2021-2022学年山东省聊城市九年级（上）第一次月考数学试卷（附答案详解）

《2021-2022学年山东省聊城市九年级（上）第一次月考数学试卷（附答案详解）》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。

2021-2022
ḕ□
ᨴὃᦪᔁ1.V^tan45°Ḅ&'A.1B.V2C.2D.2.᝞.,0121஻22஻2344B=22BC=3,DE=1,ᑣEFḄ&')A.-B.-C.6D.-3263.᝞.2AABCḄ⚔;<ᙠ>?@Ḅ?;2ᑣsinAḄ&'A.⎀10B3D•10C.34.᝞.2EᛀGH☢ḄᚁK8CMACN1MV3,AC=6m.ᑣᚁ☢ABḄPQNA.12/HB.8V3mC.45/3mD.6m5.᝞.2T48C2CEA.AB,ᚖV'E,BD1AC,ᚖV';O,CEBD
F,ᑣ.YZ[\]ᨵ_`A.6`B.5`C.4`D.3`6.aῪ[\]cdecdḄfḄKN2MV3,ᑣgḄ⚔\'A.30°B,45°C.60°D.120°7.᝞.NjklmᵨoᵯqᩭstuvᜋfQḄxy..ᙠᙢ☢;Pᜐ}~Ḅ☢2ᐝ1;A☢

1ᑮvᜋCDḄ⚔Cᜐ24B1BD,CD1BD,s=1.22BP=1.8,P0=182vᜋḄfQN()A.6B.8C.128.᝞.2E(-4,2),(2,-2),0'Z2AEF஺jᑮᩭḄᑣ;EḄ`;Ḅᙶ᪗'N()A.(2,-1)ᡈ(-2,1)B.(8,-4)ᡈ(-8,4)C.(2,-1)D.(8,-4)9.᝞.2ᙠ¤d]ABCO,ᑖ¦NAB,A£Ḅ;.4EF=2,BC=5,CD=3,ᑣsinCa§()3D110.᝞.2ᙠAABC2ZC=90°,AC=32,ABḄᚖ0ᑖ1MN¨AC§;஺2©ª47sinCBD=3,ᑣ8cḄPN()A.16B.8V2C.4V2D.811.᝞.ᡠx2¬aῪ[\]@ᱏ2cdP18cm,cdḄfP18cm,®¯cd°ᔣ²³´µ¶Qᙳ'3஺"Ḅ¹]@ᩩ2µḄ@ᩩᨵ¬N»>]2ᑣ¼¬»>]@ᩩN()A.4¬B.5¬C.6¬D.7¬

212.ᙠ☢0\ᙶ᪗½2»>]ABC஺Ḅ¾᝞.ᡠx2;AḄᙶ᪗'(1,0),;஺Ḅᙶ᪗'(0,2),¿PCB¨xÁ§;Â,û>]&B1GCÆ¿PC/1¨xÁ§;2û>]2c2G…ᢥ¼᪵ḄËÌÍβÏ2»>]42021Ð02Ñ202Ñ2020Ḅ☢Ò'()A.5x(|)2021B.5x(3)2020c.5x(^)4040D.5x(|)404213.4ÓÔYZ[\]YZK'4M5,Õj[\]Ḅ☢Ò'16,ᑣÕᜧ[\]Ḅ☢ÒN.14.᝞.2jkᙠᡭØᳫÚ.ÛᳫាÝᡭÞØ(Øf0.8m),ßàᙠáØ4â¾2ᑣ᪷ä.Ḅᦪäå2ᳫæçᳫḄfQ஻'______m.Mé0SêëF-4m-*—4m—î15.᝞ïJcos4-M+|V^tanB-3|=0,ᑣTABCḄ]ôN—16.᝞.2ᙠTABC,0E//BC,EF//AB,4E=2CE,AB=6ABC=9,¤d]BDEFḄᕜPN__.17.᝞.ᡠx2T£»"1¯DEùᑮTA8CḄ¾2gúûü,
pcᑖḄ☢ÒNTDEF☢ÒḄ|,AB=V6,ᑣý[\]ùþfAD__.DAEB18.᝞ᙠAᜐᛞCᓅ70஺ᔣAᜐ!"#20%&Ḅ()*ᓭ50஺ᔣᒴ(./1"#0ᑮ2ṹᜮ8ᜐ5#ᛞCᓅ25஺ᔣ,ᑣᛞC7ṹᜮ8Ḅ89:..%&.

