2016年全国高中数学联赛四川赛区预赛试题

{"ID":434395,"Title":"2016年全国高中数学联赛四川赛区预赛试题","Note":"2016年全国高中数学联赛四川赛区预赛试题","LearnGrade":{"ID":12,"Name":"高三","PaperTypeList":null},"PaperType":{"ID":7,"Name":"竞赛"},"Province":{"ID":510000,"Name":"四川省","ShortName":null},"PaperYear":{"ID":2016,"Name":"2016年"},"PaperLevel":{"ID":41,"Name":"普通"},"Time":"2018-12-05T19:48:19","QuesList":[{"ID":7264413,"Guid":"002a0f5a-a534-415a-b25b-34fb11242283","Title":"2016年全国高中数学联赛四川赛区预赛试题","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=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132858\" type=\"1\">三角函数</category><category id=\"132893\" type=\"1\">正弦、余弦定理</category></item>","ChildNum":1,"Time":"2018-12-05T19:50:34","QuesBody":"<div>【题文】在△ABC中，∠A、∠B、∠C的对边长分别为a、b、c.命题<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image001.png\">，且b+c=2a；命题<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image002.png\">为正三角形.则命题P是命题q的（）条件.<br>A. 充分必要<br>B. 充分但不必要<br>C. 必要但不充分<br>D. 既不充分又不必要</div>","QuesAnswer":"","QuesParse":"","UseSum":24,"AvgScore":5.0,"ParseAnswerKey":"e029eec963a424e618e138fdc9079053","QuesAttribute":2,"QuesAttributes":{"ID":2,"Name":"章内综合题"},"TitleAbbreviation":"2016·四川高三竞赛","PaperSource":[{"Id":434395,"PaperTitle":"2016年全国高中数学联赛四川赛区预赛试题","LearnGrade":12,"PaperType":7,"Province":510000,"PaperYear":2016,"PaperLevel":41,"AddTimeOn":"2018-12-05T19:48:19","SchoolId":0,"MatchingDegree":1}]},{"ID":7264414,"Guid":"6665a007-7294-46fc-9b2d-1a6889ee898b","Title":"2016年全国高中数学联赛四川赛区预赛试题","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=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132866\" type=\"1\">复数</category><category id=\"132976\" type=\"1\">复数的几个形式</category><category id=\"132981\" type=\"1\">复数的三角形式</category></item>","ChildNum":1,"Time":"2018-12-05T19:50:35","QuesBody":"<div>【题文】若复数<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image005.png\">，则<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image006.png\">（）<table name=\"optionsTable\" cellpadding=\"0\" cellspacing=\"0\" width=\"100%\"><tbody><tr><td width=\"25%\">A．-1</td><td width=\"25%\">B．<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image007.png\"></td><td width=\"25%\">C．<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image008.png\"></td><td width=\"25%\">D．1</td></tr></tbody></table></div>","QuesAnswer":"","QuesParse":"","UseSum":25,"AvgScore":5.0,"ParseAnswerKey":"53b19f8826fb0890929d1afa0edd3b00","QuesAttribute":2,"QuesAttributes":{"ID":2,"Name":"章内综合题"},"TitleAbbreviation":"2016·四川高三竞赛","PaperSource":[{"Id":434395,"PaperTitle":"2016年全国高中数学联赛四川赛区预赛试题","LearnGrade":12,"PaperType":7,"Province":510000,"PaperYear":2016,"PaperLevel":41,"AddTimeOn":"2018-12-05T19:48:19","SchoolId":0,"MatchingDegree":1}]},{"ID":7264415,"Guid":"bb4bf8fe-ecee-45ee-9e67-04034b1eba9e","Title":"2016年全国高中数学联赛四川赛区预赛试题","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=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132857\" type=\"1\">函数</category><category id=\"132881\" type=\"1\">初等函数</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132857\" type=\"1\">函数</category><category id=\"132885\" type=\"1\">函数的最大值和最小值</category></item>","ChildNum":1,"Time":"2018-12-05T19:50:35","QuesBody":"<div>【题文】已知函数<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image011.png\">，当<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image012.png\">时，记<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image013.png\">的最小值为m.则m的最大值为（）.<table name=\"optionsTable\" cellpadding=\"0\" cellspacing=\"0\" width=\"100%\"><tbody><tr><td width=\"25%\">A．