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河南省洛阳市2020届高三第三次统一考试 数学(理)试题
适用年级:高三 试卷类型:三模 试题总数:23 浏览次数:318 上传日期:2020-06-30
1 . 设集合eqIdb32afc581ff44bf2bfa9bafbe6cd27a0,集合eqId8fd070c161c842e890c4378df71bfe7e,则集合eqId170a03e31a0e4656b66452088e998e61(   )
A.eqId9f51edbe60e549a29a3e8f7146694947B.eqIddc687105e60b4f238747cc880e416835C.eqId7dcd2312d0bf4bb1befdfcc170e45791D.eqId55d55b6bb174468fa5079f56459267a6
更新:2020/06/30难度:0.94题型:单选题组卷:202
2 . 已知直线eqId74c7e0292b094e54ae596d37798a05ed:eqIdffc32b11074f4f83b92719e95b9275ca,直线eqId439fb93f7745417b8bb1747d963c6e60:eqId4beb08721ef246959bb27fe2c39501ba,若eqId0680c299a651427c9959c6986abf1c2a,则eqIdc9268c82c5bb4a9aa15b1acafdd826a9(   )
A.eqId4c0fea3781d84454a9f933aab6fe70bcB.eqId09d5a511bec44ec3ab139628a6481dd0C.eqId40e6de7d58c1473caa5566ebfcf46d50D.eqIdc98ae19514d04643b0670b8f6fcc093c
更新:2020/07/08难度:0.85题型:单选题组卷:339
3 . 已知复数eqId2cd9e2fe3d6540df9399dbefe49ada54满足eqId6693cf2429f4471f89907b8b9cf4319e,则eqId4901bc6b45d14058abf110bcad8bc39c的最小值为(   )
A.2B.1C.eqId06e478d89fff451eaa9a8a7087f7945aD.eqId05ac7be1485f4db49f0482e212043597
更新:2020/06/30难度:0.65题型:单选题组卷:171
4 . 已知eqId3a4208e0040c42ed8b09de2cae9d562eeqIdf458db68122849abb588feb2e682d9ac为两条不同直线,eqIdc13953f2514e4c8f9c8aaaf5241c33aceqId51a8330ab3364436b01f3f1c274d2b94为两个不同平面,则下列结论正确的为(   )
A.eqIdd80209f32d0945f7a14a286b64d35d96eqIde5201b75e3f74bb98544897d1817e9f8,则eqId8fcdc2ff38e54529a032f6f8e3439348
B.eqId7c0500caba714b489a707f6b864b8b55eqIdc4d7e22c85734fbca1f4a936a334a2f7eqId8fcdc2ff38e54529a032f6f8e3439348eqIdee660d81ba754fc3b222b77032bca07e,则eqIdd80209f32d0945f7a14a286b64d35d96
C.eqIdbbafc1259e8b4710ad2d6fa3ddb516c7eqId75becdb8e03a4669b491dd3c7c503418eqIdee660d81ba754fc3b222b77032bca07e,则eqIdf480d8cc26064a1fabcd202b5b2c9f6c
D.eqId75becdb8e03a4669b491dd3c7c503418eqId99480be5713447808157d05662efd647eqIdd80209f32d0945f7a14a286b64d35d96,则eqId462af0d07bbe4d46bf10d8213c48ebbe
更新:2020/06/30难度:0.65题型:单选题组卷:299
5 . 已知eqId6f13759e937144069819aed2ae5a1057是偶函数,且在eqId176a569ddabd4e4482d9ab5af6e2d6ea上单调递增,则函数eqId6f13759e937144069819aed2ae5a1057可以是(   )
A.eqIdbc2539c736d642be88ef59288f0bfe0cB.eqIdd5a75fff43324d8d952e3bbbf61e7b8c
C.eqId8936850d40b04d8d943d276a35343596D.eqId9e41c239be534a568c059576bb853876
更新:2020/06/30难度:0.85题型:单选题组卷:207
6 . 已知圆eqId19a4eb16029e4550a14f2afe4741a3c3:eqIde8b6e6f068674fe3b3f06221480bca51与直线eqId0325441219bd42b4912584bd58271769相切,则圆eqId19a4eb16029e4550a14f2afe4741a3c3与直线eqIdb0d4304bdac74844902a48e58e478a5f相交所得弦长为(   )
A.1B.eqId05ac7be1485f4db49f0482e212043597C.2D.eqId2644c4fd7d684e75ae5ed93cb3581244
更新:2020/06/30难度:0.85题型:单选题组卷:225
7 . 已知函数eqIdc2a1e81531fc4abcbe4e37b2f7f45126的导函数为eqIdfcaf3bbe14e548cc8d47beb2467db5a0,则下列结论中错误的是(   )
A.函数eqId6f13759e937144069819aed2ae5a1057eqIdfcaf3bbe14e548cc8d47beb2467db5a0有相同的值域和周期
