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          2019年全国统一高考数学试卷(文科)(新课标Ⅲ)

          适用年级:高三试卷类型:高考真题试题总数:23浏览次数:4824上传日期:2019/6/9
          一、单选题
          1 . 已知集合eqId222d38fbff2544a3bfa51d057ec7ec74,则eqIdcfb073d9fa8a44179cf4e242d45e6d3c(?)
          A.eqId24fce0e9e75c4630992de76de3b53f94B.eqId59eabb7d87ab43fa87a15fe758bfe6fbC.eqId805f8e7a66e44370bfbea58150e6feceD.eqIde19bdd270dc04752b49afb60a7c3e6ad
          难度系数:0.85使用:2489次题型:单选题更新:2019/6/9
          2 . 若eqId934bcd667b5640b0bbe6e4df5fce4d2c,则eqId705acd54ee6740c69fcd89a7a1d12157(?)
          A.eqId15974c8fbf634ca5ac2dfd4392c6abb5B.eqId5e9792326de74cd595a965e17c155e7cC.eqId6a2f6a78c7024a17b7cfb416f74433c8D.eqIda8338c00e6d5440a9d67e5a43b776472
          难度系数:0.85使用:2213次题型:单选题更新:2019/6/9
          3 . 两位男同学和两位女同学随机排成一列,则两位女同学相邻的概率是(?)
          A.eqIdcb4e6e8b758d4b20a4e7922d57412286B.eqIde41289c7307b48bd893a195b321d250fC.eqIda8012d5322b240128851ebf3cd086e12D.eqIddb6b28cbd8a14caa9cf1146f6f7916c0
          难度系数:0.85使用:1176次题型:单选题更新:2019/6/9
          4 . 《西游记》《三国演义》《水浒传》和《红楼梦》是中国古典文学瑰宝,并称为中国古典小说四大名著.某中学为了解本校学生阅读四大名著的情况,随机调查了100学生,其中阅读过《西游记》或《红楼梦》的学生共有90位,阅读过《红楼梦》的学生共有80位,阅读过《西游记》且阅读过《红楼梦》的学生共有60位,则该校阅读过《西游记》的学生人数与该校学生总数比值的估计值为(?)
          A.eqIdf746927e9c234c04bbf9ba6db28a3137B.eqIdcf85529a854e4972a5af6e1f2b99b49eC.eqId8c2918a795234a91a7e31c029f5ce7cdD.eqId39b9dcc93fba4449bef0cb475784c005
          难度系数:0.85使用:2315次题型:单选题更新:2019/6/9
          5 . 函数eqIdef580a0b6ac14a32a645ff22eee97437eqId93c5645e924f4c21a01f9bb9de4b5ac8的零点个数为(?)
          A.2B.3C.4D.5
          难度系数:0.85使用:1484次题型:单选题更新:2019/6/9
          6 . 已知各项均为正数的等比数列eqId93e38ecd74a24cb59da79181b95bfd3a的前4项和为15,且eqIdbf036aa871c0493b8cc85112f146158c,则eqIddaf9326303ae43dcba1f880ef20deee1(?)
          A.16B.8C.4D.2
          难度系数:0.85使用:2894次题型:单选题更新:2019/6/9
          7 . 已知曲线eqIdc74058e593b94956be30a055f8e59753在点eqId5ab6e76dda4a4f04bdacd4f2eb25cf40处的切线方程为eqId341817bc957542e18872bbcda5069106,则(?)
          A.eqId3641bd084df84cfd893a987391771301B.eqId95029722a4ee4cf2a3943c6dec985b1eC.eqIdeaeac4c14a5f4df09c672a69d1af0e3bD.eqId41ee6df0af0d4a01857dc5550b3a4829
          难度系数:0.85使用:2783次题型:单选题更新:2019/6/9
          8 . 如图,点eqId8eea7f6267fb49d9bce12b8ba079a43e为正方形eqId5ce7a06ae7a34393b92b5277978ac014的中心,eqId389106733e364488a3c300054aa6d96d为正三角形,平面eqId1f80f74173d444ae8b3dce1d43e89d4e平面eqIda1da90187def4bbe8489c994bbc68ac1是线段eqId6f018d9f230d41bcaafd7d15ef9f50c0的中点,则(?)
