2021-2022学年浙江省衢州市衢江区九年级（上）月考数学试卷（12月份）（附答案详解）

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2021-2022
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,ᑣ\☢]^ᡂ`Ḅ-A.-=-B.-=-C.-=-y23yy35.᝞Vᙠ0஺AB=BC,஺ᙠ஺஺4CDB=Z.AOB=()A.45°B.50°C.55°D.60°6.᝞VᙠbABCcDE//BC,d=fBC=12cm,ᑣDEḄgA.12cmB.C.4cmD.30n7.cAha/+b%+c=0Ḅij᪷-83l1,mnopqᦪy=ax2+bx+cḄVWḄrsX-tU()A.%=—3B.%=—2C.x=-1D.%=18.᝞VM-bABCḄw#,AB=18,MN"AB,ᑣMNḄy-A.9D.6

19.᝞VᙠRtAZBCZ.ACB=90\AC=BC=1,IRtABCA⌮┐30°ᑮRtbADE,BḄᑣV▢ᑖḄ☢-()10.SᱥUy=ax2+bx+cḄrsXtUx=-1,VW(1,0)ᑖVW᝞Vᡠ\ᑡᑨfজabc>0ঝ᮱—4ac>0@9a-3b+c=0টc(-0.5,yi),(-2/2)ᙳᙠSᱥUᑣ¨1>ᐜঠ5a—2b+c<0.ᐸ®5Ḅjᦪᨵ()A.2B.3C.4D.511.SᱥUy=2/-bx+3ḄrsX-tUx=l,ᑣ஺Ḅy.12.⊤µ¶·¸¹º»᪛½ᙠ86ᩩ¿\ÀÁᡂÂḄÃÄ:ÀÁḄÆᦪn200500800200012000ᡂÂḄÆᦪm187446730179010836ᡂÂḄ⚣᳛Ì0.9350.8920.9130.8950.903nᵫÎÏÐJ¹º»᪛½ÀÁᡂÂḄᭆ᳛Ñ.(Ò5ᑮ0.1)13.᝞Vᡠᙊ஺Ḅ5,AB*+,0C14B,ᚖÔE,᝞»CE=2,mnABḄg-.14.᝞VbA8CᑁÖ×00,4cABḄg.Ø2⚓ᐳ16⚓

215.opqᦪy=x2+(m—i)x+i,Üx>1yÝxḄÞᜧàÞᜧᑣáḄ>yã-.16.I2020jäg1Ḅ®Aåᢥ᝞VᡠḄAç᣸ᑡA,A,é…4020l2M,M%…%019-®AåḄ⚔îÖ4M2,4M3…4M2019ᑖïY®1(AåḄäM,A2M1&2…&019“2018×NiN,N3…N2019,òäåM1N14&2Ḅ☢-S1òäåM2N2424Ḅ☢-S2…ᑣ52019.AA1A.2Z3^4õ517.᝞VtU஺஻/2஻3tUAC÷pYᓃஹ%ஹ3×AஹBஹCútUDF÷pY஺ஹ2ஹ3×஺ஹEஹF.,cü=%DE=2,ýEFḄg.18.᝞V00ḄþABlþCQ
E,AB=CD,AD=CB.19.᝞Ḅ1.(1)ᙠ!"ADEF,&ABCS^OEF,'()*12,(2)-ᵨ/01Ḅ2345(1)6DEFḄ᜜8ᙊḄᙊ:.";<=.(1)ᵬ?@A⌱CAᝅ⚶Ḅᭆ᳛,(2)ᵬHᑖJ⌱C";ᝅ⚶K!5᪛M(ᡈᑡ⊤)QᵬஹH2S⌱CTᝅ⚶Ḅᭆ᳛.21.᝞6ABCZC=90஺AC=4cm,BC=3cm,_P?B5abIsn/sg1ᔣCi_Tj_஺?C5ab2czn/sḄg1ᔣAi_ᐸ"ᑮ

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AÔB,ᐸBḄᙶ᪗*(5,0),«ᱥ¾ÕÐ*2Ö=2.(1)«ᱥḄ¶᪆,(2)£0

