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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:16957上传日期:2019/6/9
1 . 已知集合eqId222d38fbff2544a3bfa51d057ec7ec74,则eqIdcfb073d9fa8a44179cf4e242d45e6d3c( )
A.eqId24fce0e9e75c4630992de76de3b53f94B.eqId59eabb7d87ab43fa87a15fe758bfe6fbC.eqId805f8e7a66e44370bfbea58150e6feceD.eqIde19bdd270dc04752b49afb60a7c3e6ad
难度:0.85组卷:7764题型:单选题更新:2020/1/24
2 . 若eqId934bcd667b5640b0bbe6e4df5fce4d2c,则eqId0b4fc8a120af4fab80df6ffdcf7c46f8( )
A.eqId7e1d65ed29e842fd8cc5cf647d5266d4B.eqIdb829a3f15c854a4aa2ed9ee31a6c21f3C.eqId5eedc150ab8b48d88bad1acd6d5ded11D.eqId4fde5d5c7e03464cb0a9e871ff2b4aeb
难度:0.85组卷:6414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.eqId3e866ebc4a57441386a76af413247f0eB.eqIde41289c7307b48bd893a195b321d250fC.eqIda8012d5322b240128851ebf3cd086e12D.eqId767acf51abfd4d97a757561d1a882151
难度:0.85组卷:3537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.eqIdc0d74ce4837b43509d665192a9ccaa88B.eqId445e64f710d24e178aad860c1bccf827C.eqId03d140e462bb4a23800912626e40b701D.eqId73444897aa4e43fcb9e9e21cefbdcc32
难度:0.85组卷:6494题型:单选题更新:2019/12/19
5 . 函数的零点个数为( )
A.2B.3C.4D.5
难度:0.85组卷:4470题型:单选题更新:2019/12/16
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eqIdec15b069a63a4c5fb3a6606336bb1b1a( )
A.16B.8C.4D.2
难度:0.85组卷:9896题型:单选题更新:2020/1/11
7 . 已知曲线eqIdc74058e593b94956be30a055f8e59753在点eqId5ab6e76dda4a4f04bdacd4f2eb25cf40处的切线方程为eqId10fc4a69dd2b4dde89470c957df393fc,则( )
A.eqId3641bd084df84cfd893a987391771301B.eqId95029722a4ee4cf2a3943c6dec985b1eC.eqIdeaeac4c14a5f4df09c672a69d1af0e3bD.eqId41ee6df0af0d4a01857dc5550b3a4829
难度:0.85组卷:8849题型:单选题更新:2020/2/13
8 . 如图,点eqId517584fed25c413ba8b7bb33ffa2d5c6为正方形eqId5ce7a06ae7a34393b92b5277978ac014的中心,eqId389106733e364488a3c300054aa6d96d为正三角形,平面eqId63580254e2bb49ee94083bccce408f4f平面eqIda5c43f81960147249414de29355f9e89是线段eqId28feb795484c4e8fb717a1f1282f1898的中点,则( )
figure
A.eqId23e5214cdd044328bf033aab053721f7,且直线eqId74b0ab33d2e144378b0027f24f368a0d是相交直线
B.eqIdfab442547b764708a67e44e0f9351134,且直线eqId74b0ab33d2e144378b0027f24f368a0d是相交直线
C.eqId23e5214cdd044328bf033aab053721f7,且直线eqId74b0ab33d2e144378b0027f24f368a0d是异面直线
D.eqIdfab442547b764708a67e44e0f9351134,且直线eqId74b0ab33d2e144378b0027f24f368a0d是异面直线
难度:0.65组卷:7347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eqId2c9c90efa8c2480b966e65790376f7e1eqIddfdc2d8ad8df43549f855947e01b1e21,则输出eqId08191f2c12324f94b4ddfe2f324a71cf的值等于( )
figure
A.eqId27e1e5c3e9064239a910a0da7ff7f620B.eqIdbf68cde3f4c341228496285a77e0ac71C.eqId53f965a6b0134936a0b88beda070353cD.eqId4e81d97300ef415b8e3054a76dcabd73
难度:0.85组卷:5455题型:单选题更新:2020/1/30
10 . 已知eqId63db14a5b4334f3ea583c8fb12b0d175是双曲线eqId5413695a72d44e73b4ada3c00606a205的一个焦点,点eqIdbedf755e0fdb4d078d6859360706b163eqId19a4eb16029e4550a14f2afe4741a3c3上,eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点,若eqIda0fc79709a174298a871dd58eabbc112,则eqId2a77a45fd7bc4364841e89c10c0e4f80的面积为( )
A.eqId57b3d7f61b5e48a1a1c959fa66d74726B.eqId2411e237a6024ba5812575d3840e3781C.eqId757fa3a8e0bc4df9bd2f30045051a231D.eqId0c34b200ff98472c81a84cd8f0116762
难度:0.85组卷:3767题型:单选题更新:2020/1/10
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:0.65组卷:3350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:0.65组卷:9461题型:单选题更新:2020/1/14
13 . 已知向量eqId90078e71831948c5baa444b5fed5e6d5,则eqId64592de948484ec4bc657ac0a2129381___________.
