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2019届全国100所名校最新高考模拟示范卷高三数学模拟测试文科数学(三)试题
全国 高三 月考 2020-06-04 165次

一、单选题添加题型下试题

3. 八卦的形成源于《河图》《洛书》,它用“figure”代表阳,用“figure”代表阴,用这两种符号,组成八种不同形式,每一种形式都命为一卦,分别为乾、坤、震、巽、坎、离、艮、兑,比如乾卦是“figure”,坤卦是“figure”,坎卦是“figure”.在八卦中任选一卦,则这一卦至少含有两条“figure”的概率是(   )
A.eqIddda48cced83d424b89b7d8f8c62b1056B.eqId767acf51abfd4d97a757561d1a882151C.eqIdf033d892d71d42c8ad7eeae3d48dab97D.eqId3e2697f88f04469e8dd1b2d701e62d48
4. 已知eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e是双曲线eqId58ecc109d7934cbb921c58754c302a4b的两焦点,以线段eqId42ca6838695447ed86b53bd3e1c1264b为一直角边作等腰直角三角形eqId2e119959bc854680bbd3f11d6d553bc7,若另一直角边的中点在双曲线上,则双曲线的离心率是(   )
A.eqId47eb7f5d137e421597f229247be6a46dB.eqId15755fd7039d4760803209c0bada9344C.eqId3e1543ad0883432cb23af678b3feacf4D.eqId81652b07662a4ac4a9b60bbbd08fc2f0
5. 设eqId8e15963708e9415da25069fea5906e24eqId072d7d6b911b42bc89207e72515ebf5f满足约束条件eqIda11a56090d9d4c2490d7d036e0cafcdd,则目标函数eqIdf6d45726a3f8444eb9500d5580a4a9c7的最大值为(   )
A.28B.18C.26D.24
6. 已知一个圆锥的母线长为4,且其侧面积是其轴截面面积的4倍,则该圆锥的高为(   )
A.eqId7a1ead8f5cfa47f1b68f0ca61cd1599aB.eqId45b3da198ba74223a230c3f816aedb54C.eqId022e530e1dd6453ab54467745e9df0a8D.eqId2cb51764ae3949b9b698fc2f9527dff2
8. 已知函数eqId0101ab8c701245448a2a849b1ea1444b的图象经过点eqId787fec3796eb4e9983c24c49d247da44,且在区间eqId0727a255231a4f4ebca486d580c963c9恰有两个零点,则该函数图象的一条对称轴方程可能为(   )
A.eqId004d314fa26a4434b66fc193cefa4b3dB.eqId795e60324b8d40468932f101562e2734C.eqId8e7e7921c28f4088bf1ea1cafc7121f8D.eqIdac4cb171fd8c46eca17c4bd04e28eebd
11. 在各项均为正数的等比数列eqId93e38ecd74a24cb59da79181b95bfd3a中,eqId03e42d817122488f90ed2ca2cede60f7,其前eqIdf458db68122849abb588feb2e682d9ac项和为eqIddb5481de79c946c0a760143297d5eade,若存在第eqId3a4208e0040c42ed8b09de2cae9d562e项,使得eqId3fe0aa855c8a4acfb2137b391d7acea2,则eqId3a4208e0040c42ed8b09de2cae9d562e等于(   )
A.4B.8C.16D.32
12. 下图是某多面体的三视图,图中每个小正方形的边长为1,则这个多面体的外接球的半径为(   )
figure
A.eqId7c6baff39f9d4da3bb9b86ba60839e35B.eqId7bcd573cee334383ad72cc4b179fcfb3C.eqId474d67855b28481e9eb14b9f0eca6b12D.eqIddd5e66f7537a4c578b8e995b14637000

二、填空题添加题型下试题

16. 如图,已知椭圆eqId15ddf0bba96b4162a10a0bab1fd8a511的焦点为eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e,点eqIdbedf755e0fdb4d078d6859360706b163为椭圆上任意一点,过eqIdde963a24921f4ee7a991bf9d4f43a42eeqId2d613c3320f749928aa15e77efdd2969的外角平分线的垂线,垂足为点eqId75a143b898e14ccdb032561fba9da811.过点eqId75a143b898e14ccdb032561fba9da811eqId072d7d6b911b42bc89207e72515ebf5f轴的垂线,垂足为eqId517584fed25c413ba8b7bb33ffa2d5c6,若线段eqId52b3806427e347a2a5548e83b06b4ed4的中点为eqId2381423d4cd146cab95f55527681a766,则点eqId2381423d4cd146cab95f55527681a766的轨迹方程为______.figure

