甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题
适用年级：高三试卷类型：高考模拟试题总数：23浏览次数：43上传日期：2019/6/8
一、单选题
1 . 已知集合A=
，则
=( )
| A．（2，6） | B．（2，7） | C．（-3，2] | D．（-3，2） |
难度系数：0.85使用：474次题型：单选题更新：2016/12/10
难度系数：0.94使用：60次题型：单选题更新：2019/6/8
3 . 已知正项等比数列
满足
，
与
的等差中项为
，则
的值为( )
难度系数：0.94使用：160次题型：单选题更新：2019/6/8
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type=\"0\">必修5</category><category id=\"81141\" type=\"0\">第2章 数列</category><category id=\"81150\" type=\"0\">2.3 等比数列</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81139\" type=\"0\">必修5</category><category id=\"81141\" type=\"0\">第2章 数列</category><category id=\"81150\" type=\"0\">2.3 等比数列</category><category id=\"81155\" type=\"0\">2.3.1 等比数列的概念</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81565\" type=\"0\">高中二年级第一学期</category><category id=\"81566\" type=\"0\">第7章 数列与数学归纳法</category><category id=\"81571\" type=\"0\">一 数列</category><category id=\"81575\" type=\"0\">7.1 数列</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81818\" type=\"0\">必修第四册</category><category id=\"81820\" type=\"0\">第9章 数列</category></item><item><category id=\"82158\" type=\"0\">大纲版</category><category id=\"82159\" type=\"0\">高一上册</category><category id=\"82162\" type=\"0\">第三章 数列</category></item><item><category id=\"82158\" type=\"0\">大纲版</category><category id=\"82159\" type=\"0\">高一上册</category><category id=\"82162\" type=\"0\">第三章 数列</category><category id=\"82193\" type=\"0\">3.1 数列</category></item><item><category id=\"82158\" type=\"0\">大纲版</category><category id=\"82159\" type=\"0\">高一上册</category><category id=\"82162\" type=\"0\">第三章 数列</category><category id=\"82197\" type=\"0\">3.4 等比数列</category></item>","ChildNum":1,"Time":"2019-06-08T22:27:06","QuesBody":"<div>【题文】已知正项等比数列<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/eed64493-511c-442c-854c-fc204ceed1dd/paper.files/image001.png\" alt=\"eqId1a89202786dc44fcb5cff3727cb651dc\">满足<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/eed64493-511c-442c-854c-fc204ceed1dd/paper.files/image002.png\" alt=\"eqIda675e7fb05b8430aa8e35a88d294880e\">，<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/eed64493-511c-442c-854c-fc204ceed1dd/paper.files/image003.png\" alt=\"eqId793be245a95447aea88e394dc7f856d3\">与<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/eed64493-511c-442c-854c-fc204ceed1dd/paper.files/image004.png\" alt=\"eqIda2c14d3012e84350a1d957069bd25b3d\">的等差中项为<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/eed64493-511c-442c-854c-fc204ceed1dd/paper.files/image005.png\" alt=\"eqIddb6b28cbd8a14caa9cf1146f6f7916c0\">，则<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/eed64493-511c-442c-854c-fc204ceed1dd/paper.files/image006.png\" alt=\"eqId75691f28a5bb4c8287401017aa3a2d29\">的值为( )<table name=\"optionsTable\" cellpadding=\"0\" cellspacing=\"0\" width=\"100%\"><tbody><tr><td width=\"25%\">A．4</td><td width=\"25%\">B．2</td><td width=\"25%\">C．3</td><td 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src=\"Upload/2019-06/18/b6ce6aab-dfcb-4839-bf1b-8d165b592c38/paper.files/image001.png\" alt=\"eqIdd8391135240f478580a72e90986a49d8\">，命题<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/b6ce6aab-dfcb-4839-bf1b-8d165b592c38/paper.files/image002.png\" alt=\"eqIdd05ca2be638e4f549ab5120759099c37\">，且<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/b6ce6aab-dfcb-4839-bf1b-8d165b592c38/paper.files/image003.png\" alt=\"eqIdbf4c67fe3d2342358357846ef6386ecc\">,则( )<table name=\"optionsTable\" cellpadding=\"0\" cellspacing=\"0\" width=\"100%\"><tbody><tr><td width=\"50%\">A．命题<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/b6ce6aab-dfcb-4839-bf1b-8d165b592c38/paper.files/image004.png\" alt=\"eqIdab1422f8cc56447687f57319d9341360\">是真命题</td><td width=\"50%\">B．命题<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/b6ce6aab-dfcb-4839-bf1b-8d165b592c38/paper.files/image005.png\" alt=\"eqIdb8c953f13d464148b1ef8cc2b9f70298\">是假命题</td></tr><tr><td width=\"50%\">C．命题<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/b6ce6aab-dfcb-4839-bf1b-8d165b592c38/paper.files/image006.png\" alt=\"eqId703f7945161e4a72835647dce2bd0dc9\">是假命题</td><td width=\"50%\">D．命题<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/b6ce6aab-dfcb-4839-bf1b-8d165b592c38/paper.files/image007.png\" alt=\"eqId3a9743958fe748f99fc68e1e2ddb126e\">是真命题</td></tr></tbody></table></div>","QuesAnswer":"","QuesParse":"","UseSum":67,"AvgScore":5.0,"ParseAnswerKey":"97f32635ff77df80b526f0d8035a615d","QuesAttribute":0,"PaperSource":[{"Id":524330,"PaperTitle":"甘肃省兰州市第一中学2019届高三6月最后高考冲刺模拟数学（理）试题","LearnGrade":12,"PaperType":9,"Province":620000,"PaperYear":2019,"PaperLevel":51,"AddTimeOn":"2019-06-08T22:24:15","SchoolId":71389,"MatchingDegree":0},{"Id":524331,"PaperTitle":"甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题","LearnGrade":12,"PaperType":9,"Province":620000,"PaperYear":2019,"PaperLevel":51,"AddTimeOn":"2019-06-08T22:26:16","SchoolId":71389,"MatchingDegree":0}]},{"ID":182934,"Guid":"87ad1f7e-3463-46be-9d92-d989755e7e9a","Title":"20092010学年河南省驻马店市高三上学期期末考试数学试题","From":"20092010学年河南省驻马店市高三上学期期末考试数学试题","Knowledge":"数列","QuesType":{"ID":2701,"Name":"单选题","IsSelectType":true,"OrderIndex":2,"ParentId":0},"QuesAbility":{"ID":1,"Name":"了解和识记"},"QuesDiff":{"ID":2,"DifValue":0.85,"Name":"较易"},"Categories":"<item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27930\" type=\"1\">数列</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79422\" type=\"0\">必修5</category><category id=\"79423\" type=\"0\">第一章 数列</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79422\" type=\"0\">必修5</category><category id=\"79423\" type=\"0\">第一章 数列</category><category id=\"79427\" type=\"0\">§1 数列</category></item><item><category id=\"79775\" type=\"0\">沪教版（上海）</category><category id=\"79821\" type=\"0\">高二第一学期</category><category id=\"79822\" type=\"0\">第七章 数列与数学归纳法</category><category id=\"79827\" type=\"0\">7.1 数列</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"80073\" type=\"0\">必修5</category><category id=\"80075\" type=\"0\">第二章 数列</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80669\" type=\"0\">必修5</category><category id=\"80671\" type=\"0\">第二章 数列</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80669\" type=\"0\">必修5</category><category id=\"80671\" type=\"0\">第二章 数列</category><category id=\"80679\" type=\"0\">2.1 数列</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80669\" type=\"0\">必修5</category><category id=\"80671\" type=\"0\">第二章 数列</category><category id=\"80679\" type=\"0\">2.1 数列</category><category id=\"80683\" type=\"0\">2.1.1 数列</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81139\" type=\"0\">必修5</category><category id=\"81141\" type=\"0\">第2章 数列</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81139\" type=\"0\">必修5</category><category id=\"81141\" type=\"0\">第2章 数列</category><category id=\"81148\" type=\"0\">2.1 数列</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81565\" type=\"0\">高中二年级第一学期</category><category id=\"81566\" type=\"0\">第7章 数列与数学归纳法</category><category id=\"81571\" type=\"0\">一 数列</category><category id=\"81575\" type=\"0\">7.1 数列</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81818\" type=\"0\">必修第四册</category><category id=\"81820\" type=\"0\">第9章 数列</category></item><item><category id=\"82158\" type=\"0\">大纲版</category><category id=\"82159\" type=\"0\">高一上册</category><category id=\"82162\" type=\"0\">第三章 数列</category></item><item><category id=\"82158\" type=\"0\">大纲版</category><category id=\"82159\" type=\"0\">高一上册</category><category id=\"82162\" type=\"0\">第三章 数列</category><category id=\"82193\" type=\"0\">3.1 数列</category></item>","ChildNum":1,"Time":"2010-05-11T00:14:37","QuesBody":"<div>【题文】（理）设数列<img style=\"vertical-align:middle;\" src=\"Upload/2013-07/25/17a107da-6b2c-45d1-a77d-3853017a4396/paper.files/image001.png\">满足<img style=\"vertical-align:middle;\" src=\"Upload/2013-07/25/17a107da-6b2c-45d1-a77d-3853017a4396/paper.files/image002.png\">，且对任意的<img style=\"vertical-align:middle;\" src=\"Upload/2013-07/25/17a107da-6b2c-45d1-a77d-3853017a4396/paper.files/image003.png\">，点<img style=\"vertical-align:middle;\" src=\"Upload/2013-07/25/17a107da-6b2c-45d1-a77d-3853017a4396/paper.files/image004.png\">都有<img style=\"vertical-align:middle;\" src=\"Upload/2013-07/25/17a107da-6b2c-45d1-a77d-3853017a4396/paper.files/image005.png\">，则<img style=\"vertical-align:middle;\" src=\"Upload/2013-07/25/17a107da-6b2c-45d1-a77d-3853017a4396/paper.files/image001.png\">的前<img style=\"vertical-align:middle;\" src=\"Upload/2013-07/25/17a107da-6b2c-45d1-a77d-3853017a4396/paper.files/image006.png\">项和<img style=\"vertical-align:middle;\" src=\"Upload/2013-07/25/17a107da-6b2c-45d1-a77d-3853017a4396/paper.files/image007.png\">为( )<table name=\"optionsTable\" cellpadding=\"0\" cellspacing=\"0\" width=\"100%\"><tbody><tr><td width=\"25%\">A．<img style=\"vertical-align:middle;\" src=\"Upload/2013-07/25/17a107da-6b2c-45d1-a77d-3853017a4396/paper.files/image008.png\"></td><td width=\"25%\">B．<img style=\"vertical-align:middle;\" src=\"Upload/2013-07/25/17a107da-6b2c-45d1-a77d-3853017a4396/paper.files/image009.png\"></td><td width=\"25%\">C．<img style=\"vertical-align:middle;\" src=\"Upload/2013-07/25/17a107da-6b2c-45d1-a77d-3853017a4396/paper.files/image010.png\"></td><td width=\"25%\">D．<img style=\"vertical-align:middle;\" src=\"Upload/2013-07/25/17a107da-6b2c-45d1-a77d-3853017a4396/paper.files/image011.png\"></td></tr></tbody></table></div>","QuesAnswer":"","QuesParse":"","UseSum":879,"AvgScore":5.0,"ParseAnswerKey":"396271bae16c27746ad6455754e9c2f0","QuesAttribute":0,"PaperSource":[{"Id":5424,"PaperTitle":"2009-2010学年河南省驻马店市高三上学期期末考试数学试题","LearnGrade":12,"PaperType":5,"Province":410000,"PaperYear":2010,"PaperLevel":41,"AddTimeOn":"2017-07-19T14:11:55","SchoolId":0,"MatchingDegree":0},{"Id":524331,"PaperTitle":"甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题","LearnGrade":12,"PaperType":9,"Province":620000,"PaperYear":2019,"PaperLevel":51,"AddTimeOn":"2019-06-08T22:26:16","SchoolId":71389,"MatchingDegree":0}]},{"ID":8188262,"Guid":"a218f50a-1f13-4408-9ddc-d4db982578ce","Title":"甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题","From":"","Knowledge":"","QuesType":{"ID":2701,"Name":"单选题","IsSelectType":true,"OrderIndex":2,"ParentId":0},"QuesAbility":{"ID":1,"Name":"了解和识记"},"QuesDiff":{"ID":3,"DifValue":0.65,"Name":"一般"},"Categories":"<item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27927\" type=\"1\">函数与导数</category><category id=\"28040\" type=\"1\">函数及其性质</category><category id=\"28048\" type=\"1\">函数的基本性质</category><category id=\"28086\" type=\"1\">函数的奇偶性</category><category id=\"28098\" type=\"1\">函数奇偶性的应用</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27927\" type=\"1\">函数与导数</category><category id=\"28040\" type=\"1\">函数及其性质</category><category id=\"28048\" type=\"1\">函数的基本性质</category><category id=\"28087\" type=\"1\">函数的周期性</category><category id=\"28102\" type=\"1\">函数周期性的应用</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27927\" type=\"1\">函数与导数</category><category id=\"28040\" type=\"1\">函数及其性质</category><category id=\"28048\" type=\"1\">函数的基本性质</category><category id=\"28087\" type=\"1\">函数的周期性</category><category id=\"28103\" type=\"1\">判断抽象函数的周期性</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79244\" type=\"0\">必修1</category><category