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9ᦑ,ᫀ8.᝞6ÃÄ04✌ᐜÈ0EḄɾ{ÊËᳮÈAEḄɾᓽK$CD⚪.Ì⚪⌕ὃᳮஹᚖÎᳮÏḄᵨD⚪LÐÑËP᪀⌼ÔÕÔᮣ=>ᵨᳮஹᚖÎᳮᩭᑖ᪆ஹᑨIஹ$,$⚪Ḅᐵ&.14.ூ,ᫀ௃3V2ூ$᪆௃ூᑖ᪆௃✌ᐜ᪷FᙊᕜÔᳮÈ4408Ḅ¾ᦪᯠÙ$ÔÕÔÈABḄÉ.⚪⌕ὃᙊᕜÔᳮ$⚪Ḅᐵ&È4408=90஺Ú⚪Û¾Üᜧ.ூ$,௃$L᪷F⚪ÝKAÞ40B=2Þ4cB=90°,ßA1஺4=0B=3,ᓽ4B=3V2,ᦑ,ᫀ3&.15.ூ,ᫀ௃m>-1ூ$᪆௃$LNᱥPḄQRSPx=-*=Ï•••à±yḄáxḄâᜧãâᜧ<1,2$Lm>-1.ᦑ,ᫀLm>—1.᪷F012ᦪḄឋᑭᵨ012ᦪḄQRSÜᜧs1ᑡåᓽK$.⚪ὃ012ᦪḄឋ⌕ᑭᵨ012ᦪḄâæឋçèឋ»ᑡÈÜÏ$⚪Ḅᐵ&.16•ூ,ᫀ௃éூ$᪆௃$L᝞6L(n+1)¦êÉ1Ḅqᢥ᝞6ᡠìḄ᣸ᑡ,ᵫ⚪ÝKÈLîM1E4ᑣᔩ=ᔩ"EMiAE2ᦑMM=g10⚓ᐳ16⚓

10ᦑñêMiNi/i4Ḅ☢Si=l-|xlx|=l-i=^{ûᳮKÈL᝞ü=ü³=ýEM?AE3ᦑñêM2N2424Ḅ☢S2=l-|xlxi=l-i=p2366ᑣMnNnAnAn+lḄ☢=1=+1=2020n=2019,ᡠSQ9=^,ᦑᫀS᪷⚪"#$4M1MN1S4M1EA,%&'$MMḄ(%&#$S*+ᳮ#$S2,#$SḄ/%&#$S2019Ḅ/.n3⚪4⌕ὃ789:;<Ḅᑨ>?ឋABᦪDEᓄGH#$Ḅ☢EᓄGHI⚪ᐵK.17.ூᫀ௃Ivii//i//ZNOACPQRSTஹ%WAஹBஹC;X,NO஺ZP23QR4ஹ%ஹ஺W஺ஹEஹF;XABDE:•--=--GACDF--=-DE=2,AC7f42—ߟG7DFI#DF=3.5,•••EF=DF-DE=3.5-2=1.5.ூI᪆௃ᑭᵨ^_OᑖOaᡂcd>ᳮ#ᑮf=gᯠijᨵᐵᦪlᐭnoᓽq.ACDFr⚪ὃ78^_OᑖOaᡂcd;ᩩ^_OtuᩩNOᡠ#ḄvwOaᡂcd.18.ூᫀ௃xy•.AB=CD,•AB=CD,**•AD4-AC=AC+BC,:.AD=BC,•AD=BC.ூI᪆௃{xy4D=BC,|⌕xy'=BC.r⚪ὃ7ᙊ~<ḄᐵI⚪ḄᐵKᮣᵨᡠI⚪.

1119.ூᫀ௃I(1)᝞aCEFᓽᡠ'.(2)᝞XZᓽADEFḄ᜜ᙊᙊ~.(2)ᑖ஺E,஺ZḄᚖN^ᑖOuNOḄRXᓽᡠ'ḄXP.r⚪ὃ7-9:Eᣚஹ;<Ḅ᜜ᙊ?ᙊ~9:ḄឋAB;<Ḅ᜜ᙊḄឋAIr⚪ḄᐵK.20.ூᫀ௃4ூI᪆௃I(1)ᵬ⌱¡Aᝅ⚶Ḅᭆ᳛Xᦑᫀ(2)¦᪛¨᝞©ᵬABCDªABCDABCDABCDABCDᐳᨵ16¬q®Ḅ¯°ᐸᵬஹª2²⌱¡9+ᝅ⚶Ḅ¯°ᨵ4¬³ᵬஹª2²⌱¡9+ᝅ⚶Ḅᭆ᳛ᔁ=.164(1)Nᵫᭆ᳛¶·'Iᓽq(2)¦᪛¨ᐳᨵ16¬q®Ḅ¯°ᐸᵬஹª2²⌱¡9+ᝅ⚶Ḅ¯°ᨵ4¬¸ᵫᭆ᳛¶·'Iᓽq.r⚪ὃ78᪛¨¹'ᭆ᳛.᪛¨¹qº»¼º⍡¾Ḅᑡ$ᡠᨵq®Ḅ¯°〉ᔠuÂᡈuÂÄÅᡂḄÆÇ.ᵨᑮḄXᭆ᳛=ᡠ'ÈÉᦪ?ÊÈÉᦪc.21.ூᫀ௃2tcm(3—t^cmூI᪆௃I(1)ËÌfÍiCQ=2tcm,CP=(3—t)cm,ᦑᫀ2/cm-,(3-t)cm.(2)ÎËÌfÍiu;<9:ᑣqᑖ©ᑡu¬ÈÉ%_'IজIRtAABCsRtAQPC,ᑣÏ=%,ᓽ±=9I#t=1.2BCPC33-tঝIRtAABCsRtAPQC,ÑÒ=ÓᓽᯠI#t=jQCDC2t311ᵫPXᙠBCÄḄÕÖ×lcm/s,஺Xᙠ4cÄḄÖ×4crn/s,q'$fḄ¡Ø12⚓ᐳ16⚓

