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          山西省太原市2019届高三模拟试题(一)文科数学试题

          适用年级:高三试卷类型:高考模拟试题总数:23浏览次数:281上传日期:2019/5/6
          一、单选题
          1 . 已知集合eqId7ee3f754a2d14e2bae79f89da42a73b9,eqIda8433b1b510f497983a3580e0ca0f563,则eqId170a03e31a0e4656b66452088e998e61(???)
          A.eqId92e73e2b41904318ab5e3d5894a91e80B.eqId888d683804e94e71ba7d0387c1015e1eC.eqIdd50dab1b99104684bc034b37c4da55ceD.eqId7162192b280e4a7bbb333f3c01c82d2f
          难度系数:0.94使用:116次题型:单选题更新:2019/5/6
          2 . 已知eqIdb6e15e51d29a47a7aff44f98b1aafaee为虚数单位,则复数eqId846c0894c10e4c0e8667839803c7a3bd(???)
          A.eqId1df0cecb2eae4c9e99fbe69d65ded655B.eqIdc5c2b6338e53481f8e89cee21136af2fC.eqId2e0d544c14ed4384b277f3990549b8d7D.eqId7de24fb683ba450480cf2c6615244f80
          难度系数:0.94使用:122次题型:单选题更新:2019/5/6
          3 . 下列命题中的真命题是(???)
          A.若eqId362e6b2863534f72b173ba88f1aec5e9,则向量eqIdbf80e33f8af0497793eeb1eb2a0e416eeqId26d0383ebc3f44c2984e80b88390a5f5的夹角为钝角
          B.若eqId09e871cdbe5e41eea8a95c14838b9957,则eqId448aa7f9870746a18c5f1d3b6755aef8
          C.若命题“eqId58e985f4c1274617875fade491b4d643是真命题”,则命题“eqIdc89abe1e4d584e16b3718409cb609213是真命题”
          D.命题“eqId211f758370674a1b9ef30d9349d159a4,eqId5d69c1105cb7439292e993afa4e074a7”的否定是“eqId2729f52262fd44f0a3efbe90ddffd32b,eqId0998b84c382d4500b835bf2656485e90
          难度系数:0.85使用:263次题型:单选题更新:2019/5/6
          难度系数:0.85使用:321次题型:单选题更新:2019/5/6
          5 . 已知函数eqId2732cb9cd7494c928df81fe062c04011在点eqId58f537310d654e068790cb3cebc56e79处的切线经过原点,则实数eqId70a27b6ddf6b478285353abb3b1f3741(???)
          A.1B.0C.eqId35042a9000404cec92f70f975294facdD.-1
          难度系数:0.85使用:395次题型:单选题更新:2019/5/6
          6 . 已知等比数列eqId315af7e63b0e4f1d93184bcb531e1e5a满足eqIde57c20acdb1840adbc96544793418181,eqId8a59daebf33c4f4d944b487beefaa632eqId7ff76d1a655549f6a82d004320793823(???)
          A.7B.-5C.5D.-7
          难度系数:0.65使用:351次题型:单选题更新:2019/5/6
          7 . 下图是某几何体的三视图,其中网格纸上小正方形的边长为1,则该几何体的体积为(???)
          figure
          A.12B.15C.eqId37ceff6e387b44a08b18edb28f0b8b03D.eqId6fdc6f332e91498ba99a522100d3fc6f
          难度系数:0.94使用:317次题型:单选题更新:2019/5/6
          8 . 在平面区域eqId42074857e6eb45fc880dcf58ecbedbee,内任取一点eqIda733cd9df1394d929d03733bfeda55f8,则点eqIdd7be5abad1e34f6db17a56660de8d54f的坐标eqId250f7fb784d24e0cafe915042cd755cf满足不等式eqIdf10b8dfea1894eec9dd29a9a4c543323的概率为(???)
          A.eqIdee4fb2d20e664b5b9554d6e048dadf13B.eqId1a987131f0b64a73b98104810cb0ddf1C.eqId7982f4ec26d54462a55f7cad7f2729c9D.eqId2b24119e853c4a3fac94375722970923
          难度系数:0.65使用:326次题型:单选题更新:2019/5/6
          9 . 已知数列eqId2c1230a9ef5a4968be599681d676dd2b的前eqIdf458db68122849abb588feb2e682d9ac项和eqIddb5481de79c946c0a760143297d5eade满足eqId9bdbdc81f3034c3eb1fda4e3391eda9aeqIdb1291e64e4254e018299770b7212814b,则eqId4b6ab979343243ff9fb10b1a991bd77d(???)
