2022年河南省信阳市中考数学二模试卷（附答案详解）

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2022
ᓭḕ□ὃᦪᔁ1.8ḄᦪA.-B.—8C.8D.--882.!ᐵ#$%&'“)*+Ꮇ“-.'/0123ᐳ5617835500000<=,?ᦪ!35500000ᵨABᦪC⊤EFA.35.5x107B.3.55x1073.᝞J'KLMJNḄOPJ4.RS'i஻'2,41=45஺,ᑣ42ḄYᦪF(A.45°B.75°C.105°D.135°5.\ᑡ^_`abcḄ()A.6a+3a=2aB.(2a)2=4a2C-h=&TD.(%-y)(x+2y)=/+2y26.᝞J'ᐵnoᱥqr=஺s2+8t+-\ᑡuCbcḄ

1A.a>0B.b-4ac=0C.c>0D.ab<07.ᐗ=wx2/x+6=0Ḅ᪷Ḅz{A.ᨵ}~Ḅᦪ᪷B.ᨵ}~Ḅᦪ᪷C.ᦪ᪷D.Cc8./++'ᑖ“ᦪ”“ᦻ”Ḅz{'}~<ᐜᑖᵬஹஹஹḄ<'}~<ា¢ᑮ¤Ḅᭆ᳛A.-B.-C.-D.-842169.᝞J'§DE¨Ḅ☢ªF12஺«2,EG¬ᑖNOEF,FG1EGn3G,5DG,ᑣ4DEGḄ☢ªFA.3cm2B.4cm2C.5cm2D.6cm210.᝞J'ᙠ§ABC'BC=6,AC=8,AB=10,3ᵨᙠAB¯`°'MP1BC,MNLAC,஺FPNḄ3'ᑣCQḄᨬ*²F11.³ᦪy=72x+4´µ¶xḄ²¸¹2⚓'ᐳ20⚓

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3^ᦪ2818.᝞L{|}ᦪy=x-6ḄL}ᦪy=7(m+ᦪ0)ḄLM(a,-5),N.(1)[}ᦪT᪆Nᙶ᪗.(2)[MNḄ.19.᝞L᩟10¡ᙠG¢ᜐᨵ{¤ᛞEF,¨ᨨᙠᙢ☢Aᜐ¬®)ᛞ⚔Ḅ°±+43஺ᙠ⚔஺ᜐ®)ᛞ⚔Ḅ°±+36஺ᐸEF1AF,DA14F,[ᙢ☢Aᛞ´Fµ¶Ḅ·¸(!ὃᦪº:tan36஺«0.73,cos36°«0.81,sin36°«0.59,tan430Ä0.93,cos43°«0.73,sin43°«0.68).20.᝞LᙠÅABC448c=30஺஺ÇABÈz{yAO+ÉÊ஺஺È8cËᑗC.DÇ஺஺z{A8ាÏÐᑖND4C,ÑÒDB.Ó4⚓ᐳ20⚓

4(1)[NC4DḄÖ.(2)×BC=6W[஺஺᜜ஹBCஹ3஺ÙᡂḄᑖ(▢Ûᑖ)☢Ü.21.ÝᐹᔆÒᑮ{á1500âÜᩈḄäᓫ◤⌕ᙠ15ᜩᑁHᡂênëÜᩈìâíîᨵ42ïðñÜᩈg42ÉᙊbÜᩈ.Ýᐹᔆóᙠᨵ100rô^ì^ìᜩõô92ïðñÜᩈᡈ62ÉᙊbÜᩈ÷ì^{ᜩøõô{ëÜᩈÝᐹᔆìᜩôḄïðñÜᩈgÉᙊbÜᩈᦪùïÏᐰûᝅ.ýìᜩþ᣸x
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LMNOḄᦪ(ᵨRaḄSᦪT⊤V).ঝY⌕ᙠ['ᑁᡂᓫ!\஻Ḅᨬ_`.22.᝞b!cᱥey=a/+bfg4ijkC(—1,0),kB(4,0),lym/kA,k”opcᱥeqrst▲ᑁḄg8uk!HElxm/kE,levAB/k஺!HQlym!lym/kQ.(1)\cᱥeḄxᦪy᪆T.(2)Ys{|HQOEo|!\p|Ḅ☢.(3)~O஺ஹAC,cᱥeqoᔲᙠkH,k0ஹAஹ஺⚔kḄ|ABC!Yᙠ!ᑏk”Ḅᙶ᪗!Y1ᙠ!ᳮᵫ.

