聚焦2005年高考数学平面向量的交汇性

1透视2006年高考数学平面向量的“交汇性”A1A0A2A3A4A5A3A6A7A8,A10A9A11A12A13A14A15A16A17A18A19A20A21A22,A24A23A25A26A27A28A29A18A30A31A32A33,A35A1A0A34A36A14A15A38A23A37A39A40A42A43A41A44A45A46A18A47A48,A35A1A0A49A50A51A52A44A53A54,A35A1A0A55A56A57A18A58A59,A61A60A35A1A0A62A63A64A51A65A66A67A16,A34A36A68A66A17,A70A69A71A12A18A72A73,A75A74A76A77A78A79A80A81A82A83A85A81A38A84A12A84A18A86A87A3A18A88A89A91A92A90A57A94,A1A0A13A64A51A71A12A42A69A93A14A15A42A12A95A42A68A66A17A18A96A97A48A98A81A99A101A100A102A38A100A103A18A86A87A3A104A57A106A105A107A108A109A1102006A112A111A100A102A48A85A86A113A114A115A116,A118A117A119A100一平面向量与函数的交汇例1（2005年上海市高考数学试题）A120A121A122A123BKXXFA124A125A126A127YX,A128A129A130A131A132A133A134AA135BA136JIAB22A137JI,A129A130A138A127YX,A128A139A140A128A141A142A143A124A144A145A143A146A147A136A148A14962XXXGA150A1371A147A151BK,A124A152A153A1372A147A154XA155A156XGXFA157A136A151A148A1491XFXGA124A158A159A152A150A160A161A162A143A146A124A142A143A143A146A163A164A165A166A138A167A168A169A124A170A171A135A172A170A173A174A175A124A176A177A178A179A180A168A169A142A143A124A181A182A183A184A185A150A183A186A187A188A189A133A190A191A166A192A151A193A194A162A1371A147A195A196A197A198,0,0,BKBABBBKBAA199A133A13821,22BKBKBA2002A201A202,62,2XXXXGXF得A203,42,042XFXGX则A205A206A207A208A209A210A211A212A210X21A205A203XA2131A214A215A216A205A2171XFXGA214A218A219A220A221A222A2133例2（2005年湖北省高考数学试题）A223A224A225A226BAXFTXBXXA,1,1,2A227A228A229A230A231A232A233A2341A2351A236A237A238A239A240A241A235A242TA243A244A245A246A247A248A249A248A249A250A251A252A253A254A255A106A0A1A2A3A4A241A4A5A243A6A7A8A9A42A177A10A11A241A12A13A240A241A243A14A15A16A235A61A17A18A10A19A251A240A241A243A16A20A21A22A23A24A25A26A253A243A27A28A29A250A189A30A31,11232TTXXXXTXXXF232TXXXF则01,1,1,1XFXF上可设则在上是增函数在若,23,1,1,23022XXXGXXTXF考虑函数上恒成立在区间,31XXGA32A33A34A35A36A37A38A39A40A41A192A43A44A45A46A47A48A49A1282A196A50A51XXT232A168A52A53A129A541A1281A135A45A144A55A565,1TGT即1,1,01,1,5上是增函数在即上满足在时而当XFXFXFT5TTA57A58A59A60A62A63A64A65A66A66A143A67A68A44A69A46A70A69A71A72A73A74A75A76A77A78A79A80A70A81A82A83A84A128A161A85A86A68A80A70A87A88A204A204A113A89A90A91A88A92A206A89A207A93A84A88A92A208A87A88A92A209A94A95A96A84A88A90A97一平面向量与不等式的交汇例3（2005年浙江省高考试题）A118A98A99A100ARA210ERA101|ER|A2111A102A212A103A104TA215RA105A107A108|ARA165TER|A216|ARA165ER|A109A217A110A111AARA218ERBARA218ARA165ERCERA218ARA165ERDARA219ERA218ARA165ERA112A114A115A116A117TA119RA120A121A122|ARA123TER|A124|ARA123ER|A125A126A127A130A131A132A133A1342222221,2210ATACTAACTTACTACRRRRRRRRRR即A222A136A137A138A139A140TA141RA142A145A146A147A148A149A150A151220421410CCCRRRRRR恒成立即4（A）（A）（A）A152A1531ACRRA154A155A156A157A158A159A155A160A162A163A164A166CA167例42005年江西省高考试题A169A225OABA170A171OA172A173A174A175A176A1712,0,1,SIN,COS,1PIBAA178A179A180A181OABA182A183A184A185A186A187A188A190A178A191DA193AA2306PIBA2304PICA2303PIDA2302PIA194A194A195A1952222SINCOS1SIN2|1COSSIN2ABABABRRRRRUURQA197A198A199A200A201A199A202A200A201A200A201A200A198A203A205A213A214A201A220A221A203A223A224A226A227A228A183A184A229A231A23222211111|SIN2SIN2122424SABABUURRRRA233A234A235