          A.eqIda87bdfffb405436f8d2adfebebbf34deB.eqIda840685d6efc47b18c218bc5b9c23549C.eqId1551208ee3c943a08eeb1961a294a682D.eqId21e5226783fd4114816ecda0fd9a9566
          难度系数:0.65使用:390次题型:单选题更新:2019/5/6
          10 . 已知双曲线eqId13f28c24f8d64032b78c9ea1e1261b65eqIdb17ff237fa78496abf2e4d148ec3e961的左右焦点分别为eqId0aa72756ed0c4c7a89f26aa94f43e47d,eqIdde963a24921f4ee7a991bf9d4f43a42e,直线eqId0900f1f1d3e44f0ba67b735620f0aba7过点eqId0aa72756ed0c4c7a89f26aa94f43e47d与双曲线eqId19a4eb16029e4550a14f2afe4741a3c3在第二象限相交于点eqIdd7be5abad1e34f6db17a56660de8d54f,若eqIdc467303e1cd14267903096766a5bc5f1,则双曲线eqId19a4eb16029e4550a14f2afe4741a3c3的离心率是(???)
          A.eqIda2a0ce3781fa4c26b624f5966b7dee44B.eqIdcd9b24a6a6e5426ab775be20461174e3C.2D.eqIdb7a61e896bf34cc6a774b4e37a052332
          难度系数:0.65使用:241次题型:单选题更新:2019/5/6
          11 . 已知定义在eqIdea2866d3038147a68678f20f51476ad9上的函数eqId75edd6ff38f44f73b1a72ae1266165fe满足eqIde039857476fd47a191c28315ac85a79a,且eqId328f53492658456d8ee6d10cf8fc6a3d,则eqIdbb149319aebf4ff6a1d4d02ee2c6d3aa的解集是(???)
          A.eqIdac34c85ecbbc4d688bad7cec6e371385B.eqId3ad89a9076294204a071be8cbbb5ccefC.eqIddf43fa5ed3954d49bac7d1d9882e17b5D.eqId7f3fa6c49bc640b9ad2727a4d8e2c9c3
          难度系数:0.65使用:425次题型:单选题更新:2019/5/6
          12 . 将函数eqIdcc80a421d75a4c1d8bb9423b106ff3ec的图象向右平移eqId145940d03af4447eabd753d76abd2a1deqIdf4c71d21ea4d443381cbccc0b8e97d7e个单位后得到函数eqIdfcaf3bbe14e548cc8d47beb2467db5a0的图象,若方程eqIdd9b061546c874d21828b457cf5fa2b80的根eqIdf7cbc1ad0a7b4f97b479c131b62ad882,eqIdaecaf42a9cfb4a5c8c0cade53729c9ba满足eqIdd3caaa98bdce4be89237950eba164283,则eqId145940d03af4447eabd753d76abd2a1d的值是(???)
          A.eqIdb47bf79338b1478a89eac53d16970cdfB.eqIdd3e88ecbd2db456396e01302a43b93d9C.eqId87a9bbb6dd564186905f2064b8c22182D.eqId2cb51764ae3949b9b698fc2f9527dff2
          难度系数:0.65使用:247次题型:单选题更新:2019/5/6
          二、填空题
          13 . 抛物线的准线方程为_______.
          难度系数:0.94使用:576次题型:填空题更新:2018/1/29
          14 . 已知单位向量的夹角为,则__________.
          难度系数:0.94使用:538次题型:填空题更新:2012/9/9
          15 . 已知函数eqId3075402477e84e338a5adcbb425d9eab若方程eqId545dcb49cb9e44cba01c47a4b6d5b100有两个不相等的实根eqIdf7cbc1ad0a7b4f97b479c131b62ad882,eqIdaecaf42a9cfb4a5c8c0cade53729c9ba,则eqIdb81c2234188c43d58772172ac0e739a8的最大值为__________.
