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四川省凉山州2020届高三第三次诊断性检测数学(文科)试题
适用年级:高三 试卷类型:三模 试题总数:23 浏览次数:234 上传日期:2020-06-30
1 . 设集合eqIdbca2f8eec57f4c819a73e3c468433f6b,则eqId170a03e31a0e4656b66452088e998e61(    )
A.eqId9c4f56b428bd4a5c947d36cfcedceddfB.eqId3ff1624efe59490b818b790ffcae8fa5C.eqId17f90f6a17f04d9a937a2c9f884aa4b9D.eqId2ed805d50c9a4deda071af71c424865e
更新:2020/06/30难度:0.85题型:单选题组卷:122
2 . 已知eqId6448af1207ef44b98e6c0ec9996057c2i是虚数单位),则eqId7fd6c0dadb0f4a8891639d66b8d79db4( )
A.3B.eqId5e5a9504538343ceaf6b852113919a01C.eqIda550e1844ce74ae1adb53477636f6b15D.eqIdb00c2e3e5f114d79b8a54aa4b72b2a09
更新:2020/06/30难度:0.85题型:单选题组卷:159
3 . 若eqIdc9a1976ae2ea413fa3ddd9af076ff01d,则“eqId4bf0c71176944d10b40edc90ca5e4a9beqIdfbec9c1257ab41a8bf57d2ed68d639e6”的(    )
A.充分不必要条件B.必要不充分条件
C.充分必要条件D.既不充分也不必要条件
更新:2020/06/30难度:0.85题型:单选题组卷:107
4 . 如图所示的程序框图,若输出的y的值为2,则输入的x的值为(    )
figure
A.4B.eqId30c998d35a344d80a18e14a8c8f2d14fC.2或eqId30c998d35a344d80a18e14a8c8f2d14fD.4或eqId30c998d35a344d80a18e14a8c8f2d14f
更新:2020/06/30难度:0.94题型:单选题组卷:132
5 . 已知正项等比数列eqId054d5a7de5684002909fe944c86227c2,向量eqId4ebb2da9f6384052931de4d3471ca2fa,若eqIdabb253cf12034420885753edba2cb851,则eqIdfec1408370454c6cbc934127693cc87d(    )
A.12B.16C.18D.eqId3e5cf3edfb5b497c864913b555111931
更新:2020/06/30难度:0.65题型:单选题组卷:276
6 . 已知角α的顶点与原点重合,始边与x轴正半轴重合,终边经过点eqId37fdf44cd49542f687af138cac6322ec,则eqId40f1de52cea941e996a3b302602d927d(    )
A.eqId55cdf762f6ee44b9965cb85874ed15f9B.eqId5bdf412098cc4156b5e8fd514ebc7818C.eqId2b4cdf753a8746efb449b3005ed03f26D.eqId170361f2c13a48679439924a405d8282
更新:2020/06/30难度:0.65题型:单选题组卷:172
7 . 若双曲线eqId6d0d521d22854a6992e0669a6c13d054与抛物线eqIda807245456b04e3397b6665c0a779287有相同的焦点,则该双曲线的两条渐近线的夹角为(    )
A.eqId2cb51764ae3949b9b698fc2f9527dff2B.eqId87a9bbb6dd564186905f2064b8c22182C.eqIdb47bf79338b1478a89eac53d16970cdfD.eqIdd3e88ecbd2db456396e01302a43b93d9
更新:2020/06/30难度:0.65题型:单选题组卷:156
8 . 设函数eqId7d2d99c0645b4ff2bf48ff012512c1dc与函数eqId5e1ab82ff6d04dcd9a97e3c71ce687fa的对称轴完全相同,则eqId145940d03af4447eabd753d76abd2a1d的值为(    )
A.eqId1f8348e400e54ddeb2a6241242e711b1B.eqId87a9bbb6dd564186905f2064b8c22182C.eqIdd3e88ecbd2db456396e01302a43b93d9D.eqId4f8ed4c683aa4c4b9c482734d8ac04a3
更新:2020/06/30难度:0.65题型:单选题组卷:189
9 . 已知eqIde5db6211acfa4cb6bac25ee94c7dd9bc为平面区域eqIdac1282acc18e4558b1a6e9772e458c98内的两个动点,向量eqId22ce2de394a042a8b8322f87ab64b873 ,则eqIda1b1c42e06a0473b932ce9fcbfb303fa的最大值是(    )
A.1B.2C.3D.4
更新:2020/06/30难度:0.65题型:单选题组卷:98
