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\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132858\">三角函数</category><category id=\"132893\">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 src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image001.png\" style=\"vertical-align:middle;\" />，且b+c=2a；命题<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image002.png\" style=\"vertical-align:middle;\" />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":18,"AvgScore":5.0,"ParseAnswerKey":"93a7bf9d92ebaeef647679c57889d0d9","QuesAttribute":0},{"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\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132866\">复数</category><category id=\"132976\">复数的几个形式</category><category id=\"132981\">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 src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image005.png\" style=\"vertical-align:middle;\" />，则<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image006.png\" style=\"vertical-align:middle;\" />（）<table name=\"optionsTable\" cellpadding=\"0\" cellspacing=\"0\" width=\"100%\"><tr><td width=\"25%\">A．-1</td><td width=\"25%\">B．<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image007.png\" style=\"vertical-align:middle;\" /></td><td width=\"25%\">C．<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image008.png\" style=\"vertical-align:middle;\" /></td><td width=\"25%\">D．1</td></tr></table></div>","QuesAnswer":"","QuesParse":"","UseSum":21,"AvgScore":5.0,"ParseAnswerKey":"ecca47474ae95374a1caba8effec4d94","QuesAttribute":0},{"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\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132857\">函数</category><category id=\"132881\">初等函数</category></item><item><category id=\"27925\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132857\">函数</category><category id=\"132885\">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 src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image011.png\" style=\"vertical-align:middle;\" />，当<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image012.png\" style=\"vertical-align:middle;\" />时，记<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image013.png\" style=\"vertical-align:middle;\" />的最小值为m.则m的最大值为（）.<table name=\"optionsTable\" cellpadding=\"0\" cellspacing=\"0\" width=\"100%\"><tr><td width=\"25%\">A．-2</td><td width=\"25%\">B．0</td><td width=\"25%\">C．<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image014.png\" style=\"vertical-align:middle;\" /></td><td width=\"25%\">D．l</td></tr></table></div>","QuesAnswer":"","QuesParse":"","UseSum":19,"AvgScore":5.0,"ParseAnswerKey":"3cbcd61f0a28cf484c0da140943cda25","QuesAttribute":0},{"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\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132870\">初等数论</category><category id=\"133038\">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 src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image021.png\" style=\"vertical-align:middle;\" />，<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image022.png\" style=\"vertical-align:middle;\" />表示不超过<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image023.png\" style=\"vertical-align:middle;\" />（<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image024.png\" style=\"vertical-align:middle;\" />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 src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image025.png\" style=\"vertical-align:middle;\" />（）.<table name=\"optionsTable\" cellpadding=\"0\" cellspacing=\"0\" width=\"100%\"><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></table></div>","QuesAnswer":"","QuesParse":"","UseSum":20,"AvgScore":5.0,"ParseAnswerKey":"c7e36c93c8c2562d24e96d0dedc5f880","QuesAttribute":0},{"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\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132860\">数列</category><category id=\"132898\">数列通项公式求解</category></item><item><category id=\"27925\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132860\">数列</category><category id=\"132899\">数列求和</category></item><item><category id=\"27925\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132869\">数学归纳法</category><category id=\"133030\">第一数学归纳法</category></item><item><category id=\"27925\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132870\">初等数论</category><category id=\"133037\">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 src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image027.png\" style=\"vertical-align:middle;\" />满足<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image028.png\" style=\"vertical-align:middle;\" />，<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image029.png\" style=\"vertical-align:middle;\" />.若<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image030.png\" style=\"vertical-align:middle;\" />为<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image027.png\" style=\"vertical-align:middle;\" />的前n项和，则<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image031.png\" style=\"vertical-align:middle;\" />的个位数字为（）.<table name=\"optionsTable\" cellpadding=\"0\" cellspacing=\"0\" width=\"100%\"><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></table></div>","QuesAnswer":"","QuesParse":"","UseSum":39,"AvgScore":5.0,"ParseAnswerKey":"05ae9303f1f5914c1fda0706694dd4df","QuesAttribute":0},{"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\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132862\">解析几何</category><category id=\"132927\">圆锥曲线</category></item>","ChildNum":1,"Time":"2018-12-05T19:50:37","QuesBody":"<div>【题文】已知<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image038.png\" style=\"vertical-align:middle;\" />、<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image039.png\" style=\"vertical-align:middle;\" />为椭圆与双曲线的公共焦点，P为它们的一个公共点，且<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image040.png\" style=\"vertical-align:middle;\" />.