id=\"79246\" type=\"0\">第二章 函数</category><category id=\"79260\" type=\"0\">§5 简单的幂函数</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79244\" type=\"0\">必修1</category><category id=\"79246\" type=\"0\">第二章 函数</category><category id=\"79261\" type=\"0\">本章复习与测试</category></item><item><category id=\"79775\" type=\"0\">沪教版（上海）</category><category id=\"79776\" type=\"0\">高一第一学期</category><category id=\"79779\" type=\"0\">第3章 函数的基本性质</category></item><item><category id=\"79775\" type=\"0\">沪教版（上海）</category><category id=\"79776\" type=\"0\">高一第一学期</category><category id=\"79779\" type=\"0\">第3章 函数的基本性质</category><category id=\"79798\" type=\"0\">3.4 函数的基本性质</category></item><item><category id=\"79775\" type=\"0\">沪教版（上海）</category><category id=\"79776\" type=\"0\">高一第一学期</category><category id=\"79780\" type=\"0\">第4章 幂函数、指数函数和对数函数(上）</category><category id=\"79800\" 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type=\"0\">苏教版</category><category id=\"81486\" type=\"0\">高中一年级第一学期</category><category id=\"81490\" type=\"0\">第4章 幂函数、指数函数和对数函数(上）</category><category id=\"81518\" type=\"0\">一 幂函数</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81486\" type=\"0\">高中一年级第一学期</category><category id=\"81490\" type=\"0\">第4章 幂函数、指数函数和对数函数(上）</category><category id=\"81518\" type=\"0\">一 幂函数</category><category id=\"81521\" type=\"0\">4.1 幂函数的性质与图像</category></item><item><category id=\"81682\" type=\"0\">苏教版（2004）</category><category id=\"81683\" type=\"0\">必修一</category><category id=\"81685\" type=\"0\">第二章 函数概念与基本初等函数</category><category id=\"81694\" type=\"0\">2.4 幂函数</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81721\" type=\"0\">必修第一册</category><category id=\"81722\" type=\"0\">第1章 集合与函数</category><category id=\"81726\" type=\"0\">1.2 函数的概念和性质</category><category id=\"81733\" type=\"0\">1.2.3 从图象看函数的性质</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81721\" type=\"0\">必修第一册</category><category id=\"81723\" type=\"0\">第2章 指数函数、对数函数和幂函数</category><category id=\"81741\" type=\"0\">2.3 幂函数</category></item>","ChildNum":1,"Time":"2019-06-08T22:27:08","QuesBody":"<div>【题文】已知函数<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/c0fea9f5-4b2b-4bb2-8ea9-f952b56a28bc/paper.files/image001.png\" alt=\"eqId6f13759e937144069819aed2ae5a1057\">是<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/c0fea9f5-4b2b-4bb2-8ea9-f952b56a28bc/paper.files/image002.png\" alt=\"eqId7dcd2312d0bf4bb1befdfcc170e45791\">上的偶函数，且对任意的<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/c0fea9f5-4b2b-4bb2-8ea9-f952b56a28bc/paper.files/image003.png\" alt=\"eqIdc9f6e33170ea48a797d73c1ca20d4e65\">有<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/c0fea9f5-4b2b-4bb2-8ea9-f952b56a28bc/paper.files/image004.png\" alt=\"eqId1381254e39284bb08f917afb1fc3b3a2\">，当<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/c0fea9f5-4b2b-4bb2-8ea9-f952b56a28bc/paper.files/image005.png\" alt=\"eqId94f6320d8495437ca81e6dd55e9d393f\"> 时，<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/c0fea9f5-4b2b-4bb2-8ea9-f952b56a28bc/paper.files/image006.png\" alt=\"eqIdfff2eba0ce4a4914899aba6cb51d6914\">，则<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/c0fea9f5-4b2b-4bb2-8ea9-f952b56a28bc/paper.files/image007.png\" alt=\"eqIdac2aa2a822e24f43a9ef3076d6f61699\">（ ）<table name=\"optionsTable\" cellpadding=\"0\" cellspacing=\"0\" width=\"100%\"><tbody><tr><td width=\"25%\">A．11</td><td width=\"25%\">B．5</td><td width=\"25%\">C．-9</td><td width=\"25%\">D．-1</td></tr></tbody></table></div>","QuesAnswer":"","QuesParse":"","UseSum":123,"AvgScore":5.0,"ParseAnswerKey":"2d512520edad89d220ec1cc8f0907ca0","QuesAttribute":0,"PaperSource":[{"Id":524331,"PaperTitle":"甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题","LearnGrade":12,"PaperType":9,"Province":620000,"PaperYear":2019,"PaperLevel":51,"AddTimeOn":"2019-06-08T22:26:16","SchoolId":71389,"MatchingDegree":0}]},{"ID":8188263,"Guid":"ae840e2d-9459-4a6b-bb9b-b6b6d949e504","Title":"甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题","From":"","Knowledge":"","QuesType":{"ID":2701,"Name":"单选题","IsSelectType":true,"OrderIndex":2,"ParentId":0},"QuesAbility":{"ID":1,"Name":"了解和识记"},"QuesDiff":{"ID":2,"DifValue":0.85,"Name":"较易"},"Categories":"<item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27936\" type=\"1\">算法与框图</category><category id=\"29709\" type=\"1\">算法初步</category><category id=\"29711\" type=\"1\">算法与程序框图</category><category id=\"29719\" type=\"1\">循环结构框图</category><category id=\"29744\" type=\"1\">补全循环结构的框图</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79332\" type=\"0\">必修3</category><category id=\"79334\" type=\"0\">第二章 算法初步</category><category id=\"79353\" type=\"0\">§2 算法框图的基本结构及设计</category><category id=\"79358\" type=\"0\">2.3 循环结构</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79505\" type=\"0\">选修1-2</category><category id=\"79507\" type=\"0\">第二章 框图</category></item><item><category id=\"79775\" type=\"0\">沪教版（上海）</category><category id=\"79821\" type=\"0\">高二第一学期</category><category id=\"79825\" type=\"0\">第十章 算法初步</category><category id=\"79840\" type=\"0\">10.2 程序框图</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"79992\" type=\"0\">必修3</category><category id=\"79993\" type=\"0\">第一章 算法初步</category><category id=\"79997\" type=\"0\">1.1 算法与程序框图</category><category id=\"80002\" type=\"0\">1.1.2 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type=\"0\">必修3</category><category id=\"81067\" type=\"0\">第1章 算法初步</category><category id=\"81072\" type=\"0\">1.2 流程图</category><category id=\"81078\" type=\"0\">1.2.3 循环结构</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81204\" type=\"0\">选修1-2</category><category id=\"81208\" type=\"0\">第4章 框图</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81565\" type=\"0\">高中二年级第一学期</category><category id=\"81568\" type=\"0\">第9章 矩阵和行列式初步</category><category id=\"81593\" type=\"0\">二 行列式</category><category id=\"81602\" type=\"0\">10.2 程序框图</category></item><item><category id=\"81682\" type=\"0\">苏教版（2004）</category><category id=\"81698\" type=\"0\">选修1-2</category><category id=\"81702\" type=\"0\">第4章 框图</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81837\" type=\"0\">必修第五册</category><category id=\"81838\" type=\"0\">第11章 算法初步</category><category id=\"81843\" type=\"0\">11.2 算法结构与程序框图</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81837\" type=\"0\">必修第五册</category><category id=\"81838\" type=\"0\">第11章 算法初步</category><category id=\"81843\" type=\"0\">11.2 算法结构与程序框图</category><category id=\"81849\" type=\"0\">11.2.3 循环结构</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81916\" type=\"0\">选修1-2</category><category id=\"81919\" type=\"0\">第6章 框图</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81916\" type=\"0\">选修1-2</category><category id=\"81919\" type=\"0\">第6章 框图</category><category id=\"81938\" type=\"0\">6.3 程序框图</category></item>","ChildNum":1,"Time":"2019-06-08T22:27:09","QuesBody":"<div>【题文】某程序框图如图所示，若该程序运行后输出的值是<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/dab742d9-4931-4cf9-9f4c-7992a3defd00/paper.files/image001.png\" alt=\"eqId6c827b6f6fbb4c669712c1b42fd15437\">，则<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/dab742d9-4931-4cf9-9f4c-7992a3defd00/paper.files/image002.png\" alt=\"eqId70a27b6ddf6b478285353abb3b1f3741\">的值是（ ）<br><img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/dab742d9-4931-4cf9-9f4c-7992a3defd00/paper.files/image003.png\" alt=\"figure\"><table name=\"optionsTable\" cellpadding=\"0\" cellspacing=\"0\" width=\"100%\"><tbody><tr><td width=\"25%\">A．7</td><td width=\"25%\">B．6</td><td width=\"25%\">C．5</td><td width=\"25%\">D．4</td></tr></tbody></table></div>","QuesAnswer":"","QuesParse":"","UseSum":81,"AvgScore":5.0,"ParseAnswerKey":"feded6525bb9601ec7c8d3f6f944f08b","QuesAttribute":0,"PaperSource":[{"Id":524331,"PaperTitle":"甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题","LearnGrade":12,"PaperType":9,"Province":620000,"PaperYear":2019,"PaperLevel":51,"AddTimeOn":"2019-06-08T22:26:16","SchoolId":71389,"MatchingDegree":0}]},{"ID":6688299,"Guid":"a4cac21e-bd86-4f04-bac3-595cfcf086b1","Title":"四川省成都市第七中学2018届高三下学期三诊模拟考试数学（文）试题","From":"","Knowledge":"","QuesType":{"ID":2701,"Name":"单选题","IsSelectType":true,"OrderIndex":2,"ParentId":0},"QuesAbility":{"ID":1,"Name":"了解和识记"},"QuesDiff":{"ID":3,"DifValue":0.65,"Name":"一般"},"Categories":"<item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27932\" type=\"1\">空间向量与立体几何</category><category id=\"28804\" type=\"1\">空间几何体</category><category id=\"28809\" type=\"1\">空间几何体的三视图和直观图</category><category id=\"28859\" type=\"1\">三视图</category><category id=\"28868\" type=\"1\">由三视图还原几何体</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27932\" type=\"1\">空间向量与立体几何</category><category id=\"28804\" type=\"1\">空间几何体</category><category id=\"28810\" type=\"1\">空间几何体的表面积与体积</category><category id=\"28874\" type=\"1\">柱、锥、台的表面积</category><category id=\"28878\" type=\"1\">棱柱表面积的有关计算</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79292\" type=\"0\">必修2</category><category id=\"79293\" type=\"0\">第一章 立体几何初步</category><category id=\"79302\" type=\"0\">§7 简单几何体的再认识</category><category id=\"79314\" type=\"0\">7.1 柱、锥、台的侧面展开与面积</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79292\" type=\"0\">必修2</category><category id=\"79293\" type=\"0\">第一章 立体几何初步</category><category id=\"79302\" type=\"0\">§7 简单几何体的再认识</category><category id=\"79315\" type=\"0\">7.2 柱、锥、台的体积</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"79935\" type=\"0\">必修2</category><category id=\"79936\" type=\"0\">第一章 空间几何体</category><category id=\"79943\" type=\"0\">1.3 空间几何体的表面积与体积</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"79935\" type=\"0\">必修2</category><category id=\"79936\" type=\"0\">第一章 空间几何体</category><category id=\"79941\" type=\"0\">1.1 空间几何体的结构</category><category id=\"79945\" type=\"0\">1.1.1 柱、锥、台、球的结构特征</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"79935\" type=\"0\">必修2</category><category id=\"79936\" type=\"0\">第一章 空间几何体</category><category id=\"79943\" type=\"0\">1.3 空间几何体的表面积与体积</category><category id=\"79950\" type=\"0\">1.3.1 柱体、锥体、台体的表面积与体积</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80550\" type=\"0\">必修2</category><category id=\"80551\" type=\"0\">第一章 立体几何初步</category><category id=\"80554\" type=\"0\">1.1 空间几何体</category><category id=\"80558\" type=\"0\">1.1.2 棱柱、棱锥和棱台的结构特征</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80550\" type=\"0\">必修2</category><category id=\"80551\" type=\"0\">第一章 立体几何初步</category><category id=\"80554\" type=\"0\">1.1 空间几何体</category><category id=\"80562\" type=\"0\">1.1.6 棱柱、棱锥、棱台和球的表面积</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80550\" type=\"0\">必修2</category><category id=\"80551\" type=\"0\">第一章 立体几何初步</category><category id=\"80554\" type=\"0\">1.1 空间几何体</category><category id=\"80563\" type=\"0\">1.1.7 柱、锥、台和球的体积</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81033\" type=\"0\">必修2</category><category id=\"81034\" type=\"0\">第1章 立体几何初步</category><category id=\"81039\" type=\"0\">1.3 空间几何体的表面积和体积</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81033\" type=\"0\">必修2</category><category id=\"81034\" type=\"0\">第1章 立体几何初步</category><category id=\"81037\" type=\"0\">1.1 空间几何体</category><category id=\"81041\" type=\"0\">1.1.1 棱柱、棱锥和棱台</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81033\" type=\"0\">必修2</category><category id=\"81034\" type=\"0\">第1章 立体几何初步</category><category id=\"81039\" type=\"0\">1.3 空间几何体的表面积和体积</category><category id=\"81049\" type=\"0\">1.3.1 空间几何体的表面积</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81637\" type=\"0\">高中三年级</category><category id=\"81639\" type=\"0\">第15章 简单几何体</category><category id=\"81651\" type=\"0\">三 几何体的表面积、体积和球面距离</category></item><item><category id=\"82158\" type=\"0\">大纲版</category><category id=\"82319\" type=\"0\">高二下册</category><category id=\"82320\" type=\"0\">第九章 直线、平面、简单几何体</category><category id=\"82329\" type=\"0\">9.7 棱柱</category></item><item><category id=\"82158\" type=\"0\">大纲版</category><category id=\"82319\" type=\"0\">高二下册</category><category id=\"82320\" type=\"0\">第九章 直线、平面、简单几何体</category><category id=\"82330\" type=\"0\">9.8 棱锥</category></item><item><category id=\"82158\" type=\"0\">大纲版</category><category id=\"82319\" type=\"0\">高二下册</category><category id=\"82320\" type=\"0\">第九章 直线、平面、简单几何体</category><category id=\"82331\" type=\"0\">阅读材料 柱体和锥体的体积</category></item>","ChildNum":1,"Time":"2018-08-02T10:48:09","QuesBody":"<div>【题文】《九章算术》中，将底面是直角三角形的直三棱柱称之为“堑堵”，已知某“堑堵”的三视图如图所示，则该“堑堵”的表面积为（ ）<br><img style=\"vertical-align:middle;\" src=\"Upload/2019-06/16/aefe4be1-06fb-4688-90dd-0d936563aa87/paper.files/image001.png\" alt=\"figure\"><table name=\"optionsTable\" cellpadding=\"0\" cellspacing=\"0\" width=\"100%\"><tbody><tr><td width=\"50%\">A．