全一卷
1.函数
的最小正周期为___________ .
![](http://static.xuejinqu.com/qimg/6a8/6a8dd5caabbd34273b0c0f47326c5351.png)
2.设全集
.若集合
,
,则
.
![](http://static.xuejinqu.com/qimg/737/737a8abef51754bdbebb397c47edb8d0.png)
![](http://static.xuejinqu.com/qimg/069/069da876ac69757ab9d5cbb603a0ef5e.png)
![](http://static.xuejinqu.com/qimg/85c/85ca4a48da3a3d16082a5717da9782c7.png)
![](http://static.xuejinqu.com/qimg/598/5987443db78d5059c314502ea14af2ea.png)
3.若复数
满足
,其中
是虚数单位,则
.
![](http://static.xuejinqu.com/qimg/4ad/4ad426418943f45293e90d50105ea9ee.png)
![](http://static.xuejinqu.com/qimg/501/501b36cc7cd684f78346e18ede488549.png)
![](http://static.xuejinqu.com/qimg/381/3811c40bb2c6ee0ab48b4fceeebcb350.png)
![](http://static.xuejinqu.com/qimg/0f4/0f496332fcf434b3b8585f3c8c2bb66d.png)
4.设
为
的反函数,则
.
![](http://static.xuejinqu.com/qimg/d97/d97e937e0b39a6953173069b10bb72cd.png)
![](http://static.xuejinqu.com/qimg/346/3464d1c948596561d3d41682ecd1b6ce.png)
![](http://static.xuejinqu.com/qimg/b5c/b5c9aedaed4f25d7f22fcd2e860b96d7.png)
5.若线性方程组的增广矩阵为![](//static.xuejinqu.com/qimg/14d/14dae0ab3a04f6464b354052262cdbd2.png)
![](//static.xuejinqu.com/qimg/a89/a890532d8e11603469c77154f12a2fba.png)
解为
,则
.
![](http://static.xuejinqu.com/qimg/14d/14dae0ab3a04f6464b354052262cdbd2.png)
![](http://static.xuejinqu.com/qimg/a89/a890532d8e11603469c77154f12a2fba.png)
![](http://static.xuejinqu.com/qimg/4bf/4bfa2e8ba3905204da02aa31f4766407.png)
![](http://static.xuejinqu.com/qimg/2da/2dafc6c5a701383d1a6a10a756f38bad.png)
![](http://static.xuejinqu.com/qimg/ad5/ad5f4b5e81f06319638385a475918277.png)
6.若正三棱柱的所有棱长均为
,且其体积为
,则
.
![](http://static.xuejinqu.com/qimg/e37/e37aa5c467bad983aa8d679a67cab16e.png)
![](http://static.xuejinqu.com/qimg/e1c/e1c821744cfa91647fd7684086f37623.png)
![](http://static.xuejinqu.com/qimg/7d5/7d5f9cb5cc606cfb7d664c4f79162613.png)
7.抛物线
上的动点
到焦点的距离的最小值为1,则
.
![](http://static.xuejinqu.com/qimg/c64/c642079bb8ee50cf153820c2eb2e410b.png)
![](http://static.xuejinqu.com/qimg/c35/c355450f808e12f2d3f0efe0ff891ff0.png)
![](http://static.xuejinqu.com/qimg/795/7956838c40833ea37a2d3b1f7e9ab20d.png)
8.方程
的解为 .
![](http://static.xuejinqu.com/qimg/3d2/3d2ca2dd8103f31e15490f7f63fe8cb8.png)
9.若
满足
,则目标函数
的最大值为 .
![](http://static.xuejinqu.com/qimg/edd/eddc822101550a0df8c2932c299942d3.png)
![](http://static.xuejinqu.com/qimg/d21/d21cb8cf01dae74e64725e8652c537f8.png)
![](http://static.xuejinqu.com/qimg/d54/d54b875f1b8d7e9386f674b3480b35ac.png)
10.在报名的3名男教师和6名女教师中,选取5人参加义务献血,要求男、女教师都有,则不同的选取方式的种数为 (结果用数值表示).
11.在
的二项式中,常数项等于 (结果用数值表示).
![](http://static.xuejinqu.com/qimg/175/1756af272a5276c82d002c818bef748b.png)
12.已知双曲线
、
的顶点重合,
的方程为
,若
的一条渐近线的斜率是
的一条渐近线的斜率的2倍,则
的方程为 .
