2022年浙江省金华市金东区中考数学一模试卷（附答案详解）

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2022
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15.᝞⊤567ᵬஹ:ஹ;ஹ<=>?@ABᕒᨬEFG⌱IJᡂLḄ%ᙳᦪNOP:ᵬ:;T%ᙳᦪC771185180185180OP3.63.67.48.1᪷\⊤ᦪ\⌕^⌱_>ᡂL`abᢵdeḄABᕒfghJij⌱_A.ᵬB.:C.;D.T6.᝞RtAABC“=90஺48=30°,ᑖwxyAzy80ᙊ|ᜧ~Ḅ0~MஹNyMN,BCD,AO,ᑣ/C4DḄᦪA.20°D.60°7.yP-3,yᔣ%3ᓫᔣ%2ᓫᑮyQx,-1,ᑣ¢Ḅ0A.—8B.—2C.—10D.—68.᝞¤¥ᔆᨵᜧ¨©Ḅª$«a¬ᨵ⍝¯.°⌕ᔣᵬ«±$²ᓫ³¬ᑁḄ±$µ¶·¸^±$¹ᵬº:»$«:$☢)ᓣḄ@¾N±$³¬¿¬ḄÀᦪᐵÂḄÃÄÅ10.ÆÇᙠ©Ã▲ḄyAa,c,yBb,c+1ÍᙠÀᦪyÃ)ᑣᐵ~ᐗÏGOÐ+c=0Ḅ᪷%],ᑨÔÕÖḄA.+×>1B.N+&V0C.0<%I4-%2<1D.+%2ḄÝÞÖeß2⚓ᐳ19⚓

211.ᑖâãx2-xy=.12.Àᦪy=䶵xḄåç.13.èéḄêëᨵᑖw᪗Ḽᦪî1,2,3,4Ḅ=ïðᳫᐜ^ëóô᥎öïðᳫᑣ÷ïðᳫ)Ḅᦪî¿zᜧ~5Ḅᭆ᳛0.14.⇾ûḄ᪀⌼þÿ
ஹ᝞ᵫ7ஹᜧᐰḄᡂḄḄ⚔:#BCḄ⚔&ᙠ(.*+A8᝞ᡠ/ABC:::0102cḄᦪ.15.78ᵫ891Ḅ:ᡂḄZ,=>?᝞@Aᐸ⚔E,F,G,H,/&ᙠEABCZ)Ḅ(ᑣEABCDḄ☢I.16.78K⊟MN☢OPQᑖ᝞1,ᵫ6᪷9:Tᩩ(WXYᶍ[\)ᵨ9┑`A,B,C,D,E,F,G,H,/abcᡂTᩩdX&2c7%g᪷h9TᩩḄ942cm,ᐸij᪷Tᩩ922cm,l┑`&ᙠmn9:Tᩩ1cmḄᙢ:pq᝞2ᡠ/.K⊟MOP28ᙠrsAP(uvN4CBḄᜧyz{|}~ᓄ.TᩩACEᨬN⚔TᩩᨬN⚔M4CD=90஺2MN=N4C0=30஺2MN=.1217.\2sin60°+7T°-+V12.18.ᐜᓄ☢Ḅᦪ(a+2)(a-2)+a(4-a),ᐸ¡஺=ᡈ+1.19.£¤¥ᨵ4,B§¨©B¨ᙠA¨ᓅ«¬30°:ᔣ(mA¨120¤®.ᨵj⁂±A¨|²³ᓅ:ᔣ´µj¶mn·ᑮ¹º»8¨ᓭ«³75஺:ᔣḄCᜐ.(1)NBC4ḄXᦪ.(2)BCḄ9.