523.ᙠ|ABCDL!48=4,k/ᙠ{8Cq!8M=3.AM_L஺”.Ḅ⚔kᙠkMᜐ!Ḅ;{ᡠᙠḄeᑖABஹA஺{l/kNஹP,~NP,#b(1)ᡠVḄ¡.¢k“¤[┐¦§ᑮ᝞b(2).©NkBkDᔠ[«¬!®¯°!±²³y´µ¶⚪.(1)4M=,AD=.(2)ᙠ¦§j¸L!tan^MPNḄ`oᔲ¹ºᓄ!Y1ᦋº\½8`!Yᦋº!ᳮᵫ.(3)ᑏ#¦§¡ᑮ«¬!ev/WḄLkᡠij¾eḄ¿.r6⚓!ᐳ20⚓

6´ᫀÃy᪆1.ூ´ᫀ௃Cூy᪆௃yÆ-8ḄÇᦪo8,ᦑCÉᔠ⚪Ê!ᦑ⌱ÆC.᪷Í4ᨵÉÏ1ÐḄ;8ᦪÑÇᦪ!Ò´ᫀ.O⚪ὃÔÇᦪ!ᙠg8ᦪḄÕ☢6qMÏÖo½8ᦪḄÇᦪ.2.ூ´ᫀ௃Bூy᪆௃yÆ35500000=3.55x107,ᦑ⌱ÆB.×ØÙᦪÚḄ⊤V|Tax10”Ḅ|T!ᐸL1W|a|<10,”᦮ᦪ.9nḄ`[!⌕ÜÝKᦪºᡂ஻[!_ᦪkÞu!஻ḄßE`_ᦪkÞuḄᦪÐ.©KᦪßE`à10[!woᦪá©KᦪḄßE`<1[!஻oMᦪ.â⚪ὃÔ×ØÙᦪÚḄ⊤VÚ.×ØÙᦪÚḄ⊤V|TaX10"Ḅ|T!ᐸL|a|<10,஻᦮ᦪ!⊤V[ᐵä⌕99aḄ`å஻Ḅ`.3.ூ´ᫀ௃3ூy᪆௃yÆ#q{ÜᑮḄb|⌱⚗AÉᔠ.ᦑ⌱ÆA.᪷Í#q{ÜᑮḄb|oçèb!Ò´ᫀ.O⚪ὃÔéᓫêᔠḄèb!#q{ÜᑮḄb|oçèb.4.ூ´ᫀ௃Dூy᪆௃yÆ᝞b.•••zl=45°,43=180°-Z1=135°,1•,a//b,42=43=135°.ᦑ⌱ÆD.ᐜ᪷Íì⊡î\43,ï᪷ÍðGeḄឋò42=43,ᓽÒ´ᫀ.O⚪ὃÔðGeḄឋòḄôᵨ!᪷ÍðGeḄឋò42=43oyâ⚪Ḅᐵä!õÊÆðGeḄឋòᨵÆজ;eðG!Ðö!ঝ;eðG!ᑁ┯ö!ঞ;eðG!ÐùᑁÑ⊡.5.ூ´ᫀ௃B

7ூy᪆௃yÆ6Q+3Q=2,ᦑA┯ú!1Éᔠ⚪Êá(2a)2=4a2,ᦑB9!Éᔠ⚪Êáû=&+1,ᦑC┯ú!1Éᔠ⚪Êá(x-y)(x+2y)=x2+xy-2y2,ᦑ஺┯ú!1Éᔠ⚪Êáᦑ⌱ÆB.᪷Í᦮TüýᐵḄÚᑣÃᑖÿᨵᳮᓄ⌲⚗ᑨ.⚪ὃ᦮ᑖᨵᳮᓄ⚪Ḅᐵ᦮ḄᐵᑣᑖᨵᳮᓄḄ.6.ூ!ᫀ௃Aூ᪆௃%Aஹ•••(ᱥ*+,ᔣ.a>0,ᦑA012ᔠ⚪45Bஹ•••(ᱥ*6x789:;b2-4ac>0,ᦑ8<01<ᔠ⚪45Cஹ=>?ᦪABCD%c<0,ᦑC<01<ᔠ⚪45DஹEF7ᙠy7ḄHIᑣab>0,ᦑ஺<01<ᔠ⚪4.ᦑ⌱%A.᪷MNO?ᦪḄABPᦪḄᐵPQRᑖ᪆ᓽC.⚪ὃTNO?ᦪAB6PᦪḄᐵPUNO?ᦪḄAB⌲Vᑖ᪆WᩩYḄ0Z⚪Ḅᐵ.7.ூ!ᫀ௃Cூ᪆௃%•••4=(-1)2V4x2x6=-47<0,•••[\]ᦪ᪷.ᦑ⌱%C.ᐜ_᪷Ḅᑨ`Ḅabᑮ/<0,ᯠg᪷M᪷Ḅᑨ`Ḅ4hᑨ[᪷Ḅij.⚪ὃT᪷Ḅᑨ`%VᐗNO[ax?+ᓃm+c=0®o0)Ḅ᪷64=b2-4acᨵ᝞qᐵP%r4>0s[ᨵ:t<uḄ]ᦪ᪷5r4=0s[ᨵ:tuḄ]ᦪ᪷5r4<0s[\]ᦪ᪷.8.ூ!ᫀ௃Bᵬwxyᵬwxyᵬwxyᐳᨵ16{uC|Ḅ}~ᐸ:tាᑮḄ}~ᨵ4{,8⚓ᐳ20⚓