难度:0.85组卷:3883题型:填空题更新:2020/2/6
14 . 记eqIddb5481de79c946c0a760143297d5eade为等差数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqIdf458db68122849abb588feb2e682d9ac项和,若eqIdce96a10c74724d168aea16dcc4414574,则eqId1a98035dcce642de9748cd86685de81b___________.
难度:0.85组卷:4561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:0.65组卷:8312题型:填空题更新:2020/1/11
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,eqId70523b68ecfb4812b2f27f9dac44b798eqId34a61d14c2344925ac5ecd935e4f15eb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:0.65组卷:6205题型:填空题更新:2019/6/9
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:0.65组卷:6935题型:解答题更新:2019/6/9
18 . eqId992fe44057cf4492895193f3f5398449的内角eqId10bbe48f886a4fa78fdf8c1fd064f9b4的对边分别为eqId0ce93bfa1f6a4a23b3258410dd19847a,已知eqId975db053026d4bf0ab32a09c2db70c4e
(1)求eqId8754ce8cf7f34f04abb9a0c041f57f5c
(2)若eqId992fe44057cf4492895193f3f5398449为锐角三角形,且eqIdda43591caa9542f780355a1d58dae3c1,求eqId992fe44057cf4492895193f3f5398449面积的取值范围.
难度:0.65组卷:12895题型:解答题更新:2019/12/10
19 . 图1是由矩形eqId427d6d6a9c034788933d46323d1871b1和菱形eqId29970aec73b94df480364c7d090b68d8组成的一个平面图形,其中eqId706856e90bd84d409048fe8146cd7284eqIdcf2bd5024e784a09b083df86658dfdc5,将其沿eqId8e70c8f9c5374e928143bd27cdbf7ebe折起使得eqId1dcb20a9ce8d4076af5dd64f7066c6d6eqId91a3a60f05ba4520a4dfd21420cf28ca重合,连结eqIdfe153e9ee02c43269f033306f2dbc6fd,如图2.
(1)证明图2中的eqId4dda39fe6a9b4612a439f14299511a03四点共面,且平面eqId34a0c394100b4c9ba6ae50c0e773a64a平面eqIdd6f05ef3fca445f0bf5f3a74e92295fe
(2)求图2中的四边形eqIde9b85eaa401e405b8f21a226d9af09f2的面积.figure
难度:0.65组卷:3829题型:解答题更新:2020/1/5
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:0.4组卷:4151题型:解答题更新:2020/2/8
21 . 已知曲线eqIdb44ee8c586a44804a65e7dbd7f39c453,为直线eqId0a749884d2d64fbb8b46cdeb1a88c357上的动点,过eqId0cd8063abf2b458f80091bc51b75a904eqId19a4eb16029e4550a14f2afe4741a3c3的两条切线,切点分别为eqIdeb53cb7cb0274f7d8f111c60f824c243.
(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:0.4组卷:3550题型:解答题更新:2019/6/9
22 . 如图,在极坐标系eqId3be6d92012834a92abeee2761c13bc5d中,eqIdbbd16fb84be841689dfb4e5915bb55b6eqIddc640cb3d36b4c199dee7cb8b1ae80ebeqId4f696731308748c9982bd027bcd0a8fdeqIdad7e53c912c149a3a8c3be77b8979c3e,弧eqId025eba1b1c254363907e1a37629be67aeqId0813cb0990cf489da43ac07cf0097b96eqId88f468d5e2eb47b8a4294e99948606bf所在圆的圆心分别是eqIdfedf2490eccb4e708af2c1e09bc56377eqIdeb7ec118ef374783821b0d3b381a9dbceqIda652d5d7d3c543aa8e137cee315d47ec,曲线eqId4a6b59aaf9ab4167a838a22121a0fa4b是弧eqId025eba1b1c254363907e1a37629be67a,曲线eqIdefdebd969a00456baef6e66dee747deb是弧eqId0813cb0990cf489da43ac07cf0097b96,曲线eqIdf9a374df7a8e4ce98f88af87aab1840e是弧eqId88f468d5e2eb47b8a4294e99948606bf.
figure
(1)分别写出eqId4a6b59aaf9ab4167a838a22121a0fa4beqIdefdebd969a00456baef6e66dee747debeqIdf9a374df7a8e4ce98f88af87aab1840e的极坐标方程;
(2)曲线eqId2381423d4cd146cab95f55527681a766eqId4a6b59aaf9ab4167a838a22121a0fa4beqIdefdebd969a00456baef6e66dee747debeqIdf9a374df7a8e4ce98f88af87aab1840e构成,若点eqIdd7be5abad1e34f6db17a56660de8d54feqId2381423d4cd146cab95f55527681a766上,且eqId33a1223b6170413bbf7e5a849656081c,求eqIdd7be5abad1e34f6db17a56660de8d54f的极坐标.
难度:0.65组卷:6921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:0.65组卷:5053题型:解答题更新:2019/6/9
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