天津市南开区2021-2022学年中考数学模拟试卷（一模）含解析版

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1912-30=40%,9+30=30%,ᡠµᡧ·jḄ஻?=40,n=30`ᦑᫀ\40,30`(II)•••ᙠ»1ᦪj50vy12vḄᦪᨬ•••ᐜᣎoᦪḄᦪ50ᐗ`•.•ᢥ᯿Àᑮᜧ▰ᑡᜐÅÆᜮᙢḄÆÉᦪÊ50..•.jᦪ\50ᐗ;»1ᦪḄᙳᦪ=(20x4+50x12+100x9+150x3+200x2)+30=2430+30=81(ᐗ).(HD᪷⚪:HU2500x81=202500ᐗU᪥ᐜᐳᣎo202500ᐗ.ÎÏU⚪ὃxᡧ·ᵨ᪵Zqᩗᙳᦪjᦪᦪ/ÒÓÔÕᔜÉᭆØ⚪Ḅᐵ.21.ᙠaABCjZACB=90°,ÎCḄ஺OàáâABᑗÅÎP.(1)᝞জåÎOᙠACQæç▊!2NACP=NB`5ூ᪆௃ூc௃ᑖ᪆U(1)᪷8càZCᚖëHᑮ8càᙊᑗíᵫ48à0஺ᑗÅÎP,ᑭᵨᑗïðñᳮHᑮ8c=80ᑭᵨ/âò/óHᑮeòó/íᵫNZCP+N8cp=90°,/õöᣚᓽ¬Hø`(2)ᙠjᑭᵨùúñᳮZBḄð᪷4cà8cᚖëHᑮ8Cà஺஺ᑗ,ûûOPஹAO,íᵫN8à஺஺ᑗHᑮ஺üᚖëÅN8,ýOC=x,ᑣOP=x,OB=BC-OC=6-x,RIḄᑭᵨᳮᑡᐵxḄḄᑮxḄ80Ḅ20⚓/28⚓

20᪷/C=4P,OC=OP,ᑮ/஺ᚖ#$ᑖCP,᪷☢'(CPḄᵫ⚪+,-./01/23ᔠ5CPᨬᓽ,CPḄ9.;<=1
./஺ᙠHC?50C@஺஺ḄAB"BC10C,C/Cᙠ0஺?1QODᑗ•GQ01ABHDᑗ/P,#.BC=BP,1800-Zg:•NBCP=NBPC=2ZACP+ZBCP=90°,]on°_/Ri•••ZACP=90°—ZBCP=90°--------=-=-ZB.22ᓽ2ZACP=ZB=(2)ᙠIZBCJNACB=90",AB=JAC=BC?=10,᝞L./஺ᙠC8?5OC@0OḄAB•.NC_LOC,C/஺ᙠQO?.♦./C1QODᑗMN஺0ஹAO,,/஺஺148HDᑗ/P,#.OP1AB,Q஺C=x,ᑣ஺OB=BC-OC=6-x,'#AC=AP,G.BP=/BTP=10-8=2,ᙠI஺ᜐJ,NOP/=90”,᪷ᳮ<஺0+BP?=OB2X2+22=6-4,21⚓/28⚓