4</td><td width=\"50%\">B．<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/16/aefe4be1-06fb-4688-90dd-0d936563aa87/paper.files/image002.png\" alt=\"eqIdd5688a06729e4f2b98018a07089cc71c\"></td></tr><tr><td width=\"50%\">C．<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/16/aefe4be1-06fb-4688-90dd-0d936563aa87/paper.files/image003.png\" alt=\"eqIdd9e9a2c7c5c042a8bb892737344459e2\"></td><td width=\"50%\">D．2</td></tr></tbody></table></div>","QuesAnswer":"","QuesParse":"","UseSum":560,"AvgScore":5.0,"ParseAnswerKey":"e624bcd595bb586f9e429c27ae0838dc","QuesAttribute":0,"PaperSource":[{"Id":380740,"PaperTitle":"四川省成都市第七中学2018届高三下学期三诊模拟考试数学（文）试题","LearnGrade":12,"PaperType":9,"Province":510000,"PaperYear":2018,"PaperLevel":51,"AddTimeOn":"2018-08-02T10:47:46","SchoolId":62296,"MatchingDegree":0},{"Id":407153,"PaperTitle":"四川省泸州市泸化中学2017-2018学年高一5月月考文科数学试题","LearnGrade":10,"PaperType":3,"Province":510000,"PaperYear":2018,"PaperLevel":41,"AddTimeOn":"2018-10-12T09:21:23","SchoolId":77066,"MatchingDegree":0},{"Id":480889,"PaperTitle":"安徽省定远重点中学2019届高三下学期第一次模拟考试数学（理）试题","LearnGrade":12,"PaperType":9,"Province":340000,"PaperYear":2019,"PaperLevel":41,"AddTimeOn":"2019-03-16T20:37:54","SchoolId":0,"MatchingDegree":0},{"Id":524331,"PaperTitle":"甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题","LearnGrade":12,"PaperType":9,"Province":620000,"PaperYear":2019,"PaperLevel":51,"AddTimeOn":"2019-06-08T22:26:16","SchoolId":71389,"MatchingDegree":0}]},{"ID":8188264,"Guid":"65d5e3f0-1d7a-44ad-ab64-38182c1fc418","Title":"甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题","From":"","Knowledge":"","QuesType":{"ID":2701,"Name":"单选题","IsSelectType":true,"OrderIndex":2,"ParentId":0},"QuesAbility":{"ID":1,"Name":"了解和识记"},"QuesDiff":{"ID":3,"DifValue":0.65,"Name":"一般"},"Categories":"<item><category 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type=\"0\">人教B版</category><category id=\"80624\" type=\"0\">必修4</category><category id=\"80625\" type=\"0\">第一章 基本初等函数（Ⅱ）</category><category id=\"80631\" type=\"0\">1.3 三角函数的图象与性质</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80624\" type=\"0\">必修4</category><category id=\"80625\" type=\"0\">第一章 基本初等函数（Ⅱ）</category><category id=\"80632\" type=\"0\">本章复习与测试</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80624\" type=\"0\">必修4</category><category id=\"80625\" type=\"0\">第一章 基本初等函数（Ⅱ）</category><category id=\"80631\" type=\"0\">1.3 三角函数的图象与性质</category><category id=\"80639\" type=\"0\">1.3.1 正弦函数的图象与性质</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81103\" type=\"0\">必修4</category><category id=\"81104\" type=\"0\">第1章 三角函数</category><category id=\"81110\" type=\"0\">1.3 三角函数的图象和性质</category><category id=\"81118\" type=\"0\">1.3.2 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三角函数</category><category id=\"81764\" type=\"0\">3.4 函数y=Asin(ωx+φ)的图象与性质</category><category id=\"81774\" type=\"0\">3.4.2 函数y=Asin(ωx+φ)的图象与性质</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81524\" type=\"0\">高中一年级第二学期</category><category id=\"81527\" type=\"0\">第6章 三角函数</category><category id=\"81553\" type=\"0\">一 三角函数的图像与性质</category><category id=\"81556\" type=\"0\">6.1 正弦函数和余弦函数的图像与性质</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81756\" type=\"0\">必修第二册</category><category id=\"81757\" type=\"0\">第3章 三角函数</category><category id=\"81763\" type=\"0\">3.3 三角函数的图象与性质</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81756\" type=\"0\">必修第二册</category><category id=\"81757\" type=\"0\">第3章 三角函数</category><category id=\"81764\" type=\"0\">3.4 函数y=Asin(ωx+φ)的图象与性质</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81756\" type=\"0\">必修第二册</category><category id=\"81757\" type=\"0\">第3章 三角函数</category><category id=\"81763\" type=\"0\">3.3 三角函数的图象与性质</category><category id=\"81771\" type=\"0\">3.3.1 正弦函数、余弦函数的图象与性质</category></item><item><category id=\"82158\" type=\"0\">大纲版</category><category id=\"82202\" type=\"0\">高一下册</category><category id=\"82203\" type=\"0\">第四章 三角函数</category><category id=\"82207\" type=\"0\">三 三角函数的图象和性质</category></item><item><category id=\"82158\" type=\"0\">大纲版</category><category id=\"82202\" type=\"0\">高一下册</category><category id=\"82203\" type=\"0\">第四章 三角函数</category><category id=\"82207\" type=\"0\">三 三角函数的图象和性质</category><category id=\"82216\" type=\"0\">4.8 正弦函数、余弦函数的图象和性质</category></item><item><category id=\"82158\" type=\"0\">大纲版</category><category id=\"82202\" type=\"0\">高一下册</category><category id=\"82203\" type=\"0\">第四章 三角函数</category><category id=\"82207\" type=\"0\">三 三角函数的图象和性质</category><category id=\"82217\" type=\"0\">4.9 函数y=Asin（ωx+φ）的图象</category></item>","ChildNum":1,"Time":"2019-06-08T22:27:11","QuesBody":"<div>【题文】将函数<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/8947978b-e174-4193-8984-764386f6b819/paper.files/image001.png\" alt=\"eqId7dff564489ca497c90eeaa34a7ba56f5\">的图象向右平移<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/8947978b-e174-4193-8984-764386f6b819/paper.files/image002.png\" alt=\"eqId000aef5c9f2a4aa2881d8b6ed91fe140\">个单位长度得到<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/8947978b-e174-4193-8984-764386f6b819/paper.files/image003.png\" alt=\"eqId28c4c21271884dfeac29ce0222782376\">图像，则下列判断错误的是（ ）<table name=\"optionsTable\" cellpadding=\"0\" cellspacing=\"0\" width=\"100%\"><tbody><tr><td width=\"50%\">A．函数<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/8947978b-e174-4193-8984-764386f6b819/paper.files/image003.png\" alt=\"eqId28c4c21271884dfeac29ce0222782376\">的最小正周期是<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/8947978b-e174-4193-8984-764386f6b819/paper.files/image004.png\" alt=\"eqId5a6dc96e894e4f23be3c422cad388a30\"></td><td width=\"50%\">B．<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/8947978b-e174-4193-8984-764386f6b819/paper.files/image003.png\" alt=\"eqId28c4c21271884dfeac29ce0222782376\">图像关于直线<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/8947978b-e174-4193-8984-764386f6b819/paper.files/image005.png\" alt=\"eqIda36e31de163f445dbbf0371ed2025fef\">对称</td></tr><tr><td width=\"50%\">C．函数<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/8947978b-e174-4193-8984-764386f6b819/paper.files/image003.png\" alt=\"eqId28c4c21271884dfeac29ce0222782376\">在区间<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/8947978b-e174-4193-8984-764386f6b819/paper.files/image006.png\" alt=\"eqIde01830b9b8f54a179cd9d0d94f1f48c3\">上单调递减</td><td width=\"50%\">D．<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/8947978b-e174-4193-8984-764386f6b819/paper.files/image003.png\" alt=\"eqId28c4c21271884dfeac29ce0222782376\">图像关于点<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/8947978b-e174-4193-8984-764386f6b819/paper.files/image007.png\" alt=\"eqId87d71f232f9541e99ee5cf95de04dd4d\">对称</td></tr></tbody></table></div>","QuesAnswer":"","QuesParse":"","UseSum":132,"AvgScore":5.0,"ParseAnswerKey":"893dec68dfee1c9209db9c2f5ba48427","QuesAttribute":0,"PaperSource":[{"Id":524331,"PaperTitle":"甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题","LearnGrade":12,"PaperType":9,"Province":620000,"PaperYear":2019,"PaperLevel":51,"AddTimeOn":"2019-06-08T22:26:16","SchoolId":71389,"MatchingDegree":0}]},{"ID":8188247,"Guid":"8076c67c-2c3b-4a39-81c9-06f8385c21d2","Title":"甘肃省兰州市第一中学2019届高三6月最后高考冲刺模拟数学（理）试题","From":"","Knowledge":"","QuesType":{"ID":2701,"Name":"单选题","IsSelectType":true,"OrderIndex":2,"ParentId":0},"QuesAbility":{"ID":1,"Name":"了解和识记"},"QuesDiff":{"ID":2,"DifValue":0.85,"Name":"较易"},"Categories":"<item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27929\" type=\"1\">平面向量</category><category id=\"28574\" type=\"1\">平面向量的数量积</category><category id=\"28619\" type=\"1\">平面向量数量积的运算</category><category id=\"28624\" 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type=\"0\">4.5 向量的数量积</category><category id=\"81785\" type=\"0\">4.5.3 利用坐标计算数量积</category></item><item><category id=\"82158\" type=\"0\">大纲版</category><category id=\"82202\" type=\"0\">高一下册</category><category id=\"82204\" type=\"0\">第五章 平面向量</category><category id=\"82223\" type=\"0\">一 向量及其运算</category><category id=\"82231\" type=\"0\">5.7 平面向量数量积的坐标表示</category></item>","ChildNum":1,"Time":"2019-06-08T22:25:27","QuesBody":"<div>【题文】已知非零向量<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/7c220bec-983e-4aee-97de-2cde1f27431b/paper.files/image001.png\" alt=\"eqId65157f86b1c2448bb6cb33e02d118af8\">,<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/7c220bec-983e-4aee-97de-2cde1f27431b/paper.files/image002.png\" alt=\"eqIdb368d61ee9914632a3a232f3628534da\">的夹角为<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/7c220bec-983e-4aee-97de-2cde1f27431b/paper.files/image003.png\" alt=\"eqIdb4b5468ef66640e890efc57540f9453b\">,且满足<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/7c220bec-983e-4aee-97de-2cde1f27431b/paper.files/image004.png\" alt=\"eqId71a578bdb3dd4d8ab1f4da84fbfe9bd4\">,则<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/7c220bec-983e-4aee-97de-2cde1f27431b/paper.files/image005.png\" alt=\"eqIdc1e910d329f74862be392ed6bd8fdf59\">的最大值为( )<table name=\"optionsTable\" cellpadding=\"0\" cellspacing=\"0\" width=\"100%\"><tbody><tr><td width=\"25%\">A．<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/7c220bec-983e-4aee-97de-2cde1f27431b/paper.files/image006.png\" alt=\"eqIddb6b28cbd8a14caa9cf1146f6f7916c0\"></td><td width=\"25%\">B．<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/7c220bec-983e-4aee-97de-2cde1f27431b/paper.files/image007.png\" alt=\"eqIdf1bd69290a464f71ac73b93c51985105\"></td><td width=\"25%\">C．<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/7c220bec-983e-4aee-97de-2cde1f27431b/paper.files/image008.png\" alt=\"eqIdc052ddfbd4524f67a79e0e77c2e5656a\"></td><td width=\"25%\">D．