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2018年全国高中数学联赛福建省预赛
适用年级:高三 试卷类型:竞赛 试题总数:15 浏览次数:417 上传日期:2019-03-22
1 . 将正偶数集合eqId148c2d2755f7485a9725028ef7552d37从小到大按第eqIdf458db68122849abb588feb2e682d9ac组有eqId26df77282a7a4e68a842cec192c86628个数进行分组:eqId83c71224d55149ff8d072c7e479cb931eqIde290dd24960f48bd8eedab78ef8cb52ceqIdf23dce294ad24b0095d1b1a320851894,…,则2018位于第______组.
更新:2019/03/22难度:0.85题型:填空题组卷:123
2 . 在eqId64b9b599fdb6481e9f8d9a94c102300b中,内角eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3所对的边分别是eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqIdad7cefefaba947e1a168bca491c4fca1.若eqIda08ce385279d41c789695fb651b17890eqId79b6466898ac471abcb54483316406dceqId3ded46db8bc945d498e98948069dcb1b,则eqIdc557fdbbaf4f432bb8dc61f968df0bcd______.
更新:2020/05/07难度:0.85题型:填空题组卷:93
3 . 设复数eqId2cd9e2fe3d6540df9399dbefe49ada54满足eqId521060d291f940279fc2c741b1b5e623,则eqId41e780942ea24c258865ad4232ec1f9a的最大值为______.(eqId30bb87c3252146748b8c61e7205511b8为虚数单位,eqIdc9b3e5fa614043148ac9df7054646997为复数eqId2cd9e2fe3d6540df9399dbefe49ada54的共轭复数)
更新:2019/03/22难度:0.85题型:填空题组卷:123
4 . 已知定义在eqId38a1a72a865d4179b3b243977e23dce4上的奇函数eqId4837c94ef0ff4dcf9b1dda4df363275a,它的图象关于直线eqId6b946dcfe52b4ecf9798684495f8bd22对称.当eqId5ff7f378567f4de49748e34629c2be63时,eqIde63d052c3c5c444a85c0f6d0b82fb429,则eqId16ff6490b074446fa2a9a208b9493a54______.
更新:2020/06/25难度:0.85题型:填空题组卷:95
5 . 从如图所示的,由9个单位小方格组成的,eqId07d7de046d22467db4800293517eaedc方格表的16个顶点中任取三个顶点,则这三个点构成直角三角形的概率为______.figure
更新:2019/03/22难度:0.65题型:填空题组卷:88
6 . 如图,在三棱锥eqId12175c05cfe240a0b8270ee03df1962f中,eqIde7db511e528e4748b8f85f42ef2b1913eqId64b9b599fdb6481e9f8d9a94c102300b都是边长为6的等边三角形.若二面角eqId80c7818b2d384471bbd2c217152f8eba的大小为eqIdc49bd81ea8044d68aba97695ad0e1d5e,则三棱锥eqId12175c05cfe240a0b8270ee03df1962f的外接球的面积为______.figure
更新:2019/03/22难度:0.65题型:填空题组卷:112
7 . 已知eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e分别为双曲线eqIdf1a65e6c592e439fb4d95c7a86db5ed1的左、右焦点,点eqIdd7be5abad1e34f6db17a56660de8d54f在双曲线eqId19a4eb16029e4550a14f2afe4741a3c3上,eqId92869ac114124367b45f631d030ed6bdeqId4c12bb4f299b40d2aaf895c0f6dd599a分别为eqId91b5afff2e5c47d29221db654954eb15的重心、内心.若eqId869f39e191474ac2944c96ae4dff8d9e轴,则eqId91b5afff2e5c47d29221db654954eb15的外接圆半径eqId2afb79eb3d4f4786a7474dcd6407c4de______.
更新:2019/03/22难度:0.65题型:填空题组卷:127
8 . 最近网络上有一篇文章很火.源于一道常见题目:(见图),这貌似易解的题目,里面竟然蕴藏了深奥的大道理.(本题不作为本次考试的试题,本次试题如下)
figure
eqId70a27b6ddf6b478285353abb3b1f3741eqId48f2e1ac186b4771b35f7384328d02a7,则eqId679e52b8919e4fb2baeb70bd5f3431d7的最大值为______.
更新:2019/03/22难度:0.65题型:填空题组卷:96
9 . 已知整系数多项式eqIde9c513c3dcd746f0a0889e2d12a5ad1d,若eqIdb4e9278f9217478486934216faef7b91eqId553026b4473f46efa8dc59668f8b06ee,则eqId5cd76eeacc21466990ad5fe9baa00cb5______.
更新:2019/03/22难度:0.65题型:填空题组卷:94
10 . 已知函数eqId4837c94ef0ff4dcf9b1dda4df363275a满足:对任意实数eqIdc12aac8c2448479687a40735b3572a23eqId072d7d6b911b42bc89207e72515ebf5f,都有eqIdf973fc1739c74d378ecdf65484bda1bd成立,且eqId873db9468ca2468cac3627c32a556af0,则eqId25101aee7a264987bf14de446fa072ef______.
