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河南省郑州市2019届高三第三次质量检测数学(理)试题

适用年级:高三试卷类型:高考模拟试题总数:23浏览次数:528上传日期:2019/6/7
一、单选题
1 . 已知集合eqId57ac67e1a79c4c1891563f1796b24e90,集合eqId2d3f60ac68cc47f5a5527c91f082196e,则集合eqIdc7e17aac3f664408a20c2c2cbb4f5426等于(  )
A.eqId9e3259eba44844e7bcc3a99bada008efB.eqIdf09d8f4b0c3b4196a7f47f9d39356a89C.eqIdebedefbf6bfa4afdac16c80db6a6de37D.eqIda4e2c966d65d40b5b82aaaa6f0af4cb9
难度系数:0.94使用:224次题型:单选题更新:2019/6/7
2 . 已知eqId5c98c7e0e00842daaabaca9f16d15a81,则eqId38b42e0bafa4450aa5f52780cc91913c( )
A.eqIdcc202aaf3bda411cad0ca4bf46462b14B.eqIdaf596a16cb2f41a1bfb1f66ab414032aC.eqId8f65c930571d4ff6aa6a50029d46826eD.eqId11f75c152f5341f39d020095cecda9b3
难度系数:0.94使用:255次题型:单选题更新:2019/6/7
3 . “eqIde83efc7fc3a341eeab65ee727c0dcfa7”是“方程eqIdc9c0e0779a834b6c9893eefd208f9784表示椭圆”的(  )
A.充要条件B.充分不必要条件
C.必要不充分条件D.既不充分也不必要条件
难度系数:0.94使用:1881次题型:单选题更新:2019/6/7
4 . 已知eqId313709498a0e47499ebefc26700de7e1eqId4fc444707ec24bf9bc10dde5fdb971cc,则eqId61039eca702943c08b54682159ec5535(  )
A.eqIddb6b28cbd8a14caa9cf1146f6f7916c0B.eqIddd00da4e6f1147d885f69829e181766dC.eqIdcad83c360f5e484aadfd329f9030cfc0D.eqIdcf32b3b919f04cc18988c622e750e9f1
难度系数:0.85使用:722次题型:单选题更新:2019/6/7
5 . 我国著名数学家华罗庚先生曾说:数缺形时少直观,形缺数时难入微,数形结合百般好,隔裂分家万事休,在数学的学习和研究中,常用函数的图象来研究函数的性质,也常用函数的解析式来琢磨函数的图象的特征,如函数eqId55bff78f0e174009910dd4d3115ce492的图象大致是
A.figureB.figure
C.figureD.figure
难度系数:0.85使用:448次题型:单选题更新:2019/6/7
6 . 等比数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqIdf458db68122849abb588feb2e682d9ac项和为eqIddb5481de79c946c0a760143297d5eade,若eqId74136898cd8c4f7e9fdadf45a11e3a42eqId4ea86f7987c84e33ab4567595bd39040eqId91a69de880194b29a3db0dc26f4a606a,则eqIdb2fb132dbd7f4e809993e2923f6724b1(  )
A.eqId31d650c27e5a447cb9b0b17e847e9673B.eqIdbcf62ee9123641e0a2fce2bd23e65ee4C.eqId9ef8f5c2c28e4812bb72e8056e707dc0D.eqIdda58956eb8e041a6874e39a1a494f373
难度系数:0.65使用:222次题型:单选题更新:2019/6/7
7 . 某同学eqId11f75c152f5341f39d020095cecda9b3次测评成绩的数据如茎叶图所示,总体的中位数为eqId5557c7b84f794778b10717993bbb709e,若要使该总体的标准差最小,则eqId35d1002b10e94f0593551c399763247c的值是(  )
figure
A.eqId5557c7b84f794778b10717993bbb709eB.eqId76cab3deb22044968094187ee9174798C.eqId1c1b006090344679b56b4c75d395cd8eD.eqIdd7225001a06642ef81093263e6a2f9ac
难度系数:0.65使用:354次题型:单选题更新:2019/6/7
8 . 关于圆周率,数学发展史上出现过多很有创意的求法,如著名的蒲丰试验,受其启发,我们也可以通过设计下面的试验来估计eqId5a6dc96e894e4f23be3c422cad388a30的值,试验步骤如下:①先请高二年级eqId6a64a6458938477ea9222d722f9cca2f名同学每人在小卡片上随机写下一个实数对eqIdec5d590940c34ecbbf0d6356919d07fb;②若卡片上的eqIdc12aac8c2448479687a40735b3572a23eqId072d7d6b911b42bc89207e72515ebf5f能与eqIdf1bd69290a464f71ac73b93c51985105构成锐角三角形,则将此卡片上交;③统计上交的卡片数,记为eqId3a4208e0040c42ed8b09de2cae9d562e;④根据统计数eqId6a64a6458938477ea9222d722f9cca2feqId3a4208e0040c42ed8b09de2cae9d562e估计eqId5a6dc96e894e4f23be3c422cad388a30的值.那么可以估计eqId5a6dc96e894e4f23be3c422cad388a30的值约为(  )
