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2020届全国100所名校最新高考模拟示范卷高三理科数学模拟测试试题(二)
适用年级:高三 试卷类型:月考 试题总数:23 浏览次数:76 上传日期:2020-05-23
1 . 若集合eqId31623c107197465ab779dcfe96c392d6eqId23da3134fd50467ca4ed7c6d874ed041,则eqIdd321c2c4c0c74ea09a1712449cceca7e(   )
A.eqIdbb8b724b23404623a04430ecc961d622B.eqId007e823fa1304d00a2baa8f6b8183881C.eqId63883be2e40546dca8653faa10d56c55D.eqIdad01638c3ccf49aaa82da4456093acba
更新:2020/05/23难度:0.85题型:单选题组卷:0
2 . eqIdb6e15e51d29a47a7aff44f98b1aafaee是虚数单位,eqId0773909f4ca64e76b0c922939ecba221,则eqIdaa5c49998ef74a33a88d6807d3bcaf4a(   )
A.3B.4C.5D.6
更新:2020/05/23难度:0.85题型:单选题组卷:0
3 . 第18届国际篮联篮球世界杯(世界男子篮球锦标赛更名为篮球世界杯后的第二届世界杯)于2019年8月31日至9月15日在中国的北京、广州、南京、上海、武汉、深圳、佛山、东莞八座城市举行.中国队12名球员在第一场和第二场得分的茎叶图如图所示,则下列说法错误的是(   )
figure
A.第一场得分的中位数为eqId2411e237a6024ba5812575d3840e3781B.第二场得分的平均数为eqId4db06a09df274d14a38e43ea3f70bef8
C.第一场得分的方差小于第二场得分的方差D.第一场与第二场得分的众数相等
更新:2020/05/23难度:0.85题型:单选题组卷:0
4 . 若双曲线eqId58ecc109d7934cbb921c58754c302a4b的左、右焦点分别为eqId5f04473e64c141bcbe9b0a8af27f4aa8,离心率为eqId7f4cbc932b504200bd85e1dbb4d96181,点eqId5cc3b0b8a84e46aeb65e111a4be59629,则eqId1a70d79069bd425598306abfa106c8f5(    )
A.6B.8C.9D.10
更新:2020/05/23难度:0.94题型:单选题组卷:287
5 . 已知数列eqId449e552113864c34acff3d281269effe是等差数列,其前eqIdf458db68122849abb588feb2e682d9ac项和为eqIddb5481de79c946c0a760143297d5eade,若eqId8359a461e17144d89bb65825f2499848eqIdfd0a58641ad147619b680af67333d520,则eqId6a73ce59274e4242908d2c2028fe4d91(   )
A.78B.80C.84D.86
更新:2020/05/23难度:0.85题型:单选题组卷:0
6 . 函数eqId9530903865b94c5eb6b633c7c2e74d28的图象大致为(   )
A.figureB.figure
C.figureD.figure
更新:2020/05/26难度:0.65题型:单选题组卷:92
7 . 图为祖冲之之子祖暅“开立圆术”中设计的立体模型.祖暅提出“祖氏原理”,他将牟合方盖的体积化成立方体与一个相当于四棱锥的体积之差,从而求出牟合方盖的体积等于eqIdd96d7c086eac4869a6cbd7c9807acfc5eqId096e32e1d18145d199ccbacb5a9a85fe为球的直径),并得到球的体积为eqId2e2652ab734b4909b186ccf1502e3645,这种算法比外国人早了一千多年,人们还用过一些类似的公式,根据eqIdf4969c5c1817451a8ceb3351b0dca731,判断下列公式中最精确的一个是(   )
figure
A.eqId69deb011c08a41e4b40ac080b0c54b19B.eqId155550bf93e7435d9d69c671c55f0d68C.eqIdbcbeb17428994b72a35b60ea2f9d4f28D.eqId1c53db16dd9048c3b90de9a2fbce0e85
更新:2020/05/26难度:0.85题型:单选题组卷:72
8 . eqIdd7a5e4214cdb41939b335b58120b6bb9展开式中的常数项是(   )
A.eqId1f79cb660ff34fc0a0306175262bf945B.eqId1d18010fc29e4f45abaaece953793246C.eqId717e2b409ffe450d8c3d24421e6743efD.eqId489bd971e3c5412aaf1e66be009ced9c
