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2018年全国高中数学联赛山东省预赛
适用年级:高三 试卷类型:竞赛 试题总数:14 浏览次数:737 上传日期:2019-03-27
1 . 若复数eqId2cd9e2fe3d6540df9399dbefe49ada54满足eqIdfcfac4dbee34443483536a685fe645fe,则eqId71b066f4ef034bf6b75c671bd9877701的最小值为______.
更新:2019/03/27难度:0.85题型:填空题组卷:157
2 . 在正四棱锥eqIddd5f333edd7c4a01b271754239943f8d中,已知二面角eqIdc04610fac05b4af1898e2c25f19d5c33的正弦值为eqIde0b8cd3018f64415bea8dce0a25d0538,则异面直线eqId6355576c16ff4047a4bdeff7f7b14185eqId0627be51821d4be7b3e024a354815d64所成的角为______.
更新:2019/03/27难度:0.85题型:填空题组卷:158
3 . 函数eqId938aa8585d08417aa3f0b83554759ccb的值域为______.(其中eqId7b5559fa52604169ac0cb99796b61142表示不超过实数eqIdc12aac8c2448479687a40735b3572a23的最大整数).
更新:2019/03/27难度:0.85题型:填空题组卷:167
4 . 在eqId64b9b599fdb6481e9f8d9a94c102300b中,eqIdc78160ad54674b6fbcec6b7a1e33233beqIdc009b2c31acd4c439f10218776fdac36的平分线eqIdbf4db7d066034b139ff80a09ab139d45eqId0627be51821d4be7b3e024a354815d64eqId0cd8063abf2b458f80091bc51b75a904,且有eqIdb0da467ae08d4e0181d877b4ae653e50.若eqIdfb23a1f768814f7c9f1e6eae64ce49b0,则eqId3c92a38ac4674ca3ad415c733988cfea______
更新:2019/03/27难度:0.65题型:填空题组卷:196
5 . 甲、乙两人轮流掷一枚硬币至正面朝上或者朝下,规定谁先掷出正面朝上为赢;前一场的输者,则下一场先掷.若第一场甲先掷,则甲赢得第eqIdf458db68122849abb588feb2e682d9ac场的概率为______.
更新:2019/03/27难度:0.85题型:填空题组卷:128
6 . 若直线eqId60e387d1298747b4a61b9d550c21aef5交椭圆eqIdd448b721bc2f41f8bed63e9521739ce3eqIde9c1eda3dc0c4304868ea148d833743f,且eqId1df23f37804a45ffa0371b5825863eb1eqIdaea992e70d4943e49e893817eb885ed7为整数)于点eqIdcc614bd3390c4d028df189b234dcc351eqId19a4eb16029e4550a14f2afe4741a3c3.设eqId598fad527dbf4fe8b3b60d78b1d83ecd为椭圆的上顶点,而eqId64b9b599fdb6481e9f8d9a94c102300b的重心为椭圆的右焦点eqIdde963a24921f4ee7a991bf9d4f43a42e,则椭圆的方程为______.
更新:2019/03/27难度:0.65题型:填空题组卷:205
7 . 对任意的实数eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqId94152a50056f44c086b5f0318e2354a2的最小值为______.
更新:2019/03/16难度:0.65题型:填空题组卷:137
8 . 已知eqId70a27b6ddf6b478285353abb3b1f3741eqId0d14816387a84fc88d75c2e4d7df8d4e,且eqId4d6d40a0a9ab4d5d89ef5ee949c9456a为方程eqIdeae7a1da0bf84e3b84ee95b69c3c7870的一个根,则eqIdaea992e70d4943e49e893817eb885ed7的最大可能值为______.
更新:2019/03/27难度:0.65题型:填空题组卷:156
9 . 集合eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c满足eqId1dbe262b9f084e22a8de74b9a01a41a2eqIdd0b7ff9dff15434782b506d41dd5dfa2,若eqIdcc614bd3390c4d028df189b234dcc351中的元素个数不是eqIdcc614bd3390c4d028df189b234dcc351中的元素,eqId8754ce8cf7f34f04abb9a0c041f57f5c中的元素个数不是eqId8754ce8cf7f34f04abb9a0c041f57f5c中的元素,则满足条件的所有不同的集合eqIdcc614bd3390c4d028df189b234dcc351的个数为______.
更新:2019/03/27难度:0.85题型:填空题组卷:179
10 . 设eqId92cb82a2c0354749b5125e21e5afbe86为最接近eqIdb768e01614244412b3c05e4b744a794b的整数,则eqId9aa84a86fd924e89adad8442843ebbe8______.
更新:2019/03/27难度:0.65题型:填空题组卷:114
11 . 已知圆eqIdad10a209dece4846af3de519abab6a9d与曲线eqId6cd09676800247fe89074e610f94133feqId09dada248449416383a52531442ea36aeqId03f372b1a66a4fa5b4e6a18996039b0aeqIdcc9acafc2413480295aac45a6ea0e11c为曲线eqId19a4eb16029e4550a14f2afe4741a3c3上的两点,使得圆eqId2efda802d5534f6d92d9f8af7aaec28b上任意一点到点eqIdcc614bd3390c4d028df189b234dcc351的距离与到点eqId8754ce8cf7f34f04abb9a0c041f57f5c的距离之比为定值eqId4bc929779e5e4f42af0f0966ebbed990,求eqId32454977564e4ee18da36bd51156c509的值.
更新:2019/03/27难度:0.4题型:解答题组卷:165
12 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a满足:eqId6dddd396ee0549538d94afae7cdc6257eqIde9e9db41bd984f88a34b58bf4e03e4a7eqIdccef1d0297e449349e0a2d22fc3777c7.求证:eqIda232a6fbc381431f9cac549ebba4179f
更新:2019/03/27难度:0.4题型:解答题组卷:146
13 . 实数eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqIdad7cefefaba947e1a168bca491c4fca1满足eqId1d5689360e5e4066ab850d734cfa509a,试求eqId4011cc4c29604d2c97f4d030bae256f5的最大值.
更新:2019/03/27难度:0.4题型:解答题组卷:169
14 . 证明对所有的正整数eqId1b60c21ab822484cbadf647a5940af9c,存在一个集合eqId1b7d8b87b50e4cfdbf89d48980209a52,满足如下条件:
(1)eqId1b7d8b87b50e4cfdbf89d48980209a52由都小于eqIdaaf95d5e613e4c6e8505b423d153a789eqIdf458db68122849abb588feb2e682d9ac个正整数组成;
(2)对eqId1b7d8b87b50e4cfdbf89d48980209a52的任意两个不同的非空子集eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c,集合eqIdcc614bd3390c4d028df189b234dcc351中所有元素之和不等于集合eqId8754ce8cf7f34f04abb9a0c041f57f5c中所有元素之和.
更新:2019/03/27难度:0.4题型:解答题组卷:137