A.eqId98ba9b08c5cf405a8d814c9c67f10f27B.eqId980156275a9f4005b4e658c57784fe4bC.eqId73be38f29a9e43b6abb972afe3b4857cD.eqId1f6d196119e848358fb16ff4a0a0a06d
难度系数:0.4使用:410次题型:单选题更新:2019/6/7
9 . 已知函数eqId9862b8d68f4f49e39512d94b420285c1eqIdfc3c7c5a8657450d9842424a8dc65c73的部分图象如图所示,则使eqId2c87552205cc4970ac61fdb3628add92成立的eqId70a27b6ddf6b478285353abb3b1f3741的最小正值为(   )
figure
A.eqId87a9bbb6dd564186905f2064b8c22182B.eqIdb47bf79338b1478a89eac53d16970cdfC.eqIdd3e88ecbd2db456396e01302a43b93d9D.eqId4bbbce4c9d174148a92193e26d43bd72
难度系数:0.65使用:243次题型:单选题更新:2019/9/27
10 . 如图,网格纸上小正方形的边长为eqIdf1bd69290a464f71ac73b93c51985105,粗实线画出的是某几何体的三视图,已知其俯视图是正三角形,则该几何体的外接球的体积是(  )
figure
A.eqIdf8c2d8c13ee247ea983973c4f604729dB.eqId7c23ba45fd79498581276c05ff08d911C.eqId76d24ba093564b998ec64f4fbc3899e6D.eqIdd51e601e258148a394880948006efbe9
难度系数:0.65使用:385次题型:单选题更新:2019/6/7
11 . eqIdadf5adeb3ae644dc89c819829df0a901eqId0cfe24caa0fc44de8e0fcd142d6c1377是双曲线eqId1c079cb2887d42f882bc58224292e25f的左右焦点,若双曲线上存在点eqIdd7be5abad1e34f6db17a56660de8d54f满足eqIdadce81bfacd845d98068d22d43933bde,则双曲线离心率的取值范围为(  )
A.eqId8e666adf07fc4388b4fff176be917dd2B.eqId6f12e03a234d45ecabeb33dd4f5f5f5fC.eqId146b1b67875943a1bd3f0b19999c667cD.eqId6c4cb90b5514426586c15e3d682bf688
难度系数:0.4使用:635次题型:单选题更新:2019/6/7
12 . 设函数eqId6f13759e937144069819aed2ae5a1057eqId7dcd2312d0bf4bb1befdfcc170e45791上存在导函数eqIdd4987f8ad889456da70059baf8a2d17beqId9aae6b52bfe0485fa8776694477cd407,有eqId76efaf74b63d462984ca9280a8656704,在eqId176a569ddabd4e4482d9ab5af6e2d6ea上有eqId70137164719941e29191372f61b6b3e7,若eqId040b6faf9d7740f38dac59560928657b,则实数eqId3a4208e0040c42ed8b09de2cae9d562e的取值范围为(  )
A.eqId34f3a2864310457c8962e21416a77d52B.eqId9536c46ad6fd420fa98cc86eba413088C.eqId460aaa50796e42c2ba9f4e800aaabf0dD.eqIdcfa6e12b63d84fd986681bea51689291
难度系数:0.15使用:978次题型:单选题更新:2019/6/7
二、填空题
13 . 已知向量eqIdf52af1e46e52447eb8b84fc6aa1e70d0eqId583b149be00b46dfbb939c802285a843,若eqId73df2f5d7d994aadba6956814176cc3c,则eqIda20533c285d74dbeb02bd56638216f4d__________.
难度系数:0.94使用:421次题型:填空题更新:2019/6/7
14 . eqIdeaae0a5cc74e4b709264472145934c91本相同的资料书配给三个班级,要求每班至少一本且至多六本,则不同的分配方法共有_____种.
难度系数:0.65使用:275次题型:填空题更新:2019/6/7
15 . 设函数eqId97e0bb1d0e0f40f884e25f90ab6598aa的定义域为eqId0cd8063abf2b458f80091bc51b75a904,若满足条件:存在figure,使eqId97e0bb1d0e0f40f884e25f90ab6598aafigure上的值域为figure,则称“倍胀函数”.若函数eqId4837c94ef0ff4dcf9b1dda4df363275a为“倍胀函数”,则实数eqIdbafea08741fb4f53b4ff0f97a9a503d8eqId70a27b6ddf6b478285353abb3b1f3741 的取值范围是____.
