全一卷
1.已知集合
,则![](//static.xuejinqu.com/qimg/601/6019fb5f980261116046ffd0e8ba3bcd.png)
![](http://static.xuejinqu.com/qimg/c28/c283c77b1bedaa7a545ec7a2542ee1fe.png)
![](http://static.xuejinqu.com/qimg/601/6019fb5f980261116046ffd0e8ba3bcd.png)
A.![]() | B.![]() | C.(![]() | D.![]() |
2.若复数
满足
,其中
为虚数为单位,则
=
![](http://static.xuejinqu.com/qimg/6bd/6bdb866c99fa04faaaec91cbcd1d22b6.png)
![](http://static.xuejinqu.com/qimg/9fb/9fbe08f2ff99d13251c8048945315e05.png)
![](http://static.xuejinqu.com/qimg/e83/e8338934e373e9773ec2901d188f7061.png)
![](http://static.xuejinqu.com/qimg/6bd/6bdb866c99fa04faaaec91cbcd1d22b6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
3.设
则
的大小关系是
![](https:///quesimg/Upload/formula/8da607cd9760b02ca5ea5f8b6e1d90c3.png)
![](https:///quesimg/Upload/formula/63c77f11a6e47d67432583bbd3090c82.png)
A.![]() | B.![]() | C.![]() | D.![]() |
4.要得到函数![](https:///quesimg/Upload/formula/2a8ba089510cb3a65b95e7d79fb9180e.png)
![](https:///quesimg/Upload/formula/ecdab625e32e38d1c72c901cece0e147.png)
的图象,只需要将函数
的图象
![](https:///quesimg/Upload/formula/2a8ba089510cb3a65b95e7d79fb9180e.png)
![](https:///quesimg/Upload/formula/ecdab625e32e38d1c72c901cece0e147.png)
![](https:///quesimg/Upload/formula/8fbda1a62eafd575b177a0b4e3e195f2.png)
![](https:///quesimg/Upload/formula/e8223f0d86abbb86bf95429726c9446c.png)
A.向左平移![]() |
B.向右平移![]() |
C.向左平移![]() |
D.向右平移![]() |
5.
设,命题“若
,则方程
有实根”的逆否命题是
A.若方程![]() ![]() |
B.若方程![]() ![]() |
C.若方程![]() ![]() |
D.若方程![]() ![]() |
6.在区间
上随机地取一个数
,则事件“
”发生的概率为
![](http://static.xuejinqu.com/qimg/231/2315105ad70dbe998094119282e1d782.png)
![](http://static.xuejinqu.com/qimg/c4c/c4cc3d2dfe03a702d723b5ca5a83f574.png)
![](http://static.xuejinqu.com/qimg/e00/e0011d6d6b7ea03365b5bb42155d4d4e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
7.若函数
是奇函数,则使
成立的
的取值范围为( )
![](http://static.xuejinqu.com/qimg/b4d/b4dc3190d9e5d03b09165ded8f3bee98.png)
![](http://static.xuejinqu.com/qimg/1e7/1e7c855c8addb1c8d592ec313c3e2a85.png)
![](http://static.xuejinqu.com/qimg/4cb/4cbd80f9610b2bfad04f39d54bf7eb64.png)
A.(![]() | B.(-1,0) | C.![]() | D.![]() |
8.已知等腰直角三角形的直角边的长为2,将该三角形绕其斜边所在的直线旋转一周而形成的曲面所围成的几何体的体积为
A.![]() | B.![]() | C.![]() | D.![]() |
9.设函数
,若
,则![](//static.xuejinqu.com/qimg/46a/46a40126096b57f4e29c2c7f4133150b.png)
![](http://static.xuejinqu.com/qimg/b33/b33573ac0248004128ae4fa9999b2180.png)
![](http://static.xuejinqu.com/qimg/c8b/c8bd0a9ce62410b148f3a49a4683da7b.png)
![](http://static.xuejinqu.com/qimg/46a/46a40126096b57f4e29c2c7f4133150b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
10.为比较甲、乙两地某月14时的气温状况,随机选取该月中的5天,将这5天中14时的气温数据(单位:℃)制成如图所示的茎叶图.考虑以下结论:
![](//static.xuejinqu.com/qimg/e8f/e8f26c7d9bd010296c350e75598e4516.png)
①甲地该月14时的平均气温低于乙地该月14时的平均气温;
②甲地该月14时的平均气温高于乙地该月14时的平均气温;
③甲地该月14时的平均气温的标准差小于乙地该月14时的气温的标准差;
④甲地该月14时的平均气温的标准差大于乙地该月14时的气温的标准差.