          figure
          A.eqId31a304538cc5464185dd2cea7720dbe9,且直线eqId74b0ab33d2e144378b0027f24f368a0d是相交直线
          B.eqIdfab442547b764708a67e44e0f9351134,且直线eqId74b0ab33d2e144378b0027f24f368a0d是相交直线
          C.eqId31a304538cc5464185dd2cea7720dbe9,且直线eqId74b0ab33d2e144378b0027f24f368a0d是异面直线
          D.eqIdfab442547b764708a67e44e0f9351134,且直线eqId74b0ab33d2e144378b0027f24f368a0d是异面直线
          难度系数:0.65使用:2436次题型:单选题更新:2019/6/9
          9 . 执行如图所示的程序框图,如果输入的eqId650ff57f2c964230aa05e52498fb05b7eqId80022332428548d99aa6eb2fd1b9062e,则输出eqId306e35a0bcc740e4a62cbfc4e760e1e0的值等于(?)
          figure
          A.eqId27e1e5c3e9064239a910a0da7ff7f620B.eqIdbf68cde3f4c341228496285a77e0ac71C.eqId53f965a6b0134936a0b88beda070353cD.eqId4e81d97300ef415b8e3054a76dcabd73
          难度系数:0.85使用:2108次题型:单选题更新:2019/6/9
          10 . 已知eqIdd5b10b2a13f148b78e0d5a1b820538fd是双曲线eqIddcd59c6bd4f7468391933d865544bf35的一个焦点,点eqIdd7be5abad1e34f6db17a56660de8d54feqId19a4eb16029e4550a14f2afe4741a3c3上,eqIdaad7b72a25924d078d2360cdc99f1090为坐标原点,若eqIda0fc79709a174298a871dd58eabbc112,则eqIdcef865610b524b789b23c07d553eaea4的面积为(?)
          A.eqIda1c096f0f55441fbbd4d8fd5b3606e28B.eqId38a7bfb7c42f4cf1b3186b9f8e2df68fC.eqId757fa3a8e0bc4df9bd2f30045051a231D.eqId6cce67e9138247a0bc400322a8be5b73
          难度系数:0.85使用:1078次题型:单选题更新:2019/6/9
          11 . 记不等式组eqIdd5d275e3c9eb4ea4b3f669022bc35f01表示的平面区域为eqId0cd8063abf2b458f80091bc51b75a904,命题eqId0b4ca3a6629c44a083e3bfeb88053a66;命题eqId413de9a0b873465e859f88559ab79d28.给出了四个命题:①eqId703f7945161e4a72835647dce2bd0dc9;②eqId500673a38a1c40e4aafaba1f99950f22;③eqIdab1422f8cc56447687f57319d9341360;④eqId0ca90f774f054d1085fb285c405f8bdf,这四个命题中,所有真命题的编号是(?)
          A.①③B.①②C.②③D.③④
          难度系数:0.65使用:1172次题型:单选题更新:2019/6/9
          12 . 设eqId4837c94ef0ff4dcf9b1dda4df363275a是定义域为eqId7dcd2312d0bf4bb1befdfcc170e45791的偶函数,且在eqIddca4c31f92e1447fb6eceb9fdf294175单调递减,则(?)
          A.eqId8d284b9065f8408287a906c0fb17b32a
          B.eqId9eadee0ce6974083b504b4550996e4cd
          C.eqIdfad183307fa047ab8197b14d9f1d7e00
          D.eqId0c322eb126904e9abc0e05ba13eca1c1
          难度系数:0.65使用:2910次题型:单选题更新:2019/6/9
          二、填空题
          13 . 已知向量eqId90078e71831948c5baa444b5fed5e6d5,则eqId176a2ea12e1b49899b06efe731150882___________.
          难度系数:0.85使用:1258次题型:填空题更新:2019/6/9
          14 . 记eqIddb5481de79c946c0a760143297d5eade为等差数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId6a64a6458938477ea9222d722f9cca2f项和,若eqId7c2d8c0f3bd142bd9986f086e9012e5e,则eqId862b57645f1848eda62f949391559938___________.