319.<=>(1)(1)-2+2sin600-V12+(ᐔ-2021)0I1(2)cos60°—sin245°+-tan230°+cos30°—sin30°.20.᝞ᙠRABC7RACEU—,VNE4C=NZMB.[\>&ABC-ADE.21.ᙠ᝞Ḅ"]^_`U!a"]^Ḅbcᙳe1,`fAABC(⚔f:_`hḄif)Ḅja⚔fᙶ᪗ᑖn:B(-3,l),C(-l,0),஺epUqᙠ_`ᑁstAABCḄp^ReB1GvAABC7ᐸp^Ḅxpye1>2,z<=tR&B1GḄ☢}.22.᝞~R4BDUAC1BD,BC=8,CD=4,cos4BC=£8/ebḄUh.(1)[ACḄcI(2)[tan/FBCḄ.

4BDC23.᝞ᙠ]^4BCZ)UE:bAOḄff/ᙠbC£>VCF=3FD,NBEF=90஺(1)[\>AABES^DEF(2)4B=6,cEFi8CḄchfG,[BGḄc.24.ᨵ>◥sᔁᐭὡᩭ.▁╋q¡¢.1987£e¤¥¦§¨©ᡂ«¬ᓝᕜ£¦©¯°ᙠ±²³´ᑁµ¶¬·¸Ḅ“q▁”»¼▁.¾¿᪥ᦪ¿ÂÃÄÅ"ÆeÇ“q▁”CHḄ¸)ᙠÈḄÉᙢAᜐᑮ⚔CᜐḄËÌe30஺ᙠÉᙢ8ᜐᑮ⚔CᜐḄËÌe45஺zÍAஹBjᜐx820%,[“q▁”CHḄ¸).(²Ïᶇ"ᦪf0ÑὃᦪÓ>V2«1.41,V3=1.73)25.᝞>ᙠÔ^ABC஺UAB=6m,BC=8m,ÅfÕ2m/sḄ()AftÖ*ACᔣCf×ÅØ#Åf஺lm/sḄ()fCtÖ*CBᔣf8×ÅÙPஹQjf×ÅḄ#Úe/Û(0

5

6êᫀìí᪆1.ூêᫀ௃Bூí᪆௃í>ñò=óx1=&,ᦑ⌱>B.᪷Óᱯù̬ÌúᦪûÍêᫀ.ü⚪ὃþ¶ᱯù̬Ìúᦪÿᱯᦪ⚪ᐵ.2.ூᫀ௃Bூ᪆௃•••/1஻%஻3AB_DE•**=,BCEF-AB=2,BC=3,DE=1,21=•ELFL=32ᦑ⌱8.᪷%&'ᑖ)ᡂ+,-ᳮ/0+,123ᐭ50ᓽ7.8⚪ὃ:&'ᑖ)ᡂ+,-ᳮḄ<ᵨ>?@A&'BCᩩᡠFḄG<)ᡂ+,.3.ூᫀ௃Aூ᪆௃IJABᑮ஺NOC஺᝞RSᡠTᵫ⚪?7/AC=Vl2+32=Vlo,CD=1,ᦑ⌱A.᪷%⚪?ZS[7\/ᑮCDZ4cḄJᯠaᓽ75/sin4Ḅ.8⚪ὃ:[8⚪Ḅᐵef⚪?ᑭᵨᦪ[hᔠḄjk.4.ூᫀ௃Cூ᪆௃,•ᚁ+BCAC1V3,AC=6m,BC1o=p’/BC=2V3(m),

