充值 服务号
首页>试卷详情页
2015年全国高中数学联赛福建赛区预赛试题
适用年级:高三 试卷类型:竞赛 试题总数:15 浏览次数:185 上传日期:2018-12-07
1 . 设集合eqIde649e00101f34898ac652e4362fbb203,从集合eqIdcc614bd3390c4d028df189b234dcc351中随机抽取一个元素eqIdc12aac8c2448479687a40735b3572a23,记eqIdb972c4d1c4e54ee5954bf82edf570f9b.则随机变量eqIdc688382b53d04eb9aca74b12c3b14d16的数学期望eqId32c1bfe7d4774c26ad00e1be93b7610c__________.
更新:2018/12/07难度:0.65题型:填空题组卷:36
2 . 已知eqIdc1907715c32d49c3a3bdc7a32132d399,其中,eqIde4d68848a9dd4442877939b5ab402b1f是定义在eqId38a1a72a865d4179b3b243977e23dce4上、最小正周期为2的函数.若eqId4837c94ef0ff4dcf9b1dda4df363275a在区间eqIdd3b26c1bd7c54c438066bb3f31ebc9cf上的最大值为eqIdf1bd69290a464f71ac73b93c51985105,则eqId4837c94ef0ff4dcf9b1dda4df363275a在区间eqIda17baf29ce63461abeabf9e0677fadd2上的最大值为__________.
更新:2018/12/07难度:0.65题型:填空题组卷:36
3 . 设eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e为椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqIdf18b5700afd748c9af08fbce0977010b的左、右焦点.若椭圆eqId19a4eb16029e4550a14f2afe4741a3c3上存在一点eqIdd7be5abad1e34f6db17a56660de8d54f,使得eqId2cc8ba14c6414abb87b5721861164d59,则椭圆离心率eqIdf035b8f27d4645bb9f6a66f4a3f51918的取值范围是__________.
更新:2018/12/07难度:0.65题型:填空题组卷:106
4 . 已知实数eqIdc12aac8c2448479687a40735b3572a23eqId072d7d6b911b42bc89207e72515ebf5feqId2cd9e2fe3d6540df9399dbefe49ada54满足eqId4debe216ea0c47a0a42cdb0e2a2d8fbf.则eqId8bd66638ddbc47c5a226b2c1d49af8b2的最小值为__________.
更新:2018/12/07难度:0.65题型:填空题组卷:42
5 . 已知函数eqId6099b34f1659476abd391d6945e6a397,数列eqId93e38ecd74a24cb59da79181b95bfd3a中,eqId9b90e44fc1454e15a549095adc6d29da,则数列eqId93e38ecd74a24cb59da79181b95bfd3a的前100项之和eqIdfb083f3b9e4d4a3e81da23ba4df82974____
更新:2020/05/13难度:0.4题型:填空题组卷:1001
6 . 如图,在四面体eqId5ce7a06ae7a34393b92b5277978ac014中,eqId767c242b2a814e43aac8cbdb847ecb5aeqId38a478cdb914449ab5b1571207e4fe71eqIdd6533af6b3294dafaf8e1574c57aa0e4,且eqId890174c35d994035b942963f9fddd43b与平面eqId89fbdcb029be4482b52165366491c70f所成角的余弦值为eqIde0b8cd3018f64415bea8dce0a25d0538.则该四面体外接球半径eqId2afb79eb3d4f4786a7474dcd6407c4de__________.figure
更新:2018/12/07难度:0.65题型:填空题组卷:36
7 . 在复平面内,复数eqId4f3b088061b74b91800ceb300f29522beqId4b143fb0b6bd48c3b8db24a8a95343f3eqId10333e63bd6d41a6b825514100c6983d的对应点分别为eqId2c5e235d8a884c6aaf42671328640799eqIdd5fdd748bf194d4d8dd58dd81cc7e263eqIdfb619ce27351479a8ad65e52669c5274.若eqId4057bbd1cf704c5b81f1dc9fb30386b3eqId6932adc149564d1cbeebebe9cef68110eqIdc2f98fc2a6364b83a74da5f0b04d3be4,则eqId9b0f3b96a82544dfbb3c9cc0f35d3416的取值范围是__________.