-2</td><td width=\"25%\">B．0</td><td width=\"25%\">C．<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image014.png\"></td><td width=\"25%\">D．l</td></tr></tbody></table></div>","QuesAnswer":"","QuesParse":"","UseSum":29,"AvgScore":5.0,"ParseAnswerKey":"9566a67e9032b89b7480937e258ce188","QuesAttribute":2,"QuesAttributes":{"ID":2,"Name":"章内综合题"},"TitleAbbreviation":"2016·四川高三竞赛","PaperSource":[{"Id":434395,"PaperTitle":"2016年全国高中数学联赛四川赛区预赛试题","LearnGrade":12,"PaperType":7,"Province":510000,"PaperYear":2016,"PaperLevel":41,"AddTimeOn":"2018-12-05T19:48:19","SchoolId":0,"MatchingDegree":1}]},{"ID":7264416,"Guid":"49f4e0be-d246-4186-a47b-c114e836b2a1","Title":"2016年全国高中数学联赛四川赛区预赛试题","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":4,"DifValue":0.4,"Name":"较难"},"Categories":"<item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132870\" type=\"1\">初等数论</category><category id=\"133038\" type=\"1\">素数和合数</category></item>","ChildNum":1,"Time":"2018-12-05T19:50:36","QuesBody":"<div>【题文】对任意正整数n与<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image021.png\">，<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image022.png\">表示不超过<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image023.png\">（<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image024.png\">表示不超过实数x的最大整数）且与n互素的正整数的个数.则<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image025.png\">（）.<table name=\"optionsTable\" cellpadding=\"0\" cellspacing=\"0\" width=\"100%\"><tbody><tr><td width=\"25%\">A．l1</td><td width=\"25%\">B．13</td><td width=\"25%\">C．14</td><td width=\"25%\">D．19</td></tr></tbody></table></div>","QuesAnswer":"","QuesParse":"","UseSum":30,"AvgScore":5.0,"ParseAnswerKey":"b5805b0b92adc57e937809bf5e2b1c85","QuesAttribute":0,"QuesAttributes":{"ID":0,"Name":""},"TitleAbbreviation":"2016·四川高三竞赛","PaperSource":[{"Id":434395,"PaperTitle":"2016年全国高中数学联赛四川赛区预赛试题","LearnGrade":12,"PaperType":7,"Province":510000,"PaperYear":2016,"PaperLevel":41,"AddTimeOn":"2018-12-05T19:48:19","SchoolId":0,"MatchingDegree":1}]},{"ID":7264417,"Guid":"597c9f5f-82ea-4579-a476-70b51f182b4b","Title":"2016年全国高中数学联赛四川赛区预赛试题","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=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132860\" type=\"1\">数列</category><category id=\"132898\" type=\"1\">数列通项公式求解</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132860\" type=\"1\">数列</category><category id=\"132899\" type=\"1\">数列求和</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132869\" type=\"1\">数学归纳法</category><category id=\"133030\" type=\"1\">第一数学归纳法</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132870\" type=\"1\">初等数论</category><category id=\"133037\" type=\"1\">同余及孙子定理</category></item>","ChildNum":1,"Time":"2018-12-05T19:50:36","QuesBody":"<div>【题文】设数列<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image027.png\">满足<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image028.png\">，<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image029.png\">.若<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image030.png\">为<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image027.png\">的前n项和，则<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image031.png\">的个位数字为（）.<table name=\"optionsTable\" cellpadding=\"0\" cellspacing=\"0\" width=\"100%\"><tbody><tr><td width=\"25%\">A．l</td><td width=\"25%\">B．2</td><td width=\"25%\">C．5</td><td width=\"25%\">D．