B.函数eqIdfcaf3bbe14e548cc8d47beb2467db5a0的零点都是函数eqId6f13759e937144069819aed2ae5a1057的极值点
C.把函数eqId6f13759e937144069819aed2ae5a1057的图象向左平移eqId2cb51764ae3949b9b698fc2f9527dff2个单位,就可以得到函数eqIdfcaf3bbe14e548cc8d47beb2467db5a0的图象
D.函数eqId6f13759e937144069819aed2ae5a1057eqIdfcaf3bbe14e548cc8d47beb2467db5a0在区间eqId261cfe18b4b34e529193faec06a0ee1c上都是增函数
更新:2020/06/30难度:0.65题型:单选题组卷:99
8 . 若某单位员工每月网购消费金额(单位:元)近似地服从正态分布eqId1ab45d47db9b4a0dbff5f52d8c72fc6d,现从该单位任选10名员工,记其中每月网购消费金额恰在500元至2000元之间的人数为eqIdc688382b53d04eb9aca74b12c3b14d16,则eqIdc688382b53d04eb9aca74b12c3b14d16的数学期望为(   )
参考数据:若随机变量eqId86c70780eab347ccb2043d1d7bc9ed96服从正态分布则eqIdc599a6916d1341ea9195b6e95200e680,则eqId7f3f71ecb2284411bf7908b223130150eqIdbed2f18a85c64d2dad3758855e2f0b5deqIdf6096128981840fbb0766cc724b119ef.
A.2.718B.6.827C.8.186D.9.545
更新:2020/06/30难度:0.85题型:单选题组卷:228
9 . eqId28165065505f4bd295929829c368170c的展开式中eqIdf0913d5b3fec4d158489e7ddeaad7da1系数为(   )
A.180B.90C.20D.10
更新:2020/06/30难度:0.65题型:单选题组卷:304
10 . 已知锐角三角形eqId64b9b599fdb6481e9f8d9a94c102300b的内角eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3的对边分别为eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqIdad7cefefaba947e1a168bca491c4fca1.且eqId6b0fe6d069404599aa807c16e7df5114,则eqId58bfb2c856f246ad901ef6b0ed275855的取值范围为(   )
A.eqId4b3b1a396ec64c58b7954d67c79914b7B.eqId586192b50980422aa7ebed811ea20569C.eqIda3527aac8bfe428583f0fb31747dc919D.eqId4564308734b445cd92ff7acde755c8c4
更新:2020/06/30难度:0.4题型:单选题组卷:324
11 . 设双曲线eqId93cbffaa5ae045d6ac45d1e979991c3aeqId0f14428848fa4e8cbdaccdcb9711090d的左,右焦点分别为eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e,离心率为eqIdf035b8f27d4645bb9f6a66f4a3f51918eqIdbedf755e0fdb4d078d6859360706b163在双曲线eqId93cbffaa5ae045d6ac45d1e979991c3a的右支上.且eqId2cc8ba14c6414abb87b5721861164d59eqId75a143b898e14ccdb032561fba9da811为线段eqId41c6793fbe3d400d89f837b065571453,与双曲线eqId93cbffaa5ae045d6ac45d1e979991c3a左支的交点,若eqIdb6a6e605cb6242cbbe3a19e920c39129,则eqId6ad5afac701541be8ae3bc7cdf3579b4(   )
A.eqId6c2270216d1b44498e62fce98b3f8f12B.eqId4359e5eb66ee45e4aa6f0996dcea559dC.eqId29b136556b654bf6b432c7ef4097d273D.eqId6051673b8ea04933b6df23ae0096bb7f
更新:2020/06/30难度:0.65题型:单选题组卷:133
12 . 已知函数eqIdd3b8aaf3783e4ec7a4147f9e29e66c65,若关于eqId8e15963708e9415da25069fea5906e24的方程发eqIdddc33f72fabd448189ea92c83530b504恰好有6个不相等的实根,则实数eqId3a4208e0040c42ed8b09de2cae9d562e的取值范围是(   )
A.eqId766b0d0cdc4e427dabc7fbc05539e4ecB.eqId993379a9f1a2475481069fcc98fd079f
C.eqIde889b47db8584989b55d583987393a47D.eqId29245978a058497abcb1a8e7ee04e3f3
更新:2020/06/30难度:0.4题型:单选题组卷:177
13 . 已知向量eqIdbfdcb35337334952b6d7ceab2f7c8afd,满足:eqId161033c27fa348e887f26b1b94ceb635eqId49616c2ad6be4d33a029a413cc67ace3eqId1bff5210dd044be099fcd5d188e3644e,则向量eqIdbfdcb35337334952b6d7ceab2f7c8afd的夹角为______.