更新:2020/02/11难度:0.65题型:填空题组卷:46
8 . 函数eqId466b298767f54090a2c9cd0529f07052恰有两个极值点eqId201fa446b9c440e3983d104b24e1f717,则eqId70a27b6ddf6b478285353abb3b1f3741的取值范围是__________
更新:2017/08/15难度:0.4题型:填空题组卷:816
9 . 已知eqIda29d3479b6c749f6997998c0a27ebc77.若eqIdceee23b4d8794f75b6fd2468471bef3b,则eqIdd2781a77c68c4dfa815fe3916afc45cb的取值范围是__________.
更新:2018/12/07难度:0.4题型:填空题组卷:70
10 . 若eqIdc8cfe0aea1404a1ea50553fc27185a6a,则正整数eqIdf458db68122849abb588feb2e682d9ac的最小值为__________.
更新:2018/12/07难度:0.65题型:填空题组卷:36
11 . 求函数eqId66d0c8d9536e47ca8b2f441f0169f4ff的最小值.
更新:2018/12/07难度:0.65题型:解答题组卷:40
12 . 已知过点eqIdc3514b1568dd4007bc934ec628149532、斜率为eqId4d2187284c5d4de29906363f7d21f60f的直线eqId417e80f1349244878d01fe90e0891f5f与双曲线eqId19a4eb16029e4550a14f2afe4741a3c3eqId24f04fa0265e47d4b3ee4c188a9504d7交于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c两点.
(1)求eqId4d2187284c5d4de29906363f7d21f60f的取值范围;
(2)若eqIdde963a24921f4ee7a991bf9d4f43a42e为双曲线eqId19a4eb16029e4550a14f2afe4741a3c3的右焦点,且eqId37bbd3c9fa9f476e9274ce7b5ca8da65,求eqId4d2187284c5d4de29906363f7d21f60f的值.
更新:2018/12/07难度:0.65题型:解答题组卷:40
13 . 如图,eqId4c12bb4f299b40d2aaf895c0f6dd599aeqId0cd8063abf2b458f80091bc51b75a904分别为eqId992fe44057cf4492895193f3f5398449的内心、旁心,eqId0627be51821d4be7b3e024a354815d64eqId0b03a08ae993462f957b0bd373170cc5eqId72f36042b4ed4f3693cc376dfdd083d2分别切于点eqId93cbffaa5ae045d6ac45d1e979991c3aeqIdd5b10b2a13f148b78e0d5a1b820538fdeqId92869ac114124367b45f631d030ed6bdeqIdbf4db7d066034b139ff80a09ab139d45eqId0627be51821d4be7b3e024a354815d64的交点.
figure
证明:(1)eqIdc17fbc32dbb24ccd8952945e68df27bf
(2)若eqId2381423d4cd146cab95f55527681a766eqId1a0830891ff846de8422ea80714ecab4的中点,则eqId064824c540054779916c73edea7989af.
更新:2018/12/07难度:0.4题型:解答题组卷:54
14 . 在坐标平面内,横、纵坐标均为整数的点称为整点,三个顶点均为整点的三角形称为整点三角形.求以eqId0616a8ddf13540f9bf1b188eee2e059e为内心且直角顶点在原点eqId2efda802d5534f6d92d9f8af7aaec28b的整点eqId61dcf62b30234ccfabafc9d021537bf5的个数.
更新:2018/12/07难度:0.4题型:解答题组卷:63
15 . 若对任意的正整数eqId3a4208e0040c42ed8b09de2cae9d562e,集合eqId6e578258d7dd48f1b4c6e088644770c2的任意eqId57d4a97b21354a29bb7c3962028af316元子集中,总有三个元素两两互素.求eqIdf458db68122849abb588feb2e682d9ac的最小值.
更新:2018/12/07难度:0.4题型:解答题组卷:58