+2m?,13ø7W4-17+----'m+i>4——12_V4-262r+1ú-^r3þÆÿ"=ᓽ=1,ᡂ,ᡠᨬ/n=V3-l.ᦑᫀ"#y/3-l.12717.(1)48*+,-.⌶0123Ḅᭆ᳛ᑖ8"9138ফᨵூ=᪆௃ூᑖ᪆௃(1)᪷A⊤CDᦪAFGᐺᭆIḄᭆ᳛,JKLMNOP(2)᪷A⊤CDᦪAF,JQR.2,SᑭᵨVW⊤XYᓽKMNZ.(I)᪷A⊤DᦪA4ᐳᨵ]^260^23]^ᨵ240^aN+,-.⌶0123cd"M,ᑣ2")=g=hP260138ᐳᨵ]^240^23]^ᨵ210^aB+,-.⌶0123cd"N,ᫀ8⚓ᐳ15⚓

142107ᑣP(N)=——=-240812A+,-.⌶0123Ḅᭆ᳛"1PB+,-.⌶0123Ḅᭆ᳛"m.Oফᑡὶ⊤23]^ᦪp23]^ᦪᔠQA24020260B21030240ᔠQ45050500,#n(ad-be)!(Q+b)(c+d)(a+c)(b+d)500x(240x30-210x20)2«3.205>2.706,260x240x450x50᪷AVW⊤Kuᨵ90%Ḅxyz"ᵬஹ}*~Ḅ.⌶01ᔲ2301ᡠ,-ᨵᐵ.18.(1)=᪆:(2)-78.ூ=᪆௃ூᑖ᪆௃\S,,n=1প⚪KM2S"=2஻…''ᓽKMᑮߟ“M:(2)ᵫ(1)FXD⚗ḄឋLK,ᓽKMᑮ,Ḅ¡⚗,J¢஻⚗£S᪷A¤^¥ᦪḄឋQRKM.(1)2s=#§"—~+஻=2ct"+1,ᓽ2s+஻~=2na”+n(T),ziᫀ9⚓ᐳ15⚓

15஻N2ঝজ¯ঝM2S஻+/?2-2s¯("¯=2na+஻-2(஻¯—(஻¯1),nᓽ2”“+2஻-1=2஻஺"-2(”-1”“_1+1,ᓽ2(“-1”,,-2(஻-1”,1=2("-1),ᡠ“22´஻eN*,ᡠ41",Ḅᦪᑡ.(2)=#ᵫ(1)KM஺$=4+3,%=+6,%=q+8,FG,%,"ᡂXᦪᑡᡠ¹2=%.%,ᓽ(%+6)2=(q+3).(a,+8),=Mq=-12,_0½n(«-l)1251(257625rcM2IQ”¯஻¯13,ᡠS=-12஻4-------=-n----n=-

16-----,"2222lk2J8ᡠ஻=12ᡈ஻=13(S“)ms=-78.19.(1)=᪆P(2)Ãqூ=᪆௃ூᑖ᪆௃(1)ᑖ8/ᵨ8CḄD3",N,ÅÆ,ᵫÇ☢uÉKuEM1AB,FNKBC,EM=FN,⚪KÇ☢/BCD,FNKL☢4BCD,᪷AÌ☢ᚖÎḄឋÏᳮKuEM//FN,ᓽKuÑÒÓEV2"ÇÕÑÒÓNOEFIIMN,ᨬÖ᪷AÌ☢ÇÕḄᑨÏÏᳮᓽKP(2)Sᑖ8/DQCD3K,L,ᵫ(1)uÚÛÜḄÜÝÞ.ßÜKMNL-EFG”ḄÜÝâÑã┵ÜÝḄ4åᓽK=.(1)ᫀ10⚓ᐳ15⚓

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18/=(4÷)44ø+4ùú4/*4øù2ö=1286+—ø=ø.20.(1)3ফû-1+8)ூ=᪆௃ூᑖ᪆௃(1)ᐜᵫ/(x)âḄᑗ3LᑗÌßþag(x)Ḅᑗᙶ᪗ᵫ᳛ᑗᙶ᪗ᵫᦪ஺ᓽ(2)g(x)Ḅᑗᙶ᪗ᑖᵫ“X)g(x)ᑗ⊤!ᑗ"#$ᵫᑗ"%ᔠ⊤!஺᪀⌼ᦪ)ᦪ*ᓽ+஺Ḅ,..(1)ᵫ⚪23/(-D=-l-(-l)=0,f\x)=3x2-\,r(-l)=3-l=2,ᑣy=஻x)ᙠ(-1,0)ᜐḄᑗ"#$CV=2(x+1),ᓽy=2x+2,Fᑗ"Gg(x)ᑗH(஽J(஽))g'(x)=2x,LMN2)=2O=2,P+஽=1,ᑣg(l)=l+a=2+2,P+a=3(2).r(x)=3x2-l,ᑣy=/(x)ᙠ(x/(xj)ᜐḄᑗ"#$CST(᱄T᳝)=(3x-l)(x-xJ,᦮ᳮ+V=(3X-1)X-2XZ,Fᑗ"Gg(x)ᑗH(஽,g(Z)),g'(x)=2x,ᑣ/(£)=2Gᑣᑗ"#$C”^+“)=2X(X-X),᦮ᳮ+4=2`-ὃ+Q,22ᑣcd᦮ᳮ--2$3=H_2X=%”2gh+Z,931j஻(x)=-2kTlx2,Lij//(%)=9o3-612-3%=3x(3%+1)(oT1),j஻'(x)>0,P+rl,3jl(x)<0,P+ᡈ0