          难度系数:0.85使用:1362次题型:填空题更新:2019/6/9
          15 . 设eqIdbdf2be0aa9554cd4b621ea3f01b03139为椭圆eqId873d6cd6c9664c8993dc728aebaab996的两个焦点,eqId2381423d4cd146cab95f55527681a766eqId19a4eb16029e4550a14f2afe4741a3c3上一点且在第一象限.若eqId40447e0af4494d4a802c173eaff088c6为等腰三角形,则eqId2381423d4cd146cab95f55527681a766的坐标为___________.
          难度系数:0.65使用:2327次题型:填空题更新:2019/6/9
          16 . 学生到工厂劳动实践,利用eqId34a61d14c2344925ac5ecd935e4f15eb打印技术制作模型.如图,该模型为长方体eqId1653eb2ffb674438a276f7802ff1b4ea挖去四棱锥eqId7e1048d5425b462caac86452660fe0f4后所得的几何体,其中eqIdaad7b72a25924d078d2360cdc99f1090为长方体的中心,eqIddad3add2ed014d858d9576e43f545657分别为所在棱的中点,eqId70523b68ecfb4812b2f27f9dac44b798,eqId34a61d14c2344925ac5ecd935e4f15eb打印所用原料密度为eqIdefb4ae0bc6494026b984cc7bc39d79d2,不考虑打印损耗,制作该模型所需原料的质量为___________eqIdd2f40bc0992343adafdd8a1081b8df8c.figure
          难度系数:0.65使用:2227次题型:填空题更新:2019/6/9
          三、解答题
          17 . 为了解甲、乙两种离子在小鼠体内的残留程度,进行如下试验:将200只小鼠随机分成eqIdb1303264010b459d9f702b468b17ec1f两组,每组100只,其中eqIdcc614bd3390c4d028df189b234dcc351组小鼠给服甲离子溶液,eqId8754ce8cf7f34f04abb9a0c041f57f5c组小鼠给服乙离子溶液.每只小鼠给服的溶液体积相同、摩尔浓度相同.经过一段时间后用某种科学方法测算出残留在小鼠体内离子的百分比.根据试验数据分别得到如下直方图:
          figure
          eqId19a4eb16029e4550a14f2afe4741a3c3为事件:“乙离子残留在体内的百分比不低于eqIdd250bbf1d2a6406ebedc531a3364f382”,根据直方图得到eqId2524804e0ae54d0e836cd6ef23542114的估计值为eqIda56212e618034425a3848ce06bd71b9f.
          (1)求乙离子残留百分比直方图中eqIdacb28234fbc64e47bcc9526d277d3f5a的值;
          (2)分别估计甲、乙离子残留百分比的平均值(同一组中的数据用该组区间的中点值为代表).
          难度系数:0.65使用:2442次题型:解答题更新:2019/6/9
          18 . eqId992fe44057cf4492895193f3f5398449的内角eqId38b55ed6453843a1b310edd4999dff16的对边分别为eqId0ce93bfa1f6a4a23b3258410dd19847a,已知eqId975db053026d4bf0ab32a09c2db70c4e
          (1)求eqId8754ce8cf7f34f04abb9a0c041f57f5c;
          (2)若eqId992fe44057cf4492895193f3f5398449为锐角三角形,且eqIdd49bb3d224144e9ba9e9244858dd3757,求eqId992fe44057cf4492895193f3f5398449面积的取值范围.
          难度系数:0.65使用:3425次题型:解答题更新:2019/6/9
          19 . 图1是由矩形eqId427d6d6a9c034788933d46323d1871b1和菱形eqId96fff49b5867418e8e4c23ed316fd5e9组成的一个平面图形,其中eqId706856e90bd84d409048fe8146cd7284, eqIdcf2bd5024e784a09b083df86658dfdc5,将其沿eqIdedd3474f8bc149719338361f93a191b1折起使得eqId591f0385a60a4a94bf8be12ca6a6b630eqId04f04626638f43499fac1e326b7fe20d重合,连结eqId45b717454d1e4480af6cc71af8212e49,如图2.