更新:2020/05/23难度:0.85题型:单选题组卷:0
9 . 某几何体的三视图如图所示,三个视图中的曲线都是圆弧,则该几何体的表面积为(   )
figure
A.eqId80dd56de5daf40f3b812b065dff2a500B.eqIdd01c25c6bee14243b653b043d4e96c11C.eqId4cc2f7d3399e449686cea90da9aff45dD.eqIdee3fe8f97cbd4e0ca522b85abca8919b
更新:2020/05/23难度:0.85题型:单选题组卷:0
10 . 若存在eqId3a4208e0040c42ed8b09de2cae9d562e,使得eqIdc57c30fdafd44760ab619c4d01f2c360对任意eqIdd47c09357e9f46d3b34981701baacf58恒成立,则函数eqId4837c94ef0ff4dcf9b1dda4df363275aeqId0cd8063abf2b458f80091bc51b75a904上有下界,其中eqId3a4208e0040c42ed8b09de2cae9d562e为函数eqId4837c94ef0ff4dcf9b1dda4df363275a的一个下界;若存在eqId2381423d4cd146cab95f55527681a766,使得eqIdb29123e50b3b47f3bdd04a8fd7ac464b对任意eqIdd47c09357e9f46d3b34981701baacf58恒成立,则函数eqId4837c94ef0ff4dcf9b1dda4df363275aeqId0cd8063abf2b458f80091bc51b75a904上有上界,其中eqId2381423d4cd146cab95f55527681a766为函数eqId4837c94ef0ff4dcf9b1dda4df363275a的一个上界.如果一个函数既有上界又有下界,那么称该函数有界.
下述四个结论:①1不是函数eqId8e56b063cf5f48dfb36fa29381f081d5的一个下界;②函数eqId3f12f121055f43748f346d19a330eb9f有下界,无上界;③函数eqIda8bf91f8dec24ebc883388896fdbb2fa有上界,无下界;④函数eqId97a3d19aa6b8463ba38c68f81ee31181有界.
其中所有正确结论的编号是(   )
A.①②B.②④C.③④D.②
更新:2020/05/23难度:0.4题型:单选题组卷:62
11 . 已知eqId5f04473e64c141bcbe9b0a8af27f4aa8分别为椭圆eqId97486975b6a64f85985e16d089812c4d的左、右焦点,eqId2381423d4cd146cab95f55527681a766是椭圆上一点,过点eqIdde963a24921f4ee7a991bf9d4f43a42eeqId744d37acc80c438f8c26b34b6138a011的角平分线的垂线,垂足为eqId517584fed25c413ba8b7bb33ffa2d5c6,若eqId190354f0ade34feab6bd51ffbd9655d3eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点),则eqIdb70347c485b34114a7ce11c6bc2a6321(   )
A.eqIda35cf66775a24732b08dc411968e2420B.eqIdcf32b3b919f04cc18988c622e750e9f1C.eqIda2a0ce3781fa4c26b624f5966b7dee44D.eqId7bcd573cee334383ad72cc4b179fcfb3
更新:2020/05/23难度:0.65题型:单选题组卷:327
12 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a满足条件eqId3fdd9265022344acb9ce2be3ca387ba3eqId9cca75ecdacf46d1a0d9f47e1fccc13eeqIdc73ad4de0ec14cba91db08ec61124907,则eqId54138dd4ae14450ab907ee08245b249c的最小值为(   )
A.3B.2C.1D.0
更新:2020/05/23难度:0.4题型:单选题组卷:18
13 . 已知向量eqIdc3b3041747554fa592862f9555e781df,若eqId3421663bd271480991d102671271e825,则实数eqId5f420ef2d0b94c4b8a5d8e20a5d1ce2c等于_______.
更新:2020/05/23难度:0.85题型:填空题组卷:0
14 . 若eqId8e15963708e9415da25069fea5906e24eqId072d7d6b911b42bc89207e72515ebf5f满足约束条件eqIdaadbafbb977748d2b75d732a1599b9e1,则eqId69d3b7911aff4b859d84c2c827222987的最大值为__________.