其中根据茎叶图能得到的统计结论的标号为__________ .
![](http://static.xuejinqu.com/qimg/e8f/e8f26c7d9bd010296c350e75598e4516.png)
①甲地该月14时的平均气温低于乙地该月14时的平均气温;
②甲地该月14时的平均气温高于乙地该月14时的平均气温;
③甲地该月14时的平均气温的标准差小于乙地该月14时的气温的标准差;
④甲地该月14时的平均气温的标准差大于乙地该月14时的气温的标准差.
其中根据茎叶图能得到的统计结论的标号为
11.执行右边的程序框图,若输入的
的值为
,则输出的
的值是 . ![](//static.xuejinqu.com/qimg/1da/1daed606756810fd9fda1c3d4a8cfcf1.png)
![](http://static.xuejinqu.com/qimg/4cb/4cbd80f9610b2bfad04f39d54bf7eb64.png)
![](http://static.xuejinqu.com/qimg/e11/e11dc3307f472771a21ae061141951da.png)
![](http://static.xuejinqu.com/qimg/ae3/ae3d592441dc4632c35d8b7efe75dba7.png)
![](http://static.xuejinqu.com/qimg/1da/1daed606756810fd9fda1c3d4a8cfcf1.png)
12.若
满足约束条件
则
的最大值为_______ .
![](http://static.xuejinqu.com/qimg/ea9/ea9020e9f0c812141dc8a44f3577df2f.png)
![](http://static.xuejinqu.com/qimg/409/4090ceb322fc82ae513ed8a95728bccb.png)
![](http://static.xuejinqu.com/qimg/14b/14b1a7ffce129bf07bfe0e98b79ac003.png)
13.过点
作圆
的两条切线,切点分别为
,则
= .
![](http://static.xuejinqu.com/qimg/0f5/0f575fb653a2278ffdb4ff6ee2c6651c.png)
![](http://static.xuejinqu.com/qimg/f45/f4533763a78fb2d0fc96cc91112df272.png)
![](http://static.xuejinqu.com/qimg/4b0/4b0572309e401c8f43916c900a4c3036.png)
![](http://static.xuejinqu.com/qimg/b1d/b1d3c1a9fb809da91b879e6234c012a5.png)
14.定义运算“
”:
(
).当
时,
的最小值是_______ .
![](http://static.xuejinqu.com/qimg/064/064b72dba4ab2d87e096ee9082ccf4ae.png)
![](http://static.xuejinqu.com/qimg/ff6/ff6af92c3d7516f0735a3163c8f335eb.png)
![](http://static.xuejinqu.com/qimg/ed0/ed012a9735f42b93262238a654b01325.png)
![](http://static.xuejinqu.com/qimg/171/171298193fa38c3f7899a6545ecf6d37.png)
![](http://static.xuejinqu.com/qimg/cef/cef35dad02ef9723c2212ff6b412988e.png)
15.过双曲线![](//static.xuejinqu.com/qimg/9da/9daffacbda3ae3a4e13c794a8431a076.png)
![](//static.xuejinqu.com/qimg/baf/baf3f6da6588f6f39797f6bcdbde8cb4.png)
的右焦点作一条与其渐近线平行的直线,交
于点
.若点
的横坐标为
,则
的离心率为 .
![](http://static.xuejinqu.com/qimg/9da/9daffacbda3ae3a4e13c794a8431a076.png)
![](http://static.xuejinqu.com/qimg/baf/baf3f6da6588f6f39797f6bcdbde8cb4.png)
![](http://static.xuejinqu.com/qimg/06f/06fe447e9bee8ffa71277b7771a22cdc.png)
![](http://static.xuejinqu.com/qimg/5d6/5d65dc63eb8a61e345ca22847fab9983.png)
![](http://static.xuejinqu.com/qimg/f2f/f2fb148e843b46207afb60dedd25a09e.png)
![](http://static.xuejinqu.com/qimg/f2f/f2fb148e843b46207afb60dedd25a09e.png)
![](http://static.xuejinqu.com/qimg/fdb/fdbd05c981c008fb58192e54b70f3deb.png)
![](http://static.xuejinqu.com/qimg/5d6/5d65dc63eb8a61e345ca22847fab9983.png)
16.某中学调查了某班全部
名同学参加书法社团和演讲社团的情况,数据如下表:(单位:人)
(1)从该班随机选
名同学,求该同学至少参加上述一个社团的概率;
(2)在既参加书法社团又参加演讲社团的
名同学中,有5名男同学![](https:///quesimg/Upload/formula/aa2b1e19e827ecb2c324210134710032.png)
名女同学
现从这
名男同学和
名女同学中各随机选
人,求
被选中且
未被选中的概率.