<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/7c220bec-983e-4aee-97de-2cde1f27431b/paper.files/image009.png\" alt=\"eqId8898c1dc81824f3098bbeae74e8f11fd\"></td></tr></tbody></table></div>","QuesAnswer":"","QuesParse":"","UseSum":95,"AvgScore":5.0,"ParseAnswerKey":"1648356d665620d8f93afc34017ac369","QuesAttribute":0,"PaperSource":[{"Id":524330,"PaperTitle":"甘肃省兰州市第一中学2019届高三6月最后高考冲刺模拟数学（理）试题","LearnGrade":12,"PaperType":9,"Province":620000,"PaperYear":2019,"PaperLevel":51,"AddTimeOn":"2019-06-08T22:24:15","SchoolId":71389,"MatchingDegree":0},{"Id":524331,"PaperTitle":"甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题","LearnGrade":12,"PaperType":9,"Province":620000,"PaperYear":2019,"PaperLevel":51,"AddTimeOn":"2019-06-08T22:26:16","SchoolId":71389,"MatchingDegree":0}]},{"ID":8188250,"Guid":"9c035d3f-ce27-43d0-8ba7-5d8d540f57a8","Title":"甘肃省兰州市第一中学2019届高三6月最后高考冲刺模拟数学（理）试题","From":"","Knowledge":"","QuesType":{"ID":2701,"Name":"单选题","IsSelectType":true,"OrderIndex":2,"ParentId":0},"QuesAbility":{"ID":1,"Name":"了解和识记"},"QuesDiff":{"ID":2,"DifValue":0.85,"Name":"较易"},"Categories":"<item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27933\" type=\"1\">平面解析几何</category><category id=\"29045\" type=\"1\">圆锥曲线</category><category id=\"29172\" type=\"1\">双曲线</category><category id=\"29236\" type=\"1\">双曲线的离心率</category><category id=\"29263\" type=\"1\">求双曲线的离心率或离心率的取值范围</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79458\" type=\"0\">选修1-1</category><category id=\"79460\" type=\"0\">第二章 圆锥曲线与方程</category><category id=\"79481\" type=\"0\">§3 双曲线</category><category id=\"79487\" type=\"0\">3.1 双曲线及其标准方程</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79458\" type=\"0\">选修1-1</category><category id=\"79460\" type=\"0\">第二章 圆锥曲线与方程</category><category id=\"79481\" type=\"0\">§3 双曲线</category><category id=\"79488\" type=\"0\">3.2 双曲线的简单性质</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79540\" type=\"0\">选修2-1</category><category id=\"79543\" type=\"0\">第三章 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id=\"81966\" type=\"0\">2.2.1 双曲线的定义与标准方程</category></item><item><category id=\"82158\" type=\"0\">大纲版</category><category id=\"82287\" type=\"0\">高二上册</category><category id=\"82290\" type=\"0\">第八章 圆锥曲线方程</category><category id=\"82312\" type=\"0\">8.3 双曲线及其标准方程</category></item>","ChildNum":1,"Time":"2019-06-08T22:25:31","QuesBody":"<div>【题文】已知<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/e413ddb5-9354-4c20-9915-46501386b33c/paper.files/image001.png\" alt=\"eqIda3295b0faa56453483a54207dda2feb3\">是双曲线<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/e413ddb5-9354-4c20-9915-46501386b33c/paper.files/image002.png\" alt=\"eqIdc4496dafda1c478fb528d8a8a0c9c9f5\">的左、右焦点，若点<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/e413ddb5-9354-4c20-9915-46501386b33c/paper.files/image003.png\" alt=\"eqId0cfe24caa0fc44de8e0fcd142d6c1377\">关于渐近线的对称点<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/e413ddb5-9354-4c20-9915-46501386b33c/paper.files/image004.png\" alt=\"eqId2381423d4cd146cab95f55527681a766\">也在双曲线上，则该双曲线的离心率为( )<table name=\"optionsTable\" cellpadding=\"0\" cellspacing=\"0\" width=\"100%\"><tbody><tr><td width=\"25%\">A．<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/e413ddb5-9354-4c20-9915-46501386b33c/paper.files/image005.png\" alt=\"eqId3612b2569ddf4e45a245e47a0ea9b87b\"></td><td width=\"25%\">B．<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/e413ddb5-9354-4c20-9915-46501386b33c/paper.files/image006.png\" alt=\"eqId94cd6242e9394c5b9aba165383223193\"></td><td width=\"25%\">C．<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/e413ddb5-9354-4c20-9915-46501386b33c/paper.files/image007.png\" alt=\"eqIdc052ddfbd4524f67a79e0e77c2e5656a\"></td><td width=\"25%\">D．<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/e413ddb5-9354-4c20-9915-46501386b33c/paper.files/image008.png\" 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type=\"0\">高一上册</category><category id=\"82161\" type=\"0\">第二章 函数</category><category id=\"82176\" type=\"0\">一 函数</category><category id=\"82181\" type=\"0\">2.3 函数的单调性</category></item><item><category id=\"82158\" type=\"0\">大纲版</category><category id=\"82242\" type=\"0\">高三全册</category><category id=\"82245\" type=\"0\">第三章 导数</category><category id=\"82275\" type=\"0\">3.6 函数的单调性</category></item>","ChildNum":1,"Time":"2019-06-08T22:27:12","QuesBody":"<div>【题文】定义在<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/9625c6ad-429c-420f-bad7-8893d1c0adb2/paper.files/image001.png\" alt=\"eqId419991aed46b456083d87d6c4b7ce03c\">上的函数<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/9625c6ad-429c-420f-bad7-8893d1c0adb2/paper.files/image002.png\" alt=\"eqId39a9bb676a7c47aa97d3b636db663563\">满足<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/9625c6ad-429c-420f-bad7-8893d1c0adb2/paper.files/image003.png\" alt=\"eqIddcf4fef5a2f443d78e3c14de7cd75d58\">，<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/9625c6ad-429c-420f-bad7-8893d1c0adb2/paper.files/image004.png\" alt=\"eqId3037bee4757b4b2385af1c0ed56ee403\">，则关于<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/9625c6ad-429c-420f-bad7-8893d1c0adb2/paper.files/image005.png\" alt=\"eqIdc12aac8c2448479687a40735b3572a23\">的不等式<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/9625c6ad-429c-420f-bad7-8893d1c0adb2/paper.files/image006.png\" alt=\"eqId525c40814926478faf4726ca2ec18dd8\"> 的解集为( )<table name=\"optionsTable\" cellpadding=\"0\" cellspacing=\"0\" width=\"100%\"><tbody><tr><td width=\"25%\">A．<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/9625c6ad-429c-420f-bad7-8893d1c0adb2/paper.files/image007.png\" alt=\"eqIdae9615e31481455292b5074b65e84785\"></td><td width=\"25%\">B．<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/9625c6ad-429c-420f-bad7-8893d1c0adb2/paper.files/image008.png\" alt=\"eqIdcc99955c8e5c43a8a1cb0efdf8c4003a\"></td><td width=\"25%\">C．<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/9625c6ad-429c-420f-bad7-8893d1c0adb2/paper.files/image009.png\" alt=\"eqId6a87988ee4844e29b2ac13afc5cbb9f2\"></td><td width=\"25%\">D．<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/9625c6ad-429c-420f-bad7-8893d1c0adb2/paper.files/image010.png\" 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src=\"Upload/2019-04/25/150ddc2f-5ab7-43d6-93f5-c6d50fe7cb0b/paper.files/image159.png\">的表面积为____.</div>","QuesAnswer":"","QuesParse":"","UseSum":311,"AvgScore":5.0,"ParseAnswerKey":"087b25e3c4cf3cb395ed2af80fe26567","QuesAttribute":0,"PaperSource":[{"Id":501939,"PaperTitle":"安徽省宣城市2019届高三第二次调研测试文科数学试题","LearnGrade":12,"PaperType":9,"Province":340000,"PaperYear":2019,"PaperLevel":42,"AddTimeOn":"2019-04-25T09:48:47","SchoolId":0,"MatchingDegree":0},{"Id":524331,"PaperTitle":"甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题","LearnGrade":12,"PaperType":9,"Province":620000,"PaperYear":2019,"PaperLevel":51,"AddTimeOn":"2019-06-08T22:26:16","SchoolId":71389,"MatchingDegree":0}]},{"ID":6427000,"Guid":"806820e5-e7b6-44c3-8d7a-2fb2dd0bc8fb","Title":"辽宁省丹东市2018年高三总复习质量测试（二）数学（文科）试题","From":"","Knowledge":"","QuesType":{"ID":2702,"Name":"填空题","IsSelectType":false,"OrderIndex":3,"ParentId":0},"QuesAbility":{"ID":1,"Name":"了解和识记"},"QuesDiff":{"ID":2,"DifValue":0.85,"Name":"较易"},"Categories":"<item><category 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type=\"0\">5.2 直接证明与间接证明</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81916\" type=\"0\">选修1-2</category><category id=\"81918\" type=\"0\">第5章 推理与证明</category><category id=\"81927\" type=\"0\">5.1 合情推理和演绎推理</category><category id=\"81932\" type=\"0\">5.1.3 演绎推理</category></item>","ChildNum":1,"Time":"2018-05-19T19:40:57","QuesBody":"<div>【题文】为了考查考生对于“数学知识形成过程”的掌握情况，某高校自主招生考试面试中的一个问题是：写出对数的换底公式，并加以证明．甲、乙、丙三名考生分别写出了不同的答案．公布他们的答案后，三考生之间有如下对话，甲说：“我答错了”；乙说：“我答对了”；丙说：“乙答错了”．评委看了他们的答案，听了他们之间的对话后说：你们三人的答案中只有一人是正确的，你们三人的对话中只有一人说对了．根据以上信息，面试问题答案正确的考生为_____ 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id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27933\" type=\"1\">平面解析几何</category><category id=\"29045\" type=\"1\">圆锥曲线</category><category id=\"29173\" type=\"1\">抛物线</category><category id=\"29273\" type=\"1\">抛物线标准方程的形式</category><category id=\"29282\" type=\"1\">根据抛物线方程求焦点或准线</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27933\" type=\"1\">平面解析几何</category><category id=\"29045\" type=\"1\">圆锥曲线</category><category id=\"29174\" type=\"1\">直线与圆锥曲线的位置关系</category><category id=\"29307\" type=\"1\">直线与抛物线的位置关系</category><category id=\"29343\" type=\"1\">求抛物线的切线方程</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79458\" type=\"0\">选修1-1</category><category id=\"79460\" type=\"0\">第二章 圆锥曲线与方程</category><category id=\"79480\" type=\"0\">§2 抛物线</category><category id=\"79485\" type=\"0\">2.1 抛物线及其标准方程</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79540\" type=\"0\">选修2-1</category><category id=\"79543\" type=\"0\">第三章 圆锥曲线与方程</category><category id=\"79574\" type=\"0\">§2 抛物线</category><category id=\"79580\" type=\"0\">2.1 抛物线及其标准方程</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79540\" type=\"0\">选修2-1</category><category id=\"79543\" type=\"0\">第三章 圆锥曲线与方程</category><category id=\"79576\" type=\"0\">§4 曲线与方程</category><category id=\"79586\" type=\"0\">4.3 直线与圆锥曲线的交点</category></item><item><category id=\"79775\" type=\"0\">沪教版（上海）</category><category id=\"79842\" type=\"0\">高二第二学期</category><category id=\"79844\" type=\"0\">第十二章 圆锥曲线</category><category id=\"79858\" type=\"0\">12.7抛物线的标准方程</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"80101\" type=\"0\">选修1-1</category><category id=\"80103\" type=\"0\">第二章 圆锥曲线与方程</category><category id=\"80124\" type=\"0\">2.3 抛物线</category><category id=\"80130\" type=\"0\">2.3.1 抛物线及其标准方程</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"80171\" type=\"0\">选修2-1</category><category id=\"80173\" type=\"0\">第二章 圆锥曲线与方程</category><category id=\"80195\" type=\"0\">2.4 抛物线</category><category id=\"80203\" type=\"0\">2.4.1 抛物线及其标准方程</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80699\" type=\"0\">选修1-1</category><category id=\"80701\" type=\"0\">第二章 圆锥曲线与方程</category><category id=\"80716\" type=\"0\">2.3 抛物线</category><category id=\"80722\" type=\"0\">2.3.1 抛物线及其标准方程</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80763\" type=\"0\">选修2-1</category><category id=\"80765\" type=\"0\">第二章 圆锥曲线与方程</category><category id=\"80782\" type=\"0\">2.5 直线与圆锥曲线</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80763\" type=\"0\">选修2-1</category><category id=\"80765\" type=\"0\">第二章 圆锥曲线与方程</category><category id=\"80781\" type=\"0\">2.4 抛物线</category><category id=\"80790\" type=\"0\">2.4.1 抛物线的标准方程</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81167\" type=\"0\">选修1-1</category><category id=\"81169\" type=\"0\">第2章 圆锥曲线与方程</category><category id=\"81183\" type=\"0\">2.4 抛物线</category><category id=\"81190\" type=\"0\">2.4.1 抛物线的标准方程</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81228\" type=\"0\">选修2-1</category><category id=\"81230\" type=\"0\">第2章 圆锥曲线与方程</category><category id=\"81244\" type=\"0\">2.4 抛物线</category><category id=\"81252\" type=\"0\">2.4.1 抛物线的标准方程</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81605\" type=\"0\">高中二年级第二学期</category><category id=\"81607\" type=\"0\">第12章 圆锥曲线</category><category id=\"81623\" type=\"0\">12.7 