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                                                                                                                河南省郑州市2019届高三第三次质量检测数学(文)试题

                                                                                                                适用年级:高三试卷类型:高考模拟试题总数:22浏览次数:38上传日期:2019/6/7
                                                                                                                一、单选题
                                                                                                                1 . 已知集合eqIdf53975a4ca9f4424a602aa2d74b631b1eqId9d057a42276041a981b601ec75ab410e,则eqIdcfb073d9fa8a44179cf4e242d45e6d3c(??)
                                                                                                                A.eqIdec916256d98e4e5d94759035375ad4aaB.eqIde19bdd270dc04752b49afb60a7c3e6adC.eqIdc1e3d9b5d6084b16b2e19c81cdb08a4fD.eqId4e3b32b7450c4b8fa21aac72a9431948
                                                                                                                难度系数:0.94使用:13次题型:单选题更新:2019/6/7
                                                                                                                2 . 已知eqIdcef329895f614248b69712b61bfa9883为虚数单位,复数eqId2cd9e2fe3d6540df9399dbefe49ada54满足eqId82629f8021bb413283a3c81c27fa2ccb,则在复平面内eqIdb99107e2becb4c6a83d81135996881b3对应的点在(??)
                                                                                                                A.第一象限B.第二象限C.第三象限D.第四象限
                                                                                                                难度系数:0.94使用:20次题型:单选题更新:2019/6/7
                                                                                                                3 . 我国古代有着辉煌的数学研究成果,其中的《周髀算经》、《九章算术》、《海岛算经》、《孙子算经》、《缉古算经》,有丰富多彩的内容,是了解我国古代数学的重要文献,这5部专著中有3部产生于汉、魏、晋、南北朝时期,某中学拟从这5部专著中选择2部作为“数学文化”校本课程学习内容,则所选2部专著中至少有一部是汉、魏、晋、南北朝时期专著的概率为(??)
                                                                                                                A.B.C.D.
                                                                                                                难度系数:0.94使用:217次题型:单选题更新:2019/4/14
                                                                                                                4 . 已知双曲线eqId7dc51092f8cc4683931a7d2a99be93a6的一条渐近线经过点eqIdd6be86ec372540b49e7d38c4d9ae366d,则双曲线的离心率为(??)
                                                                                                                A.eqIdcb116245290448fc88ad18e6a3789035B.eqId94cd6242e9394c5b9aba165383223193C.eqIda6cc4ecb53dd44c79f1094c31bd61e7bD.eqId8898c1dc81824f3098bbeae74e8f11fd
                                                                                                                难度系数:0.85使用:10次题型:单选题更新:2019/6/7
                                                                                                                5 . 同时具有性质“①最小正周期是eqId5a6dc96e894e4f23be3c422cad388a30”②图象关于eqId54e067d4546848e394fa75942e58f41a对称;③在eqId1bbf6368486c401e81fd8e6c902968bb上是增函数的一个函数可以是(??)
                                                                                                                A.eqId9f8e49ccdf7a4cccbf49c0e3af004afaB.eqIdcd30740d423d4fe1bf48a6874391ea96
                                                                                                                C.eqId9007d11d926842b3a1c61352edf8076cD.eqId8a3f480f0ea348af957038181f15fb5c
                                                                                                                难度系数:0.85使用:19次题型:单选题更新:2019/6/7
                                                                                                                6 . 在eqId992fe44057cf4492895193f3f5398449中,若点eqId0cd8063abf2b458f80091bc51b75a904满足eqIdceb7b9e23cab4228b8a2e764b0d01311,点eqId2381423d4cd146cab95f55527681a766eqIdcf2da96900c948a1b3ce7cbfd420c080中点,则eqId2b4a0cae6ce6469da9337e17130da9a2=(??)
                                                                                                                A.eqIdeea89aef0d214905a4d1c298ae4ee18fB.eqIdf84cc44a458a42eb9129f0eec29ee6b1C.eqId69128acb02654dac9955b0f0b0adbadfD.eqIdebc326092bc640c39adf553b22f5eba7
                                                                                                                难度系数:0.85使用:24次题型:单选题更新:2019/6/7
                                                                                                                7 . 已知定义在eqId7dcd2312d0bf4bb1befdfcc170e45791上的函数eqId4837c94ef0ff4dcf9b1dda4df363275a满足eqIdf4165c4a38444f7d9093b4ea4c1f50fd,且函数eqId4837c94ef0ff4dcf9b1dda4df363275aeqIdf0a2e15a68814b2d98a1c52e11084f4d上是减函数,若eqId2a01b2eaf41c45ca809bfdb2dd80c32beqId1ac4895808044694addae17fadcfc642eqIde527667067814617808956d09514cf3a,则eqId70a27b6ddf6b478285353abb3b1f3741eqIde3ff50261b3b48789d45dd3876c7571beqIde35f447365484e7f891dc56884132698的大小关系为(??)