320.¾¿ÀὁÂÃÄᱥḄÆÇ:ÈÉÊË£᪥ᦪᐶÎÏÐÑ´ÒÓ᪵ÕÖÕÖ×ØÙ/ÆÇ:ᨵAÚÛஹBÆÇÜஹCÝÞஹOᐸßàá£âãᜩᑁÄæὅḄÆÇ:Ñ´ÕÖè\éᑮ᝞§ê[᦮Ḅè\.ìí᪷îè\ïðḄÛñòóᑡõ⚪(1)÷øjᐳÕÖÒËúûÄæὅü(2)ì⊡ᐰᩩè\.(3)ᙠᡧè\¡Aÿ
ᡠḄᙊᦪ.(4)ᕜᑁᨵ3200ὅᵨA!B"#
Ḅὅᐳᨵ%&'21.()*+,ᨵ10-%./012345367589ᐰ;<=>ᦈᐭᩭBCDEF012#GHIJKᙢJMNO150ᐗ⊡R.MS#GᡝUᜧW᪷Y/Z[\ὃ⇋ᔜ#`a⚜cMJKḄ012├eᦈᐭ32000ᐗ/fJK#Gᡂcy(ᐗ)j#G☢lmK)noḄpᦪᐵr᝞tᡠu.(1)᪷YtvwxyjxnoḄpᦪᐵr.(2)᪷Y⚜yzwUᜧW{M#G|ᦈᐭw(ᐗ)j#G☢lK)noḄpᦪᐵr.(|ᦈᐭ=├eᦈᐭ-#Gᡂc+#G⊡R).BOḄFE,FEEG1AB,ᚖ3FF,FG,OG,4⚓ᐳ19⚓

4DG=1,DB=2.(1)wAE=AB.(2)wFBḄ.(3)wOGḄ.23.pᦪ%=mx+n(mH0)!pᦪ/="+bx+c(a*0).y=ky¦ஹ2(.3¨ᦪ)ᑣyªyi!¬2Ḅ஺pᦪ”.(1)%=%-2,¯!°Ḅ"2pᦪ"3y=3/+2x-1,wy?Ḅµ᪆.(2)·pᦪ3=2%+2!pᦪ¬4=%2-2x+3.জw3!ºḄ“pᦪ”µ᪆(ᵨ¼&Ḅ¾ᦪ⊤u).ঝÁÂkÃÄŬ3!%Ḅ“Æpᦪ”ÇᔲÉCFÇwxFᙶ᪗Ìᔲ,ÍÎᳮᵫ.ঞÁÂkÃÄÅpᦪ¬4=X2-2%+3,ḄFPᐵxÔªḄF஺ÕÖᙠ¬3!4Ḅ“,pᦪ”,wFPᙶ᪗.24.ᙠØ☢Ùᙶ᪗rÚF4(0,2),ÛFÜᙠxÔÝÞÔ,ßà0ABpFC3PBÚFäABCåACᢚçèéᑮä4CC,ÙC஺jßà0ABpëFE.(1)᝞tìFEjîF஺ïᔠñ,জwäOCP^^ADO.ঝwOP.(2)ìEC=5E஺wFÜᙶ᪗.

5óᫀ!µ᪆1.ூóᫀ௃Aூµ᪆௃µ-2Ḅ÷ÅÇ2,ᓽ|-21=2஺ᦑ⌱Ao᪷YýᦪḄ÷ÅþÿḄ
ᦪ஺⚪ὃḄឋᦪḄᦪḄḄ
ᦪ0Ḅ0஺2.ூᫀ௃Bூ᪆௃2x>3+1,2%>4,x>2.ᦑ⌱B.ᢥ᯿,-./01⚗3ᔠ567⚗38ᦪᓄ:1;.⚪ὃ,-.,<=>?,-.Ḅ@ឋA1,,-.ḄBC6DEFᡈHI6JKᦪᡈ᦮.3,-MNᔣ,P2,,-.ḄBC6DQRᡈ◀R6JKᦪ3,-MNᔣ,PT⚪ᐵV.3.ூᫀ௃Bூ᪆௃ூᑖ᪆௃⚪ὃXYZḄ[\]^3>?_`ᐵV.abᡠᨵḄeᑮḄghi⊤kᙠ[]^m.᪷op]^qᱥZḄF☢e3ᡠtᑮḄ^uvtᫀ.ூ௃JKwxᙠyz{|}FḄ┵u3Ḅp]^:BK6ᙊ.ᦑ⌱B.4.ூᫀ௃Bூ᪆௃᝞^36⚓3ᐳ19⚓