218

22(2)᪷f£¦fHᓽ,§8C=CDᯠ©᪷ª£«ᦪᓽ,C஺Ḅ.;<(1)᝞Lᵫ⚪+NE4O=45஺NFBD=3஺஺,#.ZEAC=/LEAD+ADAC=45஺+15஺=60°."AE//BF//CD,#.2FBC=NEAC=60°.ZFBD=30°#.NDBC=4FBC-Z.FBD=30°.,/ADBC=NDAB+ZADB,ZADB=\5°.#.NDAB=Z.ADB.@fῪª£¯BD=AB=2.ᓽBDḄ@2km.(2)°8±50J.OC,ᐸ²³c/O,ᙠRtaZJB஺JBD=2,NDBO=60஺,•♦•DO=2xsin60°=´8O=2xcos600=1.77ᙠRtACBOJACBO=30°,C(9=8(9tan30o=—,J3•••CD=DO-CO=y/3--=^-(km).33ᓽC,஺Ḅµkm.3/]<¶⚪ὃa#£ª£¯Ḅ·ᵨ-ᔣ£ᡂº᪀⌼#£ª£¯ᵨª£«ᦪᩭᜐᳮᡂº.23.y¾¡¿ÀᑜÂÃÄᎷÆÇὁÃÉ¿ᑮ¾Ê⚜ÌÍ✂ÏÐ5ᨵÏÐᩩY~᪵Ḅᵬஹ¥ÔÕÍ✂,Ö⌱ØᐸÙÚ᪗Û@ÜÉÜᜩ120ᐗßCàᔜâãäḄåæ<ᵬÕu35É(ç23⚓/28⚓

2335Éè¢ᑁḄᢥ᪗ÛÙÚë°35ÉḄëìᑖᢥíᢚÙÚG¥Õu45É=ç45Éè¢ᑁḄᢥ᪗ÛÙÚë°45ÉḄëìᑖᢥïᢚÙÚ.QὁÃÉ¿ḄÉᦪ@X.=1è᪷⚪+ᵨçxḄqðñᑏó⊤45ᵬÍ✂ÙÚ/120x5280ᐗ¥Í✂ÙÚ/120x120x5400ᐗ=2
.xõö5¾¡¿ᙠᵬஹ¥ÔÕÍ✂Ḅ÷øÚDùúூᫀ௃=1è108x+420,108x+420,96x+1080G2
.û35ᡈx=555¾¡¿ᙠᵬஹ¥ÔÕÍ✂Ḅ÷øÚDùூ᪆௃ூ;௃ý⚪ᑖ᪆<=1
᪷ÙÚ᪗Û,᪆qG=2
᪷ãåæ5,÷øÚDù᪷åæ5Ḅ÷øÚDùḄfᐵþ,~ᐗ᪷~ᐗ,ᫀ.ý⚪᪆<=1
108X+420,108X+420,96X+1080;=2
.·355¾¡¿ᙠᵬஹ¥ÔÕÍ✂Ḅ÷øÚDù.3545
ᵬ✂Ḅy=35x120+0.9x120x-35
,ᓽy,,=108x+420,✂Ḅyyc=45xl20+0.8x120x-45
=96x+1080,y
108x+420=96x+1080,x=55.
X435ᡈx=55
ᙠᵬஹ✂Ḅ!".ὃ%&ᦪḄ(ᵨ.24.᝞+
ᙠ,☢./ᙶ᪗23
45OABCḄ6OAஹOCᑖ8ᙠx9ஹy9Ḅ:;9
OA=4,OC=2.%P<%O=>
?x9@AB1CᓫEFḄGHᔣ%AᒴG(K
%PᑮM%A3N(K
O%P(KḄPQtB.RSTCPḄ3%U%PᢥW┐YᔣZ[90°%D,%D\%PḄ(K](K
^_DPஹDA.`24⚓/28⚓