6</td></tr></tbody></table></div>","QuesAnswer":"","QuesParse":"","UseSum":50,"AvgScore":5.0,"ParseAnswerKey":"3f83fc64d29114a3bdc8f91c8385aeb4","QuesAttribute":0,"QuesAttributes":{"ID":0,"Name":""},"TitleAbbreviation":"2016·四川高三竞赛","PaperSource":[{"Id":434395,"PaperTitle":"2016年全国高中数学联赛四川赛区预赛试题","LearnGrade":12,"PaperType":7,"Province":510000,"PaperYear":2016,"PaperLevel":41,"AddTimeOn":"2018-12-05T19:48:19","SchoolId":0,"MatchingDegree":1}]},{"ID":7264418,"Guid":"fa165665-097c-4418-9a0b-db7854f21e49","Title":"2016年全国高中数学联赛四川赛区预赛试题","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=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132862\" type=\"1\">解析几何</category><category id=\"132927\" type=\"1\">圆锥曲线</category></item>","ChildNum":1,"Time":"2018-12-05T19:50:37","QuesBody":"<div>【题文】已知<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image038.png\">、<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image039.png\">为椭圆与双曲线的公共焦点，P为它们的一个公共点，且<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image040.png\">.则该椭圆与双曲线的离心率之积的最小值为（）.<table name=\"optionsTable\" cellpadding=\"0\" cellspacing=\"0\" width=\"100%\"><tbody><tr><td width=\"25%\">A．<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image041.png\"></td><td width=\"25%\">B．<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image042.png\"></td><td width=\"25%\">C．l</td><td width=\"25%\">D．<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image043.png\"></td></tr></tbody></table></div>","QuesAnswer":"","QuesParse":"","UseSum":41,"AvgScore":5.0,"ParseAnswerKey":"9741752fcae74c2ec379be6d82e4e15c","QuesAttribute":2,"QuesAttributes":{"ID":2,"Name":"章内综合题"},"TitleAbbreviation":"2016·四川高三竞赛","PaperSource":[{"Id":434395,"PaperTitle":"2016年全国高中数学联赛四川赛区预赛试题","LearnGrade":12,"PaperType":7,"Province":510000,"PaperYear":2016,"PaperLevel":41,"AddTimeOn":"2018-12-05T19:48:19","SchoolId":0,"MatchingDegree":1}]},{"ID":6091635,"Guid":"8cf47d5d-d514-4d4c-b295-7cf73abee219","Title":"湖北省武昌2018届元月调研考试数学理科","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":4,"DifValue":0.4,"Name":"较难"},"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=\"29368\" type=\"1\">计数原理</category><category id=\"29490\" type=\"1\">二项式定理</category><category id=\"29529\" type=\"1\">二项式系数</category><category id=\"29537\" type=\"1\">求指定项的二项式系数</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=\"29368\" type=\"1\">计数原理</category><category id=\"29490\" type=\"1\">二项式定理</category><category id=\"29530\" type=\"1\">项的系数</category><category id=\"29540\" type=\"1\">求指定项的系数</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79635\" type=\"0\">选修2-3</category><category id=\"79636\" type=\"0\">第一章 计数原理</category><category id=\"79644\" type=\"0\">§5 二项式定理</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79635\" type=\"0\">选修2-3</category><category id=\"79636\" type=\"0\">第一章 计数原理</category><category id=\"79644\" type=\"0\">§5 二项式定理</category><category id=\"79648\" type=\"0\">5.1 二项式定理</category></item><item><category id=\"79243\" type=\"0\">北师大版</category><category id=\"79635\" type=\"0\">选修2-3</category><category id=\"79636\" type=\"0\">第一章 计数原理</category><category id=\"79644\" type=\"0\">§5 二项式定理</category><category id=\"79649\" type=\"0\">5.2 二项式系数的性质</category></item><item><category id=\"79775\" type=\"0\">沪教版（上海）</category><category id=\"79868\" type=\"0\">高三第一学期</category><category id=\"79871\" type=\"0\">第十六章 排列组合和二项式定理</category><category id=\"79889\" type=\"0\">16.5 二项式定理</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"80254\" type=\"0\">选修2-3</category><category id=\"80255\" type=\"0\">第一章 计数原理</category><category id=\"80261\" type=\"0\">1.3 