6•.•z2=90o-30°=60°,Z3=180°-45°-60°=75°,va//b,.•.41=43=75°,ᦑ⌱B.ᑭᵨ[uᑁ_ᳮzḄឋ⚪ᓽv.⚪ὃzḄឋ3ᐵV᪷oBz36
-.5.ூᫀ௃Aூ᪆௃ூᑖ᪆௃⚪ὃzᙳᦪN3ᳮNzᙳᦪḄb`⚪ᐵV.✌ᐜzᙳᦪ3zᙳᦪ
6D⌱NḄᕒE.ூ௃’•,¢£=%B>=xᔆqᵬ§m⌱J¨E©3vS"ᵬ=S?mᚖḄ^ឋ⚪ḄᐵV.7.ூᫀ௃Cூ᪆௃ூᑖ᪆௃ᑭᵨz1»¼;²x3y,ᓽvtᑮ½¾.

7⚪ὃ^uḄz1Pᣚ.ᙠz☢ᙶ᪗8m3^uḄz1^uFÂÃḄz1
6.z1mÃḄPᓄ»¼Äᙶ᪗Å1E3Æ1HÇᙶ᪗F1E3È1H.ூÉ௃ᔣÈz13KᓫËÌ3ÍᔣÆz12Kᓫ3⚪»¼q(a,/?)z1ᑮ(a—2,b—3),᯿»¼ÕÖv®—3—2=x,y—3=—1,ᡠRx=-5,y=2,Ù!Jxy=-10.ᦑ⌱C.8.ூᫀ௃Cூ᪆௃᪷o⚪bᑖ᪆vtᔣyÞᒴàaᐭyᑖ:3K▤¶3জᵬÞᑁy☢Fᓣ3°Þᑁy☢,PঝᵬÞᑁy☢,P3°Þᑁy☢Fᓣঞᵬஹ°y☢6DFᓣ3y☢FᓣàÌ᠒.ᦑ⌱C.᪷o⚪bᑖ᪆3ᔣᵬÞᑁay3éy☢ᑮêëìí⍝D3ᵬÞᑁy☢,P3ᑮ°ÞᑁḄyêᑮëìí⍝D3y☢ïðñFᓣ3òFᓣḄàÌóôᐜ᠒.⚪ὃPõö÷Ḅᐵ83ᐵVøùPõö÷Ḅᐵ8ᵨ^ú⊤û.9.ூᫀ௃Bூ᪆௃(ý1)ஹ•þᱥḄÿᔣ⚔ᙶ᪗-3,a>0,—=-3,ᓽ᮱=12a,4a•••ᐗa/+bx+m=0ᨵᦪ᪷b2—4am>0>BP12a—4am>0,ᓽ12—4m20,'(THW3,mḄᨬᜧ/3.(22)ᐗax?+bx+m=0ᨵᦪ᪷,67ᳮ'y=ax2+bx—>—3,m<3,•••mḄᨬᜧ/3.ᦑ⌱BB.ᐜ᪷DEᱥGḄHᔣ6Ia>0ᵫ⚔ᙶ᪗-3(K6MaᐵOP᪷Dᐗa/bx+m=0ᨵᦪ᪷6(ᑮᐵR”ḄTUVWKmḄX/Zᓽ6.+[⚪ὃ^Ḅ_EᱥGMx`Ḅ=᪷D⚪aᑨcK஺Ḅefgaஹ6ḄᐵO_'ij⚪Ḅᐵk.10.ூiᫀ௃Co8⚓ᐳ19⚓