![](http://static.xuejinqu.com/qimg/eda/edac687a42082ddc95824cef78fd3c0c.png)
![](http://static.xuejinqu.com/qimg/ff5/ff5717ba5c4a5c7b00da3eda6082fc37.png)
![](http://static.xuejinqu.com/qimg/eda/edac687a42082ddc95824cef78fd3c0c.png)
![](http://static.xuejinqu.com/qimg/eaa/eaa1aabda3a34505b867822932f2a889.png)
![](http://static.xuejinqu.com/qimg/ff5/ff5717ba5c4a5c7b00da3eda6082fc37.png)
![](http://static.xuejinqu.com/qimg/eda/edac687a42082ddc95824cef78fd3c0c.png)
![](http://static.xuejinqu.com/qimg/ff5/ff5717ba5c4a5c7b00da3eda6082fc37.png)
13.已知平面向量
、
、
满足
,且
,则
的最大值是 .
![](http://static.xuejinqu.com/qimg/814/814f761f2f7e47e94591ac2ad46771ef.png)
![](http://static.xuejinqu.com/qimg/5dc/5dcb939b29958285ccc4b00ddb7c06fc.png)
![](http://static.xuejinqu.com/qimg/862/8622bdee7dc6b1246632030f2261c81d.png)
![](http://static.xuejinqu.com/qimg/faa/faa8b7c1c18b37cdb7a4a2cf86786e78.png)
![](http://static.xuejinqu.com/qimg/844/844ca622dd6333e6c9d93e8d4eefeda5.png)
![](http://static.xuejinqu.com/qimg/a8c/a8c2ac489ccaa42c29079d6591786b25.png)
14.已知函数
.若存在
,
,
,
满足
,且![](//static.xuejinqu.com/qimg/b9b/b9bed240c65e713ee583704e40a3975f.png)
,则
的最小值为 .
![](http://static.xuejinqu.com/qimg/8a2/8a220bb37660439ff48152274e902bc8.png)
![](http://static.xuejinqu.com/qimg/eec/eec6d50d3b3ff88ffb65cc1da28aa4c3.png)
![](http://static.xuejinqu.com/qimg/73f/73f1615394a2c0f80185d4ea004e4a45.png)
![](http://static.xuejinqu.com/qimg/da0/da0d9815de405e1a6e48bae3c010ffeb.png)
![](http://static.xuejinqu.com/qimg/90d/90d732b34cf139975f5dbfb67a1b43eb.png)
![](http://static.xuejinqu.com/qimg/b00/b00e8f959000e8adc7f401d9e53b075d.png)
![](http://static.xuejinqu.com/qimg/b9b/b9bed240c65e713ee583704e40a3975f.png)
![](http://static.xuejinqu.com/qimg/8ca/8ca6403feffebcbc2e4fd36825e72e26.png)
![](http://static.xuejinqu.com/qimg/df7/df7bfe50b30a95db57277aa37183c17c.png)
15.设
、
,则“
、
均为实数”是“
是实数”的().
![](http://static.xuejinqu.com/qimg/d7a/d7acbbd1152dbf09e19a4a97db293695.png)
![](http://static.xuejinqu.com/qimg/802/802091075b88ee4075d97be5a5b040af.png)
![](http://static.xuejinqu.com/qimg/d7a/d7acbbd1152dbf09e19a4a97db293695.png)
![](http://static.xuejinqu.com/qimg/59d/59df5cff266d385398bb0bd546f1ee76.png)
![](http://static.xuejinqu.com/qimg/caa/caa65c754bdc707a6654ed6a4a38bbc5.png)
A.充分非必要条件 |
B.必要非充分条件 |
C.充要条件 |
D.既非充分又非必要条件 |
16.下列不等式中,与不等式
解集相同的是().
![](http://static.xuejinqu.com/qimg/8ad/8adfdf2d5745f6e48af712ac001ca76c.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
17.已知点
的坐标为
,将
绕坐标原点
逆时针旋转
至
,则点
的纵坐标为().
![](http://static.xuejinqu.com/qimg/2c6/2c69f9a36efbfc3e894e3e0194d420a6.png)
![](http://static.xuejinqu.com/qimg/cc7/cc741f5d79243c7cc60c82b60298d66b.png)
![](http://static.xuejinqu.com/qimg/ca5/ca55e3c1fa6468558a0775e4799f22ac.png)
![](http://static.xuejinqu.com/qimg/d79/d795b4caff4dd58b2de7de04b71a7f29.png)
![](http://static.xuejinqu.com/qimg/046/04641ef3a2c8d9840442e017544e7962.png)
![](http://static.xuejinqu.com/qimg/62f/62fc33a127038fc95a98575177777093.png)
![](http://static.xuejinqu.com/qimg/63b/63befa494958409f73e42119bad22041.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
18.设
是直线
与圆
在第一象限的交点,则极限
( ).
