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陕西省西安市八校2020届高三(6月份)高考数学(理科)联考试卷
陕西 高三 其他 2020-08-01 50次

一、单选题添加题型下试题

3. 已知i为虚数单位,eqIde9edd995034840cfb557ea415074294a,若复数eqId79e4acec41574d60894a896a6fdaa650的共轭复数eqIdd97c066590474beb8b6a5abd6461c259在复平面内对应的点位于第三象限,且eqId2a4833373b3e4d7baac9f3c8d71acc66,则z=(   )
A.eqIdf7a2d5f2819a4df28ae537ec45af5efbB.eqId753e1efdb9f844a9b8d6968e0b317448C.eqId7de24fb683ba450480cf2c6615244f80D.eqIdcb1a3327144b455cab317b2d44c5b739
4. 已知eqId3a4208e0040c42ed8b09de2cae9d562eeqIdf458db68122849abb588feb2e682d9ac为不同的直线,eqIdc13953f2514e4c8f9c8aaaf5241c33aceqId4eb56f42ca674f2f9c9101b548763159为不同的平面,给出下列命题:
eqId7e5d6394897e4dceaf45b5173c4d4459;②eqId7dda310e51bf40f5989ba74df6646919;③eqId7b6be41cb0604f2c880ba55e7de35490;④eqId395d42dd3ff04b15a377207000cb891d
其中的正确命题序号是(   )
A.②③B.①②③C.②④D.①②④
6. 设eqId673b4d5765014a41acc0e7ef4a8ed501是平面内两个不共线的向量,eqIda5127ba534dc40e5a722e9624602aa04a>0,b>0),若ABC三点共线,则eqIdb6a8e1de6fa4436ab3d43d3d5e3d6ec3的最小值是(   )
A.2B.4C.6D.8
7. 已知pa=±1,q:函数eqId3fda3a9a9c994f318e934f51dc5ef3ac为奇函数,则pq成立的(   )
A.充分不必要条件B.必要不充分条件
C.充分必要条件D.既不充分也不必要条件
9. 已知sinα、cosα是方程5x2eqIdcd9b24a6a6e5426ab775be20461174e3x﹣2=0的两个实根,且α∈(0,π),则cos(α+eqIdb47bf79338b1478a89eac53d16970cdf)=(   )
A.eqIdd9014531eb8f4ecfaa1496f0f3b63ac4B.﹣eqIdd9014531eb8f4ecfaa1496f0f3b63ac4C.eqId984f3d2a94a14e92890974be2ab293aaD.﹣eqId984f3d2a94a14e92890974be2ab293aa
10. 对于函数fx)=cos2x+eqIda2a0ce3781fa4c26b624f5966b7dee44sinxcosxxR,下列命题错误的是(   )
A.函数fx)的最大值是eqId57b3d7f61b5e48a1a1c959fa66d74726
B.不存在eqId1d6821eab5b242188a4c1e0a838173f0使得fx0)=0
C.函数fx)在[eqIdd3e88ecbd2db456396e01302a43b93d9eqId2cb51764ae3949b9b698fc2f9527dff2]上单调递减
D.函数fx)的图象关于点(eqId6a74f495d52d4fafa37efa264e3f9b9d,0)对称
11. 已知eqIdde963a24921f4ee7a991bf9d4f43a42eeqId0aa72756ed0c4c7a89f26aa94f43e47d是双曲线eqIdf3d8bc15671340c09adcd8020bf22336的上、下两个焦点,过eqId0aa72756ed0c4c7a89f26aa94f43e47d的直线与双曲线的上下两支分别交于点eqId8754ce8cf7f34f04abb9a0c041f57f5ceqIdcc614bd3390c4d028df189b234dcc351,若eqId59297415787c4fe698150fe68c3757d4为等边三角形,则双曲线的渐近线方程为eqIdd996f15bd38249f7b7e35e6afefa8c0b  eqId8fbdf36fcfa44dddb74ad17d601f601d
A.eqId2747a0a5e7f048c3bea5d78f1368668cB.eqId72f96e6b2ecd4cd3880ce0739954106aC.eqId9f0403da34c5479ca534e5521ce50d1fD.eqIde2edc78f66c34593b8ca6020f65ba541

二、填空题添加题型下试题

13. 已知实数xy满足不等式组eqId75f0e957498241ca90467033d4c1bd9b,则zx+y的最小值为_____.
14. 从eqIda8012d5322b240128851ebf3cd086e12eqId49b7b111d23b44a9990c2312dc3b7ed9、2、3、5、9中任取两个不同的数,分别记为mn,则“logmn>0”的概率为_____.
15. 已知点ABC在球心为O的球面上,若ABAC=5,BC=6,球心O到截面ABC的距离为1,则该球的表面积为_____.