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%\"><tr><td width=\"25%\">A．<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image041.png\" style=\"vertical-align:middle;\" /></td><td width=\"25%\">B．<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image042.png\" style=\"vertical-align:middle;\" /></td><td width=\"25%\">C．l</td><td width=\"25%\">D．<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image043.png\" style=\"vertical-align:middle;\" /></td></tr></table></div>","QuesAnswer":"","QuesParse":"","UseSum":33,"AvgScore":5.0,"ParseAnswerKey":"216e145274691d51fe45e34b72ec5c03","QuesAttribute":0},{"ID":6091635,"Guid":"ebc359c2-ffc0-49c2-abde-9779590446a9","Title":"【全国市级联考】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\">高中数学综合库</category><category id=\"27934\">计数原理与概率统计</category><category id=\"29368\">计数原理</category><category id=\"29490\">二项式定理</category><category id=\"29529\">二项式系数</category><category id=\"29537\">求指定项的二项式系数</category></item><item><category id=\"27925\">高中数学综合库</category><category id=\"27934\">计数原理与概率统计</category><category id=\"29368\">计数原理</category><category id=\"29490\">二项式定理</category><category id=\"29530\">项的系数</category><category id=\"29540\">求指定项的系数</category></item><item><category id=\"79243\">北师大版</category><category id=\"79635\">选修2-3</category><category id=\"79636\">第一章 计数原理</category><category id=\"79644\">§5 二项式定理</category></item><item><category id=\"79243\">北师大版</category><category id=\"79635\">选修2-3</category><category id=\"79636\">第一章 计数原理</category><category id=\"79644\">§5 二项式定理</category><category id=\"79648\">5.1 二项式定理</category></item><item><category id=\"79243\">北师大版</category><category id=\"79635\">选修2-3</category><category id=\"79636\">第一章 计数原理</category><category id=\"79644\">§5 二项式定理</category><category id=\"79649\">5.2 二项式系数的性质</category></item><item><category id=\"79775\">沪教版（上海）</category><category id=\"79868\">高三第一学期</category><category id=\"79871\">第十六章 排列组合和二项式定理</category><category id=\"79889\">16.5 二项式定理</category></item><item><category id=\"79903\">人教A版</category><category id=\"80254\">选修2-3</category><category id=\"80255\">第一章 计数原理</category><category id=\"80261\">1.3 二项式定理</category></item><item><category id=\"79903\">人教A版</category><category id=\"80254\">选修2-3</category><category id=\"80255\">第一章 计数原理</category><category id=\"80261\">1.3 二项式定理</category><category id=\"80265\">1.3.1 二项式定理</category></item><item><category id=\"79903\">人教A版</category><category id=\"80254\">选修2-3</category><category id=\"80255\">第一章 计数原理</category><category id=\"80261\">1.3 二项式定理</category><category id=\"80266\">1.3.2 “杨辉三角”与二项式系数的性质</category></item><item><category id=\"80512\">人教B版</category><category id=\"80844\">选修2-3</category><category id=\"80845\">第一章 计数原理</category><category id=\"80851\">1.3 二项式定理</category></item><item><category id=\"80512\">人教B版</category><category id=\"80844\">选修2-3</category><category id=\"80845\">第一章 计数原理</category><category id=\"80851\">1.3 二项式定理</category><category id=\"80855\">1.3.1 二项式定理</category></item><item><category id=\"81004\">苏教版</category><category id=\"81303\">选修2-3</category><category id=\"81304\">第1章 计数原理</category><category id=\"81312\">1.5 二项式定理</category></item><item><category id=\"81004\">苏教版</category><category id=\"81303\">选修2-3</category><category id=\"81304\">第1章 计数原理</category><category id=\"81312\">1.5 二项式定理</category><category id=\"81314\">1.5.1 二项式定理</category></item><item><category id=\"81004\">苏教版</category><category id=\"81303\">选修2-3</category><category id=\"81304\">第1章 计数原理</category><category id=\"81312\">1.5 二项式定理</category><category id=\"81315\">1.5.2 二项式系数的性质及应用</category></item><item><category id=\"81004\">苏教版</category><category id=\"81637\">高中三年级</category><category id=\"81640\">第16章 排列组合和二项式定理</category><category id=\"81665\">16.5 二项式定理</category></item><item><category id=\"81720\">湘教版</category><category id=\"82019\">选修2-3</category><category id=\"82020\">第7章 计数原理</category><category id=\"82026\">7.4 二项式定理</category></item><item><category id=\"82158\">大纲版</category><category id=\"82319\">高二下册</category><category id=\"82321\">第十章 排列、组合和二项式定理</category><category id=\"82341\">10.4 二项式定理</category></item>","ChildNum":1,"Time":"2018-02-27T11:53:01","QuesBody":"<div>【题文】在<img src=\"Upload/2018-07/20/285f463e-c6e6-4955-be34-754e93c5e372/paper.files/image001.png\" style=\"vertical-align:middle;\" />的展开式中，<img src=\"Upload/2018-07/20/285f463e-c6e6-4955-be34-754e93c5e372/paper.files/image002.png\" style=\"vertical-align:middle;\" />的系数是__________．</div>","QuesAnswer":"","QuesParse":"","UseSum":699,"AvgScore":5.0,"ParseAnswerKey":"15faec88751a0fd6a54135b4934c29b0","QuesAttribute":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\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132858\">三角函数</category><category id=\"132892\">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 src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image073.png\" style=\"vertical-align:middle;\" />、<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image074.png\" style=\"vertical-align:middle;\" />、<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image075.png\" style=\"vertical-align:middle;\" />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":17,"AvgScore":5.0,"ParseAnswerKey":"812e9718bc4ce5c572dd7ec02b523806","QuesAttribute":0},{"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\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132863\">立体几何</category><category id=\"132940\">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 