抛物线的标准方程</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81878\" type=\"0\">选修1-1</category><category id=\"81880\" type=\"0\">第2章 圆锥曲线与方程</category><category id=\"81894\" type=\"0\">2.4 圆锥曲线的应用</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81878\" type=\"0\">选修1-1</category><category id=\"81880\" type=\"0\">第2章 圆锥曲线与方程</category><category id=\"81893\" type=\"0\">2.3 抛物线</category><category id=\"81900\" type=\"0\">2.3.1 抛物线的定义与标准方程</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81945\" type=\"0\">选修2-1</category><category id=\"81947\" type=\"0\">第2章 圆锥曲线与方程</category><category id=\"81961\" type=\"0\">2.4 圆锥曲线的应用</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81945\" type=\"0\">选修2-1</category><category id=\"81947\" type=\"0\">第2章 圆锥曲线与方程</category><category id=\"81960\" type=\"0\">2.3 抛物线</category><category id=\"81968\" type=\"0\">2.3.1 抛物线的定义与标准方程</category></item><item><category id=\"82158\" type=\"0\">大纲版</category><category id=\"82287\" type=\"0\">高二上册</category><category id=\"82290\" type=\"0\">第八章 圆锥曲线方程</category><category id=\"82314\" type=\"0\">8.5 抛物线及其标准方程</category></item>","ChildNum":1,"Time":"2019-04-17T09:45:25","QuesBody":"<div>【题文】已知抛物线<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/17/149cfd48-2198-47f1-8bfd-14f5e1f80886/paper.files/image155.png\">的焦点为<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/17/149cfd48-2198-47f1-8bfd-14f5e1f80886/paper.files/image156.png\">，<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/17/149cfd48-2198-47f1-8bfd-14f5e1f80886/paper.files/image157.png\">为<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/17/149cfd48-2198-47f1-8bfd-14f5e1f80886/paper.files/image158.png\">轴正半轴上的一点．且<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/17/149cfd48-2198-47f1-8bfd-14f5e1f80886/paper.files/image159.png\">（<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/17/149cfd48-2198-47f1-8bfd-14f5e1f80886/paper.files/image160.png\">为坐标原点），若抛物线<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/17/149cfd48-2198-47f1-8bfd-14f5e1f80886/paper.files/image041.png\">上存在一点<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/17/149cfd48-2198-47f1-8bfd-14f5e1f80886/paper.files/image161.png\">，其中<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/17/149cfd48-2198-47f1-8bfd-14f5e1f80886/paper.files/image162.png\">，使过点<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/17/149cfd48-2198-47f1-8bfd-14f5e1f80886/paper.files/image163.png\">的切线<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/17/149cfd48-2198-47f1-8bfd-14f5e1f80886/paper.files/image164.png\">，则切线<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/17/149cfd48-2198-47f1-8bfd-14f5e1f80886/paper.files/image165.png\">在<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/17/149cfd48-2198-47f1-8bfd-14f5e1f80886/paper.files/image158.png\">轴的截距为_____．</div>","QuesAnswer":"","QuesParse":"","UseSum":145,"AvgScore":5.0,"ParseAnswerKey":"becdb76d453fe1fae2f118a679d53c16","QuesAttribute":0,"PaperSource":[{"Id":496783,"PaperTitle":"北京师范大学附属实验中学2019届高三3月高考模拟试卷（一）数学（理科）试题","LearnGrade":12,"PaperType":9,"Province":110000,"PaperYear":2019,"PaperLevel":51,"AddTimeOn":"2019-04-17T09:44:44","SchoolId":126,"MatchingDegree":0},{"Id":524331,"PaperTitle":"甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题","LearnGrade":12,"PaperType":9,"Province":620000,"PaperYear":2019,"PaperLevel":51,"AddTimeOn":"2019-06-08T22:26:16","SchoolId":71389,"MatchingDegree":0}]},{"ID":7806651,"Guid":"7cdcc986-8acb-41bf-86b2-4597c99885c6","Title":"安徽省合肥市2019届高三第二次教学质量检测数学（文）试题","From":"","Knowledge":"","QuesType":{"ID":2703,"Name":"解答题","IsSelectType":false,"OrderIndex":4,"ParentId":0},"QuesAbility":{"ID":1,"Name":"了解和识记"},"QuesDiff":{"ID":3,"DifValue":0.65,"Name":"一般"},"Categories":"<item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27928\" type=\"1\">三角函数与解三角形</category><category id=\"28322\" type=\"1\">三角恒等变换</category><category id=\"28505\" type=\"1\">两角和与差的三角函数</category><category id=\"28512\" type=\"1\">两角和与差的正弦公式</category><category id=\"28521\" type=\"1\">逆用和、差角的正弦公式化简、求值</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27928\" type=\"1\">三角函数与解三角形</category><category id=\"28323\" type=\"1\">解三角形</category><category id=\"28546\" type=\"1\">正弦定理和余弦定理</category><category id=\"28548\" type=\"1\">正弦定理</category><category id=\"28555\" type=\"1\">正弦定理边角互化的应用</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27928\" type=\"1\">三角函数与解三角形</category><category id=\"28323\" type=\"1\">解三角形</category><category id=\"28546\" type=\"1\">正弦定理和余弦定理</category><category id=\"28550\" type=\"1\">余弦定理</category><category id=\"28559\" type=\"1\">余弦定理解三角形</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79422\" type=\"0\">必修5</category><category id=\"79424\" type=\"0\">第二章 解三角形</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79422\" type=\"0\">必修5</category><category id=\"79424\" type=\"0\">第二章 解三角形</category><category id=\"79438\" type=\"0\">§1 正弦定理与余弦定理</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79422\" type=\"0\">必修5</category><category id=\"79424\" type=\"0\">第二章 解三角形</category><category id=\"79438\" type=\"0\">§1 正弦定理与余弦定理</category><category id=\"79443\" type=\"0\">1.2 余弦定理</category></item><item><category id=\"79775\" type=\"0\">沪教版（上海）</category><category id=\"79804\" type=\"0\">高一第二学期</category><category id=\"79806\" type=\"0\">第五章 三角比</category><category id=\"79816\" type=\"0\">5.3 解斜三角形</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"80073\" type=\"0\">必修5</category><category id=\"80074\" type=\"0\">第一章 解三角形</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"80073\" type=\"0\">必修5</category><category id=\"80074\" type=\"0\">第一章 解三角形</category><category id=\"80078\" type=\"0\">1.1 正弦定理和余弦定理</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"80073\" type=\"0\">必修5</category><category id=\"80074\" type=\"0\">第一章 解三角形</category><category id=\"80078\" type=\"0\">1.1 正弦定理和余弦定理</category><category id=\"80082\" type=\"0\">1.1.2 余弦定理</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80669\" type=\"0\">必修5</category><category id=\"80670\" type=\"0\">第一章 解三角形</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80669\" type=\"0\">必修5</category><category id=\"80670\" type=\"0\">第一章 解三角形</category><category id=\"80674\" type=\"0\">1.1 正弦定理和余弦定理</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80669\" type=\"0\">必修5</category><category id=\"80670\" type=\"0\">第一章 解三角形</category><category id=\"80674\" type=\"0\">1.1 正弦定理和余弦定理</category><category id=\"80678\" type=\"0\">1.1.2 余弦定理</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81139\" type=\"0\">必修5</category><category id=\"81140\" type=\"0\">第1章 解三角形</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81139\" type=\"0\">必修5</category><category id=\"81140\" type=\"0\">第1章 解三角形</category><category id=\"81145\" type=\"0\">1.2 余弦定理</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81524\" type=\"0\">高中一年级第二学期</category><category id=\"81526\" type=\"0\">第5章 三角比</category><category id=\"81543\" type=\"0\">三 解斜三角形</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81524\" type=\"0\">高中一年级第二学期</category><category id=\"81526\" type=\"0\">第5章 三角比</category><category id=\"81543\" type=\"0\">三 解斜三角形</category><category id=\"81550\" type=\"0\">5.6 正弦定理、余弦定理和解斜三角形</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81818\" type=\"0\">必修第四册</category><category id=\"81819\" type=\"0\">第8章 解三角形</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81818\" type=\"0\">必修第四册</category><category id=\"81819\" type=\"0\">第8章 解三角形</category><category id=\"81824\" type=\"0\">8.2 余弦定理</category></item><item><category id=\"82158\" type=\"0\">大纲版</category><category id=\"82202\" type=\"0\">高一下册</category><category id=\"82204\" type=\"0\">第五章 平面向量</category><category id=\"82224\" type=\"0\">二 解斜三角形</category></item><item><category id=\"82158\" type=\"0\">大纲版</category><category id=\"82202\" type=\"0\">高一下册</category><category id=\"82204\" type=\"0\">第五章 平面向量</category><category id=\"82224\" type=\"0\">二 解斜三角形</category><category id=\"82234\" type=\"0\">5.9 正弦定理、余弦定理</category></item>","ChildNum":1,"Time":"2019-03-30T22:17:41","QuesBody":"<div>【题文】在<img style=\"vertical-align:middle;\" src=\"Upload/2019-03/30/79348340-81fb-402d-8990-a9c3d9338d66/paper.files/image026.png\">中，角<img style=\"vertical-align:middle;\" src=\"Upload/2019-03/30/79348340-81fb-402d-8990-a9c3d9338d66/paper.files/image009.png\">，<img style=\"vertical-align:middle;\" src=\"Upload/2019-03/30/79348340-81fb-402d-8990-a9c3d9338d66/paper.files/image010.png\">，<img style=\"vertical-align:middle;\" src=\"Upload/2019-03/30/79348340-81fb-402d-8990-a9c3d9338d66/paper.files/image123.png\">的对边分别是<img style=\"vertical-align:middle;\" src=\"Upload/2019-03/30/79348340-81fb-402d-8990-a9c3d9338d66/paper.files/image200.png\">，<img style=\"vertical-align:middle;\" src=\"Upload/2019-03/30/79348340-81fb-402d-8990-a9c3d9338d66/paper.files/image079.png\">，<img style=\"vertical-align:middle;\" src=\"Upload/2019-03/30/79348340-81fb-402d-8990-a9c3d9338d66/paper.files/image201.png\">.已知<img style=\"vertical-align:middle;\" src=\"Upload/2019-03/30/79348340-81fb-402d-8990-a9c3d9338d66/paper.files/image202.png\">.<br>（Ⅰ）求角<img style=\"vertical-align:middle;\" src=\"Upload/2019-03/30/79348340-81fb-402d-8990-a9c3d9338d66/paper.files/image123.png\">的值；<br>（Ⅱ）若<img style=\"vertical-align:middle;\" src=\"Upload/2019-03/30/79348340-81fb-402d-8990-a9c3d9338d66/paper.files/image203.png\">，<img style=\"vertical-align:middle;\" src=\"Upload/2019-03/30/79348340-81fb-402d-8990-a9c3d9338d66/paper.files/image204.png\">，求<img style=\"vertical-align:middle;\" src=\"Upload/2019-03/30/79348340-81fb-402d-8990-a9c3d9338d66/paper.files/image026.png\">的面积.