                                                                                                                A.eqIdf2d0452490a644fc93c289a699184792B.eqId5f41c357450f4a2bbc83cc2bf71569d3C.eqId988282e31d4c4be898187be93d8893a8D.eqId8326d27a34624d9390591c8250142736
                                                                                                                难度系数:0.65使用:11次题型:单选题更新:2019/6/7
                                                                                                                8 . 在轴截面顶角为直角的圆锥内,作一内接圆柱,若圆柱的表面积等于圆锥的侧面积,则圆锥的底面半径与圆柱的底面半径之比为(??)
                                                                                                                A.eqId94cd6242e9394c5b9aba165383223193B.eqIdc052ddfbd4524f67a79e0e77c2e5656aC.eqId2644c4fd7d684e75ae5ed93cb3581244D.eqIdddd35c5d043e4ebeac32a99367053c68
                                                                                                                难度系数:0.65使用:22次题型:单选题更新:2019/6/7
                                                                                                                9 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3aeqIdeeb4ca98872f4e6d91cea28f43fc0b63满足eqIdc3fe975b34aa4288b929e9b6682ec6bceqIdcd4972fa5e644131bcd61dcacab7fbcdeqId5212c995e2184aafac28beaa8ac65de8.则数列eqIdc2cbf03707ac4dd5931e93ce13542bc5的前eqId11f75c152f5341f39d020095cecda9b3项和为(??)
                                                                                                                A.eqId9a9b25031dec478a879aa613dfa5bd45B.eqId33d46e71fa9a4174ad6ca3af7ad32687C.eqIdb3cea48dab0747d9a3efbbb65045e9caD.eqIdef62e01be2e2485fb1d8edaef1bdd91e
                                                                                                                难度系数:0.85使用:15次题型:单选题更新:2019/6/7
                                                                                                                10 . 如图所示,网格纸上小正方形的边长为eqId2f746fef440e46f2963d399de1459b2f,粗线画出的是某几何体的三视图,则该几何体的体积为(??)
                                                                                                                figure
                                                                                                                A.eqIda87c95e7a5f041a2afeb1bb41b0805a4B.eqId77eb12453bd54f66be53a8232c5ed641C.eqId8d9106e1c5b44ff5aefbf80a7e170bacD.eqId1ffd2abe185c4ab287b4ce1affd111af
                                                                                                                难度系数:0.4使用:340次题型:单选题更新:2019/4/11
                                                                                                                11 . 已知椭圆eqId2d06a65effcb497696160a90dc2a5ba1与双曲线eqId4137bd96c24f4bffbab2fd90ffe744cc有公共焦点,eqId0913b82c12b848baac239b9723f28c64的一条渐近线与以eqId89f304d65276434e9d4128cdd7fe2e9e的长轴为直径的圆相交于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,若eqId89f304d65276434e9d4128cdd7fe2e9e恰好将线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3三等分,则(???)
                                                                                                                A.eqId66d279f98d3d4c64ae56a9982ff3c32dB.eqId2a65ee8a79da48d5a2d204ce9ad01bc1C.eqId0d197b3d84034917a7d310743bb1de75D.eqId564601dfbe204563a679c8400dc03b33
                                                                                                                难度系数:0.65使用:9次题型:单选题更新:2019/6/7
                                                                                                                二、填空题
                                                                                                                12 . 若实数eqIdc12aac8c2448479687a40735b3572a23eqId072d7d6b911b42bc89207e72515ebf5f满足条件eqIdb1e8e9ce38c34375a72ea6756655bebceqId42ee41dc3a7d452d9e1f20b37fb532a2的最大值为__________.