二项式定理</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"80254\" type=\"0\">选修2-3</category><category id=\"80255\" type=\"0\">第一章 计数原理</category><category id=\"80261\" type=\"0\">1.3 二项式定理</category><category id=\"80265\" type=\"0\">1.3.1 二项式定理</category></item><item><category id=\"79903\" type=\"0\">人教A版</category><category id=\"80254\" type=\"0\">选修2-3</category><category id=\"80255\" type=\"0\">第一章 计数原理</category><category id=\"80261\" type=\"0\">1.3 二项式定理</category><category id=\"80266\" type=\"0\">1.3.2 “杨辉三角”与二项式系数的性质</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80844\" type=\"0\">选修2-3</category><category id=\"80845\" type=\"0\">第一章 计数原理</category><category id=\"80851\" type=\"0\">1.3 二项式定理</category></item><item><category id=\"80512\" type=\"0\">人教B版</category><category id=\"80844\" type=\"0\">选修2-3</category><category id=\"80845\" type=\"0\">第一章 计数原理</category><category id=\"80851\" type=\"0\">1.3 二项式定理</category><category id=\"80855\" type=\"0\">1.3.1 二项式定理</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81303\" type=\"0\">选修2-3</category><category id=\"81304\" type=\"0\">第1章 计数原理</category><category id=\"81312\" type=\"0\">1.5 二项式定理</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81303\" type=\"0\">选修2-3</category><category id=\"81304\" type=\"0\">第1章 计数原理</category><category id=\"81312\" type=\"0\">1.5 二项式定理</category><category id=\"81314\" type=\"0\">1.5.1 二项式定理</category></item><item><category id=\"81004\" type=\"0\">苏教版</category><category id=\"81303\" type=\"0\">选修2-3</category><category id=\"81304\" type=\"0\">第1章 计数原理</category><category id=\"81312\" type=\"0\">1.5 二项式定理</category><category id=\"81315\" type=\"0\">1.5.2 二项式系数的性质及应用</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=\"81640\" type=\"0\">第16章 排列组合和二项式定理</category><category id=\"81665\" type=\"0\">16.5 二项式定理</category></item><item><category id=\"81720\" type=\"0\">湘教版</category><category id=\"82019\" type=\"0\">选修2-3</category><category id=\"82020\" type=\"0\">第7章 计数原理</category><category id=\"82026\" type=\"0\">7.4 二项式定理</category></item><item><category id=\"82158\" type=\"0\">大纲版</category><category id=\"82319\" type=\"0\">高二下册</category><category id=\"82321\" type=\"0\">第十章 排列、组合和二项式定理</category><category id=\"82341\" type=\"0\">10.4 二项式定理</category></item>","ChildNum":1,"Time":"2018-02-27T11:53:01","QuesBody":"<div>【题文】在<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/28/a313b190-0146-4644-9dc1-c30bd517ed8d/paper.files/image001.png\" alt=\"eqIdae9c235942b643d7869cbf0a6baeb58f\">的展开式中<img style=\"vertical-align:middle;\" src=\"Upload/2019-06/28/a313b190-0146-4644-9dc1-c30bd517ed8d/paper.files/image002.png\" alt=\"eqIdf0913d5b3fec4d158489e7ddeaad7da1\">的系数是______．（用具体数作答）</div>","QuesAnswer":"","QuesParse":"","UseSum":805,"AvgScore":5.0,"ParseAnswerKey":"44dc23b87875ee8b3f6c56482b590303","QuesAttribute":0,"QuesAttributes":{"ID":0,"Name":""},"TitleAbbreviation":"2018·湖北高考模拟（理）","PaperSource":[{"Id":321232,"PaperTitle":"湖北省武昌2018届高三元月调研考试数学理科试题","LearnGrade":12,"PaperType":9,"Province":420000,"PaperYear":2018,"PaperLevel":61,"AddTimeOn":"2018-02-27T11:51:15","SchoolId":0,"MatchingDegree":0},{"Id":378213,"PaperTitle":"湖北省宜昌市一中2018届高三考前适应性训练1数学(理)试题","LearnGrade":12,"PaperType":9,"Province":420000,"PaperYear":2018,"PaperLevel":62,"AddTimeOn":"2018-07-24T11:37:55","SchoolId":46926,"MatchingDegree":0},{"Id":434395,"PaperTitle":"2016年全国高中数学联赛四川赛区预赛试题","LearnGrade":12,"PaperType":7,"Province":510000,"PaperYear":2016,"PaperLevel":41,"AddTimeOn":"2018-12-05T19:48:19","SchoolId":0,"MatchingDegree":0},{"Id":537140,"PaperTitle":"宁夏石嘴山市第三中学2018-2019学年高二下学期期中考试数学（理）试题","LearnGrade":11,"PaperType":4,"Province":640000,"PaperYear":2019,"PaperLevel":62,"AddTimeOn":"2019-07-04T16:03:46","SchoolId":73051,"MatchingDegree":0}]},{"ID":7264419,"Guid":"b312971d-a0ce-43a3-a1f4-5689719ecc81","Title":"2016年全国高中数学联赛四川赛区预赛试题","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":3,"DifValue":0.65,"Name":"一般"},"Categories":"<item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132858\" type=\"1\">三角函数</category><category