7ᵫtu-ᳮ/AB=>JAC2+BC2=4V3(m),ᦑ⌱C.᪷%ᚁvḄᭆx50BC᪷%tu-ᳮyz/ᑮᫀ.8⚪ὃ:Ḅ[Ḅ<ᵨ-ᚁvᚁ|⚪}~ᚁvḄᭆx⚪Ḅᐵ.5.ூᫀ௃Aூ᪆௃•BD1AC,CE1AB,AAAEC=/.ADB=90°,BEF=CDF=90°,vZ.A=Z-A,Z-EFB=DFC,•.AECSAADB,BEFsுCDF,vZ-EBF=ABD,BEF=Z.ADB=90°,•BEFsுBDA^LCEASுCDF,•••ᐳᨵ6G[ᦑ⌱4᪷%[Ḅᑨ-@@eᓽ7.8⚪ὃ:[Ḅᑨ-⚪Ḅᐵ}~[Ḅᑨ-,ὃὃ⚪.6.ூᫀ௃Cூ᪆௃᝞SAB=AC,AD1BC,BDC•.BD=CD,vBCAD=2V3,•tanB=—=V3,BD:.B=60°,••AB=AC,•/BC[ABAC=60°,ᦑ⌱C.eABC[7/h.8⚪ὃ:[Ὺ[Ḅឋ[Ḅᑨ-Zឋ⚪Ḅᐵ

8eABC[.7.ூᫀ௃Cூ᪆௃ᵫ⚪?ᐝAPᐝPC,Z.APB=^CPD,^ABP=Z.CDP,RtABPsRtCDP,.ABCD,BPPD..CD=1^1=12().1.8ᦑ⌱c.ᵫ/ABPSACDP,ᑣ᪷%[Ḅឋ7/,=ᓽ7.BPPD8⚪ὃ:[Ḅ<ᵨ>?ᑭᵨ&☢¡¢£Z[Ḅ/0[⚪ᐵ.8.ூᫀ௃Aூ᪆௃E(-4,2)\஺¤¥¦§AEFO¨©ᑮªᩭḄ¬ᑣ¬EḄG<¬Ḅᙶ᪗¤(—4xi,2xi)(—4x(ߟ^),2x(—}),ᓽᡈ(-2,1),ᦑ⌱A.᪷%¥°ᣚḄឋyzᓽ7.8⚪ὃ:Ḅ¥°ᣚḄឋᙠ&☢ᙶ᪗³᝞´¥°ᣚ\ª¬¤¥¦+¤k,µ¶¥S[G<¬Ḅᙶ᪗Ḅ+ᡃᡈ-k.9.ூᫀ௃Cூ᪆௃NO8஺■:Eஹ/ᑖ¹ABஹAOḄ¬,EF//BD,EF=^BD,vEF=2,•••BD=4,»•••BC=5,CD=3,BD2+CD2=BC2,BDC*+,+-,ᦑ⌱C.᝞SNO8£),ᵫ[¥-ᳮ/ᑮ80ḄJvᯠaᑭᵨtu-ᳮḄ⌮-ᳮ½ABCD¤[ᨬaᵫ┦ᦪḄ-ÀÁ'.

9Â⚪Ã⌕ὃ:┦[Ḅ-À\Å[¥Ḅឋ\Åtu-ᳮ⌮-ᳮ᪷%/0BDC[⚪ᐵ.10.ூᫀ௃Bூ᪆௃.MN)Ḅᚖ&ᑖ•••AD—BD.7ᙠ••sin"BD=§,CD_CD_7''JD=AD=9'"AC=AD+CD=32,CD=14,AD=BD=18.ᙠ/?[BCDBC=y/BD2-CD2="82-142=V128=8É.ᦑ⌱B.᪷%)ᚖ&ᑖḄឋ/ᑮ4D=BD,ᑭᵨ[ḄÊᐵ³Å/CBDḄË7/ᑮCD.A஺Ḅᐵ³Ì50ÍÎḄJᨬaᑭᵨtu-ᳮ50BCḄJ.8⚪ὃ:tu-ᳮஹ)ᚖ&ᑖḄឋÅ[}~)ᚖ&ᑖḄឋÅtu-ᳮÏ8⚪Ḅᐵ.11.ூᫀ௃Bூ᪆௃ூᑖ᪆௃8⚪ὃ:[<ᵨÐẠ⚪.᪷%⚪?7/Á'5ᓽ7.ூ௃ÒÓÔ[ÕᩩÖ஻ÔÍḄ@¤Eᐘ¬Eᙠ48جÙᙠACØᑣEÙ=3,EFᑮBCḄÚÛ¤3Ü