A234A235A234A236A237A238A239A240A239A235A241A2420SIN20122SPIPIQA243A244A244A244A244A245A246A247A244A248A249A250A251A191DA193二平面向量与三角的交汇A252A253A254A226A227A182A255A1A0A2A180A3A4A5A6A7A182A8A9A10A11A24A12A12A13A14A15A16A17A65A18A19A20A21A22A42A70A23A17A25A26A27A28A93A42A15A16A17A29A65A18A30A27A28A93A42A15A16A17A65A18A19A20A27A31A32A17A33A34A27A28A93A35A36A37A38A39例5（2005年山东省高考试题）A230A118A40A41A43COS,SINMURA452SIN,COS,2NPIPIRA1283A16382,5MNURRA44COS28PIA46A47A237A48A238COSSIN2,COSSINMNURRA16722COSSIN2COSSINMNURR422COSSIN44COS4PI21COS4PIA159A49A5082,5MNURRA239A1607COS425PIA2222COS2COS1428PIPIQ216COS2825PI,2PIPI598288PIPIPIA107COS0OBOAA26A43A44OA25A46A58A28A70KA22A47A48A49A50A51A52A143A53A54A55A56A35A32A36A57A59A31A32A60A61A62A63A22A64A65A27A67A68A69A71A72A73A62A74KA22A40A75A76A27A77A78A79A40A75A76A70A80KA22A49A50A27A81A143A83A84A85A86A85A86A87A87A88A90A91A92A88A91A92A91A92A93A93A136A94A95A108KA96A97A25A98A55A39A99A100A22A101A102A27A177A103A70A101A102A22A48A104A70A80KA22A49A50A136A105A105A106A106A107A109A109A110A110A111A105A143A30A31A32CA22A33A34A251322YXA107A107A112A112A110A108得代入13222YXKXY09263122KXXKA113A35A32LA36A30A31A32A42A74A40A41A22A38A58A720136313626,0312222KKKKA11413122BABABABAYYXXOBOAKXXKKXXA120A1215A203221222BABABABABABAXXKXXKKXKXXXYYXX1373231262319122222KKKKKKKA127A122解此不等式得即,01393,213732222KKKKA1233312KA124A125A116A126A124A1601312KA130KA131A132A133A134A138A1391,3333,1A140A141A142A144A145A146A147A148A131A149A148A150A151A152A153A154A155A131A156A157A158A162A164A119A165A166A167A169A152A170A149KA131A132A133A134A138A131A171A172A141A119A173A174A175A176A178A179A180A181A182A183A184A185A186A187A188A189A190A175A176A178A191A192A193A194A195A183A197A199A200A201A202A204A205A206A201A183A207A199A208A209A210四平面向量与平面几何的交汇A179A180A181A182A202A179A180A193A194A183A211A212A213A209A189A214A175A176A179A180A181A182A183A184A185A202A187A188A189A190A175A176A178A179A180A193A194A215A216A189A218A219A175A176A178A181A182A215A216A220A179A180A193A194A208A209A195A183A187A221例9（2005年湖南省高考试题）PA223A225ABCA224A226A227A228A229A230A231A232A233PAPCPCPBPBPAA234A235PA236A237ABCA238A239A240AA241A242A244BA241A246A244CA241A247A244DA241A249A244A250由条件PAPCPCPBPBPAA252A2530PBPAPCPBCAUUURUUURUUURUUURUUUR0PCPBPAPCABUUURUUURUUURUUURUUURA234A254PBCAPCABUUURUUURUUURUUURA234PA255PA236A237ABCA238A249A244例10（2005年江苏省高考试题）A168A225ABCA38A128OA82A38A0AMA144A1A2A3A27A58A128A243AMA2112A128A217OCOBOAA19A4A5A6A7A8A143A28A122A9A245|,|202OAXOMXXUUURUUUUR则，（）2MBCOCOMUURUUURUUUURQ为的中点，OBA90180COS222XXOMOAOCOBOA202124222XXXXA138X1A141A9A171A4A5A6A102五平面向量与导数的交汇A11A12A42A178A13A29A7A14A15A16A14A17A18A20A9A24A30A29A7A21A22A19A23A25A26A31A136A132A141A32A7A14A33A89A34A19A35A36A21A22A19A37A39A40MABCEOA4111A436例11（2005年江西理科试题）A118A44A45A462COS,TAN,2SIN,TAN,2242424XXXXABPIPIPIRRFXABRRA47A48A49A50A51A52A530,0的导函数是其中使XFXFXFXFXPIA54A50A51A55A56A57A59XA60A61A137A54A62A50A51A55A56A63A64A65A66A66A67A6742TAN42TAN42SIN2COS22PIPIPIXXXXBAXF21TANTAN1222222COSSINCOS222221TAN1TAN222SINCOS2COS1SINCOS222XXXXXXXXXXXX0,SINCOSCOSSIN2COS0FXFXFXFXXXXXX令即0,02,2XFXFXXA68A69A70A71A72A73A74A75A76PIPIPI六平面向量与学科外的