8ூ'᪆௃'B•.•4(Q,C)ᙠot▲ḄvwG•Q>0,c>0,ac=1,ᓽa=•8(4c+1)ᙠxyᦪztḄ{᜜vᓽot▲•.bV0,c+1>0,b(c+l)=—1,ᓽ8=-Wcஹ},be•1•%2z=>0%1i4-Xz?=—=—aac+1•0V+%2v1ᦑ⌱BC.᪷DZ(Q,C)ᙠot▲ḄvwG(KQ>0,c>0,PB(8c+1)ᙠxyᦪztḄ{᜜v(Kb<0,C+l>0,P᪷Dx௃+%2=—1ᓽ6(Kiᫀ.[⚪ὃ^᪷MOᦪḄᐵO᪷MOᦪḄᐵO<ᔜt▲Ḅᱯ_[⚪ḄᐵkX1%2_ᐵRXḄᐗa/+bx+c=0(a)0,a,b,cᦪ)Ḅᦪ᪷ᑣXi+=x-x=11211.ூiᫀ௃x(x-y)
'᪆1'Bx2-xy=x(x-y).᪷D6IV_X,jKXᓽ6(Kiᫀ.j⚪ὃ^Ḅ_VḄX.67(KVᯠ67'⚪.2_'j⚪>Ḅ2.12.ூiᫀ௃XH2ூ'᪆௃ூ⚪'᪆௃ூᑖ᪆௃[⚪ὃ^yᦪḄZ¡☢ὃ⇋B(1)¤yᦪ⊤¦V_᦮V¨6Xᐰªᦪ(2)¤yᦪ⊤¦V_ᑖV¨ὃ⇋ᑖVḄᑖ«T¬0(3)¤yᦪ⊤¦V_᪷V¨Hᦪ®¯.᪷DHᦪᜧRUR0,ᑖ«TUR0ᑡTUV±²ᓽ6('.ூ'i௃'Bᵫ⚪a(ᑐ+120´-2µ0,'(%>1¶*2.ᦑiᫀx>1´*2.13.ூiᫀᔩூ'᪆௃'Bᑡ⊤(B

912341--(2,1)(3,1)(4,1)2(1,2)(3,2)(4,2)3(1,3)(2,3)(4,3)4(1,4)(2,4)(3,4)ᡠᨵU6¬Ḅº»ᦪᨵ12¼ᐸ¾¿ÀᳫᦪÂÃ<ᜧR5Ḅº»ᨵ4¼,ᦑiᫀBᑡ⊤(KᡠᨵU6¬Ḅº»ᦪÅK¿ÀᳫᦪÂÃ<ᜧR5Ḅº»ᦪᓽ6WKᡠWḄᭆ᳛.j⚪ὃ^ᑡ⊤2M᪛Éz2ᵨᑮḄIËBᭆ᳛=ᡠWº»ᦪM̺»ᦪÃÍ.14.ூiᫀ௃10ூ'᪆௃'B᝞zAB_ÐÑÒ¨Cᐳᨵ6ÔÕjC'T,cஹᓽᨵ6ÐÑ¡ÑÙ'••'ஹ▼•ஹஹAB_ÛÒ¨Cᐳᨵ4ÔÕjBᓽᨵ4ÐÑ¡ÑÙABJ\BjIÝᡠÞ¤ß/BC_ÐÑ¡ÑÙ¨஺Ḅᦪ10.ᦑiᫀB10.᪷DàáÒÙḄឋãᑖA8_ÐÑÒ<ÛÒ¼º»åæK஺ḄÔÕ.[⚪ὃ^àçÒÙ<ᙊéᙠRᑖA3_ÐÑÒ<ÛÒ¼º»êëìíàáÒÙḄឋã_'⚪ḄᐵkîKzÙïÙtÐ.15.ூiᫀ௃ðூ'᪆௃'Bñ⚪a6(28=4஺=90஺v
EFB+Z-CFG=90°,Z.EFB+
BEF=90°,♦
CFG=
BEF,ᙠABEF<ß0¾2B=
C(BEF=
CFG,EF=FG•BEFdCFG(AAS),÷=x,CF—y,ᑣGøCG=x,BE=y,vZ-FGC+Z-DGH=90°,
CFG+
FGC=90°,♦
CFG=
DGH,••ZC=zZ)=90°,o10⚓ᐳ19⚓