10•••EF“BC,•••AEFSAABC,.EF_18-3n_3"BC-18-18,/71=5,ᓽÓÔ[ÕᩩÖ5Ô.ᦑ⌱B.12.ூᫀ௃Dூ᪆௃,••[ABC஺Ḅ¬AḄᙶ᪗¤(1,0),¬஺Ḅᙶ᪗¤(0,2),OA=1>OD-2,AD—V5,—=OD2IJCBâxä¬å,æ[4&C1C,•••DAO,.3@,AB2VAD-AB=y/s,-AB-y,X••Ö1è[Ḅ☢é¤Si=&C2=5•(|)2,ëᳮ7/A2c2=(|V5+|x|V5)2,Öìè[☢é¤S=5-(|)4,2Ö஻è[☢é¤S=5-(|)2n,n.•Ö2021è[Ḅ☢é¤Szo2i=5-(|)4042,ᦑ⌱D.᪷%[Ḅᑨ-ªᳮ/0AABSAAI&BIðñ/NB441=48⍗⍗2ᑭᵨtu-ᳮyz0[ḄJᨬaᑭᵨ[Ḅ☢éô1yzè[Ḅ☢éõö0÷ø|⚪ùúûᑓñ.8⚪ýᔠὃ:[Ḅᑨ-ஹtu-ᳮஹ[Ḅឋ¬þ᜜ᙠ⚪

11⌕᢬᣾⚪◚Ḅ᪵⚪Ḅ⚪ᦔ᳛.13.ூᫀ௃25ூ᪆௃$•.•&'()*+,Ḅ()-.4$5,&'()*+,Ḅ☢0-.16$25,12ᜧ*+,Ḅ☢0.4•••25*+,Ḅ☢0616,••16$25=16$x.7x=25.ᦑᫀ6$25.᪷:()*+,☢0Ḅ-;<()-Ḅ=>?@☢0-᪷:⚪ABCᓽ.E⚪ὃGḄ.()*+,ḄឋI()*+,ᕜKḄ-;<()-ஹ()*+,☢0Ḅ-;<()-Ḅ=>ஹ()*+,MNḄ-ஹMNOḄ-ஹMN+=ᑖOḄ-Q;<()-.14.ூᫀ௃1.6ூ᪆௃$•R-DE//BC,ADESAACB,DEAE••—~~~9BCAB0.84—=--h4+4h=1.6
TUᦑᫀ6$16᪷:ᳫWXYᳫZᳫ[Ḅᚖ]O^=_ᓽ`aADE^i,ACB,᪷:ᐸ()-ᓽ?.E⚪ὃGc()*+,ᙠdeZḄNᵨ⚪Zᐵh.i@()Ḅ*+,ᯠk᪷:MNlᡂ-nᑡ@>pq〉sḄᦪuvwᩭyz⚪.15.ூᫀ௃;l*+,ூ᪆௃ூᑖ᪆௃E⚪ὃGcᱯ|+Ḅ*+}ᦪ~E⚪Ḅᐵh.ᱯ|+Ḅ*+}ᦪ~ᦪḄឋI.᪷:ᱯ|+Ḅ*+}ᦪ~ᦪḄឋI?.ூ௃$ᵫ⚪A7cos/1=\tanB=V3,:4=60°,Z.B—60°,