更新:2020/06/30难度:0.85题型:填空题组卷:178
更新:2020/06/30难度:0.85题型:填空题组卷:147
15 . 已知直线eqId417e80f1349244878d01fe90e0891f5f经过抛物线eqId19a4eb16029e4550a14f2afe4741a3c3:eqIdd050af449075401299cc78c647d310e8的焦点eqId63db14a5b4334f3ea583c8fb12b0d175eqId417e80f1349244878d01fe90e0891f5feqId19a4eb16029e4550a14f2afe4741a3c3交于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,其中点eqIdcc614bd3390c4d028df189b234dcc351在第四象限,若eqId5e3cc0734ba44883aba34e69420567f8,则直线eqId417e80f1349244878d01fe90e0891f5f的斜率为______.
更新:2020/06/30难度:0.65题型:填空题组卷:87
16 . 如图,在三棱锥eqId97af93bc48424679a970c09ac8f447cd中,eqId1191e33196564e489097b976d8ab5430eqId58e3386d90274d468c8f497eb4c5d567eqIddd5cae5e7cac4a6faf8e0c081565834ceqId93cbffaa5ae045d6ac45d1e979991c3aeqId63db14a5b4334f3ea583c8fb12b0d175分别是eqId99a3187c2b8f4bcc9703c74c3b72f1f3eqId34c6b6e427744abfb88dc90b8c7c2111的中点.若用一个与直线eqId1a0830891ff846de8422ea80714ecab4垂直的平面去截该三棱锥,与棱eqIdcf2da96900c948a1b3ce7cbfd420c080eqIdbf4db7d066034b139ff80a09ab139d45eqId1b51efe7c2fa42748ac5a6be262e2fa4eqId0627be51821d4be7b3e024a354815d64分别交于eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6eqIdbedf755e0fdb4d078d6859360706b163eqId75a143b898e14ccdb032561fba9da811四点,则四边形eqId6a7a973d97224292a8f23fb074bf99ea面积的最大值为______.figure
更新:2020/06/30难度:0.65题型:填空题组卷:75
17 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的首项eqId77b3f6b9955e499dbdab033a38779496,其前eqIdf458db68122849abb588feb2e682d9ac项和为eqIddb5481de79c946c0a760143297d5eade,且满足eqIdf415893acb7443b39f9406600a127b58
(1)求证:数列eqId47af774d9826496f909ef4ce3d8b0009是等比数列;
(2)令eqId8a581be49e554ca5a1575ec5d4e1da1a,求数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前eqIdf458db68122849abb588feb2e682d9ac项和eqId92ed363a54bd4a8a93df9463bb3af1f5
更新:2020/06/30难度:0.65题型:解答题组卷:278
18 . 如图.长方体eqId588284d93dc5489295f8f224f8e30d13的底面eqId5ce7a06ae7a34393b92b5277978ac014为正方形,eqId348bf2c3045d49f797736d5858af3ce8eqId8b9939c474e64920a8674fc1242c2c9ceqId93cbffaa5ae045d6ac45d1e979991c3a为棱eqIdea82c30b37894b1bb742dee61200db07上一点,eqId2b5bc0c60ad54d5380ad2a70ea4c180aeqId63db14a5b4334f3ea583c8fb12b0d175为棱eqIdbd70ef61616a454bae30f5691884094b上任意一点.
figure
(1)求证:eqIdcbe2ed0c472b432eafff3c5dd7022271
(2)求二面角eqIdc9a5329bf9b049a69caabbe9db7b0a57的余弦值.
更新:2020/06/30难度:0.65题型:解答题组卷:86
19 . 已知平面内动点eqIdbedf755e0fdb4d078d6859360706b163与点eqIdd7b47c94341b4d3ba815e9a13b8b0542eqIdcd41fd5b7a704b179bf50c0dc7130d8b连线的斜率之积为eqId6c134c414a5e4643849c88caa4d6a5f0.