id=\"132892\" type=\"1\">三角恒等式、不等式、最值</category></item>","ChildNum":1,"Time":"2018-12-05T19:50:38","QuesBody":"<div>【题文】若实数<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image073.png\">、<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image074.png\">、<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image075.png\">构成以2为公比的等比数列，sinα、sinβ、sinγ构成等比数列，则cosa=_____.</div>","QuesAnswer":"","QuesParse":"","UseSum":20,"AvgScore":5.0,"ParseAnswerKey":"1c6c90d70c7cb1bc3466954a4d616eb4","QuesAttribute":2,"QuesAttributes":{"ID":2,"Name":"章内综合题"},"TitleAbbreviation":"2016·四川高三竞赛","PaperSource":[{"Id":434395,"PaperTitle":"2016年全国高中数学联赛四川赛区预赛试题","LearnGrade":12,"PaperType":7,"Province":510000,"PaperYear":2016,"PaperLevel":41,"AddTimeOn":"2018-12-05T19:48:19","SchoolId":0,"MatchingDegree":1}]},{"ID":7264420,"Guid":"cc3ea2de-6cd0-48b2-a8de-47e94dd83af9","Title":"2016年全国高中数学联赛四川赛区预赛试题","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":3,"DifValue":0.65,"Name":"一般"},"Categories":"<item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132863\" type=\"1\">立体几何</category><category id=\"132940\" type=\"1\">表面展开图</category></item>","ChildNum":1,"Time":"2018-12-05T19:50:38","QuesBody":"<div>【题文】已知正四棱锥S-ABCD的侧棱长为4，<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image085.png\">，在侧棱SB、SC、SD分别取点E、F、G则空间四边形AEFG周长的最小值为________.</div>","QuesAnswer":"","QuesParse":"","UseSum":25,"AvgScore":5.0,"ParseAnswerKey":"1a0da2489e641dd07430c29aa8019516","QuesAttribute":2,"QuesAttributes":{"ID":2,"Name":"章内综合题"},"TitleAbbreviation":"2016·四川高三竞赛","PaperSource":[{"Id":434395,"PaperTitle":"2016年全国高中数学联赛四川赛区预赛试题","LearnGrade":12,"PaperType":7,"Province":510000,"PaperYear":2016,"PaperLevel":41,"AddTimeOn":"2018-12-05T19:48:19","SchoolId":0,"MatchingDegree":1}]},{"ID":7264421,"Guid":"39a1625e-8b31-4870-9270-cfadefcf6276","Title":"2016年全国高中数学联赛四川赛区预赛试题","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":3,"DifValue":0.65,"Name":"一般"},"Categories":"<item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132859\" type=\"1\">向量</category><category id=\"132896\" type=\"1\">向量的运算</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132859\" type=\"1\">向量</category><category id=\"132897\" type=\"1\">向量的坐标表示，数量积</category></item>","ChildNum":1,"Time":"2018-12-05T19:50:39","QuesBody":"<div>【题文】已知△ABC的外心为O，且<img style=\"vertical-align:middle;\" src=\"Upload/2019-01/14/808ef1db-a7d7-4bac-9f86-3abf98214d6a/paper.files/image001.png\">，则<img style=\"vertical-align:middle;\" src=\"Upload/2019-01/14/808ef1db-a7d7-4bac-9f86-3abf98214d6a/paper.files/image002.png\">________.