12C=180°-60°-60°=60஺.ᦑaABC6;l*+,.ᦑᫀ6;l*+,.16.ூᫀ௃16ூ᪆௃$••4E=2CE,CE1=,AE2vEF//AB.AE_BF_2•BC-5BC=9,:.BF=6,•DE//BCBDCE1ABAC3vAB=6,BD=2vEF//AB,DE//BC••l,BZJEF.=_l,•••BD=EF=2,DE=BF=6,l,BOEFḄᕜK2(2+6)=16,ᦑᫀ6$16.ᵫ=_OᑖO^ᡂ-n7@-nᯠkl,2DEF.=_l,7@MNl(;ᓽ7@.E⚪⌕ὃG=_OᑖO^ᡂ-n=_OᑖO^ḄO^MNᡂ-n.⚪ḄᐵhAO^ḄMNᐵ.17.ூᫀ௃V6-2ூ᪆௃$•••ADEDE=ᑮAABCḄ.-.AC//DF,DEFsுAEG,

13♦.•^££=2,DE=AB=V6,S&DEF3.g_2"&=3'••AE=2,AD=^6-2.ᦑᫀ6$V6—2.aOEFSAZEG,ᵫᐸ()-?7AE,§¨?74DE⚪⌕ὃG()*+,ḄᑨªXឋIஹ=ḄឋIᐵhᙠᔣ+z⚪>ᔣ+Ḅᭆ¹ஹº»┦+*+}ᦪḄªµ.⚪Ḅᐵh.19.ூᫀ௃$(1)(1)-2+2sin600-V12+(re-2021)°=4+2xf—2½+1=4+V3—2\/3+1=5-V3(2)cos60°-sin245°+^tan230°+cos30°-sin30°1V2.1¾ஹ241Z2~(T)+4X(T)+T-2

141111V31=-------1--X---1--------224322V35=-------212,ூ᪆௃(1)ᐜᓄÈᔜᯠkʧ_BCᓽ;(2)ᱯ|+Ḅ*+}ᦪ~Ìᐭ§_BCᓽ.E⚪ὃGcÎᦪḄÏCᱯ|+Ḅ*+}ᦪ~ÐᢣᦪÒ᦮ᦪᢣᦪÔÕÖº×ᙢᓄÈᔜ.⚪Ḅᐵh.20.ூᫀ௃$Z.EAC=Z.DAB,••Z.EAC+Z.BAE=Z-DAB+BAE,•Z.BAC=Z.DAEJ..AB_AC**—,ADAEABCADE.ூ᪆௃᪷:()*+,Ḅᑨªᓽ?@ᫀ.E⚪ὃG()*+,Ḅᑨªªᳮ⚪Ḅᐵh.º×Ïᵨ()*+,Ḅᑨª.21.ூᫀ௃$a&B1G᝞àᡠâA/liBiCiḄ☢0=4x4-3x2x4-Tx2x4-gx2x2=ூ᪆௃êKAOᑮ°4ë7஺&=204,ìí¯@°BiGᓽyz⚪E⚪ὃG¯à-)îᣚ*+,Ḅ☢0;`ð⚪Ḅᐵh.ᳮ⚪Aᵨᑖᒘí?*+,Ḅ☢0ò<ὃóὃ⚪w.22.ூᫀ௃$(1)vAC1BD,cos^ABC==BC=8,•AB=10,

15ᙠRt^ACBᵫõöªᳮ7,AC=y/AB2-BC2=V102-82=6,ᓽACḄK66(2)᝞à,÷øCF,F°¯8஺ḄᚖOᚖùE,•••B6AOlúḄOᓽ6Ḅ°•••CF=-AD=FD,2ᙠRtAACDᵫõöªᳮ7AD=yjAC2+CD2=V62+42=2V13,•••*+,CFO6;Ὺ*+,FELCD,1/.CE=-CD=2,2ᙠRMEûCEF="2CE2="3-4=3,••tan7FBD=—=---=—.BEBC+CE10ூ᪆௃(1)┦+*+}ᦪ7(2)÷øCF,F¯BDḄᚖOᚖù6E,᪷:]+*+,ülO;<ülý7CF=FD,ᵫõöªᳮ74஺=2gEF=3,ᓽ?tanNFBD.E⚪ὃG]+*+,E⚪ᐵh᪷:⚪A¯þÿ
┦ᦪᳮ.23.ூᫀ௃(1).•!ABCQ"#$!,•.Z.A=Z.D=90°,•Z,BEF=90°,/.ABE+Z.AEB=AAEB+7DEF=90°,••Z-ABE=7DEF,ABE^LDEF(2).•!ABC஺"#$!
..AB=AD=CD=6,AD//BG,••CF=3FD,