10 . 小明有一卷纸,纸非常的薄且紧紧缠绕着一个圆柱体轴心卷成一卷,它的整体外貌如图所示,纸卷的直径为12厘米,轴的直径为4厘米.当小明用掉eqIddda48cced83d424b89b7d8f8c62b1056的纸后,则剩下的这卷纸的直径最接近于(    )
figure
A.6厘米B.7厘米C.8厘米D.9厘米
更新:2020/06/30难度:0.65题型:单选题组卷:132
11 . 已知长方体eqId588284d93dc5489295f8f224f8e30d13的体积eqIda1d896eea5764eafab3b85f1abeb568d,若四面体eqId1c0c1be4d05e4c7b8cfa8662510ab064的外接球的表面积为S,则S的最小值为(    )
A.eqIdf02c7a6cd286450983fa0c3df26806cdB.eqId9050468529364d52bb5f07ad6c942cc0C.eqIde835a5f3bdf34b269917bf97d468b3ccD.eqIdccc069abde5c4b1e8760566e8713e4df
更新:2020/06/30难度:0.65题型:单选题组卷:108
12 . 已知函数eqIddbafae43f8304c2f9d8659a66a1e866e的图象关于直线eqId5db4a4f976ba42089c0439595abeb40b对称,且当eqId45f4ca0a3e5c4a4fa9585073df543039时,eqId2708cd74323647b3b75ec623cf03e2b2.若eqId93de039eb6244070bbb535c56e7347b4eqId3519381d4acc46b09d5e3d881e76f3a8eqId291665b436a7400195a30c1d0497b719,则eqId0ce93bfa1f6a4a23b3258410dd19847a的大小关系是(    )
A.eqId2b09921788f943369b8b2d69257fdda4B.eqId18513915a070416db1e6b2d279419695C.eqId96f25c3294b2457ca92c563e42cd8713D.eqIdd267db4f512541f8825f9d0ff4192c96
更新:2020/06/30难度:0.85题型:单选题组卷:215
13 . 已知eqIdef9ffb46f48a48828357da10684fec98,若eqIde6fbd9e2cf684c26a661206a73eada7e,则eqIdd33c7c1015944e2b81de4ff8695de842_____.
更新:2020/06/30难度:0.85题型:填空题组卷:103
14 . 如图,eqId99a3187c2b8f4bcc9703c74c3b72f1f3是圆O的直径,eqId11482994d1ba4e02b4d6580bc253c1da,假设向该圆随机撒一粒黄豆,则它落到阴影部分的概率为_______.figure
更新:2020/06/30难度:0.85题型:填空题组卷:110
15 . 设eqId64b9b599fdb6481e9f8d9a94c102300b的内角eqId10bbe48f886a4fa78fdf8c1fd064f9b4所对的边分别为eqId0ce93bfa1f6a4a23b3258410dd19847a,若eqIdc4667aa1f592454e8feaa23207703b10eqId12b446e4969e4739bdd25795efd776f8eqIdcbdef76009be4bd4af0aa94ff122ddf2,则eqId43030e1d3ce84bd395f1afe81562fea7______.
更新:2020/06/30难度:0.85题型:填空题组卷:95
16 . 阿波罗尼斯(古希腊数学家,约公元前262-190年)的著作《圆锥曲线论》是古代世界光辉的科学成果,它将圆锥曲线的性质网罗殆尽,几乎使后人没有插足的余地.他证明过这样一个命题:平面内与两定点距离的比为常数eqId2cfa6dd83d7e41e7983fac745bc86155的点的轨迹是圆,后人将这个圆称为阿波罗尼斯圆.①若定点为eqIde03a3609ffa041ea870e577c70f1117a,写出eqId0bb2c724a5ec49248f87ffbde98943f7的一个阿波罗尼斯圆的标准方程__________;②△eqId89fbdcb029be4482b52165366491c70f中,eqId1176aec79f8645a5b61c0bc6da81af7f,则当△eqId89fbdcb029be4482b52165366491c70f面积的最大值为eqId2644c4fd7d684e75ae5ed93cb3581244时,eqIdf3ccc5889ff44339b4e5a8c578f48e0e______.
更新:2020/06/30难度:0.65题型:双空题组卷:76
17 . eqIddb5481de79c946c0a760143297d5eade为等差数列eqId93e38ecd74a24cb59da79181b95bfd3a的前n项和,已知eqId669d59b45536467cafdeef96b34da33c.
(1)求eqIdef9cef8e6d054d8dac46b8cde14953adeqIddb5481de79c946c0a760143297d5eade
(2)设eqIdd85095493d7a422dba1a844fe067e937,数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前n项和为eqId92ed363a54bd4a8a93df9463bb3af1f5,证明:eqIdba8f4a77f7dc4c08afde81d7200e11d8.