          难度系数:0.65使用:284次题型:填空题更新:2019/5/6
          16 . 如图,正方体eqId588284d93dc5489295f8f224f8e30d13的棱长为4,点eqIdca9308a4ebd84ed8a28d8a519a8dbb39在棱eqIdea82c30b37894b1bb742dee61200db07上,且eqId92804d73f4d94ebc95fe3c153dce1bf9,eqId45bf04ad61254d1db36b6029a42ca9b4是面eqId50dcbbdb425943e8b5a0e6b8b508d09f内的正方形,且eqIdac72548e3b824bfabb3c578db21b990a,eqIdd7be5abad1e34f6db17a56660de8d54f是面eqId50dcbbdb425943e8b5a0e6b8b508d09f内的动点,且eqIdd7be5abad1e34f6db17a56660de8d54f到平面eqId0645bf529ddb4f81b26e3a3c58a047b5的距离等于线段eqId7b71ac6238b649bba16fd5463c7b0b56的长,则线段eqId4ea1af672e334fb1a6a3ab675d494e72长度的最小值为__________.figure
          难度系数:0.65使用:210次题型:填空题更新:2019/5/6
          三、解答题
          17 . 如图,已知eqId64b9b599fdb6481e9f8d9a94c102300b的内角eqIdcc614bd3390c4d028df189b234dcc351,eqId8754ce8cf7f34f04abb9a0c041f57f5c,eqId19a4eb16029e4550a14f2afe4741a3c3的对边分别是eqId70a27b6ddf6b478285353abb3b1f3741,eqIdaea992e70d4943e49e893817eb885ed7,eqIdad7cefefaba947e1a168bca491c4fca1,且eqIde6aed394bd734d18b6f436a813376ed0,点eqId0cd8063abf2b458f80091bc51b75a904eqIdcf2da96900c948a1b3ce7cbfd420c080的中点,eqId8f0d92f3bcb04a19a496b597fac94202,交eqId99a3187c2b8f4bcc9703c74c3b72f1f3于点eqId93cbffaa5ae045d6ac45d1e979991c3a,且eqIddad31040fd02475ea52d192682cf59c6,eqId55cf7e04ebcb44eb8a5ffad2b591255e.
          figure
          (1)求eqId8754ce8cf7f34f04abb9a0c041f57f5c;
          (2)求eqId64b9b599fdb6481e9f8d9a94c102300b的面积.
          难度系数:0.65使用:434次题型:解答题更新:2019/5/6
          18 . 如图,在四棱锥eqId770e29d14b274c728d9b8ce2b191fda6中,底面eqId5ce7a06ae7a34393b92b5277978ac014是平行四边形,eqId2381423d4cd146cab95f55527681a766,eqId517584fed25c413ba8b7bb33ffa2d5c6分别是eqId0627be51821d4be7b3e024a354815d64,eqId66d409c343f04cfda647f9bfc7da6b2a的中点,eqId7ad7a82e0b5e414991c43a0bbb3b1db1是等边三角形,面eqId8895fef48d16470a9671f932b178e485eqIdc99c444e10d84680a6fdc44586d46ce1,eqId51b787c23e694051b0599ec6ec434478,eqId83c5e611f64a491ca0bf18c26e874bda.
          figure
          (1)证明:eqId9ca2fcc94017421c98babfce4c93d037eqId9734ae9e5b784be5afa257a9ac88a7c4;
          (2)求三棱锥eqId3cc0b843d920413b844eda786533bc4c的体积.
          难度系数:0.65使用:305次题型:解答题更新:2019/5/6
          19 . 近年来随着互联网的高速发展,旧货交易市场也得以快速发展.某网络旧货交易平台对2018年某种机械设备的线上交易进行了统计,得到如图所示的频率分布直方图,和如图所示的散点图.现把直方图中各组的频率视为概率,用eqIdc12aac8c2448479687a40735b3572a23(单位:年)表示该设备的使用时间,eqId072d7d6b911b42bc89207e72515ebf5f(单位:万元)表示其相应的平均交易价格.
          figurefigure
          (1)已知2018年在此网络旧货交易平台成交的该种机械设备为100台,现从这100台设备中,按分层抽样抽取使用时间eqId39b9e52c8cae4a19bd9999919ae81be9的4台设备,再从这4台设备中随机抽取2台,求这2台设备的使用时间都在eqId938b0b9210834e2e8b040bb57b3cb761的概率.
          (2)由散点图分析后,可用eqId73e3745a0ae74e0ca6159a3a39f81125作为此网络旧货交易平台上该种机械设备的平均交易价格eqId072d7d6b911b42bc89207e72515ebf5f关于其使用时间eqIdc12aac8c2448479687a40735b3572a23的回归方程.
          figure
          表中eqIdc026b316dc954dffa2900a7e727a3622,eqIdea9d7b13626a4e9eb5706ded06dd38a2
          (i)根据上述相关数据,求eqId072d7d6b911b42bc89207e72515ebf5f关于eqIdc12aac8c2448479687a40735b3572a23的回归方程;
          (ii)根据上述回归方程,求当使用时间eqIdb963099e95254e4a9a413e2b96f768f0时,该种机械设备的平均交易价格的预报值(精确到0.01).
          附:对于一组数据eqId02db5f466e554ff3b2a989456ea3d6d8,eqIdb866aeb994db431a851950eb5eff1395,…,eqId51adb0b519e14fe8a58ea111aecd9c27,其回归直线eqId6c349e1c31e94326b8ce45a6ea92753b的斜率和截距的最小二乘估计分别为eqId1b07677782ea41bd8cd9a80fd3b8f904
          参考数据:eqId40418469fec5493c8c6c1aeb4dc7ec65,eqId031abdb1ca7d4381a80c6d8cda908f54,eqId3713e55ad81b49c9a2684db36b194fc0.