24(1)fᵨgtḄiᦪj⊤l=%DḄᙶ᪗n(2)ptqrs
4DPAḄ☢w
qxy(3)ᙠ%P<0ᔣA(KḄ|}3
4DPA~ᔲᡂq.//5~
ptḄs.~
f▊ᳮᵫn(4)f._ᑏ=\Ḽ%PḄ(K
%D(KSḄF.ூᫀ௃(1)Dᙶ᪗q(t+1)n(2)t=2,ZXDPAḄ☢w
sq1n(3)2Bᡈ3B,ZXPAD2.//5n(4)%D(KSḄFq2ூ᪆௃ூᑖ᪆௃(1)O=P%ᙶ᪗
p=CPḄ3%ᙶ᪗
᪷Ḅឋᓽp=D%ᙶ᪗(2)᪷D%Ḅᙶ᪗/5Ḅ☢w¡j._pᓽn(3)ᐜᑨ¤=~q./Ḅ/
᪷¥¦§ᳮpn(4)᪷%DḄ(KS¨OB,«!¬ᓽ.ூ௃(1)•••%P<%0=>
?x9@AB1CᓫEFḄGHᔣ%AᒴG(K
/.OP=t,]0C=2,#.P(t,0),OCPḄ3%qF,ᑣF%Ḅᙶ᪗q(2
1),2²RSTCPḄ3%FU%PᢥW┐YᔣZ[90஺%D,ᐸᙶ᪗q(t+1,-)n2(2)%ᙶ᪗q(t+1,-),OA=4,2.,.SADPA=-^PX-=-(4-Z)X-=-^(4Z-/2)=-^-(/-2)2+1,.,.t=2
S=ln(3)~᪀ᡂ.//5.`25⚓/28⚓

25জNPDA=90஺
PC஻AD,ᵫ¥¦§ᳮ
PD2+AD2=AP2>ᓽᨴ+1+(4—/—Ip+=(1)2,
t=2ᡈt=-6(ÀÁ).n.t=2B.ঝZPAD=90஺
Ã%DᙠAB
Ä
ÅCOPs^PAD,/.CP:PD=CO:PA,.••2:1=2:PA,PA=1,ᓽt+l=4,t=3B.Æ
Ätq2Bᡈ3B
4DPA~ᡂq.//5.(4)᪷%DḄ(KS¨OB,«!¬
OB=2Ç
.•.%D(KSḄFq2È.ὃ%²É&ᦪḄᨬsn˧2ᦪÌp&ᦪ᪆jn.//5Ḅឋn45Ḅឋ.25.ÍIJÉ&ᦪy=ax2-4ax+3a.(I)pβÉ&ᦪḄÏÐ9n(II)βÉ&ᦪḄ+ÑÒÓᔣÔ
1WXW4
yḄs2,«1WXW4
&ᦪ+ÑḄ%q%P
%q%Q
pÅOPQḄ☢wn`26⚓/28⚓

26HIÏÕÎÖᱥSḄ%Pxiyi,QX2,2tWxiWt+1,X2Ø5,ᙳÚÛPØÜ,f+Ñ
._ᑏ=tḄs.ூᫀ௃ÝIÞÏÐ9x=2@ÝID6OPQḄ☢wq10@HDtḄsq4.ூ᪆௃ூ௃ᑖ᪆1᪷ÖᱥSḄÏÐ9¡j._ᑏ=ᓽ.2ÖᱥSḄÒÓᔣÔ
ÏÐ9ᙠ10ß4Ḅáᑁ
ãÎᙠÏÐ9ᜐås
ᓽp=⚔%ᙶ᪗
iᐭp=஺Ḅs
ᑖ᪆²É&ᦪᙠ1/4ḄáᑁḄᨬès
p=%04,—6.6OPQḄ☢w@ᵨFY5Ḅ☢wéÁ3C.//5Ḅ☢wᓽ.3+
ᙳÚÛê2%ÖᱥSÒÓᔣÔ
%Pᙠ%஺ë6ᡈìᔠ
ÚÛᩩï
ᓽᑡ=¬j
pᓽ.ÝIÞÏÐ9x=-᝞=2.2aII•.•Î²É&ᦪḄ+ÑÒÓᔣÔ
«ÏÐ9q.SB=2,ñ2
yåᑮᙠ1ᙛ4Ḅsq2,ᓽP2,2,4஺-8஺+3஺=2,/.a=—2,**•y——2x~+8x—6,•.•l

27%úû⚪ýÕ²É&ᦪÆᔠ⚪
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ᦪḄᔜ⚪Ḅᐵ.28⚓/!28⚓