![](http://static.xuejinqu.com/qimg/83d/83d932bf2700b4b5639497ed0c8ae338.png)
![](http://static.xuejinqu.com/qimg/661/66184938f4f6d3c4bb5722da7c213ab8.png)
![](http://static.xuejinqu.com/qimg/1df/1dffce6077456fb25ed104e9d3e7175e.png)
![](http://static.xuejinqu.com/qimg/af3/af3640acba00fae09d611f0a34a6bd6d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
19.如图,圆锥的顶点为
,底面的一条直径为
,
为半圆弧
的中点,
为劣弧
的中点.已知
,
,求三棱锥
的体积,并求异面直线
与
所成角的大小.![](//static.xuejinqu.com/qimg/088/0886f0a4fa8057fbf70e0389fbe01c31.png)
![](http://static.xuejinqu.com/qimg/267/2671ed9ca948a7c93c63d42491400282.png)
![](http://static.xuejinqu.com/qimg/948/948ac91770c53df52fd53f778633b822.png)
![](http://static.xuejinqu.com/qimg/7c1/7c1cacaf46ce934e0e62ecee13aa6230.png)
![](http://static.xuejinqu.com/qimg/948/948ac91770c53df52fd53f778633b822.png)
![](http://static.xuejinqu.com/qimg/9e0/9e01ef98b1252ab6762d0b482174710f.png)
![](http://static.xuejinqu.com/qimg/807/8070ed040c6224c98e5b54569f165862.png)
![](http://static.xuejinqu.com/qimg/48f/48f5b88f155e540bb007ea05283eaeba.png)
![](http://static.xuejinqu.com/qimg/31b/31b76183eaffe62697bd46724822c71c.png)
![](http://static.xuejinqu.com/qimg/c6f/c6f48853ec470a8d21265b879efd6f84.png)
![](http://static.xuejinqu.com/qimg/5c9/5c96c27adc850c4e6bb19f9fc5dafd36.png)
![](http://static.xuejinqu.com/qimg/84c/84c8db814902c690c04b050c22542d7d.png)
![](http://static.xuejinqu.com/qimg/088/0886f0a4fa8057fbf70e0389fbe01c31.png)
20.已知函数
,其中
为实数.
(1)根据
的不同取值,判断函数
的奇偶性,并说明理由;
(2)若
,判断函数
在
上的单调性,并说明理由.
![](http://static.xuejinqu.com/qimg/393/3936fedad4e577a17467ba00f361d27b.png)
![](http://static.xuejinqu.com/qimg/e37/e37aa5c467bad983aa8d679a67cab16e.png)
(1)根据
![](http://static.xuejinqu.com/qimg/e37/e37aa5c467bad983aa8d679a67cab16e.png)
![](http://static.xuejinqu.com/qimg/10c/10cac31fc4cad12203d7b71cdba1115a.png)
(2)若
![](http://static.xuejinqu.com/qimg/d4a/d4a6c86803fd9c8430fa685421b83069.png)
![](http://static.xuejinqu.com/qimg/10c/10cac31fc4cad12203d7b71cdba1115a.png)
![](http://static.xuejinqu.com/qimg/c2a/c2a6e0a284f9022b43c5b0a18aee1f8e.png)
21.
如图,
三地有直道相通,
千米,
千米,
千米.现甲、乙两警员同时从
地出发匀速前往
地,经过
小时,他们之间的距离为
(单位:千米).甲的路线是
,速度为5千米/小时,乙的路线是
,速度为8千米/小时.乙到达
地后原地等待.设
时乙到达
地.
![](//static.xuejinqu.com/qimg/d7c/d7c605f368c748032f4ccbc83aff25e6.png)
(1)求
与
的值;
(2)已知警员的对讲机的有效通话距离是3千米.当
时,求
的表达式,并判断
在
上得最大值是否超过3?说明理由.