19“(X)-0+0-0+5/M)/-1/274ᑣX)Ḅ*C1,”)7ᦑ஺Ḅ,.C1,ᱥ).21.(l)/=4x<(2)AB:x-yfly+4.ூP᪆௃ூᑖ᪆௃(1)ᵫᱥ"Ḅ+ᓽ+P(2)Ḅᙶ᪗"ḄZ=+1,ᵫᳮ᳛+£=23.,ᵫḄᑗ+8="ᔠᳮP.(1)ᱥ"Ḅ¡"Cx=-5,¢MDGx£ᚖwMḄ¥ᙶ᪗Cp,¦w|M|ᓺ+^=3,ᡠ஺=2,ᡠᱥ"CḄ#$C/=4x<ফ஻«“¬5■®"A/N:x=/wy+l,x=my+1ᵫ¯?,+V—4஻2y—4=0,°±(),²³2=-4,[y=4xk:²f_4²T¶_4ᵫ᳛+.T·¸T²+%,"Tº¸T»+¶4444""஺:x=º¼-J+2,½ᐭᱥ"#$+¿-Àd2).),-8=0,²²°±஺ᨴ%=-8,ᡠN=2%,Âᳮ+®=2%7ᫀ13⚓ᐳ15⚓

2044ᡠ&$=%+¶2(M+%)2ÅÆC"MMḄÇᑖC஺,ÈULIஹIickgtanccᡠK,=tan4=g=kÌ⌕Î"Ïᨬᜧᑣ᜛e(0,?,tanÔT6"tana-tan--k_1<1,£L=2M=2&>0,ᑣ^^^^--fT2F-l/fF^T4~1+tanatan/7+212\k¢ÙÚ¢!=2kᓽA=জw¬ᡂàk2ᡠ¢a-4ᨬᜧw◀=^!"/á=஺+஻½ᐭᱥ"#$+â-4&y-4஻=0,°>0,%^=-4஻=4%C=-16,ᡠ஻=4,ᡠ"AB:x=6y+4.ூã௃ᐵåãZPæ⚪Ḅᐵåçᑭᵨᱥ"#$ê᳛ëìᓄíᑭᵨᳮ+ᙶ᪗îḄᐵï.22.(1)/=6x-2(y>0):(2)C3cḄòᙶ᪗Có(বGCḄòᙶ᪗C(-1,-2).ூP᪆௃ூᑖ᪆௃(I)÷øᓽ+ᑮGḄúû#$;(2)ýþ"C2C,Ḅ#$ᓄᡂúû#$ὶ
ᓽ.(1)X=",>=஻ᡠx="ᡈᓽGḄF=6x-2(yzo).66(2)x=-=",y=M,ᡠ6x=-2—/,ᓽGḄV=-6x-2(y40),6ᵫ2cos0—sin஺=0=2pcos᜛2psin᜛=0,ᓽGḄ2x—y=0.3ᫀ514⚓ᐳ15⚓

21ὶ:6>2;0)./x=-[x=1=>2ᡈஹᓽABᙶ᪗2x-y=01[1y=2@=iὶ@=>6X-2(>40),=>1;ᡈ]*=>ᓽABᙶ᪗(-1,-2).2x-y=0[y=-2I2)23.(1)I᪆(2)I᪆ூ᪆௃ூᑖ᪆௃(1)cr+b2+4c2=a2+i2+(2c)2,ᑭᵨQRSTUᓽV=W>(2)ᵫ(1)XᔠZ[V=0ᵫQRSTUᨵ“+/+(2c)2](12+12+i2)“a+6+2c)2,ᡠa+b+2c43,klmk஻=b=2c=lopTqᡠ஺+6+2c43r(2)Wg>b=2c,஺>0,b>0,c>0,ᵫ(1)=a+b+2c=a+4cW3,ᓽ0