</div>","QuesAnswer":"","QuesParse":"","UseSum":43,"AvgScore":5.0,"ParseAnswerKey":"d46726dbd5ef4bd649cc40f5fc8631b1","QuesAttribute":0,"QuesAttributes":{"ID":0,"Name":""},"TitleAbbreviation":"2016·四川高三竞赛","PaperSource":[{"Id":434395,"PaperTitle":"2016年全国高中数学联赛四川赛区预赛试题","LearnGrade":12,"PaperType":7,"Province":510000,"PaperYear":2016,"PaperLevel":41,"AddTimeOn":"2018-12-05T19:48:19","SchoolId":0,"MatchingDegree":1}]},{"ID":7264422,"Guid":"31f60875-b6cc-4c0a-94dd-c9e6cfc0740e","Title":"2016年全国高中数学联赛四川赛区预赛试题","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":4,"DifValue":0.4,"Name":"较难"},"Categories":"<item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132861\" type=\"1\">不等式</category><category id=\"132903\" type=\"1\">重要不等式</category><category id=\"132906\" type=\"1\">均值不等式</category></item>","ChildNum":1,"Time":"2018-12-05T19:50:39","QuesBody":"<div>【题文】设实数x、y、z、w满足<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image100.png\">.则<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image101.png\">的最大值为________.</div>","QuesAnswer":"","QuesParse":"","UseSum":34,"AvgScore":5.0,"ParseAnswerKey":"a664aface759b9a8c90b495a4b75057f","QuesAttribute":0,"QuesAttributes":{"ID":0,"Name":""},"TitleAbbreviation":"2016·四川高三竞赛","PaperSource":[{"Id":434395,"PaperTitle":"2016年全国高中数学联赛四川赛区预赛试题","LearnGrade":12,"PaperType":7,"Province":510000,"PaperYear":2016,"PaperLevel":41,"AddTimeOn":"2018-12-05T19:48:19","SchoolId":0,"MatchingDegree":1}]},{"ID":7264423,"Guid":"2cbd4a46-b292-4b54-ab46-99581a4c7f2e","Title":"2016年全国高中数学联赛四川赛区预赛试题","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":5,"DifValue":0.15,"Name":"困难"},"Categories":"<item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132455\" type=\"1\">集合</category><category id=\"132875\" type=\"1\">子集，子集族</category></item>","ChildNum":1,"Time":"2018-12-05T19:50:40","QuesBody":"<div>【题文】对于任何集合S，用<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image110.png\">表示集合S中的元素个数，用n（S）表示集合S的子集个数.若A、B、C为三个有限集，且满足（1）<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image111.png\">；（2）<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image112.png\">.则<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image113.png\">的最大值为_______.</div>","QuesAnswer":"","QuesParse":"","UseSum":53,"AvgScore":5.0,"ParseAnswerKey":"7c2c11a8a2bc4940dcc62398d42a99e1","QuesAttribute":0,"QuesAttributes":{"ID":0,"Name":""},"TitleAbbreviation":"2016·四川高三竞赛","PaperSource":[{"Id":434395,"PaperTitle":"2016年全国高中数学联赛四川赛区预赛试题","LearnGrade":12,"PaperType":7,"Province":510000,"PaperYear":2016,"PaperLevel":41,"AddTimeOn":"2018-12-05T19:48:19","SchoolId":0,"MatchingDegree":1}]},{"ID":7264424,"Guid":"cb225661-b9ef-4c9a-8629-2dea051b0ad7","Title":"2016年全国高中数学联赛四川赛区预赛试题","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=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132860\" type=\"1\">数列</category><category id=\"132899\" type=\"1\">数列求和</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132861\" type=\"1\">不等式</category><category id=\"132904\" type=\"1\">证明不等式的常用方法</category><category id=\"132926\" type=\"1\">构造法</category></item>","ChildNum":1,"Time":"2018-12-05T19:50:40","QuesBody":"<div>【题文】设等比数列<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image027.png\">的前n项和为<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image126.png\">（r为常数）.记<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image127.png\">.<br>（1）求数列<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image128.png\">的前n项和<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image129.png\">；<br>（2）若对于任意的正整数n，均有<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image130.png\">，求实数k的最大值.