                                                                                                                难度系数:0.94使用:16次题型:填空题更新:2019/6/7
                                                                                                                13 . 在三棱锥eqId45c4760a833c4f3ab3f2efef403d69c9中,eqId6c155f0ef2bc455ba6a717afde8cdaac,eqId5917bc5b0c184db0adfea9d3d7975870,则三棱锥eqId45c4760a833c4f3ab3f2efef403d69c9外接球的表面积为__________.
                                                                                                                难度系数:0.65使用:15次题型:填空题更新:2019/6/7
                                                                                                                14 . 在数列eqId93e38ecd74a24cb59da79181b95bfd3a中,满足eqIdaebe3dd7d7eb458d91d8b31a52b1f0e6eqIdf85fb472fce740a1991fd2c3cde332aceqId4e7aa1db7874488792358387c382192beqId275f6f3282c444ad8a2fd8e75251a738eqId5212c995e2184aafac28beaa8ac65de8),则figure__________.
                                                                                                                难度系数:0.65使用:13次题型:填空题更新:2019/6/7
                                                                                                                15 . 已知函数eqIde1be6e27002043efa5eab0926ec61794,若在区间eqIdd9c8e246392c4473b9c9b64f4cd089a8上函数eqId4837c94ef0ff4dcf9b1dda4df363275a的图象恒在直线eqIdffecf7be5ed549f7ab426cf304352437的图象的下方,则实数eqId70a27b6ddf6b478285353abb3b1f3741的取值范围是__________.
                                                                                                                难度系数:0.65使用:10次题型:填空题更新:2019/6/7
                                                                                                                三、解答题
                                                                                                                16 . 在eqId992fe44057cf4492895193f3f5398449中,内角eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3的对边分别为eqId70a27b6ddf6b478285353abb3b1f3741eqIde3ff50261b3b48789d45dd3876c7571beqIde35f447365484e7f891dc56884132698eqId77154d518d6c4636a654f723fc05176deqIdb97d6dff165d4cf8ae23c6473f206799.点eqId0cd8063abf2b458f80091bc51b75a904的线段eqIde84e0278d905475dbdfd36c2a4101592上,且eqIdae9b1ca7efc944588e6c46d64ca73e06eqId46dcf669a6ce45c6895e74b31e947427.
                                                                                                                (Ⅰ)求AB的长;
                                                                                                                (Ⅱ)求eqId39726fa171f74d35ae623009d5bf7637的面积.
                                                                                                                难度系数:0.85使用:13次题型:解答题更新:2019/6/7
                                                                                                                17 . 如图,菱形eqId5ce7a06ae7a34393b92b5277978ac014的对角线eqIdcf2da96900c948a1b3ce7cbfd420c080eqId1b51efe7c2fa42748ac5a6be262e2fa4相交于点eqIdaad7b72a25924d078d2360cdc99f1090eqId6079efc800734d2fa9869f1d78bc234c平面eqId5ce7a06ae7a34393b92b5277978ac014,四边形eqId985871b73b0245bdb99253a9a0f92565为平行四边形.
                                                                                                                figure
                                                                                                                (Ⅰ)求证:平面eqId667a51daaeda428da1df341cc6fedafc平面eqId8308cd625b6a4519b8c8d3ca60574e6e
                                                                                                                (Ⅱ)若eqId5e94b90aa1a24a258c676342de713897,点eqId624ead457bfc42928d5a00d01f311cf1在线段eqId04f04626638f43499fac1e326b7fe20d上,且eqId84197664aebd4acda199bcbe24d2db56,三棱锥eqId36cc5fb0525e4cc391aed08c2a74d0c6的体积等于四棱锥eqId65cc642d79f74b05b21d5f41f98baf17体积的一半,求eqId5f420ef2d0b94c4b8a5d8e20a5d1ce2c的值.
