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湖南省益阳市2020届高三下学期5月高考模拟理科数学试题
适用年级:高三 试卷类型:三模 试题总数:23 浏览次数:91 上传日期:2020-08-02
1 . 设集合eqIdc360c6bbc9384bbebc38b70e891d5a3f,则eqId170a03e31a0e4656b66452088e998e61(   )
A.{1,2}B.{0,1,2}C.(﹣∞,0)D.(0,3)
更新:2020/08/02难度:0.85题型:单选题组卷:151
2 . 已知eqIdb6e15e51d29a47a7aff44f98b1aafaee为虚数单位,eqIdf45ff360a8cd4da59868e47df89d4519,则eqId783c5f01aa1e49b29f88c27d2eca4354(   )
A.1B.﹣1C.2D.﹣2
更新:2020/08/02难度:0.85题型:单选题组卷:25
3 . 已知向量eqId9adc1365000c4e7997522746c5c2dbf3与向量eqId8b4536f2c690430e8f0ce38f16e00883共线,则实数x的值为(   )
A.﹣eqId57b3d7f61b5e48a1a1c959fa66d74726B.eqId57b3d7f61b5e48a1a1c959fa66d74726或﹣eqId57b3d7f61b5e48a1a1c959fa66d74726C.eqId57b3d7f61b5e48a1a1c959fa66d74726D.eqId57b3d7f61b5e48a1a1c959fa66d74726或0
更新:2020/08/02难度:0.94题型:单选题组卷:49
4 . 刘徽《九章算术•商功》中将底面为长方形,两个三角面与底面垂直的四棱锥叫做阳马.如图,是一个阳马的三视图,则此阳马的体积为(   )
说明: figure
A.eqId234f115648b84034995067419adb9bf4B.eqId58e0fe62beab48bcb3d84ad45180503eC.8D.16
更新:2020/08/02难度:0.85题型:单选题组卷:51
更新:2020/08/02难度:0.85题型:单选题组卷:96
6 . 已知函数eqId565d8a5edd6c4f99849a6a07cb322180,则函数eqId4837c94ef0ff4dcf9b1dda4df363275a的图象在点eqId2cb0b5c25a7e411abb9bf0c694c7c4ac处的切线斜率为(   )
A.eqId49b7b111d23b44a9990c2312dc3b7ed9B.eqIdfcc58431683b452ca65d1d9977a280bdC.eqId0884c4d6d4e844e29cb9046f8982ac0dD.eqIdb9e14f6c12e943509b9f5c3c0fe99fa8
更新:2020/08/02难度:0.85题型:单选题组卷:632
7 . 轴截面是正方形的圆柱叫做等边圆柱,已知某等边圆柱eqIdd926282bace544d98b4bb819e8bfaafa中,以底面圆eqId2efda802d5534f6d92d9f8af7aaec28b为底面圆,eqIde687d88b00354877b5e9fe1bff2531ee的中点eqId75c5faa59a8949f2a231b896be997e28为顶点作圆锥eqIda3435eea4c5a414db848c88456920237,现在等边圆柱eqIdd926282bace544d98b4bb819e8bfaafa中随机取一点,则该点取自圆锥eqIda3435eea4c5a414db848c88456920237内的概率是(   )
A.eqId49b7b111d23b44a9990c2312dc3b7ed9B.eqIda8012d5322b240128851ebf3cd086e12C.eqId3e866ebc4a57441386a76af413247f0eD.eqIdd056375c2cc745268c01dc2cbaa35258
更新:2020/08/02难度:0.94题型:单选题组卷:16
8 . 若等比数列eqId93e38ecd74a24cb59da79181b95bfd3a满足:eqId77b3f6b9955e499dbdab033a38779496eqId9a32d6c81f9746ea939e0ffe0a17f0d8,则eqId9d51ad182bd541949184738b462bbab8(   )
A.eqId401586f7a7f248b7904a4cfeaa2ed2f0B.eqIdc2b8234067d34cfca7c48ff6dd80f285C.eqId401586f7a7f248b7904a4cfeaa2ed2f0eqIdc2b8234067d34cfca7c48ff6dd80f285D.eqIdccb3cb63e81a4d48bfc4944fc0a6b03aeqIdc2b8234067d34cfca7c48ff6dd80f285
更新:2020/08/02难度:0.85题型:单选题组卷:93
9 . 定义在R上的奇函数fx)满足eqId43709baf316a44a29fe104ef48ab5f3c,且当eqId2edfef78e0424dcaae778d0f7afd528e时,eqIdbf6d9b5d7124406cbb3e99b8ef065575,则eqId5412608fea8543259f12f8c941f45e9a(   )
A.eqIddda48cced83d424b89b7d8f8c62b1056B.﹣eqIddda48cced83d424b89b7d8f8c62b1056C.eqIde41289c7307b48bd893a195b321d250fD.﹣eqIde41289c7307b48bd893a195b321d250f
更新:2020/08/02难度:0.85题型:单选题组卷:163
10 . 若随机变量eqIdc688382b53d04eb9aca74b12c3b14d16服从正态分布eqId995155952a92435790e9f7f7527f4f49,则eqId81c1860b070b44dd8505572de3fc3310eqId1bdfe8e573ab44e0be3c2aee825c1b2f,设eqId735c0b31e2d143c280159bc20fb82271,且eqId37f1deb06a2646c6b09ae052d9f13bde,在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,若圆eqIdbc4735a014b2464880ad3c0ec57c88f5上恰有两个点到直线eqId7432a1d1465f4ac2a5359b95b9f3fc91的距离为eqId37705e1ef6a84bbdbe88433e75932cdf,则实数eqIdad7cefefaba947e1a168bca491c4fca1的取值范围为(   )