8••.:tាᑮḄᭆ᳛=i,164ᦑ⌱%B.᪛Aᐳᨵ16{uC|Ḅ}~ᐸ:tាᑮḄ}~ᨵ4{ᵫᭆ᳛ᓽC.⚪ὃḄᵨ᪛Aᭆ᳛.᪛AC¡<¢£<⍡¥Ḅᑡ§ᡠᨵC|Ḅ}~,〉ᔠ:ªᡈ:ª¡.¬ᡂḄ®¯5⚪s⌕±4⚪²³´µ¶<²³´µ.ᵨᑮḄD·;%ᭆ᳛=ᡠijᦪ6¸ijᦪ¹º.9ூ!ᫀ௃Dூ᪆௃%᝞A»FG8EQ9;H,•••EGÁᑖNCEF,FG1EG9;G,4HEG=
FEG,
EGH=4EGF=90°,ᙠAHEGAFEG(Z.HEG=
FEGEG=EG,I
EGH=AEGF.^HEG^^FEG(ASA),S»HEG—S^FEG—5S4HEF#HG=FG,SADGH=SADFG=2^ADHF#DEGḄ☢Ê%S&DGH+S/^HEG=ASADHF+]SAEHF~^SAOEF=wX12=6cm2.ᦑ⌱%D.»FG8ED9;H,ᐜΧÏHEGFEG,QÐCbHEG=S^EG=^SAHEF"G=FG,᪷MÒÓÔḄ*CbSAOGH=SADFG=15,ᨬg᪷M^DEGḄ☢Êu9ADHFSADGH+S&HEG=2^ADHF+×S^EHF=DØᱏ_ᓽCߟ⚪Û⌕ὃᐰuÒÓÔḄᑨÝ6ឋßஹÒÓÔḄ*᪀⌼ᔠ〉Ḅâã*⚪ᐵ.10.ூ!ᫀ௃C

9ூ᪆௃%äCåCMJL4B9M,CM8PN9W,QPNḄ;PQ=NQ,•••BC=6,AC=8,AB=10,•••BC2+AC2=AB2,•.ÏABCæÓÒÓÔw4cB=90஺CQ=»N,vMPIBC,MN1AC,.Z.CPM=)CNP=90°,NWçÔCPMNèÔPN=CM,PW=NW,CW=MW,••PQ=MQ,:.QW¢ᔠiCQ=%CM,⌕éC஺aᨬêë⌕CMᨬêìC¡rCM_L48sCMᨬêíᚖ*ïᨬðñ11vS&ABC=5xACxBC=-xABxCM,6x8=10xCM,kA,24**•CM=—,5•••CQḄᨬêa=ᦑ⌱%c.᪷MèÔḄឋßb§CM=PN,§CQ=%CM,⌕éCQḄaᨬêë⌕CMḄaᨬêᓽC᪷Mᚖ*ïᨬðb§CM_L48sCMᨬê᪷MÒÓÔḄ☢ʧCMᓽC.⚪ὃTòóÝᳮḄ⌮ÝᳮèÔḄឋßᑨÝᚖ*ïᨬðÒÓÔḄ☢ÊuD·;|§CQ=^CM⚪Ḅᐵ.11.ூ!ᫀ௃x>-2ூ᪆௃%᪷M⚪4b%2x+4N0,bx>-2.10⚓ᐳ20⚓