src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image085.png\" style=\"vertical-align:middle;\" />，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":18,"AvgScore":5.0,"ParseAnswerKey":"335e864444cc2012e5a08bcc099232d0","QuesAttribute":0},{"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\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132859\">向量</category><category id=\"132896\">向量的运算</category></item><item><category id=\"27925\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132859\">向量</category><category id=\"132897\">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 src=\"Upload/2019-01/14/808ef1db-a7d7-4bac-9f86-3abf98214d6a/paper.files/image001.png\" style=\"vertical-align:middle;\" />，则<img src=\"Upload/2019-01/14/808ef1db-a7d7-4bac-9f86-3abf98214d6a/paper.files/image002.png\" style=\"vertical-align:middle;\" />________.</div>","QuesAnswer":"","QuesParse":"","UseSum":29,"AvgScore":5.0,"ParseAnswerKey":"54b38afbcd0eb27aa9250da74c717d06","QuesAttribute":0},{"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\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132861\">不等式</category><category id=\"132903\">重要不等式</category><category id=\"132906\">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 src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image100.png\" style=\"vertical-align:middle;\" />.则<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image101.png\" style=\"vertical-align:middle;\" />的最大值为________.</div>","QuesAnswer":"","QuesParse":"","UseSum":24,"AvgScore":5.0,"ParseAnswerKey":"cc7014889ee29fd9f97dd9005e572685","QuesAttribute":0},{"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\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132455\">集合</category><category id=\"132875\">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 src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image110.png\" style=\"vertical-align:middle;\" />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 src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image111.png\" style=\"vertical-align:middle;\" />；（2）<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image112.png\" style=\"vertical-align:middle;\" />.则<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image113.png\" style=\"vertical-align:middle;\" />的最大值为_______.</div>","QuesAnswer":"","QuesParse":"","UseSum":32,"AvgScore":5.0,"ParseAnswerKey":"b3ad6c4c08196fcdd39c6b94befdbc38","QuesAttribute":0},{"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\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132860\">数列</category><category id=\"132899\">数列求和</category></item><item><category id=\"27925\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132861\">不等式</category><category id=\"132904\">证明不等式的常用方法</category><category id=\"132926\">构造法</category></item>","ChildNum":1,"Time":"2018-12-05T19:50:40","QuesBody":"<div>【题文】设等比数列<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image027.png\" style=\"vertical-align:middle;\" />的前n项和为<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image126.png\" style=\"vertical-align:middle;\" />（r为常数）.记<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image127.png\" style=\"vertical-align:middle;\" />.<br />（1）求数列<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image128.png\" style=\"vertical-align:middle;\" />的前n项和<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image129.png\" style=\"vertical-align:middle;\" />；<br />（2）若对于任意的正整数n，均有<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image130.png\" style=\"vertical-align:middle;\" />，求实数k的最大值.</div>","QuesAnswer":"","QuesParse":"","UseSum":22,"AvgScore":5.0,"ParseAnswerKey":"d09334a6991007f8e651fd22a9cd67a7","QuesAttribute":0},{"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\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132861\">不等式</category><category id=\"132903\">重要不等式</category><category id=\"132906\">均值不等式</category></item><item><category id=\"27925\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132861\">不等式</category><category id=\"132904\">证明不等式的常用方法</category><category id=\"132924\">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 src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image151.png\" style=\"vertical-align:middle;\" />.</div>","QuesAnswer":"","QuesParse":"","UseSum":18,"AvgScore":5.0,"ParseAnswerKey":"054eee44c22715e138c86115b50cdc9b","QuesAttribute":0},{"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\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132862\">解析几何</category><category id=\"132928\">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 src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image177.png\" style=\"vertical-align:middle;\" />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":29,"AvgScore":5.0,"ParseAnswerKey":"f06aa451e5f4350043c65ecefba650a4","QuesAttribute":0},{"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\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132871\">导数与极限</category><category id=\"133053\">导数的应用</category></item><item><category id=\"27925\">高中数学综合库</category><category id=\"132454\">竞赛知识点</category><category id=\"132871\">导数与极限</category><category id=\"133053\">导数的应用</category><category id=\"133078\">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 src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image200.png\" style=\"vertical-align:middle;\" />.请讨论函数<img src=\"Upload/2018-12/05/e16d55bf-02da-4795-a2b9-9f262ce2b30e/paper.files/image013.png\" style=\"vertical-align:middle;\" />单调性.</div>","QuesAnswer":"","QuesParse":"","UseSum":27,"AvgScore":5.0,"ParseAnswerKey":"01fcda7ead6efacf752e726e3bf840b6","QuesAttribute":0}],"bankId":0,"PaperQuesCount":16,"ReadSum":166,"schoolId":0}