10•ßCFG^ADGH,•••BEF^LCFG,•BEFsுDGH,üý6þBEFS^A/E,rn.iAEEl1DGHG217vj-----,==---,BFEF4CFGF42ᑣAE=-,DG=442-AB=CD,XyA-y=X++ᓽ3%=2y,2yy
ᙠRtAFCG¾FC2+CG2=FG2,:.y24-%2=42,y2+(|y)2=16,'(Bÿ=%=,••8=BC=1,4BCZ)Ḅ☢.᪷⚪BEF2CFG,BF=x,CF=y,ᑣCG=x,BE=y,34BEFs4DGH^hAIE,᪷Ḅឋ=9DG=\ᵫ4B=CD,ᐵ"X#yḄ$%&'X#y()Ḅᐵ*ᙠRtAFCG,ᑭᵨ/01ᳮx#yḄ34'5$Ḅ5#6ᓽ89☢.:⚪ὃ<=ᐰḄᑨ1#ឋ/01ᳮ@AᑭᵨḄឋ89BḄ5CD@⚪ḄᐵE.16.ூGᫀ௃62V2cm(31V6-31V2)c?nூ@᪆௃@K᝞MN5AE#N”O"PK,ᑣMK=NK=62(cm),জRN4CC=90஺TNK=90஺ᙠRtAMNK,᪷/01ᳮMN=y/MK2+NK2=V622+622=62Ucm),MxGxDxAH\7EK'^

11ঝRW4CD=30஺T4K=30஺XMTINK"PT,5.MT=^MK=31cm,KT=31V3cm,•••NT=62-316(cm),ᙠRtAMN7,᪷/01ᳮMN=yjMT2+NT2=312+(62-31V3)2=31Y-31e(cm),N5AE#NHO"PK,ᑣMK=NK=62cm,RW4CD=90஺ᡈW4CC=30஺T@ᓽ.:⚪ὃ<=@A\ᐸBᵨᐵED^_▭a⚪bᓄᦪea⚪.17.ூGᫀ௃@K2sin60°+7r°-(-|)-2+VT2V36=2x——F1—4+2A/3=V3+l-4+2V3=3A/3-3.ூ@᪆௃✌ᐜhijᢣᦪlஹn᦮ᦪᢣᦪpஹq$#ᱯsḄtᦪ3ᯠvhiwxᨬv&zᔣ|}~hi89iḄ3ᓽ.⚪⌕ὃ<=_ᦪḄi@G⚪ḄᐵED⌕Kᙠ4_ᦪiT#ᨵᳮᦪi᪵⌕&ᑮᓽᐜiw$ஹq$iw◀ᨬviᨵḄ⌕ᐜi☢Ḅi⌕ᢥ᯿&zᑮ|Ḅ4.᜜ᨵᳮᦪḄiᙠ_ᦪᑁᯠ〉ᵨ.18.ூGᫀ௃@K(a+2)(a—2)+a(4—a),=a2—4+4a—a2,=4a—4¢Ra=£+1T¥=4(V2+1)-4=4V2+4-4=4V2.ூ@᪆௃᪷¦$§¨#ᓫ⚗w«⚗Ḅxᑣᓄ¬^஺3ᐭhiᓽ.:⚪ὃ<=¦$§¨ᓫ⚗w«⚗¯°¨#xᑣD@⚪ḄᐵE±i²\³Ḅᜐᳮ.19.ூGᫀ௃@K(1)᝞M•••4E4B=30஺AE//BF,4FBA=Z.EAB=30°,l12⚓ᐳ19⚓