三、解答题添加题型下试题

17. 已知eqId64b9b599fdb6481e9f8d9a94c102300b的内角eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3的对应边分别为eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqIdad7cefefaba947e1a168bca491c4fca1eqId64b9b599fdb6481e9f8d9a94c102300b的面积为eqId1b7d8b87b50e4cfdbf89d48980209a52,且eqId25b656c733474b958f42ad2e43ff7c43.
(1)若eqIdc897a2d468924a06b2f9aa94baed6a6b,求eqId695cde8d903a47019dcc3eb41c9ddb63
(2)若eqId38f936987f3142dbbe99c97acc1bc8fe,求eqId1b7d8b87b50e4cfdbf89d48980209a52的最大值
18. 某城市对一项惠民市政工程满意程度(分值:eqId6c34dabd941c43a8a88cc2a44d3f83ab分)进行网上调查,有2000位市民参加了投票,经统计,得到如下频率分布直方图(部分图):
figure
现用分层抽样的方法从所有参与网上投票的市民中随机抽取eqIdf458db68122849abb588feb2e682d9ac位市民召开座谈会,其中满意程度在eqId1f48c3aa48c14105a10c80196c7b6f3c的有5人.
(1)求eqIdf458db68122849abb588feb2e682d9ac的值,并填写下表(2000位参与投票分数和人数分布统计);
满意程度(分数)
eqId1f48c3aa48c14105a10c80196c7b6f3c
eqId707ded8fc22444dbba48cb0f05707734
eqIdf4f63176e95d4e63986c90a0ab4a87ae
eqIdb31ee0d5fa2a4cba9314f2e6f67129a2
eqIdf14ba95a614e4229ace506a7df0c596c
人数
 
 
 
 
 
 
(2)求市民投票满意程度的平均分(各分数段取中点值);
(3)若满意程度在eqId1f48c3aa48c14105a10c80196c7b6f3c的5人中恰有2位为女性,座谈会将从这5位市民中任选两位发言,求男性甲或女性乙被选中的概率.
19. 如图,四棱柱eqId588284d93dc5489295f8f224f8e30d13中,eqId1899674d873d4961bd824facc92df528平面eqId5ce7a06ae7a34393b92b5277978ac014,底面eqId5ce7a06ae7a34393b92b5277978ac014是边长为1的正方形,eqId727d90e152a44c358c15c17dc69b74d4.
figure
(1)求证:平面eqId81dac8f6b9e94a8c814fe471937c55e6平面eqIdaee242bf59a24f429307b6e1a8db092f.
(2)求点eqId0cd8063abf2b458f80091bc51b75a904到平面eqIdc08e5e3af7c94e998cb5d0a54c148ba8的距离.
20. 已知抛物线eqId91d153665f12451bb66d663cf54c2b6a的焦点到直线eqIda3d3c0edc40a44a88c85f42b1dd77693的距离为eqIdcd9b24a6a6e5426ab775be20461174e3,过点eqId44fac052e9094ebaa0092e76c8f0b9a0的直线eqId439fb93f7745417b8bb1747d963c6e60eqId19a4eb16029e4550a14f2afe4741a3c3交于eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6两点.
(1)求抛物线eqId19a4eb16029e4550a14f2afe4741a3c3的准线方程;
(2)设直线eqId34f0716ff7f042578cd4f3404d3b83e7的斜率为eqId0cadcd5e7c5e4f8690f3f9e84b9a54f6,直线eqId6a0cd541cc20416fad3e358d4270147b的斜率为eqId57228a1a035d477a97cee2c3e05b6f4b,若eqId847d8cdc65ef4a09a7e7fda263b62710,且eqId74c7e0292b094e54ae596d37798a05edeqId439fb93f7745417b8bb1747d963c6e60的交点在抛物线eqId19a4eb16029e4550a14f2afe4741a3c3上,求直线eqId439fb93f7745417b8bb1747d963c6e60的斜率和点eqIdcc614bd3390c4d028df189b234dcc351的坐标.
21. 已知函数eqIdcf4e5a93767748f497c8052df53b5d40eqIde9edd995034840cfb557ea415074294a.
(1)若eqIda08ce385279d41c789695fb651b17890,求曲线eqId9b37d03e47a347fc8fab9f814ba5fac4在点eqId2cb0b5c25a7e411abb9bf0c694c7c4ac处的切线方程;
(2)若方程eqId73c522d6c6b848d197f565b6d2e56078有一个实数根,求eqId70a27b6ddf6b478285353abb3b1f3741的取值范围.
22. 在平面直角坐标系中,以坐标原点eqId2efda802d5534f6d92d9f8af7aaec28b为极点,eqId8e15963708e9415da25069fea5906e24轴的正半轴为极轴建立极坐标系,直线eqId417e80f1349244878d01fe90e0891f5f的参数方程为eqIdf5629b350586463daf1c98b112293a9feqId0049fc19eba84da7b19470dcb07a2a6d为参数),曲线eqId35433dec53414eb99b30fb3d7c994376eqId145940d03af4447eabd753d76abd2a1d为参数).
(1)求直线eqId417e80f1349244878d01fe90e0891f5f及曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的极坐标方程;
(2)若曲线eqId59b98344e8bc4bf5ba7da779cc5c0e2b与直线eqId417e80f1349244878d01fe90e0891f5f和曲线eqIdcfc8599bedfb4ab4944abf141f348a9a分别交于异于原点eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c的两点,求eqId4819509fefec4542acccfcf3d67cd699的值.
23. 已知函数eqIde9a51feebccb4a7b86b4714a919dbaa8,函数eqIdad6469db9b1f432daebf09f7e3e55463.
(1)已知常数eqIdc450006af2d44fcc984984be95e8b6c1,解关于eqId8e15963708e9415da25069fea5906e24的不等式eqId74f2140872f9400a9aebcdefed78ca91
(2)若函数eqId4837c94ef0ff4dcf9b1dda4df363275a的图象恒在函数eqId28c4c21271884dfeac29ce0222782376图象的上方,求实数eqId3a4208e0040c42ed8b09de2cae9d562e的取值范围.