更新:2020/05/23难度:0.65题型:填空题组卷:30
15 . 已知函数eqId7db54f1b4f3e4671b914585a69abe0f7,点eqId49f6536fc6d245b6befdd144a6abae3ceqId3ae2e10d09754e9c9c666621a78984c1是函数eqId6f13759e937144069819aed2ae5a1057图象上相邻的两个对称中心,则eqIdabb4172ea4c548e38ccc32fc6414f2b9_________.
更新:2020/05/23难度:0.85题型:填空题组卷:0
16 . 在正三棱柱eqId9881c5faa5cb449bb37fa59b41c76e43中,eqIdbfafc9c818504a68969d0160bf2b7a65eqIdc0ccc58b8e954a0a83b879635b3538b8eqIdc3bc315778fd47ef9822f0554c98bd79分别为eqId1ed5c9a541554ff2bbacbddf4d0638c6eqId17ceafc9b1a74a37a89907801af1e742的中点,平面eqIdc13953f2514e4c8f9c8aaaf5241c33ac过点eqIdcfc8599bedfb4ab4944abf141f348a9a,且平面eqId4557eb7263864026ae6d9a61d9a9e01d平面eqId97e21e66e1164f35995c0c7a871561e7,平面eqId03357d8b829e41e4abc14e6e38205eaa平面eqId5b130797c3d947d68cf4a6d4310410f5,则异面直线eqId1a0830891ff846de8422ea80714ecab4eqId417e80f1349244878d01fe90e0891f5f所成角的余弦值为________.
更新:2020/05/26难度:0.65题型:填空题组卷:98
17 . 在eqId64b9b599fdb6481e9f8d9a94c102300b中,eqId0ce93bfa1f6a4a23b3258410dd19847a分别为内角eqId10bbe48f886a4fa78fdf8c1fd064f9b4的对边,且eqId04854bdf89a64a3c9b00ac2791b169da.
(1)求角eqIdcc614bd3390c4d028df189b234dcc351的大小;
(2)若eqIde28611a1795f427ba422c1488f89e639eqId2efda802d5534f6d92d9f8af7aaec28beqId64b9b599fdb6481e9f8d9a94c102300b的内心,求eqIdc89a7c57dad540a0b06d5a6444d4c1f2的最大值.
更新:2020/05/23难度:0.85题型:解答题组卷:324
18 . 如图,在四棱锥eqIdac097205e9cb41279269aadcac3fb6f1中,eqIde78cce043a6c43329b55788351ff3484底面eqId5ce7a06ae7a34393b92b5277978ac014,底面eqId5ce7a06ae7a34393b92b5277978ac014为直角梯形,eqId445d8e9d6e264ad496892fc95f52033aeqId0627be51821d4be7b3e024a354815d64eqIdbf4db7d066034b139ff80a09ab139d45eqId2404423e6a634896a3585f857957bde5eqId790707287e604e1a97e1484c1457c054eqId93cbffaa5ae045d6ac45d1e979991c3aeqId63db14a5b4334f3ea583c8fb12b0d175eqId92869ac114124367b45f631d030ed6bd分别为线段eqIdbf4db7d066034b139ff80a09ab139d45eqIde3de99d6c54049cc9915165f22199e1feqIde9b50933e347462ea824ccc9bf51fc93的中点.
figure
(1)证明:平面eqIda8aeeb3348c24061b40e16d689171576∥平面eqId3cb897b0b52644e1bfa84f1def450e67
(2)求直线eqId70df4038c7334041b6b1cfcf3f197832与平面eqId83e13ba429bb426fb39bd7720a82c64c所成角的正弦值.
更新:2020/05/23难度:0.65题型:解答题组卷:103
19 . 已知点eqIdaf2cea7e5a3b460c9edd46a9761db3e5是抛物线eqId7e148e9b5def4bf1af4353dbf1ccc544上一点,点eqId63db14a5b4334f3ea583c8fb12b0d175为抛物线eqId19a4eb16029e4550a14f2afe4741a3c3的焦点,eqId0df3642d8ef246919ceb4fdda8264a23.
(1)求直线eqId7b71ac6238b649bba16fd5463c7b0b56的方程;
(2)若直线eqId7b71ac6238b649bba16fd5463c7b0b56与抛物线eqId19a4eb16029e4550a14f2afe4741a3c3的另一个交点为eqId75a143b898e14ccdb032561fba9da811,曲线eqId19a4eb16029e4550a14f2afe4741a3c3在点eqIdbedf755e0fdb4d078d6859360706b163与点eqId75a143b898e14ccdb032561fba9da811处的切线分别为eqId79df476224874da48567d2482d95e8aa,直线eqId79df476224874da48567d2482d95e8aa相交于点eqId92869ac114124367b45f631d030ed6bd,求eqId61e60c9cc1194366ae600144291f0a1a的面积.