          (1)证明图2中的eqId4dda39fe6a9b4612a439f14299511a03四点共面,且平面eqId1686246f15404e0d892538aa1e3c60f5平面eqIdb4916d70031b44ce81841267966f4a11;
          (2)求图2中的四边形eqId27a6710bb3274a27bbefbca026d86b20的面积.figure
          难度系数:0.65使用:1156次题型:解答题更新:2019/6/9
          20 . 已知函数eqId164ab17b78c94b408b128f22cfa0fc73.
          (1)讨论eqId6f13759e937144069819aed2ae5a1057的单调性;
          (2)当eqId18b0ec124f9a4f89a1bc90cd0f639404时,记eqId6f13759e937144069819aed2ae5a1057在区间eqId55c1c8d277914621b117cb963bfff120的最大值为eqId2381423d4cd146cab95f55527681a766,最小值为eqId3a4208e0040c42ed8b09de2cae9d562e,求eqId75131b27935740a989cc98f865925217的取值范围.
          难度系数:0.4使用:1305次题型:解答题更新:2019/6/9
          21 . 已知曲线eqIdb44ee8c586a44804a65e7dbd7f39c453,为直线eqId8f30f709ef4647f082c6f0000a1d1736上的动点,过eqId0cd8063abf2b458f80091bc51b75a904eqId19a4eb16029e4550a14f2afe4741a3c3的两条切线,切点分别为eqIdb1303264010b459d9f702b468b17ec1f.
          (1)证明:直线eqId99a3187c2b8f4bcc9703c74c3b72f1f3过定点:
          (2)若以eqId7dfb680270784f1eab0c846f7280da3d为圆心的圆与直线eqId99a3187c2b8f4bcc9703c74c3b72f1f3相切,且切点为线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3的中点,求该圆的方程.
          难度系数:0.4使用:1033次题型:解答题更新:2019/6/9
          22 . 如图,在极坐标系eqId3be6d92012834a92abeee2761c13bc5d中,eqIdbbd16fb84be841689dfb4e5915bb55b6,eqIddc640cb3d36b4c199dee7cb8b1ae80eb,eqId4f696731308748c9982bd027bcd0a8fd,eqIdad7e53c912c149a3a8c3be77b8979c3e,弧eqId025eba1b1c254363907e1a37629be67a,eqId0813cb0990cf489da43ac07cf0097b96,eqId88f468d5e2eb47b8a4294e99948606bf所在圆的圆心分别是eqIdfedf2490eccb4e708af2c1e09bc56377,eqIdeb7ec118ef374783821b0d3b381a9dbc,eqIda652d5d7d3c543aa8e137cee315d47ec,曲线eqId4a6b59aaf9ab4167a838a22121a0fa4b是弧eqId025eba1b1c254363907e1a37629be67a,曲线eqIdefdebd969a00456baef6e66dee747deb是弧eqId0813cb0990cf489da43ac07cf0097b96,曲线eqIdf9a374df7a8e4ce98f88af87aab1840e是弧eqId88f468d5e2eb47b8a4294e99948606bf.
          figure
          (1)分别写出eqId4a6b59aaf9ab4167a838a22121a0fa4b,eqIdefdebd969a00456baef6e66dee747deb,eqIdf9a374df7a8e4ce98f88af87aab1840e的极坐标方程;
          (2)曲线eqId2381423d4cd146cab95f55527681a766eqId4a6b59aaf9ab4167a838a22121a0fa4b,eqIdefdebd969a00456baef6e66dee747deb,eqIdf9a374df7a8e4ce98f88af87aab1840e构成,若点eqIdd7be5abad1e34f6db17a56660de8d54feqId2381423d4cd146cab95f55527681a766上,且eqId33a1223b6170413bbf7e5a849656081c,求eqIdd7be5abad1e34f6db17a56660de8d54f的极坐标.
          难度系数:0.65使用:2628次题型:解答题更新:2019/6/9
          23 . 设eqIda3d712063a1c48f2bc74dfecd9f714f8,且eqId40156dcad4644c46b0479d3839e1d2ce.
          (1)求eqId12b52d0492914c2699bee302da760990的最小值;
          (2)若eqId68cf1791bf0c499f9986ab74af59f43f成立,证明:eqId90a14661685b4fde9dd17dcd136e7fd8eqId5a6398e244614e1888ed5578c91a5364.
          难度系数:0.65使用:2027次题型:解答题更新:2019/6/9
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