三、解答题添加题型下试题

17. 如图,eqIde78cce043a6c43329b55788351ff3484平面eqId5ce7a06ae7a34393b92b5277978ac014,四边形eqId5ce7a06ae7a34393b92b5277978ac014是矩形,eqId93cbffaa5ae045d6ac45d1e979991c3aeqId63db14a5b4334f3ea583c8fb12b0d175分别是eqId99a3187c2b8f4bcc9703c74c3b72f1f3eqIdd293923b221045898dcc5442f88aa67a的中点.
说明: figure
(1)求证:eqIdfec789eef46d41f085a9535585488fc5平面eqIdef6a7c356a884ffc866777aa14a0f89b
(2)若二面角eqIdd903ee2337bb4f858e56206f1281ada1eqIdb7fe117dc1a94fbf93716ecbbcced6bd角,eqIdded28dbc6ca54681ab966fe6545c6cdceqId2e976cd2db184d5e8ad025a3ddedfb8a,求eqIdd293923b221045898dcc5442f88aa67a与平面eqIdef6a7c356a884ffc866777aa14a0f89b所成角的正弦值.
18. 已知{an}是各项都为正数的数列,其前n项和为Sn,且eqIda94f656741674c48b7e7c458554de72c
(1)求数列{Sn}的通项公式;
(2)设bneqId663d69c049bf4a6cba05d6723bae89c4,求{bn}的前n项和Tn
19. 为调查某校学生每周体育锻炼落实的情况,采用分层抽样的方法,收集100位学生每周平均锻炼时间的样本数据(单位:eqId2b1922fa59af4c5098f7af850d2fcd98).根据这100个样本数据,制作出学生每周平均锻炼时间的频率分布直方图(如图所示).
figure
(Ⅰ)估计这100名学生每周平均锻炼时间的平均数eqId647171a68e7e4225bb098f8cf03a975f和样本方差eqId43deeaabbc3c42ab8df8775638303a68(同一组中的数据用该组区间的中点值作代表);
(Ⅱ)由频率分布直方图知,该校学生每周平均锻炼时间eqId7fc4561966aa4ea2924541be8d21ddae近似服从正态分布eqId995155952a92435790e9f7f7527f4f49,其中eqId22d6117c1dd94466972a94a4e1de0edb近似为样本平均数eqId647171a68e7e4225bb098f8cf03a975feqIde1662d8502ad467dbc3a62827c855e4d近似为样本方差eqId43deeaabbc3c42ab8df8775638303a68.
(i)求eqId1d9a437ec62845e8be3b89a493ffe7ce
(ii)若该校共有5000名学生,记每周平均锻炼时间在区间eqId26333243867e405aa4db0c43d739c9f4的人数为eqIdc688382b53d04eb9aca74b12c3b14d16,试求eqIdd052a25b226749878579eedf20825f55.
附:eqId405cf03cd6334d8ea9f29688a8b54400,若eqId7fc4561966aa4ea2924541be8d21ddae~eqId995155952a92435790e9f7f7527f4f49eqId4cd9e641f50a48ddb1e22942764ff322eqIdf4a2ad70f9984318a1a3dce17f261ffe.
20. 在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,已知椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqId15bfbddeee0143e08c809ecf76ffb129的离心率为eqIdd1ebfa5c81a04d18900d19595d070677,直线eqId417e80f1349244878d01fe90e0891f5f和椭圆eqId19a4eb16029e4550a14f2afe4741a3c3交于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,当直线eqId417e80f1349244878d01fe90e0891f5f过椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的焦点,且与eqId8e15963708e9415da25069fea5906e24轴垂直时,eqIdac709ecd57644f199f922ee58934c3d3.
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)是否存在与eqId8e15963708e9415da25069fea5906e24轴不垂直的直线eqId417e80f1349244878d01fe90e0891f5f,使弦eqId99a3187c2b8f4bcc9703c74c3b72f1f3的垂直平分线过椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的右焦点?若存在,求出直线eqId417e80f1349244878d01fe90e0891f5f的方程;若不存在,请说明理由.
23. 已知函数fx)=|x﹣1|.
(1)求不等式f(2x)﹣fx+1)≥2的解集.
(2)若a>0,b>0且a+bf(3),求证:eqId51970eff873345498296a2a5a01760c6