16/.DF=1.5,(DE=%,ABE^ADEF,DFDE=*AEAB+,1.5x6-X6-x=3,.•DE—3,-AD//BG,•7DEF=Z.G,v7DFE=7CFG•..CGF0°ADEF,.DE_DF••/—CF
•CF=3FD,31A⁰=7:CG=9,BG=BC+CG=15.ூ᪆௃(1)ᑭᵨ“*7”ᓽ:;<(2)ᵫ4B=CD=6,஺>=3>஺?@஺>஺>ḄB
ᑭᵨZBES^DEF?@஺CḄBD
EᵫCGFS^OEF?@CGḄBD
ᓽ:?@8GḄB.⚪ὃHI#$!ḄឋK
LM!ḄᑨOឋK
PQ#RSᑮLM!UV⚪ḄᐵX.24.ூᫀ௃(C”"xm,ᵫ⚪Y-N4HC=90஺
ZCFH=45°,z/1=30°,BH=CH=xm,AH=V3CH=V3xm,vAH-BH=AB,:.y[3x—x=20,-x=10(V3+1)«27.3m,:“*[▁”C஻Ḅ^D_"27.3m.ூ᪆௃(C”"`a;@BH=CH=xm,AH=y[3CH=V3xm,Eᵫa”*BH=48-@$b
$bᓽ:.⚪ὃHḄU7!Ḅcᵨ*def⚪ஹῪ7!ḄOឋKஹi30஺Ḅ7

17!ḄឋKj;@=CH,4H=kCHUl⚪ḄᐵX.25.ூᫀ௃(1)ᙠRtAABCn
AC=y/AB2+BC2=V62+82=10,vZ-PCQ=7ACB,.•.o“QC=NBp
ACQPs&CBA,ᑣr=sᓽtj=5,-t=^(s)jACCDluo13oNPQC=NB4Cp
4CQPS4CAB,ᑣ{=|
ᓽ}3=~-t=(s)jCBCA8107"Mᡈᐝp
QஹC"⚔Ḅ!OAABCLM;(2)!ABQPO.CPQḄ☢PL.ᳮᵫ᝞PH1BCH,᝞
vPH//AB,•CPHsுCAB..PH_PCpr.PH_10-2t••—,P>U-,ABAC610PH=ᵨ
o!A8QPO.CPQḄ☢Lp
S—BC—S&CPQ=S&CPQᓽS-BC=2s>CPQc130-6t1,c252᦮ᳮ-t2-5t+20=0,lp$bᦪ,!ABQP.4CPQḄ☢PL.ூ᪆௃(1)ᐜᑭᵨᳮ@AC=10
ᵫNPCQ=N4CB,᪷!LMḄᑨ
o7PQC=48p:ᑨCQPs&CBA,ᑭᵨLM-ᑮo=~<7PQC=4BACp:ᑨ4CQPSACAB,ᑭᵨLM-ᑮ?=!
ᯠCᑖ$b?@tḄ¡ᓽ:jO10(2)PH_LBCH,᝞
ᐜ;<.CPHSASB,ᑭᵨLM:-ᑮp”=¤|
Eᑭᵨ!48஺2O4CPQḄ☢L-ᑮ஻48c=2SACPQ
ᑭᵨ!☢¦§-ᑮ24tᜫ}=
68,ᯠCᐵrḄ$b:ᑨ!48஺2O^CPQḄ☢PᔲL.⚪ὃHILM!Ḅᑨᨵ¬®cLḄ¬¯!LM.cᵨLM°ḄB.