</div>","QuesAnswer":"","QuesParse":"","UseSum":486,"AvgScore":5.0,"ParseAnswerKey":"7682691d1b90d060db5e0a9a44051c6b","QuesAttribute":0,"PaperSource":[{"Id":487953,"PaperTitle":"安徽省合肥市2019届高三第二次教学质量检测数学（文）试题","LearnGrade":12,"PaperType":9,"Province":340000,"PaperYear":2019,"PaperLevel":41,"AddTimeOn":"2019-03-30T22:16:55","SchoolId":0,"MatchingDegree":0},{"Id":524330,"PaperTitle":"甘肃省兰州市第一中学2019届高三6月最后高考冲刺模拟数学（理）试题","LearnGrade":12,"PaperType":9,"Province":620000,"PaperYear":2019,"PaperLevel":51,"AddTimeOn":"2019-06-08T22:24:15","SchoolId":71389,"MatchingDegree":0},{"Id":524331,"PaperTitle":"甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题","LearnGrade":12,"PaperType":9,"Province":620000,"PaperYear":2019,"PaperLevel":51,"AddTimeOn":"2019-06-08T22:26:16","SchoolId":71389,"MatchingDegree":0}]},{"ID":8188266,"Guid":"4c89952e-adbf-43bb-8547-936c04930e16","Title":"甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题","From":"","Knowledge":"","QuesType":{"ID":2703,"Name":"解答题","IsSelectType":false,"OrderIndex":4,"ParentId":0},"QuesAbility":{"ID":1,"Name":"了解和识记"},"QuesDiff":{"ID":3,"DifValue":0.65,"Name":"一般"},"Categories":"<item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27934\" type=\"1\">计数原理与概率统计</category><category id=\"29366\" type=\"1\">统计</category><category id=\"29373\" type=\"1\">变量间的相关关系</category><category id=\"29455\" type=\"1\">回归直线方程</category><category id=\"29464\" type=\"1\">用回归直线方程对总体进行估计</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27934\" type=\"1\">计数原理与概率统计</category><category id=\"29366\" type=\"1\">统计</category><category id=\"29373\" type=\"1\">变量间的相关关系</category><category id=\"29456\" type=\"1\">最小二乘法</category><category id=\"29466\" type=\"1\">求回归直线方程</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27934\" type=\"1\">计数原理与概率统计</category><category id=\"29369\" type=\"1\">概率</category><category id=\"29553\" type=\"1\">古典概型</category><category id=\"29585\" type=\"1\">古典概型的概率计算公式</category><category id=\"29589\" type=\"1\">计算古典概型问题的概率</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79332\" type=\"0\">必修3</category><category id=\"79335\" type=\"0\">第三章 概率</category><category id=\"79362\" type=\"0\">§2 古典概型</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79332\" type=\"0\">必修3</category><category id=\"79335\" type=\"0\">第三章 概率</category><category id=\"79362\" type=\"0\">§2 古典概型</category><category id=\"79367\" type=\"0\">2.1 古典概型的特征和概率计算公式</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79332\" type=\"0\">必修3</category><category id=\"79335\" type=\"0\">第三章 概率</category><category id=\"79362\" type=\"0\">§2 古典概型</category><category id=\"79368\" type=\"0\">2.2 建立概率模型</category></item><item><category id=\"79775\" type=\"0\">沪教版（上海）</category><category id=\"79891\" type=\"0\">高三第二学期</category><category id=\"79892\" type=\"0\">第十七章 概率论初步</category><category id=\"79895\" type=\"0\">17.1 古典概念</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"79992\" type=\"0\">必修3</category><category id=\"79995\" type=\"0\">第三章 概率</category><category id=\"80018\" type=\"0\">3.2 古典概型</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"79992\" type=\"0\">必修3</category><category id=\"79995\" type=\"0\">第三章 概率</category><category id=\"80018\" type=\"0\">3.2 古典概型</category><category id=\"80024\" type=\"0\">3.2.1 古典概型</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80584\" type=\"0\">必修3</category><category id=\"80587\" type=\"0\">第三章 概率</category><category id=\"80612\" type=\"0\">3.2 古典概型</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80584\" type=\"0\">必修3</category><category id=\"80587\" type=\"0\">第三章 概率</category><category id=\"80612\" type=\"0\">3.2 古典概型</category><category id=\"80620\" type=\"0\">3.2.1 古典概型</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80584\" type=\"0\">必修3</category><category id=\"80587\" type=\"0\">第三章 概率</category><category id=\"80612\" type=\"0\">3.2 古典概型</category><category id=\"80621\" type=\"0\">3.2.2 概率的一般加法公式（选学）</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81066\" type=\"0\">必修3</category><category id=\"81069\" type=\"0\">第3章 概率</category><category id=\"81097\" type=\"0\">3.2 古典概型</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81637\" type=\"0\">高中三年级</category><category id=\"81641\" type=\"0\">第17章 概率论初步</category><category id=\"81669\" type=\"0\">17.1 古典概念</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81837\" type=\"0\">必修第五册</category><category id=\"81840\" type=\"0\">第13章 概率</category><category id=\"81871\" type=\"0\">13.2 概率及其应用</category><category id=\"81876\" type=\"0\">13.2.1 古典概率模型</category></item>","ChildNum":1,"Time":"2019-06-08T22:27:14","QuesBody":"<div>【题文】某商场营销人员进行某商品的市场营销调查时发现，每回馈消费者一定的点数，该商品每天的销量就会发生一定的变化，经过试点统计得到以下表：<br><table border=\"1\" cellpadding=\"0\" cellspacing=\"0\"><tbody><tr style=\"height:18.0pt\"><td style=\"width:88.5pt;border:solid black 1.0pt;padding:3.75pt 5.4pt 3.75pt 5.4pt; height:18.0pt\" width=\"118\">反馈点数t<br></td><td style=\"width:34.5pt;border:solid black 1.0pt;border-left:none; padding:3.75pt 5.4pt 3.75pt 5.4pt;height:18.0pt\" width=\"46\">1<br></td><td style=\"width:49.5pt;border:solid black 1.0pt;border-left:none; padding:3.75pt 5.4pt 3.75pt 5.4pt;height:18.0pt\" width=\"66\">2<br></td><td style=\"width:51.0pt;border:solid black 1.0pt;border-left:none; padding:3.75pt 5.4pt 3.75pt 5.4pt;height:18.0pt\" width=\"68\">3<br></td><td style=\"width:48.75pt;border:solid black 1.0pt;border-left:none; padding:3.75pt 5.4pt 3.75pt 5.4pt;height:18.0pt\" width=\"65\">4<br></td><td style=\"width:47.25pt;border:solid black 1.0pt;border-left:none; padding:3.75pt 5.4pt 3.75pt 5.4pt;height:18.0pt\" width=\"63\">5<br></td></tr><tr style=\"height:18.0pt\"><td style=\"width:88.5pt;border:solid black 1.0pt;border-top:none; padding:3.75pt 5.4pt 3.75pt 5.4pt;height:18.0pt\" width=\"118\">销量（百件）/天<br></td><td style=\"width:34.5pt;border-top:none;border-left:none;border-bottom: solid black 1.0pt;border-right:solid black 1.0pt;padding:3.75pt 5.4pt 3.75pt 5.4pt; height:18.0pt\" width=\"46\">0.5<br></td><td style=\"width:49.5pt;border-top:none;border-left:none;border-bottom: solid black 1.0pt;border-right:solid black 1.0pt;padding:3.75pt 5.4pt 3.75pt 5.4pt; height:18.0pt\" width=\"66\">0.6<br></td><td style=\"width:51.0pt;border-top:none;border-left:none;border-bottom: solid black 1.0pt;border-right:solid black 1.0pt;padding:3.75pt 5.4pt 3.75pt 5.4pt; height:18.0pt\" width=\"68\">1<br></td><td style=\"width:48.75pt;border-top:none;border-left:none; border-bottom:solid black 1.0pt;border-right:solid black 1.0pt;padding:3.75pt 5.4pt 3.75pt 5.4pt; height:18.0pt\" width=\"65\">1.4<br></td><td style=\"width:47.25pt;border-top:none;border-left:none; border-bottom:solid black 1.0pt;border-right:solid black 1.0pt;padding:3.75pt 5.4pt 3.75pt 5.4pt; height:18.0pt\" width=\"63\">1.7<br></td></tr></tbody></table> <br>（Ⅰ）经分析发现，可用线性回归模型<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/1a98bb27-1400-42df-bafd-e10df765cfcc/paper.files/image001.png\" alt=\"eqIddc99153f9bcb48299b98ec2ec4033513\">拟合当地该商品销量<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/1a98bb27-1400-42df-bafd-e10df765cfcc/paper.files/image002.png\" alt=\"eqId072d7d6b911b42bc89207e72515ebf5f\">（千件）与返还点数<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/1a98bb27-1400-42df-bafd-e10df765cfcc/paper.files/image003.png\" alt=\"eqId32454977564e4ee18da36bd51156c509\">之间的相关关系.试预测若返回6个点时该商品每天的销量；<br>（Ⅱ）若节日期间营销部对商品进行新一轮调整.已知某地拟购买该商品的消费群体十分庞大，经营销调研机构对其中的200名消费者的返点数额的心理预期值进行了一个抽样调查，得到如下一份频数表：<br><table border=\"1\" cellpadding=\"0\" cellspacing=\"0\"><tbody><tr style=\"height:30.0pt\"><td style=\"width:107.25pt;border:solid black 1.0pt;padding:3.75pt 5.4pt 3.75pt 5.4pt; height:30.0pt\" width=\"143\">返还点数预期值区间<br>（百分比）<br></td><td style=\"width:38.25pt;border:solid black 1.0pt;border-left:none; padding:3.75pt 5.4pt 3.75pt 5.4pt;height:30.0pt\" width=\"51\">[1,3)<br></td><td style=\"width:48.0pt;border:solid black 1.0pt;border-left:none; padding:3.75pt 5.4pt 3.75pt 5.4pt;height:30.0pt\" width=\"64\">[3,5)<br></td><td style=\"width:40.5pt;border:solid black 1.0pt;border-left:none; padding:3.75pt 5.4pt 3.75pt 5.4pt;height:30.0pt\" width=\"54\">[5,7)<br></td><td style=\"width:42.75pt;border:solid black 1.0pt;border-left:none; padding:3.75pt 5.4pt 3.75pt 5.4pt;height:30.0pt\" width=\"57\">[7,9)<br></td><td style=\"width:42.75pt;border:solid black 1.0pt;border-left:none; padding:3.75pt 5.4pt 3.75pt 5.4pt;height:30.0pt\" width=\"57\">[9,11)<br></td><td style=\"width:49.5pt;border:solid black 1.0pt;border-left:none; padding:3.75pt 5.4pt 3.75pt 5.4pt;height:30.0pt\" width=\"66\">[11,13)<br></td></tr><tr style=\"height:24.0pt\"><td style=\"width:107.25pt;border:solid black 1.0pt;border-top:none; padding:3.75pt 5.4pt 3.75pt 5.4pt;height:24.0pt\" width=\"143\">频数<br></td><td style=\"width:38.25pt;border-top:none;border-left:none; border-bottom:solid black 1.0pt;border-right:solid black 1.0pt;padding:3.75pt 5.4pt 3.75pt 5.4pt; height:24.0pt\" width=\"51\">20<br></td><td style=\"width:48.0pt;border-top:none;border-left:none;border-bottom: solid black 1.0pt;border-right:solid black 1.0pt;padding:3.75pt 5.4pt 3.75pt 5.4pt; height:24.0pt\" width=\"64\">60<br></td><td style=\"width:40.5pt;border-top:none;border-left:none;border-bottom: solid black 1.0pt;border-right:solid black 1.0pt;padding:3.75pt 5.4pt 3.75pt 5.4pt; height:24.0pt\" width=\"54\">60<br></td><td style=\"width:42.75pt;border-top:none;border-left:none; border-bottom:solid black 1.0pt;border-right:solid black 1.0pt;padding:3.75pt 5.4pt 3.75pt 5.4pt; height:24.0pt\" width=\"57\">30<br></td><td style=\"width:42.75pt;border-top:none;border-left:none; border-bottom:solid black 1.0pt;border-right:solid black 1.0pt;padding:3.75pt 5.4pt 3.75pt 5.4pt; height:24.0pt\" width=\"57\">20<br></td><td style=\"width:49.5pt;border-top:none;border-left:none;border-bottom: solid black 1.0pt;border-right:solid black 1.0pt;padding:3.75pt 5.4pt 3.75pt 5.4pt; height:24.0pt\" width=\"66\">10<br></td></tr></tbody></table> <br>将对返点点数的心理预期值在<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/1a98bb27-1400-42df-bafd-e10df765cfcc/paper.files/image004.png\" alt=\"eqIdba02b4a2f80c4071a5adde28105f9795\">和<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/1a98bb27-1400-42df-bafd-e10df765cfcc/paper.files/image005.png\" alt=\"eqIdd2a78391654a4ff29a6a989bfb7fff01\">的消费者分别定义为“欲望紧缩型”消费者和“欲望膨胀型”消费者，现采用分层抽样的方法从位于这两个区间的30名消费者中随机抽取6名，再从这6人中随机抽取3名进行跟踪调查，求抽出的3人中至少有1名“欲望膨胀型”消费者的概率.</div>","QuesAnswer":"","QuesParse":"","UseSum":52,"AvgScore":5.0,"ParseAnswerKey":"0f0c9e0bbd1664bd5e6d583177f22a8d","QuesAttribute":0,"PaperSource":[{"Id":524331,"PaperTitle":"甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题","LearnGrade":12,"PaperType":9,"Province":620000,"PaperYear":2019,"PaperLevel":51,"AddTimeOn":"2019-06-08T22:26:16","SchoolId":71389,"MatchingDegree":0}]},{"ID":8106164,"Guid":"a1e980e9-4d04-42e3-84e2-568e56af8ec5","Title":"步步高高二数学暑假作业：暑假学习效果验收考试","From":"","Knowledge":"","QuesType":{"ID":2703,"Name":"解答题","IsSelectType":false,"OrderIndex":4,"ParentId":0},"QuesAbility":{"ID":1,"Name":"了解和识记"},"QuesDiff":{"ID":2,"DifValue":0.85,"Name":"较易"},"Categories":"<item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27932\" type=\"1\">空间向量与立体几何</category><category id=\"28804\" type=\"1\">空间几何体</category><category id=\"28810\" type=\"1\">空间几何体的表面积与体积</category><category id=\"28875\" type=\"1\">柱、锥、台的体积</category><category id=\"28884\" type=\"1\">柱体体积的有关计算</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27932\" type=\"1\">空间向量与立体几何</category><category id=\"28804\" type=\"1\">空间几何体</category><category id=\"28810\" type=\"1\">空间几何体的表面积与体积</category><category id=\"28875\" type=\"1\">柱、锥、台的体积</category><category id=\"28885\" type=\"1\">锥体体积的有关计算</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27932\" type=\"1\">空间向量与立体几何</category><category id=\"28805\" type=\"1\">点、直线、平面之间的位置关系</category><category id=\"28900\" type=\"1\">直线、平面垂直的判定与性质</category><category id=\"28954\" type=\"1\">线面垂直的性质</category><category id=\"28973\" type=\"1\">线面垂直证明线线垂直</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79540\" type=\"0\">选修2-1</category><category id=\"79542\" type=\"0\">第二章 空间向量与立体几何</category><category id=\"79564\" type=\"0\">§5 夹角的计算</category><category id=\"79572\" type=\"0\">5.3 直线与平面的夹角</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"79935\" type=\"0\">必修2</category><category id=\"79937\" type=\"0\">第二章 点、直线、平面之间的位置关系</category><category id=\"79954\" type=\"0\">2.3 直线、平面垂直的判定及其性质</category><category id=\"79966\" type=\"0\">2.3.3 直线与平面垂直的性质</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80550\" type=\"0\">必修2</category><category id=\"80551\" type=\"0\">第一章 立体几何初步</category><category id=\"80555\" type=\"0\">1.2 点、线、面之间的位置关系</category><category id=\"80566\" type=\"0\">1.2.3 空间中的垂直关系</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80763\" type=\"0\">选修2-1</category><category id=\"80766\" type=\"0\">第三章 空间向量与立体几何</category><category id=\"80793\" type=\"0\">3.2 空间向量在立体几何中的应用</category><category id=\"80801\" type=\"0\">3.2.3 直线与平面的夹角</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81228\" type=\"0\">选修2-1</category><category id=\"81231\" type=\"0\">第3章 空间向量与立体几何</category><category id=\"81258\" type=\"0\">3.2 空间向量的应用</category><category id=\"81265\" type=\"0\">3.2.1 直线的方向向量与平面的法向量</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81792\" type=\"0\">必修第三册</category><category id=\"81793\" type=\"0\">第6章 立体几何初步</category><category id=\"81797\" type=\"0\">6.2 空间的直线与平面</category><category id=\"81804\" type=\"0\">6.2.3 垂直关系</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81945\" type=\"0\">选修2-1</category><category id=\"81948\" type=\"0\">第3章 空间向量与立体几何</category><category id=\"81973\" type=\"0\">3.4 直线的方向向量</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81945\" type=\"0\">选修2-1</category><category id=\"81948\" type=\"0\">第3章 空间向量与立体几何</category><category id=\"81974\" type=\"0\">3.5 直线与平面的垂直关系</category></item>","ChildNum":1,"Time":"2019-05-23T17:50:40","QuesBody":"<div>【题文】如图，三棱柱<i>ABC</i>－<i>A</i><sub>1</sub><i>B</i><sub>1</sub><i>C</i><sub>1</sub>中，侧棱垂直于底面，∠<i>ACB</i>＝90°，<i>AC</i>＝<i>BC</i>＝<img style=\"vertical-align:middle;\" src=\"Upload/2019-05/25/cdb1796d-8b72-4d4c-9b66-32145d853a99/paper.files/image001.png\"><i>AA</i><sub>1</sub>，<i>D</i>是棱<i>AA</i><sub>1</sub>的中点．