</div>","QuesAnswer":"","QuesParse":"","UseSum":34,"AvgScore":5.0,"ParseAnswerKey":"8bd83507a4ec3b33c86528fd29c32ec3","QuesAttribute":0,"QuesAttributes":{"ID":0,"Name":""},"TitleAbbreviation":"2016·四川高三竞赛","PaperSource":[{"Id":434395,"PaperTitle":"2016年全国高中数学联赛四川赛区预赛试题","LearnGrade":12,"PaperType":7,"Province":510000,"PaperYear":2016,"PaperLevel":41,"AddTimeOn":"2018-12-05T19:48:19","SchoolId":0,"MatchingDegree":1}]},{"ID":7264425,"Guid":"00597ed9-fbaf-43d0-bf33-0f8ee658e2e5","Title":"2016年全国高中数学联赛四川赛区预赛试题","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":4,"DifValue":0.4,"Name":"较难"},"Categories":"<item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132861\" type=\"1\">不等式</category><category id=\"132903\" type=\"1\">重要不等式</category><category id=\"132906\" type=\"1\">均值不等式</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132861\" type=\"1\">不等式</category><category id=\"132904\" type=\"1\">证明不等式的常用方法</category><category id=\"132924\" type=\"1\">其他</category></item>","ChildNum":1,"Time":"2018-12-05T19:50:41","QuesBody":"<div>【题文】已知a、b、c为正实数.证明：<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image151.png\">.</div>","QuesAnswer":"","QuesParse":"","UseSum":23,"AvgScore":5.0,"ParseAnswerKey":"c67288209a09717caf89119f4d6e20cb","QuesAttribute":0,"QuesAttributes":{"ID":0,"Name":""},"TitleAbbreviation":"2016·四川高三竞赛","PaperSource":[{"Id":434395,"PaperTitle":"2016年全国高中数学联赛四川赛区预赛试题","LearnGrade":12,"PaperType":7,"Province":510000,"PaperYear":2016,"PaperLevel":41,"AddTimeOn":"2018-12-05T19:48:19","SchoolId":0,"MatchingDegree":1}]},{"ID":7264426,"Guid":"87a80e97-cb72-44f6-b180-c6519fc985be","Title":"2016年全国高中数学联赛四川赛区预赛试题","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=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132862\" type=\"1\">解析几何</category><category id=\"132928\" type=\"1\">直线与二次曲线方程及性质</category></item>","ChildNum":1,"Time":"2018-12-05T19:50:42","QuesBody":"<div>【题文】已知拋物线<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image177.png\">过定点C（l，2），在抛物线上任取不同于点C的一点A，直线AC与直线y=x+3交于点P，过点P作x轴的平行线，与抛物线交于点B.<br>（1）证明：直线AB过定点；<br>（2）求△ABC面积的最小值.</div>","QuesAnswer":"","QuesParse":"","UseSum":34,"AvgScore":5.0,"ParseAnswerKey":"8a6d88b7cddfbae696b3ee482d57e75e","QuesAttribute":2,"QuesAttributes":{"ID":2,"Name":"章内综合题"},"TitleAbbreviation":"2016·四川高三竞赛","PaperSource":[{"Id":434395,"PaperTitle":"2016年全国高中数学联赛四川赛区预赛试题","LearnGrade":12,"PaperType":7,"Province":510000,"PaperYear":2016,"PaperLevel":41,"AddTimeOn":"2018-12-05T19:48:19","SchoolId":0,"MatchingDegree":1}]},{"ID":7264427,"Guid":"ace329dd-83b5-471d-93db-8cc5c2584c75","Title":"2016年全国高中数学联赛四川赛区预赛试题","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":4,"DifValue":0.4,"Name":"较难"},"Categories":"<item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132871\" type=\"1\">导数与极限</category><category id=\"133053\" type=\"1\">导数的应用</category></item><item><category id=\"27925\" type=\"1\">高中数学综合库</category><category id=\"132454\" type=\"1\">竞赛知识点</category><category id=\"132871\" type=\"1\">导数与极限</category><category id=\"133053\" type=\"1\">导数的应用</category><category id=\"133078\" type=\"1\">判断单调性</category></item>","ChildNum":1,"Time":"2018-12-05T19:50:42","QuesBody":"<div>【题文】已知a为实数，函数<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image200.png\">.请讨论函数<img style=\"vertical-align:middle;\" src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image013.png\">单调性.</div>","QuesAnswer":"","QuesParse":"","UseSum":38,"AvgScore":5.0,"ParseAnswerKey":"b72c8cde1297933396e3e09011328a79","QuesAttribute":0,"QuesAttributes":{"ID":0,"Name":""},"TitleAbbreviation":"2016·四川高三竞赛","PaperSource":[{"Id":434395,"PaperTitle":"2016年全国高中数学联赛四川赛区预赛试题","LearnGrade":12,"PaperType":7,"Province":510000,"PaperYear":2016,"PaperLevel":41,"AddTimeOn":"2018-12-05T19:48:19","SchoolId":0,"MatchingDegree":1}]}],"bankId":0,"PaperQuesCount":16,"ReadSum":243,"schoolId":0}