全国名校近两年（20222022）中考数学模拟试卷分类汇编综合性问题

综合型问题一、选择题12022年，瑞安市模考）在函数①y2x1②y2x1③y④yx中,、（21x经过点（1，－1）的函数解析式的个数是.3CD1答案：B22022年吴中区一模如图，在平行四边形ABCD中，BD＝4cm，将平行四边形ABCD绕其对称中心O旋转90°，则点D经过的路径长为▲A4πcmB3πcmC2πcmDπcm答案：D4（2022年，广东一模）函数＝－错误!中自变量的取值范围是DADOGHEBFC（第7题图）BAACyOBA．≥0-1Dy1PC·CByCEOADAQCBABAB-1ABN1EOxEOxPMD题图第24ACCD1B(2)1x．y2O(3)BC4xyx21y1155515第24题图by2x83413OABCyxx29cm4cm450Cyx17yx2bxcyx2bxc2x1321b＝bc0yx22x3x1x1yx22x3yx393bc0c3x1x1(x，x22x3)(3x0)yx3y2SBPCS四边形BPCOSBOCS四边形BPCO9S四边形BPCO21BE1OE(PES四边形BPCO＝SRtBPES直角梯形PEOCPEOC)221(x3)(x22x3)1(x)(x22x33)3(x3)2927x32222282S四边形BPCO927927927x3x22x315(3，15)11282828242422DPBD,DP2PACPACya(x4)213a(04)21a1OCBO334y1(x4)211x22x31(x4)210x12x26444AB322213BEC90AOByyByABD90CBE90ABOABAO90ABOBAOCBEBBCFPPAOBBECCECE62BNDDOBAB2CAD13QFEPAH811BQMECE2x322m3EyPmCx132-2MODBQN4OCE1POCx3OAm21m(1m21m23m（第O24题备用）AxPQ32m3)（第24题）2442SPACSPAQSPCQ1(1m23m)63(m3)227m3PAC2732424441x2x40x22x80x12x24A(4,0)B(0,4)ykxb4kb0b442k1yx4P(x,x)xx4Q(x,x)xx42x4E(x,x)xx4b42222222x8PCx(x4)2x4PDPCSPCD1PC22(x2)213771681682168Sx22(x2)2x28x8(x)22xSmax4447773778x4QN(x4)xx4QMQNSQMN1QN21(x4)232222S1(x4)2Smax8yxmyx1yk2b2b2xk1b0k12292yx2x11OBMD21n22myk24k2y12OA2PD2PGPN22x3xOB1MDPOPBA'B'OC'A'B'OC'OC'DAMA'A'B'OC'ABOCyax2bxc(a0)abc0a1c3b2yx22x3OBOA2AB2109a3bc0c3OC'DOCABC'ODBOA△C'OD∽△BOAOC'OC1C'OD的周长=OC'1410C'OD410=1210(m，n)BOA的周长OB10105nm22m3SAMA'SAMOSOMA'SAOA'yAy图Ay11A图1图2AAC666OGOMHFBBBPEDC4xBEDCCBO4xQO4xAODBDH（图12）1OAm1OA'n图a3(m备用图1OAOA'n)93(mn3)2222223(m23m)3(m32270m3m315315271122)8n4，8222224SAMF:SOAB16:34a2b0323323kb332339a3b333332kb033323323132313238332383838332313332332333333333323231838333233

3,3,34a2bc0,1bc0,b0,15339a3bc3,1bc0.c1.222222422c0.23433313|CF||OD|42

234323431|OE|3333|CF|2|CF|23x243x3x23x23x3x233332

1|CF||ED|233934x3235325314,8322

22CM5125MHCMsinMCHBM5

55

MHMBMAMB2108223333344532MHMA55244444bbbb163333b4b5b163233233343131y111120204y242ABABxxxx3x522223