<br><img style=\"vertical-align:middle;\" src=\"Upload/2019-05/25/cdb1796d-8b72-4d4c-9b66-32145d853a99/paper.files/image002.jpg\"><br>(1)证明：平面<i>BDC</i><sub>1</sub>⊥平面<i>BDC</i>；<br>(2)平面<i>BDC</i><sub>1</sub>分此棱柱为两部分，求这两部分体积的比．</div>","QuesAnswer":"","QuesParse":"","UseSum":196,"AvgScore":5.0,"ParseAnswerKey":"1acc9b5d9190551d6f571b12b93768ec","QuesAttribute":0,"PaperSource":[{"Id":524331,"PaperTitle":"甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题","LearnGrade":12,"PaperType":9,"Province":620000,"PaperYear":2019,"PaperLevel":51,"AddTimeOn":"2019-06-08T22:26:16","SchoolId":71389,"MatchingDegree":0}]},{"ID":8188267,"Guid":"049e1245-9c60-41f1-8ac4-1992f8eed696","Title":"甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题","From":"","Knowledge":"","QuesType":{"ID":2703,"Name":"解答题","IsSelectType":false,"OrderIndex":4,"ParentId":0},"QuesAbility":{"ID":1,"Name":"了解和识记"},"QuesDiff":{"ID":3,"DifValue":0.65,"Name":"一般"},"Categories":"<item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27933\" type=\"1\">平面解析几何</category><category id=\"29045\" type=\"1\">圆锥曲线</category><category id=\"29171\" type=\"1\">椭圆</category><category id=\"29189\" type=\"1\">椭圆的标准方程</category><category id=\"29207\" type=\"1\">根据a、b、c求椭圆标准方程</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27933\" type=\"1\">平面解析几何</category><category id=\"29045\" type=\"1\">圆锥曲线</category><category id=\"29174\" type=\"1\">直线与圆锥曲线的位置关系</category><category id=\"29295\" type=\"1\">直线与椭圆的位置关系</category><category id=\"29317\" type=\"1\">根据直线与椭圆的位置关系求参数或范围</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27933\" type=\"1\">平面解析几何</category><category id=\"29045\" type=\"1\">圆锥曲线</category><category id=\"29174\" type=\"1\">直线与圆锥曲线的位置关系</category><category id=\"29299\" type=\"1\">椭圆中的定点、定值</category><category id=\"29326\" type=\"1\">椭圆中的定值问题</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79458\" type=\"0\">选修1-1</category><category id=\"79460\" type=\"0\">第二章 圆锥曲线与方程</category><category id=\"79482\" type=\"0\">本章复习与测试</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79540\" type=\"0\">选修2-1</category><category id=\"79543\" type=\"0\">第三章 圆锥曲线与方程</category><category id=\"79576\" type=\"0\">§4 曲线与方程</category><category id=\"79586\" type=\"0\">4.3 直线与圆锥曲线的交点</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"80101\" type=\"0\">选修1-1</category><category id=\"80103\" type=\"0\">第二章 圆锥曲线与方程</category><category id=\"80125\" type=\"0\">本章复习与测试</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"80171\" type=\"0\">选修2-1</category><category id=\"80173\" type=\"0\">第二章 圆锥曲线与方程</category><category id=\"80196\" type=\"0\">本章复习与测试</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80699\" type=\"0\">选修1-1</category><category id=\"80701\" type=\"0\">第二章 圆锥曲线与方程</category><category id=\"80717\" type=\"0\">本章复习与测试</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80763\" type=\"0\">选修2-1</category><category id=\"80765\" type=\"0\">第二章 圆锥曲线与方程</category><category id=\"80782\" type=\"0\">2.5 直线与圆锥曲线</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81228\" type=\"0\">选修2-1</category><category id=\"81230\" type=\"0\">第2章 圆锥曲线与方程</category><category id=\"81247\" type=\"0\">本章复习与测试</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81878\" type=\"0\">选修1-1</category><category id=\"81880\" type=\"0\">第2章 圆锥曲线与方程</category><category id=\"81894\" type=\"0\">2.4 圆锥曲线的应用</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81945\" type=\"0\">选修2-1</category><category id=\"81947\" type=\"0\">第2章 圆锥曲线与方程</category><category id=\"81961\" type=\"0\">2.4 圆锥曲线的应用</category></item>","ChildNum":1,"Time":"2019-06-08T22:27:15","QuesBody":"<div>【题文】椭圆C:<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/fb2b9e9c-0be4-4aba-bd9c-0e938078da76/paper.files/image001.png\" alt=\"eqIde9b1737ca0154a95ad75cc03d12cccb4\">(a>b>0)的左、右焦点分别为<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/fb2b9e9c-0be4-4aba-bd9c-0e938078da76/paper.files/image002.png\" alt=\"eqIda3295b0faa56453483a54207dda2feb3\">，离心率为<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/fb2b9e9c-0be4-4aba-bd9c-0e938078da76/paper.files/image003.png\" alt=\"eqIdcf32b3b919f04cc18988c622e750e9f1\">，过焦点<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/fb2b9e9c-0be4-4aba-bd9c-0e938078da76/paper.files/image004.png\" alt=\"eqId0cfe24caa0fc44de8e0fcd142d6c1377\">且垂直于x轴的直线被椭圆C截得的线段长为1．<br>（Ⅰ）求椭圆C的方程；<br>（Ⅱ）已知点M（0，-1），直线l经过点N（2，1）且与椭圆C相交于A,B两点（异于点M），记直线MA的斜率为<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/fb2b9e9c-0be4-4aba-bd9c-0e938078da76/paper.files/image005.png\" alt=\"eqIdd4bf9298f0db4fb5afb67e0d739f3074\">，直线MB的斜率为<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/fb2b9e9c-0be4-4aba-bd9c-0e938078da76/paper.files/image006.png\" alt=\"eqId75fdb198d83447e59e31c1f4923cc3bc\">，证明<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/fb2b9e9c-0be4-4aba-bd9c-0e938078da76/paper.files/image007.png\" alt=\"eqIde493a2c801c647e181aa02327145bfec\"> 为定值，并求出该定值.</div>","QuesAnswer":"","QuesParse":"","UseSum":38,"AvgScore":5.0,"ParseAnswerKey":"1cea7484faa2ea1a9823154a1e0aeb12","QuesAttribute":0,"PaperSource":[{"Id":524331,"PaperTitle":"甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题","LearnGrade":12,"PaperType":9,"Province":620000,"PaperYear":2019,"PaperLevel":51,"AddTimeOn":"2019-06-08T22:26:16","SchoolId":71389,"MatchingDegree":0}]},{"ID":7893272,"Guid":"de1dd881-4082-4e82-9a2d-f334bce2ec0d","Title":"黑龙江省齐齐哈尔市2019届高三第二次模拟考试数学（文科）试题","From":"","Knowledge":"","QuesType":{"ID":2703,"Name":"解答题","IsSelectType":false,"OrderIndex":4,"ParentId":0},"QuesAbility":{"ID":1,"Name":"了解和识记"},"QuesDiff":{"ID":3,"DifValue":0.65,"Name":"一般"},"Categories":"<item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27927\" type=\"1\">函数与导数</category><category id=\"28044\" type=\"1\">导数及其应用</category><category id=\"28259\" type=\"1\">导数在研究函数中的作用</category><category id=\"28278\" type=\"1\">利用导数研究函数的单调性</category><category id=\"28282\" type=\"1\">利用导数求函数的单调区间</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"27927\" type=\"1\">函数与导数</category><category id=\"28044\" type=\"1\">导数及其应用</category><category id=\"28260\" type=\"1\">导数的综合应用</category><category id=\"28294\" type=\"1\">导数在函数中的其他应用</category><category id=\"28299\" type=\"1\">利用导数研究函数的零点</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79244\" type=\"0\">必修1</category><category id=\"79246\" type=\"0\">第二章 函数</category><category id=\"79258\" type=\"0\">§3 函数的单调性</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79458\" type=\"0\">选修1-1</category><category id=\"79462\" type=\"0\">第四章 导数应用</category><category id=\"79500\" type=\"0\">本章复习与测试</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79458\" type=\"0\">选修1-1</category><category id=\"79462\" type=\"0\">第四章 导数应用</category><category id=\"79498\" type=\"0\">§1 函数的单调性与极值</category><category id=\"79501\" type=\"0\">1.1 导数与函数的单调性</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79587\" type=\"0\">选修2-2</category><category id=\"79590\" type=\"0\">第三章 导数应用</category><category id=\"79615\" type=\"0\">本章复习与测试</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79587\" type=\"0\">选修2-2</category><category id=\"79590\" type=\"0\">第三章 导数应用</category><category id=\"79613\" type=\"0\">§1 函数的单调性与极值</category><category id=\"79616\" type=\"0\">1.1 导数与函数的单调性</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"79904\" type=\"0\">必修1</category><category id=\"79905\" type=\"0\">第一章 集合与函数概念</category><category id=\"79911\" type=\"0\">1.3 函数的基本性质</category><category id=\"79918\" type=\"0\">1.3.1 单调性与最大（小）值</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"80101\" type=\"0\">选修1-1</category><category id=\"80104\" 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id=\"80699\" type=\"0\">选修1-1</category><category id=\"80702\" type=\"0\">第三章 导数及其应用</category><category id=\"80727\" type=\"0\">本章复习与测试</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80699\" type=\"0\">选修1-1</category><category id=\"80702\" type=\"0\">第三章 导数及其应用</category><category id=\"80726\" type=\"0\">3.3 导数的应用</category><category id=\"80734\" type=\"0\">3.3.1 利用导数判断函数的单调性</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80804\" type=\"0\">选修2-2</category><category id=\"80805\" type=\"0\">第一章 导数及其应用</category><category id=\"80813\" type=\"0\">本章复习与测试</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80804\" type=\"0\">选修2-2</category><category id=\"80805\" type=\"0\">第一章 导数及其应用</category><category id=\"80811\" type=\"0\">1.3 导数的应用</category><category id=\"80820\" type=\"0\">1.3.1 利用导数判断函数的单调性</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81005\" type=\"0\">必修1</category><category id=\"81007\" type=\"0\">第2章 函数</category><category id=\"81015\" type=\"0\">2.2 函数的简单性质</category><category id=\"81020\" type=\"0\">2.2.1 函数的单调性</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81167\" type=\"0\">选修1-1</category><category id=\"81170\" type=\"0\">第3章 导数及其应用</category><category id=\"81196\" type=\"0\">本章复习与测试</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81167\" type=\"0\">选修1-1</category><category id=\"81170\" type=\"0\">第3章 导数及其应用</category><category id=\"81194\" type=\"0\">3.3 导数在研究函数中的应用</category><category id=\"81201\" type=\"0\">3.3.1 单调性</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81268\" type=\"0\">选修2-2</category><category id=\"81269\" type=\"0\">第1章 导数及其应用</category><category id=\"81278\" type=\"0\">本章复习与测试</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81268\" type=\"0\">选修2-2</category><category id=\"81269\" type=\"0\">第1章 导数及其应用</category><category id=\"81275\" type=\"0\">1.3 导数在研究函数中的应用</category><category id=\"81284\" type=\"0\">1.3.1 单调性</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81878\" type=\"0\">选修1-1</category><category id=\"81881\" type=\"0\">第3章 导数及其应用</category><category id=\"81904\" type=\"0\">3.3 导数在研究函数中的应用</category><category id=\"81913\" type=\"0\">3.3.1 利用导数研究函数的单调性</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81980\" type=\"0\">选修2-2</category><category id=\"81981\" type=\"0\">第4章 导数及其应用</category><category id=\"81987\" type=\"0\">4.3 导数在研究函数中的应用</category><category id=\"81997\" type=\"0\">4.3.1 利用导数研究函数的单调性</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81878\" type=\"0\">选修1-1</category><category id=\"81881\" type=\"0\">第3章 导数及其应用</category><category id=\"81906\" type=\"0\">本章复习与测试</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"81980\" type=\"0\">选修2-2</category><category id=\"81981\" type=\"0\">第4章 导数及其应用</category><category id=\"81990\" type=\"0\">本章复习与测试</category></item><item><category id=\"82158\" type=\"0\">大纲版</category><category id=\"82159\" type=\"0\">高一上册</category><category id=\"82161\" type=\"0\">第二章 函数</category><category id=\"82176\" type=\"0\">一 函数</category><category id=\"82181\" type=\"0\">2.3 函数的单调性</category></item><item><category id=\"82158\" type=\"0\">大纲版</category><category id=\"82242\" type=\"0\">高三全册</category><category id=\"82245\" type=\"0\">第三章 导数</category><category id=\"82275\" type=\"0\">3.6 函数的单调性</category></item>","ChildNum":1,"Time":"2019-04-16T20:23:54","QuesBody":"<div>【题文】已知函数<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/16/9f7b2256-8de6-4b66-a4cf-a83d1cc00ced/paper.files/image354.png\">.