10ᦑ!ᫀx>-2.᪷MøùúḄûaý?ᦪᐵPÛ⌕ᨵNO᪷.᪷MNO᪷Ḅ4hþ+ᦪÿᦪ.⚪ὃᦪḄ⚪ᦪḄ☢ὃ⇋(1)ᦪ⊤!"#᦮"%&ᐰ()ᦪ*(2)ᦪ⊤!"#ᑖ"%ὃ⇋ᑖ"Ḅᑖ-./00*(3)ᦪ⊤!"#34᪷"%67ᦪ08ᦪ.12.ூ;ᫀ௃m<1ூ@᪆௃@ᵫ-x>4m,Hx<-4m,IJ<-4,K.L"MḄ@N0x<-4,•••—4m>-4,@Hm<1,ᦑ;ᫀ0m<1.ᑖRSTU.L"Ḅ@N᪷VWXYᜧᜧஹY\\ஹᜧ\\ᜧ]^_ஹᜧᜧ\\_.ᑮab.L"MḄ@N.⚪ὃḄ#@ᐗ4.L"MdaSTU.L"@N#eẠgh“Yᜧᜧ*Y\\*ᜧ\\ᜧ]^_*ᜧᜧ\\_.ᑮ”Ḅkᑣ#@;m⚪Ḅᐵo.13.ூ;ᫀ௃2(1+x)2=4.5ூ@᪆௃@᪷V⚪shtuᵨwxyᦻᐹᖪ}Ḅᢗ!2(1+x)ᐗuᵨwxyᦻᐹᖪ}Ḅᢗ!2(1+x)2ᐗᑣ2(1+x)2=4.5.ᦑ;ᫀ02(1+%)2=4.5.᪷V“uᵨwxyᦻᐹᖪ}Ḅᢗ!4.5ᐗKUuᵨwxyᦻᐹᖪ}ḄᢗḄᙳ᳛0x”&ᑡᐗ34.⚪ὃᵫ)▭⚪Tᐗ34_LᐵdaᑡTᐗ34#@⚪Ḅᐵo.14.ூ;ᫀ௃31°ூ@᪆௃@OB,■■■AC=AB,/,AOC=62°,

114஺3=44஺஺=62஺48஺4=44஺8=31°,2ᦑ;ᫀ031஺.஺8᪷Vᙊᕜbᳮᓽ&ST4BD4⚪ὃᙊᕜbᳮᙊ¡^ḄᐵLh¢@⚪Ḅᐵo#£¤¥¦§ᵨ¨©ª«w]ὃ§ὃ⚪¬.15.ூ;ᫀ௃2ᡈ6ூ@᪆௃@•.•MD=AD=6,3&hMḄ¯°#±஺0ᙊ60²³ḄᙊজMC=MB%ᑣMᙠBCḄᚖ·ᑖª¸,4DMP=30°,•••APDM=60°,•••)ADN=)MDN=30",AN=[AD=2V3*ঝCM=CB=6%DM=AD=6,º»¼AMMO0d¼,AN=AD=6*ঞ•••BMḄᨬ\06¾-6=6(V5-1)>6,•••M8./LwBC0ᦑ;ᫀ024ᡈ6.᪷VMD=AD=6,&hMḄ¯°#±஺0ᙊ60²³Ḅᙊᑖ¿ÀÁÂÃᓽ&.⚪ὃᢚÅḄឋÇḄÈᵨஹ¯°ḄÈᵨஹLῪ¼ḄឋÇLᐵo#ᑖÊÂÃḄÈᵨ.Ë12⚓ᐳ20⚓