更新:2020/05/23难度:0.65题型:解答题组卷:0
20 . 垃圾分类,是指按一定规定或标准将垃圾分类储存、分类投放和分类搬运,从而转变成公共资源的一系列活动的总称.分类的目的是提高垃圾的资源价值和经济价值,力争物尽其用.2019年6月25日,生活垃圾分类制度入法.到2020年底,先行先试的46个重点城市,要基本建成垃圾分类处理系统;其他地级城市实现公共机构生活垃圾分类全覆盖.某机构欲组建一个有关“垃圾分类”相关事宜的项目组,对各个地区“垃圾分类”的处理模式进行相关报道.该机构从600名员工中进行筛选,筛选方法:每位员工测试eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3三项工作,3项测试中至少2项测试“不合格”的员工,将被认定为“暂定”,有且只有一项测试“不合格”的员工将再测试eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c两项,如果这两项中有1项以上(含1项)测试“不合格”,将也被认定为“暂定”,每位员工测试eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3三项工作相互独立,每一项测试“不合格”的概率均为eqIdf249169661be4a5ea4b0e9525f0c88c4
(1)记某位员工被认定为“暂定”的概率为eqId5d91b7fc22a04c85aee8d5bd751cea6a,求eqId5d91b7fc22a04c85aee8d5bd751cea6a
(2)每位员工不需要重新测试的费用为90元,需要重新测试的总费用为150元,除测试费用外,其他费用总计为1万元,若该机构的预算为8万元,且该600名员工全部参与测试,问上述方案是否会超过预算?请说明理由.
更新:2020/05/23难度:0.4题型:解答题组卷:298
21 . 已知函数eqIdff8d8bc3e7794c3b9a35254bde4ea7b7.
(1)若eqId99c1da4b95cc4a5ba9ecc4c82b51175e恒成立,eqId2c07a82215514a4eaf0b1325853b8f48.求eqId84bb3bf2bcd4450c85dd7570191c36fc的最大值;
(2)若函数eqIdc99a6c8f225a48b98b4671e655bcbd71有且只有一个零点,且满足条件的eqId4959a8a13c0b40f3a3b076626a4b616c,使不等式eqId93bb0cda914d4ee3a00345db8bbb8c16恒成立,求实数eqId3a4208e0040c42ed8b09de2cae9d562e的值.
更新:2020/05/23难度:0.4题型:解答题组卷:0
22 . 在直角坐标系eqId2272a344734c4fb088737b84294f7219中,曲线eqId19a4eb16029e4550a14f2afe4741a3c3的参数方程为eqId1abecaa938d64107b2335b71241381f2eqIdc13953f2514e4c8f9c8aaaf5241c33ac为参数),在以坐标原点为极点,eqId8e15963708e9415da25069fea5906e24轴的正半轴为极轴的极坐标系中,直线eqId417e80f1349244878d01fe90e0891f5f的极坐标方程为eqIdfba44fd7940143f99d99668c88a52ece
(1)若直线eqId417e80f1349244878d01fe90e0891f5f与曲线eqId19a4eb16029e4550a14f2afe4741a3c3至多只有一个公共点,求实数eqId3a4208e0040c42ed8b09de2cae9d562e的取值范围;
(2)若直线eqId417e80f1349244878d01fe90e0891f5f与曲线eqId19a4eb16029e4550a14f2afe4741a3c3相交于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,且eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c的中点为eqIdbedf755e0fdb4d078d6859360706b163,求点eqIdbedf755e0fdb4d078d6859360706b163的轨迹方程.
更新:2020/05/26难度:0.65题型:解答题组卷:144
23 . 已知eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7为正实数,eqId8390abd13e03461580ac5858ed7a8de3
(1)证明:eqIdbb3aa0dd5ab0436f989adb40449500a0
(2)证明:eqId16bac46a07ab40f3be044760c7df5c97
更新:2020/05/26难度:0.65题型:解答题组卷:40