          难度系数:0.65使用:707次题型:解答题更新:2019/5/6
          20 . 已知椭圆eqId76662bc293df4139b90c65ed8b136d3beqIdae57f5b0c81947a6986bec0b052d5019的左、右焦点分别是eqId0aa72756ed0c4c7a89f26aa94f43e47d,eqIdd5b10b2a13f148b78e0d5a1b820538fd,其离心率为eqIddb6b28cbd8a14caa9cf1146f6f7916c0,点eqIdd7be5abad1e34f6db17a56660de8d54f是椭圆eqId19a4eb16029e4550a14f2afe4741a3c3上任一点,且eqIda0630b0433694e2c93052b19dec269c6面积的最大值为eqIda2a0ce3781fa4c26b624f5966b7dee44.
          (1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
          (2)若斜率不为0的直线与椭圆eqId19a4eb16029e4550a14f2afe4741a3c3相交于eqId2381423d4cd146cab95f55527681a766,eqId517584fed25c413ba8b7bb33ffa2d5c6两个不同点,且eqId42dcd6f502594116b8d8351e4a91c8e7是平行四边形,证明:四边形eqId42dcd6f502594116b8d8351e4a91c8e7的面积为定值.
          难度系数:0.4使用:315次题型:解答题更新:2019/5/6
          21 . 已知函数eqIdcdfad39453ce444096dc87e1a7fe8b9c,eqId7aee35ef0014493a9e716473f2eb1766.
          (1)讨论函数eqId6f13759e937144069819aed2ae5a1057的单调性;
          (2)当eqId982da3835b7946d999cc8604a2ece266,时,若对于任意eqIdc6c39367598f467695233f1162898e25,都存在eqId27f9fb4cbe854d58a364f79efe4f515b,使得eqId6bc21b355ff94ff8bae5760c09554a00,证明:eqIdc3c65b61a47c4051ba77cbd4536f5500.
          难度系数:0.4使用:277次题型:解答题更新:2019/5/6
          22 . 在平面直角坐标系eqId94e28bb883384a7580bda6b481c94427中,曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的参数方程为eqId7d497917f9ec48e6b8c1340d08e60a47,以原点0为极点,eqIdc12aac8c2448479687a40735b3572a23轴的正半轴为极轴建立极坐标系,曲线eqIdfe33ac7524b14f658e64c52c37499d5c的极坐标方程为eqIdb9fcdf6f84644541ad1a4f6020336aed.
          (1)若曲线eqIdcfc8599bedfb4ab4944abf141f348a9a方程中的参数是eqIdc13953f2514e4c8f9c8aaaf5241c33ac,且eqIdcfc8599bedfb4ab4944abf141f348a9aeqIdfe33ac7524b14f658e64c52c37499d5c有且只有一个公共点,求eqIdcfc8599bedfb4ab4944abf141f348a9a的普通方程;
          (2)已知点eqId3deaf6d16cf84f17a60709d6c1f8f277,若曲线eqIdcfc8599bedfb4ab4944abf141f348a9a方程中的参数是eqId32454977564e4ee18da36bd51156c509,eqId7a4e13687ef44ed2acdbfd4630b5ff2c,且eqIdcfc8599bedfb4ab4944abf141f348a9aeqIdfe33ac7524b14f658e64c52c37499d5c相交于eqIdd7be5abad1e34f6db17a56660de8d54f,eqIdca9308a4ebd84ed8a28d8a519a8dbb39两个不同点,求eqId063d33d623dc4a01836e553e3630786a的最大值.
          难度系数:0.65使用:393次题型:解答题更新:2019/5/6
          23 . 已知函数eqId799282a0f48f40e3b7ec823d4eeaacb7.
          (1)求不等式eqIdcbd76f89e7a44dacb5360a0c0cad8b54的解集;
          (2)若存在实数eqId761b2917a82b4524b8dbab7e6380f014,使得eqIdb432c32270e8448db50cb44be1e2e867成立的eqId3a4208e0040c42ed8b09de2cae9d562e的最大值为eqId2381423d4cd146cab95f55527681a766,且实数eqId70a27b6ddf6b478285353abb3b1f3741,eqIdaea992e70d4943e49e893817eb885ed7满足eqId469c1897dc3f4184a4c1149203dffe53,证明:eqIda70c50fea00543189694cac21c3efd2f.
          难度系数:0.65使用:228次题型:解答题更新:2019/5/6
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