A

A

ADDDDACBCCADDPOOAxO图①BPCBC第2题图OCACAO4BC313610ACB90ACBCPOC5PB425

ENPMF5·P1GMCCGN4图②F2

ABPPPMM1QFF213PBBE2GNEBECxNBARCBACBPMCMCNCNP90MPN901FPN902FPN9012CP2CNCM1NEMF1xCE2xCFCGCGxyx2xGPEFCE901PEGPNGNx1x1G1FGFECGCEEG2CP22GPEFCE90123214551452523454FCCP2FM12EN12CFCG21EG22(0t5)RtABEPNGNGNAEAO5，AB4BEAE2AB252－42＝3CE2RtDCEDC2CE2DE2DEOD(4OD)222OD2OD5(0,5)APM∽AED22PMAPAP55APMt5t5tPMNE4Pt，ED＝，AEPECEDAE2522321A12F3B4-2-1O4D1t25tS-2S矩形PMNEPMPEt(5t)1(t5)225055222矩形PMNE22382525MARtAEDMEMAPMAE,AP215tS矩形PMNEMEAE2122851555第5题图555APPMxy2-2-1,)AMAE5MM2422424222-O14OD2AO25)2525-2RtAODAD(5APM∽AEDAPAM22第3AEAD题图AMAE5525PM1t5xM525yM5t25tAPAD55225t25(5,5)(525，5)120255(525，5)t224mxy1,(x2y)2(x2y)2yx24x3APDACBOCAOCD△OBCOBC45CB32AEBCAECE2(2，2)△AEC∽△AFPPFAFPFA(1，0)△ADCOCAOCD45△CBD∽△COABCDOCAOCAOCD45yx155222t12t1252t1523135t25231t1223135352t124t252t1221152211721119219CBt2t0tt2P2h/cm1AmBts15AB511C11s112219t379t4s11219B494At5s5225t125t552tt10t2101052OA12xy0.50.1图1P1x1001my10x5002x83x2y1.10.1m25cm10cm5cmy0.43418O10t/25?hA10?v8?vhA4cm3/sC的容积是容器容积的1图210?(12hA)v104tc1tc),解得tc6t18tc186245?tc106,解得hc12(1841.4’136h12hc121224APB90或270552150503’5’8’11’x(012021)50505092第56BD22BF2SEBFBF102EE22OA4AC=CDFPA=xCDy33AF3SCFAAFSACF3DAOCDF1tanPACCDDOCPOCPCOC4POCDOCPADPOOBDODCCDy16y4yy252252OE图8CEDE1DPDOCDy2PBPCx44x28x16PPPBCPEO902yyPEPO4x442424x4tanPOE15POE15AB6BC22PEtanPE35DAB45EFPOAx11111111yax2bxcyax2bxc44244422yabc022ab1yax2a1x14aaA1a1c14aF4aC52a1SAMCSABCa151a23a10a3501a04x4a4O2aEBDa325a325AC2AB2BC2y0ax2a1x10x11,x21a121121AC1a,BC1a2,AB2(1a)2(1a2)a1tanFOBt1222ttOB2tSOAB2t(0t2)OEEF2t222OB2tEBEF第28题2图tOEEFBE2tEB1BE2tBO4t2t4tt3EB1EFEBt2t2t22AAD=2CDCDC=2CDBBHFGQQEBEDAHPBAEPGBABM1）NBADCCBF（备用图O（备用图2）图②OAADDC图①HEEOBOEEB3t2t3t2t22t23OBOEEB5t2t5t2t22t65DHPBPHEB

48xkk12x2yxxm1yx(x4)412xCG2BG25b111212x135yx2kb0k,b1xxxx4244x23515151515y12y135352224m4m4m4mABCDABCADBEC3EADABACAB6cosB5AEBEADAEBBBEADAB3cosBBH3BH18BAC90cosBcosBAHBCAB56BHBC55AFMO3614BEEC55

CEGB（第24题图）OMOBABCOM∥BCAMOAEB△ABCABACAE⊥BCAEB90°AMO90°OM⊥AE△ABCABACBE1BC，ABCCBC4，cosC1BE1，cosABC1△ABE233AEB90°ABBEAO6rOM∥BC△AOM∽△ABE6cosABCOMAOr6r331D8BD米BBEAB2解得r22米6EEACAOCODBEACO第19题图ABCDyEEBCMHPBM△ABEABCDPDPECyADCAD2xb图1图23b0O1题图Ax1222mxP(m1PHyCO3CO2.5HCy24xx10,x24,A(4,0)yx1,)2x2HPCH13,OA4,OH13CHHC1.5,COHCHO2OAHPm24CH0.5COHPCH,HPm1,OA2m,CO3,CH1m11,m3HPCH,OACO22m1.5OACOHPm1,OA2m,CO2.5HCm11,m50m1COHC,2m2.5yyHPCHCO2.5HCCH0,CH0,CO2.5HC1m0,HPm1,OA2m,OACOCHmP11PCO2.5HC,m5H2m2.59P1155)CO2.5HC,COHC,HC,COCC(0,m1714214AAOxOxHPCHHPm1,OA2m,CO2.5HCm11,mAOA,（图3）2m5CO2.5CO2.5HC,COHC1HC1,CO55C55)m,36C(0,C(0,（图)4）26914m5C(0,5)6yax22ax3a(a0)DCCB3a1aa21a1yx22x30（>3）时，OAOD3a3－3=－－223，1=0，2=3都不合题意舍去1分符合条件的点P为（－2，－5）1分5、（2022·湖州市中考模拟试卷10）将正方形绕中心O顺时针旋转角获得正方形ABCDA1B1C1D1，如图1所示（1）当=45时如图2，若线段与边的交点为，线段与的交点为，可得以下结论建立①EOPFOP；②PAPA1，试选择一个证明（2）当0o90o时,第（1）小题中的结论PAPA1还建立吗假如建立，请证明;假如不建立，请说明原因（3）在旋转过程中，记正方形A1B1C1D1与AB边订交于P,Q两点，研究POQ的度数能否发生变化假如变化，请描绘它与之间的关系;假如不变，请直接写出POQ的度数图1图2答案：（1）若证明①EOPFOP当=45时,即AOA145o,又PAO45oPFO90o,同理PEO90o∴E