更新:2019/03/22难度:0.65题型:填空题组卷:88
11 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqIdf458db68122849abb588feb2e682d9ac项和eqIddb5481de79c946c0a760143297d5eade满足eqId60e90f53cc3a415b9e8eb0d051efea3ceqId2783a65b248b43f5bacb0fc4d5bae2fd,且eqIdc60df934817a48528e3bd750cf12052a
(1)求数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式;
(2)设eqId8a8a7795f1c6434786e93788e7319f1ceqId92ed363a54bd4a8a93df9463bb3af1f5为数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前eqIdf458db68122849abb588feb2e682d9ac项和,求使eqIdfd8c2697316b46f98ae2219386441294成立的最小正整数eqIdf458db68122849abb588feb2e682d9ac的值.
更新:2019/03/22难度:0.65题型:解答题组卷:108
12 . 已知eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e分别为椭圆eqIdfd8674e21002436f9476310a52d934ec的左、右焦点,点eqIdcd61f0ff38584b4ea5416db8512cf5b2在椭圆eqId19a4eb16029e4550a14f2afe4741a3c3上,且eqId91b5afff2e5c47d29221db654954eb15的垂心为eqId1df8963cbe44430da4b3926a6094708c
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)设eqIdcc614bd3390c4d028df189b234dcc351为椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的左顶点,过点eqIdde963a24921f4ee7a991bf9d4f43a42e的直线eqId417e80f1349244878d01fe90e0891f5f交椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqId0cd8063abf2b458f80091bc51b75a904eqId0cd8063abf2b458f80091bc51b75a904两点.记直线eqIdbf4db7d066034b139ff80a09ab139d45eqId7fd836b3d4ac4d398fb8e461e090364c的斜率分别为eqIdd4bf9298f0db4fb5afb67e0d739f3074eqId75fdb198d83447e59e31c1f4923cc3bc,若eqId78940b8e7fc6405087bc871d06aace30,求直线eqId417e80f1349244878d01fe90e0891f5f的方程.
更新:2019/03/22难度:0.65题型:解答题组卷:125
13 . 如图,在锐角eqId64b9b599fdb6481e9f8d9a94c102300b中,eqId93cbffaa5ae045d6ac45d1e979991c3aeqId93cbffaa5ae045d6ac45d1e979991c3a是边eqId0627be51821d4be7b3e024a354815d64上的点,eqId64b9b599fdb6481e9f8d9a94c102300beqIdc1606811a17a43ab89872b189e4eecc5eqId19081cc6b1ee4c34b85e9245d585572d的外心分别为eqIdaad7b72a25924d078d2360cdc99f1090eqIdd7be5abad1e34f6db17a56660de8d54feqIdca9308a4ebd84ed8a28d8a519a8dbb39.证明:
figure
(1)eqIde1f031a20157400d9c533d7e896fbddbeqId64b9b599fdb6481e9f8d9a94c102300b
(2)若eqId51471b557b734c16824eb704214b9208,则eqIdb160d85a50a047df9b4e82f530fc3fed
更新:2019/03/22难度:0.65题型:解答题组卷:102
14 . 已知eqId3787f3de20284879b2ee970ee3997eef
(1)当eqId2d569479cd1c43c1af15895792b64db6时,不等式eqId73b05e6a4f0243b2a0903c6ef7201ade恒成立,求实数eqId3a4208e0040c42ed8b09de2cae9d562e的取值范围;
(2)若eqIdf7cbc1ad0a7b4f97b479c131b62ad882eqIdaecaf42a9cfb4a5c8c0cade53729c9ba是函数eqId4837c94ef0ff4dcf9b1dda4df363275a的两个零点,求证:eqId58de71391109416cbb0641a5a9c5059b
更新:2019/03/22难度:0.65题型:解答题组卷:161
15 . 设eqId2381423d4cd146cab95f55527681a766是由有限个正整数构成的集合,且eqId2017dd8d6a804c378a5763eb8f5dcf0d,这里eqIdcfeb19fee73446b69322999ffca48e00eqId2a9b3f5753ea444ab14c9f60e2cdf286eqId4dbcf768f0d64d188031f05c52d11601,2,…,20.并对任意的eqId62e1d182d314494aa502648940b0725e,都有eqIdc76d4fc02a2545c9851f57ceb3680cb9eqIdd21cb19a1bf4480db21e36af186fb2e9,已知对任意的eqId3f5832b546f5482a8e1dd1ea9495c981eqId32c75c7abece4de0900ac1ab51a51888,若eqId0be890d60d55448e8e52e0f9d5df5268,则eqId58521edaf7344d5c9a5989ba969c0bdd.求集合eqId2381423d4cd146cab95f55527681a766的元素个数的最小值.(这里,eqId2759c11395b84cf196a4d3f4b8f01ea9表示集合eqId86c70780eab347ccb2043d1d7bc9ed96的元素个数)
更新:2019/03/22难度:0.4题型:解答题组卷:99