更新:2020/06/30难度:0.65题型:解答题组卷:285
18 . 州电视台为了解州卫视一档中华诗词类节目的收视情况,抽查东西区各5个县,统计观看该节目的人数的数据得到如下的茎叶图(单位:百人).其中一个数字被污损.
figure
(1)求西部各县观看该节目的观众的平均人数超过东部各县观看该节目的平均人数的概率;
(2)该节目的播出极大地激发了观众对中华诗词学习的热情,现从观看节目的观众中随机统计了4位观众学习诗词的周平均时间y(单位:小时)与年龄x(单位:岁)的关系,如下表所示:
x
20
30
40
50
y
2.5
3
4
4.5
 
根据表中的数据,试求线性回归方程eqIdd1251868f5af4d44b51b8a50ace7eb65,并预测年龄为60岁的观众学习诗词的时间.
(参考公式eqId141d85ee527140478be809c9938da708
更新:2020/06/30难度:0.65题型:解答题组卷:198
19 . 如图,四面体eqId5ce7a06ae7a34393b92b5277978ac014中,eqId82920e5b77524eec94f5e6cd469047d5分别是eqId2f1b7b718ca4439da7dfaeb20fdcf97b的中点,eqId6f956d77ea7e4f669c0dd0e5786d79b3,eqId51ea4ae358204a54bc26b4f2a137feea.
figure
(1)求证:eqId8beda2d2be2044da805962ee52e53b73平面eqIdd128ff4f83ef4c12aad8920a558a97b7
(2)求直线eqId7fd836b3d4ac4d398fb8e461e090364c与平面eqIdff691949259a43a589da1c62a1b70d2d所成角的余弦值.
更新:2020/06/30难度:0.85题型:解答题组卷:255
20 . 已知函数eqId9496e3b2d97c4824b86dc832527b2ef1.
(1)设函数eqIdeef86c99aabf4afbbbb2c53a1cb559d4在点eqIdfd4ccdd44ad348f88e3b6f7f0112a97c处的切线方程为eqIdc14739b2ae5b4fde972e08210a7f67d5,求a的值.
(2)若曲线eqId144eff5c0e4649138a21f2b1b6a06907与曲线eqId1aacfd8f79754517ab57903022e76d98至少有一条公共切线,求a的取值范围.
更新:2020/06/30难度:0.65题型:解答题组卷:217
21 . 已知椭圆eqId211c15b061ee47039dccbca908ea32b4,右顶点eqIdbbd16fb84be841689dfb4e5915bb55b6,上顶点为B,左右焦点分别为eqId5f04473e64c141bcbe9b0a8af27f4aa8,且eqIdda3c8a27d3de491ba3f393c373912d95,过点A作斜率为eqIdbc3831956bed4d45a9b00b3f1c759288的直线l交椭圆于点D,交y轴于点E.
(1)求椭圆C的方程;
(2)设PeqIdbf4db7d066034b139ff80a09ab139d45的中点,是否存在定点Q,对于任意的eqIdbc3831956bed4d45a9b00b3f1c759288都有eqId1c67c298861d43ffa903fe04caf98c32?若存在,求出点Q;若不存在,请说明理由.
更新:2020/06/30难度:0.4题型:解答题组卷:155
22 . 在平面直角坐标系中,以坐标原点O为极点,x轴的正半轴为极轴建立极坐标系.eqId8e6acd891f5c4ee58e49a1a58ccdf866两点的极坐标分别为eqIde6ee4da1498d478fa5c522f011db824aeqId6c860c29d95f4473b3051cf205b74456曲线C的参数方程为eqIdeb6e1afe812848f692b9ba7f5b68297deqIdf9db0aee08264a238b9741675591065e为参数).
(1)求eqId8e6acd891f5c4ee58e49a1a58ccdf866两点的直角坐标及曲线C的普通方程;
(2)设P是曲线C上任意一点(P不在y轴上),若直线eqId6f782d71f5a7422aa78bd8204949ce26eqIde9b50933e347462ea824ccc9bf51fc93分别交eqId8e15963708e9415da25069fea5906e24轴于点eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6,试问eqId592ddbcf85744928ad91695e87afcbdc是否为定值?若是,请求出这个定值;若不是,请说明理由.
更新:2020/06/30难度:0.85题型:解答题组卷:167
23 . 已知函数eqIdbd281c6e49284c0dab868b9ccbff05ea.
(1)当eqId316e2199840e418e87252dba1d7d7ffd时,求不等式eqId6f588829720c462ba5eb75cec39feb52的解集;
(2)设不等式eqId38d53735f6ba4ba8b179ffd8152b3ca3的解集为M,若eqIde9e608426a344a71b1c7ca15d31f8c2b,求实数a的取值范围.
更新:2020/06/30难度:0.65题型:解答题组卷:97