A.eqId0ff5d18326b64ff18c02aef7ce59ce40B.eqId6a06033480574c5dac872532d36bcef2
C.eqId89ffe95847ea4e818949d81ec3a0e3cdD.eqId0d2ff26aca70463ea5b00e1459dffbfb
更新:2020/08/02难度:0.65题型:单选题组卷:26
11 . 如图,已知eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e为椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqIdd448b721bc2f41f8bed63e9521739ce3eqId207ddd75d0ee42629ce30bec7dcdaba1)的左、右焦点,过原点eqId2efda802d5534f6d92d9f8af7aaec28b 的直线eqId417e80f1349244878d01fe90e0891f5f与椭圆eqId19a4eb16029e4550a14f2afe4741a3c3交于eqIdeb53cb7cb0274f7d8f111c60f824c243两点(eqIdfb97767077bf4f21808288145baabb76),若eqId5b07121e1cd24279942a2b41c25d28e5eqId015bbd2ac7834ae8878fb7dbe7361d14,则eqId3d1ecd47ec654047bccd094a7737d411(   )
说明: figure
A.eqIde41289c7307b48bd893a195b321d250fB.eqIda8012d5322b240128851ebf3cd086e12C.eqId35f9084319e54f21aab3f44e2493b171D.eqId18d201ad69d542128329dbe73c1061fb
更新:2020/08/02难度:0.65题型:单选题组卷:46
12 . 若eqId37ee4988379449d4af9a121085062a2a表示不超过eqId8e15963708e9415da25069fea5906e24的最大整数(例如:eqId29b8cc5efb7647589298b7e7b69fef76),数列eqId054d5a7de5684002909fe944c86227c2满足:eqId1b870f8b46dc466aa4eb8cceaae660c7eqIda48d15c3a0dd415abecbbf754077cb9d,则eqId29409a2478ab440aa840fc2bad235a58(   )
A.eqId6b818ef040ce4f60a7990abe0b159667B.eqIde5c7ce5e432a4affbcddbe32992203b8C.eqIddc462ee98f894815bd3f1d5cfb50a2c6D.eqIdc311bf8e1e094a7ca2aa20f661cce51b
更新:2020/08/02难度:0.65题型:单选题组卷:212
13 . 若二项式eqIde4eded527da74a3da7c9984a384e8fd0展开式中,eqId5b55a800c13841a9a950777de0f0dec7项的系数为eqId7b1aaf239a69442fa58e336bf69f9cdf,则实数eqId70a27b6ddf6b478285353abb3b1f3741的值为_____.
更新:2020/08/02难度:0.85题型:填空题组卷:42
14 . 已知双曲线eqIdc3b97a393de447caa56c33f22b32bf2deqId9aca4748e10b4a46802f26823a3e28c6eqId786c47b04d16439ca7b2f93b9716ec01的一条渐近线与圆eqId55961763a2794d469615fae0c5728b18eqId022ba0308c40478699d9b8004d554425相切,切点在第三象限,则eqId783c5f01aa1e49b29f88c27d2eca4354 _____.
更新:2020/08/02难度:0.85题型:填空题组卷:21
15 . 已知函数eqIdf7eea50693ef4ddaaba47d776c45d158的图象向右平移eqIdb47bf79338b1478a89eac53d16970cdf个长度单位,得到函数eqId28c4c21271884dfeac29ce0222782376的图象,若函数eqId28c4c21271884dfeac29ce0222782376在区间eqId92c54a690c7347fc8bffd81275c80ace上单调递增,则eqIdf15782a6b93b49aeb4285c6f304dbe29的值为_____.
更新:2020/08/02难度:0.65题型:填空题组卷:72
16 . 在三棱锥SABC中,AC=2AB=4,BC=2eqIdcd9b24a6a6e5426ab775be20461174e3ASSC,平面ABC⊥平面SAC,则当△CBS的面积最大时,三棱锥SABC内切球的半径约为_____.(参考数据:eqIde8f7c99cfdc5476f962dee89cd67c616≈0.25)
更新:2020/08/02难度:0.65题型:填空题组卷:19
17 . 已知eqId0ce93bfa1f6a4a23b3258410dd19847a分别是eqId64b9b599fdb6481e9f8d9a94c102300b内角eqId10bbe48f886a4fa78fdf8c1fd064f9b4的对边,eqIda79b98f250ca4b56b8158a7642c51d0eeqIdb616a94271174fe78871039108c99810
(1)求eqId280ff125eb854a3183f21d737d8c5517
(2)若eqId64b9b599fdb6481e9f8d9a94c102300b的面积为eqIdb343117ae75e4bb28fe61eb8f47b9aff,求eqIdad7cefefaba947e1a168bca491c4fca1
更新:2020/08/02难度:0.65题型:解答题组卷:127
18 . 如图,在长方体eqId588284d93dc5489295f8f224f8e30d13中.