                                                                                                                难度系数:0.85使用:19次题型:解答题更新:2019/6/7
                                                                                                                18 . 某企业为确定下一年投入某种产品的研发费用,需了解年研发费用eqIdc12aac8c2448479687a40735b3572a23(单位:千万元)对年销售量eqId072d7d6b911b42bc89207e72515ebf5f(单位:千万件)的影响,统计了近eqId11f75c152f5341f39d020095cecda9b3年投入的年研发费用eqIda318598c955c4e3fb6fca24d898dc391与年销售量eqId9b281d892c79444abea810b59a7349da的数据,得到散点图如图所示:
                                                                                                                figure
                                                                                                                (Ⅰ)利用散点图判断,eqIdc572ead52d774ab7b909af63e266e399eqId25e69afc3f604892a41767b5ff796cc0(其中eqIde35f447365484e7f891dc56884132698eqId096e32e1d18145d199ccbacb5a9a85fe为大于eqIda86879ae304449a4a6e6461c485a1f13的常数)哪一个更适合作为年研发费用eqIdc12aac8c2448479687a40735b3572a23和年销售量eqId072d7d6b911b42bc89207e72515ebf5f的回归方程类型(只要给出判断即可,不必说明理由);
                                                                                                                (Ⅱ)对数据作出如下处理:令eqIda5d4481a3d2d4ff7bf8f36888d68fc22eqIdb641dcea74cb4628ace22ddfac4a938f,得到相关统计量的值如下表:
                                                                                                                figure
                                                                                                                根据(Ⅰ)的判断结果及表中数据,求eqId072d7d6b911b42bc89207e72515ebf5f关于eqIdc12aac8c2448479687a40735b3572a23的回归方程;
                                                                                                                (Ⅲ)已知企业年利润eqId2cd9e2fe3d6540df9399dbefe49ada54(单位:千万元)与eqIdc12aac8c2448479687a40735b3572a23eqId072d7d6b911b42bc89207e72515ebf5f的关系为eqId7442ce62fb394eceb7f57578f204f2f4(其中eqId7a133913a9f94bcc8266f4f61af61ada),根据(Ⅱ)的结果,要使得该企业下一年的年利润最大,预计下一年应投入多少研发费用?
                                                                                                                附:对于一组数据eqIdf16d77ae947e482999d9787c75122a83,其回归直线eqIda9877e70d3504ea6929d4debc77081da的斜率和截距的最小二乘估计分别为eqId5bb3dccab75a451291eb08675d3d0aeceqIdcf9225b188124cdd99a938fdbbc5a323
                                                                                                                难度系数:0.65使用:18次题型:解答题更新:2019/6/7
                                                                                                                19 . 已知抛物线eqId1832cb9298c24d33a91c7f736a1d695e的焦点为eqIdd5b10b2a13f148b78e0d5a1b820538fdeqIdc12aac8c2448479687a40735b3572a23轴上方的点eqId0fda1586ec2147749d8c671c3aec9d89在抛物线上,且eqId8980875d106648f8b2451ee0284c93a3,直线eqId417e80f1349244878d01fe90e0891f5f与抛物线交于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c两点(点eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId2381423d4cd146cab95f55527681a766不重合),设直线eqId4cec7f78f05f4905884972b23407f11deqId1fa29b89d8c1441fb756373fabf9a446的斜率分别为eqIdd4bf9298f0db4fb5afb67e0d739f3074eqId75fdb198d83447e59e31c1f4923cc3bc.
                                                                                                                (Ⅰ)求抛物线的方程;
                                                                                                                (Ⅱ)当eqId321bc71ebecf43bb9b07f547b7406f69时,求证:直线eqId417e80f1349244878d01fe90e0891f5f恒过定点并求出该定点的坐标.
                                                                                                                难度系数:0.4使用:11次题型:解答题更新:2019/6/7
                                                                                                                20 . 设函数eqIdb207495800e84ffb95fd1cc9be7a1556eqId934e69c483664cf9af85cc90ba4e6501.
                                                                                                                (Ⅰ)设eqIde79f51a45bf34d7a8744515170482adf,函数eqId97e0bb1d0e0f40f884e25f90ab6598aaeqId52a55495e3914940b0afe31ffb895c15处切线方程为eqIde28f0060e7f54b819dc25b5df032975c,求eqId70a27b6ddf6b478285353abb3b1f3741eqIde3ff50261b3b48789d45dd3876c7571b的值;
                                                                                                                (Ⅱ)若eqId61d5e792ea11486ca32b1ceac215d22feqId4d2187284c5d4de29906363f7d21f60f为整数,当eqId2d569479cd1c43c1af15895792b64db6时,eqId8b5be4910d6245de8eab05d3b5e6424e成立,求eqId4d2187284c5d4de29906363f7d21f60f的最大值.
                                                                                                                难度系数:0.4使用:19次题型:解答题更新:2019/6/7
                                                                                                                21 . 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:22次题型:解答题更新:2019/6/7
                                                                                                                22 . 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:22次题型:解答题更新:2019/6/7
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