12/ÛwÜ0éឋA9:;<ḄឋAI⚪ḄᐵKᱯ(2)ë"ᑖìíî.22.ூᫀ௃I(1)᪷⚪"ᳫ$ðXஹᨬòXéóᙌḄᙶ᪗ᑖ4(0÷)B(4,4),C(7,3)γQùᦪI᪆·y=a(x-hY+k,úX(0,ûlᐭq#16a+4=üI#a=—,³ýᱥOI᪆·y=-l(x-4)2+4(2)úC(7,3)Xᙶ᪗lᐭýᱥOI᪆·#1,³ÿK(7-4)+4=39
=ᓽCᙠᱥᳫᢗ(3)ᡂᳮᵫx=2ᐭy=—(x—4)2+4y=315•••3->3.19!ᡂ.ூ$᪆௃(1)᪷)ᱥḄ⚔ᙶ᪗.ᳫ/01Ḅᙶ᪗23ᱥḄ$᪆4(2)5x=7,6/yḄ783஻?;<ᓽ2=/ᑨ?(3)x=2ᐭy=-1(-4)2+4y=3@A/Bᫀ.XD⚪ὃGHIJᦪ$᪆4Ḅ6L.ᐸN▭Pᵨ.⚪RᦪSTU⚪VWIJᦪ$XN▭Y⚪.23.ூBᫀ௃9SyS0

13ூ$᪆௃$(1)•••8ᙶ᪗R(5,0),ᱥ\]^R_x=2,•••Aᙶ᪗R(-1,0),`ᱥ$᪆4Ry=a(x+l)(x-5),(0,-5)ᐭ$᪆45=a(0+1)(0-5),$a=1,:Gy=(x+1)(%—5)=x2—4x—5.(2)ax=2ᐭ$᪆42y=22—2x4-5=-9,9RJᦪᨬc7v5—2>2—0,dx=51yeᨬᜧ7y=52-5x4-5=0,-92-0,%=51ஹeᨬᜧ7.(3)ᐜ6/BCᡠᙠ_$᪆4ᯠ|ᵨ_ᙶ᪗-ᱥ\Pᙶ᪗.D⚪ὃGIJᦪḄᔠPᵨ$⚪ᐵIJᦪḄឋᦪᔠ6$.14⚓ᐳ16⚓

1424.ூBᫀ௃1$᝞1,18஺ᙠRtABCD᪷)ᳮBD2=BC2+CD2=20,ᙠRtZiAB஺᪷)ᳮAD=y/BD2-AB2=V20-9=VT1(2)জ¡᝞2,3£),vZ.BAC=45",•••3BDC=3BAC=45",•••BC=CD,•••4CBD=3BDC=45°,3BCD=90°,•••BDRO஺Ḅ_£•••/.BAD=90°=3BCD,••¤ABCD¥_¦¤ঝ$ᙠ¨ABCAB=AC,ABAC=45°,2•••3ABC="180°-3BAC)=67.5஺ᵫজ©Z.CBD=45°,•••4ABD=Z.ABC-Z.CBD=22.5°,OA,ᑣ44஺஺=2AABD=45°,A=AH1ODMH,Z.AHO=90°,N04H=45°=Z.AOH,AH=OH,`AH=OH=x,ᑣ஺4=V2x,•••OD=OA=y/2x,DH=OD-OH=(N-l)x,ᙠRtAAHO᪷)ᳮAH2+DH2=AD2,•••x2+[(V2-l)x]2=l2,22+V2AX
=----2

15BD=20B=20A=2y/2x,᪷)ᳮAB=7BD?-AD?=V8x2-1=V3+2V2=V2+1ᙠRt¨BCDBC=CD=2%,SPQ=ABCD=S^ABD+S&BCD11=-BD-AH-V-BCCD17-=-(2v2x-x+2x-2x)1R,=-(2V2+4)x2=(2+>/2)x2=3+2V2.ூ$᪆௃(1)B£>,᪷)ᳮ6/BZ)2=20,~᪷)ᳮᓽ26/Bᫀ(2)জB஺/NBDC=NBAC=45஺~ᑨ?/zCB஺=NBOC=45஺@Aᑨ?/8஺R஺஺Ḅ_£ᓽ2/ªঝᐜ6/«4BD=22.5°,@A/«4OD=45஺A=4"1஺஺¬H,ᑨ?/4H=OH,`AH=OH=x,@Aᵨᳮ6/2=®6/A8,ᨬ|ᵨ☢°Ḅ±6/¤4BCDḄ☢°.⚪ᙊḄᔠ⚪³⌕ὃGHᳮᙊḄᨵᐵឋµ¶·¦Ḅ☢°¸46/x$ᨬ|¹⚪Ḅᐵ.16⚓ᐳ16⚓