说明: figure
(1)求证:eqId6cbe61f5278c40dd9ac3e0c8f6e37ea3平面eqId8af9f53d7aa74d1ca7f111c20d5ab576
(2)若eqId88b8d5bea78b485c8f6851a60d257101,求直线eqIdf12c98a2bca444d1bc8a7dbd264d9955与平面eqId8af9f53d7aa74d1ca7f111c20d5ab576所成角的正弦值.
更新:2020/08/02难度:0.65题型:解答题组卷:87
19 . 抛物线eqIdd050af449075401299cc78c647d310e8的焦点为eqId63db14a5b4334f3ea583c8fb12b0d175,斜率为eqIdf3d28f4edef84cd5a5a1acd0f604b7bd的直线eqId417e80f1349244878d01fe90e0891f5f过点eqId63db14a5b4334f3ea583c8fb12b0d175且交抛物线于eqIde48bfb65dcde45fc9cab85499b67171b两点.
(1)若eqIdb67802f812494769b93485483fe3d0e2,求eqId4d2187284c5d4de29906363f7d21f60f
(2)过焦点eqId63db14a5b4334f3ea583c8fb12b0d175eqId417e80f1349244878d01fe90e0891f5f垂直的直线交抛物线eqId622e4033039a42f18743cf8d2f224d27两点,求eqId10196690a31145dbae17ac7242f01b54的最小值.
更新:2020/08/02难度:0.4题型:解答题组卷:21
20 . 已知函数eqId6e24034d34a7481aab3448c67124659c
(1)若函数eqId4837c94ef0ff4dcf9b1dda4df363275aeqIddf124ef8bdc74951994dc00978fea6b3上单调递增,求实数eqId70a27b6ddf6b478285353abb3b1f3741的取值范围;
(2)当eqId316e2199840e418e87252dba1d7d7ffd时,若eqIdc3ba5be319b04158aea14ab6fb28dea2(其中eqId70c08d40596445378a3ebc3942e99852),证明:eqId87da705fc8774b19926763fe1de27331
更新:2020/08/02难度:0.65题型:解答题组卷:77
21 . 某校班主任利用周末时间对该班级2019年最后一次月考的语文作文分数进行了一次统计,发现分数都位于20﹣55之间,现将所有分数情况分为[20,25),[25,30),[30,35),[35,40),[40,45),[45,50),[50,55)七组,其频率分布直方图如图所示,已知m=2n,[30,35)这组的参加者是12人.
说明: figure
(1)根据此频率分布直方图求图中mn的值,并求该班级这次月考作文分数的中位数;
(2)组织者从[35,40)这组的参加者(其中共有5名女学生,其余为男学生)中随机选出1人(为公平起见,把每个人编号,通过号码确定),如果选到男学生,则该学生留在本组,如果选到女生,则该女生交换一个男生到该组中去(已知本班男生人数多于女生人数),重复上述过程n次后,该组中的男生人数为Xn
①求随机变量X1的概率分布及数学期望EX1);
②求随机变量Xn的数学期望EXn)关于n的表达式.
更新:2020/08/02难度:0.15题型:解答题组卷:34
22 . 在平面直角坐标系xOy中,曲线eqId19a4eb16029e4550a14f2afe4741a3c3的参数方程为eqId1b09af9563d941fd99477a917e0562d4eqIdc13953f2514e4c8f9c8aaaf5241c33ac为参数),以坐标原点O为极点,x轴的正半轴为极轴建立极坐标系,直线eqId417e80f1349244878d01fe90e0891f5f的极坐标方程为eqIde908f89cf38f4701ae9984efe4a1025b
(1)求曲线eqId19a4eb16029e4550a14f2afe4741a3c3的普通方程和直线eqId417e80f1349244878d01fe90e0891f5f的直角坐标方程;
(2)求直线eqId417e80f1349244878d01fe90e0891f5f与曲线eqId19a4eb16029e4550a14f2afe4741a3c3相交所得的弦长.
更新:2020/08/02难度:0.65题型:解答题组卷:31
23 . 已知函数eqId9614e0e4be694d6ba578eb45136dfafa
(1)求不等式eqId292c5db283234fb88a3473ff3827c428的解集;
(2)若恰好存在7个不同的整数n,使得fn)<1,求实数m的取值范围.
更新:2020/08/02难度:0.65题型:解答题组卷:20