<br>（1）当<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/16/9f7b2256-8de6-4b66-a4cf-a83d1cc00ced/paper.files/image355.png\">时，讨论函数<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/16/9f7b2256-8de6-4b66-a4cf-a83d1cc00ced/paper.files/image049.png\">的单调性；<br>（2）若函数<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/16/9f7b2256-8de6-4b66-a4cf-a83d1cc00ced/paper.files/image356.png\">在<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/16/9f7b2256-8de6-4b66-a4cf-a83d1cc00ced/paper.files/image357.png\">（<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/16/9f7b2256-8de6-4b66-a4cf-a83d1cc00ced/paper.files/image358.png\">为自然对数的底）时取得极值，且函数<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/16/9f7b2256-8de6-4b66-a4cf-a83d1cc00ced/paper.files/image359.png\">在<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/16/9f7b2256-8de6-4b66-a4cf-a83d1cc00ced/paper.files/image360.png\">上有两个零点，求实数<img style=\"vertical-align:middle;\" src=\"Upload/2019-04/16/9f7b2256-8de6-4b66-a4cf-a83d1cc00ced/paper.files/image361.png\">的取值范围.</div>","QuesAnswer":"","QuesParse":"","UseSum":399,"AvgScore":5.0,"ParseAnswerKey":"ac21d51f735eba9eda12e8411d26a1d9","QuesAttribute":0,"PaperSource":[{"Id":496538,"PaperTitle":"黑龙江省齐齐哈尔市2019届高三第二次模拟考试数学（文科）试题","LearnGrade":12,"PaperType":9,"Province":230000,"PaperYear":2019,"PaperLevel":41,"AddTimeOn":"2019-04-16T20:23:04","SchoolId":0,"MatchingDegree":0},{"Id":524331,"PaperTitle":"甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题","LearnGrade":12,"PaperType":9,"Province":620000,"PaperYear":2019,"PaperLevel":51,"AddTimeOn":"2019-06-08T22:26:16","SchoolId":71389,"MatchingDegree":0}]},{"ID":4988466,"Guid":"040edd67-9f48-47c2-bd91-ce9dbe924b44","Title":"河南省豫南九校（中原名校）2017届高三下学期质量考评八数学（文）试题","From":"","Knowledge":"","QuesType":{"ID":2703,"Name":"解答题","IsSelectType":false,"OrderIndex":4,"ParentId":0},"QuesAbility":{"ID":1,"Name":"了解和识记"},"QuesDiff":{"ID":3,"DifValue":0.65,"Name":"一般"},"Categories":"<item><category 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type=\"0\">选修4-4</category><category id=\"80937\" type=\"0\">第二章 参数方程</category><category id=\"80953\" type=\"0\">2.1 曲线的参数方程</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80935\" type=\"0\">选修4-4</category><category id=\"80937\" type=\"0\">第二章 参数方程</category><category id=\"80954\" type=\"0\">2.2 直线和圆的参数方程</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80935\" type=\"0\">选修4-4</category><category id=\"80937\" type=\"0\">第二章 参数方程</category><category id=\"80955\" type=\"0\">2.3 圆锥曲线的参数方程</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80935\" type=\"0\">选修4-4</category><category id=\"80937\" type=\"0\">第二章 参数方程</category><category id=\"80953\" type=\"0\">2.1 曲线的参数方程</category><category id=\"80959\" type=\"0\">2.1.2 曲线的参数方程</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80935\" type=\"0\">选修4-4</category><category id=\"80937\" type=\"0\">第二章 参数方程</category><category id=\"80954\" type=\"0\">2.2 直线和圆的参数方程</category><category id=\"80960\" type=\"0\">2.2.1 直线的参数方程</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80935\" type=\"0\">选修4-4</category><category id=\"80937\" type=\"0\">第二章 参数方程</category><category id=\"80954\" type=\"0\">2.2 直线和圆的参数方程</category><category id=\"80961\" type=\"0\">2.2.2 圆的参数方程</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80935\" type=\"0\">选修4-4</category><category id=\"80937\" type=\"0\">第二章 参数方程</category><category id=\"80955\" type=\"0\">2.3 圆锥曲线的参数方程</category><category id=\"80962\" type=\"0\">2.3.1 椭圆的参数方程</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80935\" type=\"0\">选修4-4</category><category id=\"80937\" type=\"0\">第二章 参数方程</category><category id=\"80955\" type=\"0\">2.3 圆锥曲线的参数方程</category><category id=\"80963\" type=\"0\">2.3.2 抛物线的参数方程</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80935\" type=\"0\">选修4-4</category><category id=\"80937\" type=\"0\">第二章 参数方程</category><category id=\"80955\" type=\"0\">2.3 圆锥曲线的参数方程</category><category id=\"80964\" type=\"0\">2.3.3 双曲线的参数方程</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"82093\" type=\"0\">选修4-4</category><category id=\"82095\" type=\"0\">第2章 参数方程</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"82093\" type=\"0\">选修4-4</category><category id=\"82095\" type=\"0\">第2章 参数方程</category><category id=\"82105\" type=\"0\">2.2 直线的参数方程</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"82093\" type=\"0\">选修4-4</category><category id=\"82095\" type=\"0\">第2章 参数方程</category><category id=\"82106\" type=\"0\">2.3 圆锥曲线的参数方程</category></item>","ChildNum":1,"Time":"2017-04-28T06:37:05","QuesBody":"<div>【题文】己知直线<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/23/15b597b0-ca7e-4472-9501-3412d6aec48d/paper.files/image001.png\" alt=\"eqId417e80f1349244878d01fe90e0891f5f\">的参数方程为<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/23/15b597b0-ca7e-4472-9501-3412d6aec48d/paper.files/image002.png\" alt=\"eqIde09fdb2bee85401b88b05f8df2489df4\">（t为参数），曲线C的极坐标方程为<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/23/15b597b0-ca7e-4472-9501-3412d6aec48d/paper.files/image003.png\" alt=\"eqId1cfb7807a04645cf869d1c798459df0b\">，直线<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/23/15b597b0-ca7e-4472-9501-3412d6aec48d/paper.files/image001.png\" alt=\"eqId417e80f1349244878d01fe90e0891f5f\">与曲线C交于A、B两点，点<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/23/15b597b0-ca7e-4472-9501-3412d6aec48d/paper.files/image004.png\" alt=\"eqIdeab66d0e6a4f41d98b27cb1d9a511830\">．<br>（1）求直线<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/23/15b597b0-ca7e-4472-9501-3412d6aec48d/paper.files/image001.png\" alt=\"eqId417e80f1349244878d01fe90e0891f5f\">的普通方程和曲线C的直角坐标方程；<br>（2）求<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/23/15b597b0-ca7e-4472-9501-3412d6aec48d/paper.files/image005.png\" alt=\"eqId3b403ca75d384bcfa75092d4ebd8e540\">的值．</div>","QuesAnswer":"","QuesParse":"","UseSum":969,"AvgScore":5.0,"ParseAnswerKey":"8d26ee6b5c042f0080d368d08276c5d7","QuesAttribute":2,"PaperSource":[{"Id":229459,"PaperTitle":"2017届河南省豫南九校（中原名校）高三下学期质量考评八数学（文）试卷（带解析）","LearnGrade":12,"PaperType":3,"Province":410000,"PaperYear":2017,"PaperLevel":41,"AddTimeOn":"2017-05-13T11:46:08","SchoolId":0,"MatchingDegree":0},{"Id":264272,"PaperTitle":"河南省中原名校（即豫南九校）2018届高三上学期第二次质量考评数学（文）试题","LearnGrade":12,"PaperType":9,"Province":410000,"PaperYear":2017,"PaperLevel":41,"AddTimeOn":"2017-09-30T09:52:56","SchoolId":0,"MatchingDegree":0},{"Id":382499,"PaperTitle":"河南省中原名校2018届高三高考预测金卷 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type=\"0\">选修4-5</category><category id=\"80485\" type=\"0\">第三讲 柯西不等式与排序不等式</category><category id=\"80500\" type=\"0\">一 二维形式的柯西不等式</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"80482\" type=\"0\">选修4-5</category><category id=\"80485\" type=\"0\">第三讲 柯西不等式与排序不等式</category><category id=\"80501\" type=\"0\">二 一般形式的柯西不等式</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80967\" type=\"0\">选修4-5</category><category id=\"80969\" type=\"0\">第二章 柯西不等式与排序不等式及其应用</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80967\" type=\"0\">选修4-5</category><category id=\"80969\" type=\"0\">第二章 柯西不等式与排序不等式及其应用</category><category id=\"80985\" type=\"0\">2.1 柯西不等式</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80967\" type=\"0\">选修4-5</category><category id=\"80969\" type=\"0\">第二章 柯西不等式与排序不等式及其应用</category><category id=\"80985\" type=\"0\">2.1 柯西不等式</category><category id=\"80990\" type=\"0\">2.1.1 平面上的柯西不等式的代数和向量形式</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81462\" type=\"0\">选修4-5</category><category id=\"81466\" type=\"0\">5.4 几个著名的不等式</category><category id=\"81476\" type=\"0\">5.4.1 柯西不等式</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81462\" type=\"0\">选修4-5</category><category id=\"81467\" type=\"0\">5.5 运用不等式求最大（小）值</category><category id=\"81480\" type=\"0\">5.5.2 运用柯西不等式求最大（小）值</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"82110\" type=\"0\">选修4-5</category><category id=\"82115\" type=\"0\">第5章 三个重要不等式</category><category id=\"82133\" type=\"0\">5.1 柯西不等式</category></item>","ChildNum":1,"Time":"2019-06-08T22:25:43","QuesBody":"<div>【题文】已知函数<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/d6ffee61-6436-4349-9a30-3fa8a9dd33eb/paper.files/image001.png\" alt=\"eqIdd33a8931d4094787b5607b2ae60060b4\">.<br>（Ⅰ）解不等式<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/d6ffee61-6436-4349-9a30-3fa8a9dd33eb/paper.files/image002.png\" alt=\"eqId11ccb1b45b954bc3930930f5108719a3\">；<br>（Ⅱ）记函数<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/d6ffee61-6436-4349-9a30-3fa8a9dd33eb/paper.files/image003.png\" alt=\"eqId6f13759e937144069819aed2ae5a1057\">的最小值为<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/d6ffee61-6436-4349-9a30-3fa8a9dd33eb/paper.files/image004.png\" alt=\"eqId3a4208e0040c42ed8b09de2cae9d562e\">，若<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/d6ffee61-6436-4349-9a30-3fa8a9dd33eb/paper.files/image005.png\" alt=\"eqId0ce93bfa1f6a4a23b3258410dd19847a\">均为正实数，且<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/d6ffee61-6436-4349-9a30-3fa8a9dd33eb/paper.files/image006.png\" alt=\"eqId3da22b1fc98f4acfa050e5ca807ad3da\">，求<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/18/d6ffee61-6436-4349-9a30-3fa8a9dd33eb/paper.files/image007.png\" alt=\"eqId497e16532fd649c09952d5e173c3eef8\">的最小值.</div>","QuesAnswer":"","QuesParse":"","UseSum":72,"AvgScore":5.0,"ParseAnswerKey":"8dcf72c467c16d7cba14337b190ef5b7","QuesAttribute":0,"PaperSource":[{"Id":524330,"PaperTitle":"甘肃省兰州市第一中学2019届高三6月最后高考冲刺模拟数学（理）试题","LearnGrade":12,"PaperType":9,"Province":620000,"PaperYear":2019,"PaperLevel":51,"AddTimeOn":"2019-06-08T22:24:15","SchoolId":71389,"MatchingDegree":0},{"Id":524331,"PaperTitle":"甘肃省兰州市第一中学2019届高三6月高考冲刺模拟数学（文）试题","LearnGrade":12,"PaperType":9,"Province":620000,"PaperYear":2019,"PaperLevel":51,"AddTimeOn":"2019-06-08T22:26:16","SchoolId":71389,"MatchingDegree":0}]}],"bankId":0,"PaperQuesCount":23,"ReadSum":43,"schoolId":0}
，复数
满足
，则
( )