难度系数:0.4使用:343次题型:填空题更新:2019/6/7
16 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a满足eqIdaebe3dd7d7eb458d91d8b31a52b1f0e6eqIddc847817c19d4ddaab67eb8b3f1b90ed,若集合eqId7556ec09776c479d83999992d3c80814中有eqId8898c1dc81824f3098bbeae74e8f11fd个元素,则实数eqId32454977564e4ee18da36bd51156c509的取值范围是__________.
难度系数:0.15使用:514次题型:填空题更新:2019/6/7
三、解答题
17 . 在eqId992fe44057cf4492895193f3f5398449中,eqIdee29121fd0d247dc815fe3c7596abb06eqIdca3b74cb75a340e9b504a3ffa03d18eaeqIdbe4ba88cdb9043789f28c09ad3bb7810eqId992fe44057cf4492895193f3f5398449的内角平分线,eqId2281e9af81ba45058952a310c8820c10.
(Ⅰ)求eqId182337b5d6c245e69b1c87b406c882c6的值
(Ⅱ)求角eqIdcc614bd3390c4d028df189b234dcc351的大小
难度系数:0.85使用:516次题型:解答题更新:2019/6/7
18 . 如图,eqId992fe44057cf4492895193f3f5398449eqId1a59f675e3ea4309bfb83ff3b4953b43eqId6e82d3b62ac24ed5b35425ee7b513530eqId93cbffaa5ae045d6ac45d1e979991c3aeqIdd5b10b2a13f148b78e0d5a1b820538fd分别为eqId99a3187c2b8f4bcc9703c74c3b72f1f3eqIdcf2da96900c948a1b3ce7cbfd420c080边的中点,以eqId1a0830891ff846de8422ea80714ecab4为折痕把eqId59ba42088e944332a1be671aeb031182折起,使点eqIdcc614bd3390c4d028df189b234dcc351到达点eqIdd7be5abad1e34f6db17a56660de8d54f的位置,且eqId8abab2acfe5e4930844e46990a7541d6..
figure
(Ⅰ)证明:eqId6ff1c35a6aec46b287d5fb3ab114dcdb平面eqId652e1d89a8df43c3b0575cc7729feb5c
(Ⅱ)设eqId517584fed25c413ba8b7bb33ffa2d5c6为线段eqId7b71ac6238b649bba16fd5463c7b0b56上动点,求直线eqIde18c3dc1d0a24201bc03dae6e727fc33与平面eqIdbe3defbca74843cfa3ff8fb1e8520461所成角的正弦值的最大值.
难度系数:0.65使用:300次题型:解答题更新:2019/6/7
19 . 在我国,大学生就业压力日益严峻,伴随着政府政策引导与社会观念的转变,大学生创业意识,就业方向也悄然发生转变.某大学生在国家提供的税收,担保贷款等很多方面的政策扶持下选择加盟某专营店自主创业,该专营店统计了近五年来创收利润数eqIdcee2232199ff4be0ac694c983d786be8(单位:万元)与时间eqIde0223a1879b144d3905ef5af94b09106(单位:年)的数据,列表如下:
figure
(Ⅰ)依据表中给出的数据,是否可用线性回归模型拟合eqId072d7d6b911b42bc89207e72515ebf5feqId32454977564e4ee18da36bd51156c509的关系,请计算相关系数eqIdd9026ce1966847eb86a5e13345fed583并加以说明(计算结果精确到eqId80022332428548d99aa6eb2fd1b9062e).(若eqId35ce079bac394085b4711719ad9b6fb9,则线性相关程度很高,可用线性回归模型拟合);
附:相关系数公式eqIde5c4a276913c4a3c9ff3a9fe95481c56eqId5eac35a2c32d4f8e82b02cfe36c84718
参考数据eqId14a394e84567410595774a3d71b1e36b.
(Ⅱ)该专营店为吸引顾客,特推出两种促销方案.
方案一:每满eqId7c7bb070a42641baac658b969a1385c6元可减eqIdd6c0e3ca15b3431487f3ef7f69c1d8a5元;
方案二:每满eqId7c7bb070a42641baac658b969a1385c6元可抽奖一次,每次中奖的概率都为eqIdc4029d4942be4b7ab551922941e74e51,中奖就可以获得eqId9b60a1d8f8a546adad03a8a544135b62元现金奖励,假设顾客每次抽奖的结果相互独立.