![](https:///quesimg/Upload/formula/5021dda43ea360fb7b1102c1a462693a.png)
参加书法社团 | 未参加书法社团 | |
参加演讲社团 | ![]() | ![]() |
未参加演讲社团 | ![]() | ![]() |
(1)从该班随机选
![](https:///quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
(2)在既参加书法社团又参加演讲社团的
![](https:///quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https:///quesimg/Upload/formula/aa2b1e19e827ecb2c324210134710032.png)
![](https:///quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https:///quesimg/Upload/formula/9aade62f339761df74997fef1e69464e.png)
![](https:///quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https:///quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https:///quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https:///quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https:///quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
17.(本小题满分12分)
中,角
所对的边分别为
.已知
求
和
的值.
![](http://static.xuejinqu.com/qimg/16c/16c308318e303ef15f97f68ae859a7c1.png)
![](http://static.xuejinqu.com/qimg/137/13738505dfcdb036901a1897e52ba7d1.png)
![](http://static.xuejinqu.com/qimg/8af/8af3a728a3d9fbcb90d43f88e6f7e045.png)
![](http://static.xuejinqu.com/qimg/44c/44cc92a1b44f395262fc4fe706ad42c6.png)
![](http://static.xuejinqu.com/qimg/97d/97dccb41579f54ae6679b1ae2d57d80e.png)
![](http://static.xuejinqu.com/qimg/7c2/7c2b10b9c6ad7dc2ed397b32dc70616a.png)
18.如图,三棱台
中,
分别为
的中点.
![](//static.xuejinqu.com/qimg/268/2680743e3489ed5aa116637a2cd69832.png)
(Ⅰ)求证:
平面
;
(Ⅱ)若
求证:平面
平面
.
![](http://static.xuejinqu.com/qimg/ab1/ab109779407c9355796904e2a11d4f0e.png)
![](http://static.xuejinqu.com/qimg/928/928b1b45564cbd29b6835518c803edcb.png)
![](http://static.xuejinqu.com/qimg/c23/c23745a35f452a2b395eba95d6027d73.png)
![](http://static.xuejinqu.com/qimg/268/2680743e3489ed5aa116637a2cd69832.png)
(Ⅰ)求证:
![](http://static.xuejinqu.com/qimg/513/513ef78849fa2325dcc575af0c7d004c.png)
![](http://static.xuejinqu.com/qimg/e95/e9566b3f7be3776fb5da653fa8b3eadf.png)
(Ⅱ)若
![](http://static.xuejinqu.com/qimg/92c/92c196aeb6b4cbeec95be4c91da3d61b.png)
![](http://static.xuejinqu.com/qimg/46a/46ae073beaa65663c39745d23ead08f2.png)
![](http://static.xuejinqu.com/qimg/bf2/bf2321deece0dfd39e7a3a44b3d2c52f.png)
19.已知数列
是首项为正数的等差数列,数列
的前
项和为
.
(1)求数列
的通项公式;
(2)设
,求数列
的前
项和
.
![](https:///quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https:///quesimg/Upload/formula/8ef5561a645f3f67290f31631d465fca.png)
![](https:///quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https:///quesimg/Upload/formula/958b23fabde33988b941240a6f82c44b.png)
(1)求数列
![](https:///quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
(2)设
![](https:///quesimg/Upload/formula/802fe1d43065964fd79c25932f3bc13b.png)
![](https:///quesimg/Upload/formula/bee4464b3b4eb6e52ee02f095aae84f0.png)
![](https:///quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https:///quesimg/Upload/formula/cb26cd1601fe7e76e1e2dc0b4909324a.png)
20.设函数
. 已知曲线
在点
处的切线与直线
平行.
(Ⅰ)求
的值;
(Ⅱ)是否存在自然数
,使得方程
在
内存在唯一的根?如果存在,求出
;如果不存在,请说明理由;
(Ⅲ)设函数
(
表示,
中的较小值),求
的最大值.