12·•:7FBC=75°,•Z.ABC=7FBC-Z.FBA=45°,ᓅ·^BAC=/.BAE+Z-CAE=30°+45°=75°,»:.LACB=180°-45°-75°=60°¢D\(2)᝞MX4D1BC"D.\Pᓃ//ᙠRtZkABD,vZ.ABD=45°,AB=120À\M/86ᓃÁ»AD=BD=AB-sin45°=120Xy=60ᡈ(À)AᙠRtÄCD,•••/•(7=60°,4஺=60ÅÀCD=AD-tan300=60V2Xy=20e(À),BC=BD+CD=60V2+20Ç(À).GKBCḄ5(60ᡈ+20È)À.ூ@᪆௃(1)ᵫ¦Ḅឋ²\$ᔣḄ1É9"84=^EAB=30஺4FBC=75஺,ÊËN4BC=45°,·᪷$ᔣḄ1É948"=Z.BAE+/.CAE=75°,ᑭᵨᑁ#1ᳮ89N4CB=60°¢(2)X4஺1BCOBC"P஺9RtAABD,9BD=AD,@Rt^AC஺9C3,4'9BC=BD+CD.:⚪ὃ<ḄD@AḄBᵨ-$ᔣa⚪¦Ḅឋᑁ#1ᳮ┦tᦪ1É᪀⌼Aᑭᵨtᦪ89BOÏCQḄ5CD@⚪ḄᐵE.20.ூGᫀ௃@K(1)56+28%=200,ᓽ:ᩩ
~ᐳÐ<=200ÑÒÓὅ¢001(2)஺$ÕÖḄᨵK200x20%=40(×)801601601"A$ÕÖḄᨵK200-56-44-40=60(40140L20O×)⊡ᐰḄᩩÚhM᝞|MᡠÜ(3)ᙠᡧÚhM,AÞÕÖ$ᡠßBḄᙊáK360°xâ=108°,ᦑGᫀK108¢(4)3200xä=1856(Ñ)GKåᵨA#BæÞÕÖ$ḄÒÓὅᐳᨵ1856Ñ.ூ@᪆௃(1)᪷BḄᦪç#ᡠᓰḄéᑖë²8:~Ð<ḄÒÓὅḄ×ᦪ¢(2)᪷ÚhM,Ḅᦪ²8⌱íA#஺Ḅ×ᦪ&'²îᩩÚhM⊡ᐙð᦮,(3)8ᙠᡧÚhM,4ÞÕÖ$ᡠßBḄᙊáḄCᦪ¢(4)᪷ÚhM,Ḅᦪ²hi9åᵨA#8æÞÕÖ$ḄÒÓὅᐳᨵ«ñÑ.

13:⚪ὃ<ᡧÚhMஹᩩÚhMஹᵨ᪵:òhóô@G:⚪ḄᐵED⚪ᑭᵨᦪõᔠḄ÷ø@G.21.ூGᫀ௃(1)tᦪᐵ*ù=/^+8,᪷MûütᦪMûýP(200,1000),(240,880),îþæPᦪtᦪᐵ*K(200k+b=1000l240/c+b=880'@:ÿ
ᦑᦪᐵy=-3x+1600(2)├ᦈᐭ:2000xᡂy-x=(ߟ3x+1600)-x=-3x2+1600x,⊡150x
ᦈᐭ=├ᦈᐭ•ᡂ+⊡
ᡠw=2000x-(-3+1600x)+150x,᦮ᳮ"w=3%2+55Ox.ூ$᪆௃(1)ᑭᵨ)*ᦪ+ᓽ-.$(2)ᑖ0.1├ᦈᐭஹᡂஹ⊡
3᪷5ᦈᐭ├ᦈᐭᡂ⊡67ᓽ-.⚪:⌕ὃ=>?ᦪḄA▭CᵨD)*ᦪ+.$᪆
$⚪ḄᐵEFGH$I⚪J,L1ᔜNᦪ⊤PQRᦪ.22.ூSᫀ௃$(1)•••48FUᙊ஺ḄXY
^ADB=90°,•••CD=BD,•Z.CAD=
BAD,ᙠ[4E0Q[ADB\
2EAD=
BADAD=AD:Z-ADB=Z.ADE=90°•AE=AB.(2)
GED=
FEB,
EDG=Z-EFB=90°,•EDGs&EFB,DG_EDT**=:FBEFVED=DB=2,EF=y/EB2-FB2=<42-FB2,....L,2FB=V16-FB2]14⚓
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