①某位顾客购买了eqId95ca1aab1ed749c5a05d646fe8feb55b元的产品,该顾客选择参加两次抽奖,求该顾客获得eqId9b60a1d8f8a546adad03a8a544135b62元现金奖励的概率.
②某位顾客购买了eqIdde02dcb652014b73ac90b1cf2560c15a元的产品,作为专营店老板,是希望该顾客直接选择返回eqId4ae541456de84214b67f4d8d8e9c2d39元现金,还是选择参加三次抽奖?说明理由.
难度系数:0.85使用:410次题型:解答题更新:2019/6/7
20 . 已知抛物线figure,圆eqId2d8c5ed1855442f39201ec851ee4e264.
(Ⅰ)eqIdd5b10b2a13f148b78e0d5a1b820538fd是抛物线eqId19a4eb16029e4550a14f2afe4741a3c3的焦点,eqIdcc614bd3390c4d028df189b234dcc351是抛物线eqId19a4eb16029e4550a14f2afe4741a3c3上的定点,eqIdac4f6a68bcfc49aeb2950ceda6243661,求抛物线eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(Ⅱ)在(Ⅰ)的条件下,过点eqIdd5b10b2a13f148b78e0d5a1b820538fd的直线eqId417e80f1349244878d01fe90e0891f5f与圆eqId93cbffaa5ae045d6ac45d1e979991c3a相切,设直线eqId417e80f1349244878d01fe90e0891f5f交抛物线eqId19a4eb16029e4550a14f2afe4741a3c3eqIdd7be5abad1e34f6db17a56660de8d54feqIdca9308a4ebd84ed8a28d8a519a8dbb39两点,则在eqIdc12aac8c2448479687a40735b3572a23轴上是否存在点eqId2381423d4cd146cab95f55527681a766使eqId0678c449e1544f1a8f75fcf14aaf2fb1?若存在,求出点eqId2381423d4cd146cab95f55527681a766的坐标;若不存在,请说明理由.
难度系数:0.4使用:261次题型:解答题更新:2019/6/7
21 . 已知函数eqId4a3e781737934c49ab0be06eea9df99eeqIde9edd995034840cfb557ea415074294a.
(Ⅰ)当eqId7aa0304bbc2f497d81252f9c24541f51时,求eqId4837c94ef0ff4dcf9b1dda4df363275a的最小值;
(Ⅱ)若eqId4837c94ef0ff4dcf9b1dda4df363275a有两个零点,求参数eqId70a27b6ddf6b478285353abb3b1f3741的取值范围
难度系数:0.15使用:720次题型:解答题更新:2019/6/7
22 . 在平面直角坐标系eqId99aa1a5c138c47c883843229fec9a5d6中,直线eqId417e80f1349244878d01fe90e0891f5f的参数方程为eqId655c4081e960459c9f5d2361a9992dc2eqId32454977564e4ee18da36bd51156c509为参数),曲线eqId0831715c83144509a334aca7de95ea3b.以坐标原点为极点,eqIdc12aac8c2448479687a40735b3572a23轴正半轴为极轴立极坐标系,曲线eqId0913b82c12b848baac239b9723f28c64的极坐标方程为eqIdccd5210b1685442193ebce704b260ce3.
(Ⅰ)若直线eqId417e80f1349244878d01fe90e0891f5feqIdc12aac8c2448479687a40735b3572a23eqId072d7d6b911b42bc89207e72515ebf5f轴的交点分别为eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c,点eqIdd7be5abad1e34f6db17a56660de8d54feqId89f304d65276434e9d4128cdd7fe2e9e上,求eqId422df40fa8ed4a1da7c6230efaa77002的取值范围;
(Ⅱ)若直线eqId417e80f1349244878d01fe90e0891f5feqId0913b82c12b848baac239b9723f28c64交于eqId2381423d4cd146cab95f55527681a766eqId8eea7f6267fb49d9bce12b8ba079a43e两点,点eqIdca9308a4ebd84ed8a28d8a519a8dbb39的直角坐标为eqIdb0a7048df4af4f1fb21343c07b4cccdc,求eqId6c4f39e0339749ce8d2589b15659a7e2的值.
难度系数:0.65使用:467次题型:解答题更新:2019/6/7
23 . 已知函数eqIda2a5c94b21e54faf8f8723de864d8738.
(Ⅰ)求eqId61d5e792ea11486ca32b1ceac215d22f时,eqIdfad572d341ed447397d9f7c1619794ee的解集;
(Ⅱ)若eqId4837c94ef0ff4dcf9b1dda4df363275a有最小值,求eqId70a27b6ddf6b478285353abb3b1f3741的取值范围,并写出相应的最小值.
难度系数:0.65使用:226次题型:解答题更新:2019/6/7
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