![](http://static.xuejinqu.com/qimg/dba/dbabae5773a1b3925e440b53335cdc50.png)
![](http://static.xuejinqu.com/qimg/df7/df78e228e4493109cfa4907fefbe4f41.png)
![](http://static.xuejinqu.com/qimg/53f/53f100305e6177ff19492fd14fd8da5f.png)
![](http://static.xuejinqu.com/qimg/f13/f13bc19923408b4b26de1d7cfc66ad99.png)
(Ⅰ)求
![](http://static.xuejinqu.com/qimg/f7e/f7ebe3f1509f13bb46fb292fc2a3f596.png)
(Ⅱ)是否存在自然数
![](http://static.xuejinqu.com/qimg/93c/93c0a0677a1a991b4911061811aa1f77.png)
![](http://static.xuejinqu.com/qimg/ffd/ffdd2ab5ab5bde9aaee63ce74f81832c.png)
![](http://static.xuejinqu.com/qimg/daf/dafd5196940a7cd3eb8b8cd0f383c62b.png)
![](http://static.xuejinqu.com/qimg/93c/93c0a0677a1a991b4911061811aa1f77.png)
(Ⅲ)设函数
![](http://static.xuejinqu.com/qimg/887/887ea94d99ebad04379f554b09020056.png)
![](http://static.xuejinqu.com/qimg/df7/df78e228e4493109cfa4907fefbe4f41.png)
![](http://static.xuejinqu.com/qimg/f6a/f6a4f11f3325e8a388fd9f3f145614fd.png)
![](http://static.xuejinqu.com/qimg/2d1/2d139b28108752eff25e41ca236c30b6.png)
21.平面直角坐标系
中,已知椭圆
:
的离心率为
,且点(
,
)在椭圆
上.
(Ⅰ)求椭圆
的方程;
(Ⅱ)设椭圆
:
,
为椭圆
上任意一点,过点
的直线
交椭圆
于
两点,射线
交椭圆
于点
.
(ⅰ)求
的值;
(ⅱ)求
面积的最大值.
![](http://static.xuejinqu.com/qimg/59d/59de59fb2862ad656a90d9bb1b18568a.png)
![](http://static.xuejinqu.com/qimg/7f4/7f4ba58e204b9831a2d04610deeb3622.png)
![](http://static.xuejinqu.com/qimg/938/938b7bdf555ae449d389beafb5c02642.png)
![](http://static.xuejinqu.com/qimg/368/36891736c0b0d0f8b7fcde28fcf6015f.png)
![](http://static.xuejinqu.com/qimg/002/00224d1b854a5133f3a31f399df4b9b0.png)
![](http://static.xuejinqu.com/qimg/ae9/ae9afa911c676e39af2d9f3bc42e0939.png)
![](http://static.xuejinqu.com/qimg/7f4/7f4ba58e204b9831a2d04610deeb3622.png)
(Ⅰ)求椭圆
![](http://static.xuejinqu.com/qimg/7f4/7f4ba58e204b9831a2d04610deeb3622.png)
(Ⅱ)设椭圆
![](http://static.xuejinqu.com/qimg/00e/00ec78cc7c5ca95d140f4a5d92fd938e.png)
![](http://static.xuejinqu.com/qimg/efe/efe24b0705474d8b45502a6bd1428199.png)
![](http://static.xuejinqu.com/qimg/b97/b978c7440ace3ed1c03be3beec86c9b7.png)
![](http://static.xuejinqu.com/qimg/7f4/7f4ba58e204b9831a2d04610deeb3622.png)
![](http://static.xuejinqu.com/qimg/b97/b978c7440ace3ed1c03be3beec86c9b7.png)
![](http://static.xuejinqu.com/qimg/4b3/4b3cede5b981089496bd98ca5886128f.png)
![](http://static.xuejinqu.com/qimg/00e/00ec78cc7c5ca95d140f4a5d92fd938e.png)
![](http://static.xuejinqu.com/qimg/d47/d47fd34dba4fa534f0500674371c13e2.png)
![](http://static.xuejinqu.com/qimg/321/321c64157d7c4a83a644f6eebd8b7b49.png)
![](http://static.xuejinqu.com/qimg/00e/00ec78cc7c5ca95d140f4a5d92fd938e.png)
![](http://static.xuejinqu.com/qimg/e45/e456ad23356ff84d95e8dc9ff9f6a849.png)
(ⅰ)求
![](http://static.xuejinqu.com/qimg/9cf/9cf8fd9bc48f2a392acaa0e3af1ce90d.png)
(ⅱ)求
![](http://static.xuejinqu.com/qimg/a1f/a1f8b7021abb96f6a2a58c31ff13caa9.png)