(1)求动点eqIdbedf755e0fdb4d078d6859360706b163的轨迹eqId93cbffaa5ae045d6ac45d1e979991c3a的方程;
(2)过点eqIdba800e03c70e4b36ad99f5d841729878的直线与曲线eqId93cbffaa5ae045d6ac45d1e979991c3a交于eqIdbedf755e0fdb4d078d6859360706b163eqId75a143b898e14ccdb032561fba9da811两点,直线eqId6e01ec176a0c41d4b4c511e5b8adf517eqId0c43edec1bef4ede93a413694f6f5d55与直线eqIdd59777a92d8f4da290823fc3dc6b5c26分别交于eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6两点.求证:以eqId996e2048847f41d5a5fe0e2282909254为直径的圆恒过定点.
更新:2020/06/30难度:0.15题型:解答题组卷:114
20 . 某地为鼓励群众参与“全民读书活动”,增加参与读书的趣味性.主办方设计这样一个小游戏:参与者抛掷一枚质地均匀的骰子(正方体,六个面上分别标注1,2,3,4,5,6六个数字).若朝上的点数为偶数.则继续抛掷一次.若朝上的点数为奇数,则停止游戏,照这样的规则进行,最多允许抛掷3次.每位参与者只能参加一次游戏.
(1)求游戏结束时朝上点数之和为5的概率;
(2)参与者可以选择两种方案:方案一:游戏结束时,若朝上的点数之和为偶数,奖励3本不同的畅销书;若朝上的点数之和为奇数,奖励1本畅销书.方案二:游戏结束时,最后一次朝上的点数为偶数,奖励5本不同的畅销书,否则,无奖励.试分析哪一种方案能使游戏参与者获得更多畅销书奖励?并说明判断的理由.
更新:2020/06/30难度:0.65题型:解答题组卷:165
21 . 设函数eqId8ce5498577434d408d50db76041f36a8eqIda12a0daa63e243f2959834fd35a0f7d6.
(1)若对任意eqId45f4ca0a3e5c4a4fa9585073df543039eqId502640d344474fdd8c352a93a2d27165恒成立,求eqId70a27b6ddf6b478285353abb3b1f3741的取值集合;
(2)设eqId8f52e14bc0f847bda67f8136900b2f7c,点eqId642acb49838e48ccb8908cb8d48e9da8,点eqId7629757da116474daabb821776882b91,直线eqId30f91f320fc94f72ae5e9d07539dc8bb的斜率为eqId8ea8a8058cf142b292d96faba17b7dc9求证: eqIdb0b4bd8e92b146ed911b2507b26d5841.
更新:2020/06/30难度:0.4题型:解答题组卷:82
22 . 在平面直角坐标系中,曲线eqId19a4eb16029e4550a14f2afe4741a3c3的参数方程为eqIdb3ccc1120cc04974b809660cdfc57c32(eqIdc13953f2514e4c8f9c8aaaf5241c33ac为参数),以坐标原点eqId2efda802d5534f6d92d9f8af7aaec28b为极点,以eqId8e15963708e9415da25069fea5906e24轴正半轴为极轴建立极坐标系,直线eqId417e80f1349244878d01fe90e0891f5f的极坐标方程为eqIddc96266435e845d5b5fad5f2f3e2ed1a
(1)求曲线eqId19a4eb16029e4550a14f2afe4741a3c3的普通方程和直线eqId417e80f1349244878d01fe90e0891f5f的直角坐标方程;
(2)已知点eqId25b63077c8ca4563ba82dfd04ed69343,点eqId8754ce8cf7f34f04abb9a0c041f57f5c为曲线eqId19a4eb16029e4550a14f2afe4741a3c3上的动点,求线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3的中点eqId2381423d4cd146cab95f55527681a766到直线eqId417e80f1349244878d01fe90e0891f5f的距离的最大值.并求此时点eqId8754ce8cf7f34f04abb9a0c041f57f5c的坐标.
更新:2020/06/30难度:0.85题型:解答题组卷:255
23 . 已知是eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqIdad7cefefaba947e1a168bca491c4fca1正实数,且eqId2f3f4e68c7604ed592e9c3078195ac90.
eqId4f304408ff99439fb00d393e23b5ef99eqIdadee5b3fb0d54783ba6673e3f7ff4deb的最小值;
eqIdfe8a430550574b23a069a9e28efd7dcb求证:eqIdebfff324ff224ef79366c4e7bd0b8390.
更新:2020/06/30难度:0.65题型:解答题组卷:138