1216.ூ;ᫀ௃M(l)(27r-6)°+(i)-1-|V8-V9|=1+4-(3-2V2)1+4-3+2V2=2+2V2*2x2-6x+9(A/Ùk2%—6%(%—2)=x-2.Q-2(%—3)%(%—2)x—2(%—3)2_2XX-3ூ@᪆௃(1)ᐜÝÞᢣᦪà᦮ᦪᢣᦪ'â34᪷"Ḅᓄäåæçèݦéᓽ&;(2)ᐜëᑖì/ᑖ@Ḅíîᑖ@èïᑖᓽ&.⚪ð⌕ὃᑖ"ḄòᔠôÝ@;Ḅᐵo#çõÈḄôÝöᑣḄ÷ø.17.ூ;ᫀ௃@প•••6úḄûüᦪ04+10%=40(ü),3CLþüᦪ040-(4+28+2)=6(ü)⊡ᐰ
᝞(2)ḄᑖᡂḄᦪ3ᦪ84+24.(3)1500x^=1050(())*+,ᨵ1050(ᡂᙠ80ᑖ(/80ᑖ)01.ூ4᪆௃(1)ᐜᵫA:ᦪ;ᐸᡠᓰ?ᑖ@ABC:ᦪD᪷FGH:ᦪIJC:ᦪABC:ᦪLM⊡ᐰ
(2)᪷FᦪJᦪḄOP4)ᓽR(3)ᵨ᪵U*VCWᓽR.U⚪ὃZḄ[ᩩ]+
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jklmM(a,—5),:#—5=a—6,4n஺=1,M(l,-5).•q@riᦪy=stᦪumH0)Ḅ
jlmM(l,—5),m=1x(-5)=—5,vq@riᦪḄ4᪆wsy=-j._545ᡈ+1“=%—6vmNᙶ᪗s(2)᝞
lmz{PM஻y}~x}NPmP.♦.•mM(l,-5),N(5,—1),PM=4,PN=4.ᙠRtPMNMN=yJPM2+PN2=4^2.ூ4᪆௃(1)ᵫghiᦪy=x-6AnMḄᙶ᪗AᯠᑭᵨOᦪABḄ,nᑮq@riᦪḄ4᪆w(2)lm{PM//y}~x}NPmP,ᵫMஹNḄᙶ᪗AnPM=4,PN=4,ᯠ᪷FOᳮᓽRA4.U⚪[q@riᦪghiᦪḄ~m⚪ὃZghiᦪ
j1mḄᙶ᪗ᱯOᦪAq@riᦪḄ4᪆wOᳮḄᵨᦪᔠ[4⚪Ḅᐵd.19.ூ)ᫀ௃4l஺{DHJ.EH,•••EF1AF,DA1AF,vGAOHF[•••HF=AD=10DH=AF,DH=4F=xᙠRMAEFtanz.EAF=ᓽtan43°=*0.93,¢14⚓,F

14EF=0.934ᡝᙠRtAEDHtan^EDH=—,DHBPtan36°=—®0.73,AFEH=0.73AF,•••FH=EF-EH=0.93AF-0.734F=10,•••AF=50)¥¦§ᙢ☢Amᛞ«mI¬Ḅ®s50.ூ4᪆௃l஺{DH1EFH,᪷FḄឋ°nᑮHF=4D=10DH=AF,DH=AF=%4²³´³ᓽRnᑮµ.U⚪ὃZḄ[4²³´³Ḅᵨ-·³¸³⚪_`·³¸³Ḅᭆºஹ»¼┦³´³iᦪḄOP[4⚪Ḅᐵd.20.ூ)ᫀ௃4(1)¾¿0஺OC,■■BC஺஺aᑗmC,AOCB=90°,•••Z.ABC=30°,•••COB=90°-AABC=60",•••/.CAB=-Z.COB=30",2•48ᑖNDAC=24G4B=60°,"4DḄs60஺(2)ᙠBC=6^3,/-ABC=30°,OC=BC•tan30°=6A/3Xy=6,•4/MC=60°,4DOC=2NG4D=120°,•Z,BOC=60°,♦
DOB=
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1511207rx62=2x-BCOC------——2360=BC•0C—12ᑍ=36V3—12ᐔ,.••▢ÂᑖḄ☢Ãs368-127r.ூ4᪆௃(1)¾¿O஺0C,᪷FᑗḄឋ°RnNOCB=90஺ᯠᑭᵨ²³´³OÆH┦³ÇÈRnNCOB=60஺LMᑭᵨᙊᕜ³OᳮRnZZMB=30஺ᨬᑭᵨ³ᑖḄOPᓽR4);(2)ᙠRtaOBCᑭᵨ┦³´³iᦪḄOPABOCḄÍD᪷Fᙊᕜ³OᳮABZ.DOC=2)CAD=120°,LMRnNBOC=Î஺஺ÏᯠᑭᵨSASÐÑᨬᑭᵨ▢ÂᑖḄ☢Ã=2BOCḄ☢Ã-ᡧDOCḄ☢ÃÒ+VᓽR4).U⚪ὃZᑗḄឋ°ᙊᕜ³Oᳮᡧ☢ÃḄ+V᪷F⚪ÓḄÔÕᩩÖ×ᔠ
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