如图,
![](http://static.xuejinqu.com/qimg/fe5/fe55049a1c38176cb9b88fc842d7dc30.png)
![](http://static.xuejinqu.com/qimg/35c/35c5f30c20d61d12f8e04e7fed4352b2.png)
![](http://static.xuejinqu.com/qimg/434/434654aa22c610dc8cf393d2e1369b56.png)
![](http://static.xuejinqu.com/qimg/b16/b1609805a76667a6360df67296b204c1.png)
![](http://static.xuejinqu.com/qimg/2c6/2c69f9a36efbfc3e894e3e0194d420a6.png)
![](http://static.xuejinqu.com/qimg/63b/63befa494958409f73e42119bad22041.png)
![](http://static.xuejinqu.com/qimg/069/0699401c5b8267a5a9a736d8dfe1a4bf.png)
![](http://static.xuejinqu.com/qimg/d1d/d1dffaf08ab2bf9311b4dd9348c8ef67.png)
![](http://static.xuejinqu.com/qimg/948/948ac91770c53df52fd53f778633b822.png)
![](http://static.xuejinqu.com/qimg/cb5/cb563d6838eec5d7063c12dd35f0ee69.png)
![](http://static.xuejinqu.com/qimg/63b/63befa494958409f73e42119bad22041.png)
![](http://static.xuejinqu.com/qimg/109/1090a92a4f3cacef47c612d0ae144f07.png)
![](http://static.xuejinqu.com/qimg/7c1/7c1cacaf46ce934e0e62ecee13aa6230.png)
![](http://static.xuejinqu.com/qimg/d7c/d7c605f368c748032f4ccbc83aff25e6.png)
(1)求
![](http://static.xuejinqu.com/qimg/518/5189de39939674eb4eed4196a757a3b0.png)
![](http://static.xuejinqu.com/qimg/12a/12a937bc3f0f006490683c521d3ffc89.png)
(2)已知警员的对讲机的有效通话距离是3千米.当
![](http://static.xuejinqu.com/qimg/58d/58d9eb7b010c3d00f7b7a5dd51ce8989.png)
![](http://static.xuejinqu.com/qimg/d1d/d1dffaf08ab2bf9311b4dd9348c8ef67.png)
![](http://static.xuejinqu.com/qimg/d1d/d1dffaf08ab2bf9311b4dd9348c8ef67.png)
![](http://static.xuejinqu.com/qimg/e2f/e2f8cc0aa2cad9d8beb3b075ccc73aa3.png)
22.已知椭圆
,过原点的两条直线
和
分别于椭圆交于
、
和
、
,设
的面积为
.
(1)设
,
,用
、
的坐标表示点
到直线
的距离,并证明
;
(2)设
,
,
,求
的值;
(3)设
与
的斜率之积为
,求
的值,使得无论
与
如何变动,面积
保持不变.
![](http://static.xuejinqu.com/qimg/de7/de7ce3c9ef8817d0807ac92eaba7cd77.png)
![](http://static.xuejinqu.com/qimg/1c1/1c1fc79529545e2c0921f12fb6653cda.png)
![](http://static.xuejinqu.com/qimg/ca0/ca0117ba97dcc5c90fb296197e73aaac.png)
![](http://static.xuejinqu.com/qimg/2c6/2c69f9a36efbfc3e894e3e0194d420a6.png)
![](http://static.xuejinqu.com/qimg/63b/63befa494958409f73e42119bad22041.png)
![](http://static.xuejinqu.com/qimg/7c1/7c1cacaf46ce934e0e62ecee13aa6230.png)
![](http://static.xuejinqu.com/qimg/687/687d3bea245f61cf3f6f819ed803fc37.png)
![](http://static.xuejinqu.com/qimg/37a/37aefd0a3501ef070be6d8ab65459ff7.png)
![](http://static.xuejinqu.com/qimg/2ad/2ad8bafcedadbaec921904ce79cb212d.png)
(1)设
![](http://static.xuejinqu.com/qimg/25f/25f4a1c11044ecea30706978e3b266f0.png)
![](http://static.xuejinqu.com/qimg/9f9/9f9a65db202b4b4d8a897192c5ba7a9c.png)
![](http://static.xuejinqu.com/qimg/2c6/2c69f9a36efbfc3e894e3e0194d420a6.png)
![](http://static.xuejinqu.com/qimg/7c1/7c1cacaf46ce934e0e62ecee13aa6230.png)
![](http://static.xuejinqu.com/qimg/7c1/7c1cacaf46ce934e0e62ecee13aa6230.png)
![](http://static.xuejinqu.com/qimg/1c1/1c1fc79529545e2c0921f12fb6653cda.png)
![](http://static.xuejinqu.com/qimg/f99/f994e48592ea6ec114dd6fd178421f0a.png)
(2)设
![](http://static.xuejinqu.com/qimg/d1b/d1bb3c2455dc843dadf2d890c3bd0828.png)
![](http://static.xuejinqu.com/qimg/df0/df0a4d218e53aad80e8da925d06ba99f.png)
![](http://static.xuejinqu.com/qimg/b0b/b0b51a06e1d807413a46c7b43e3aa781.png)
![](http://static.xuejinqu.com/qimg/330/330651d36a713394d1e8b3377ad0cc7a.png)
(3)设
![](http://static.xuejinqu.com/qimg/1c1/1c1fc79529545e2c0921f12fb6653cda.png)
![](http://static.xuejinqu.com/qimg/ca0/ca0117ba97dcc5c90fb296197e73aaac.png)
![](http://static.xuejinqu.com/qimg/df7/df7bfe50b30a95db57277aa37183c17c.png)
![](http://static.xuejinqu.com/qimg/df7/df7bfe50b30a95db57277aa37183c17c.png)
![](http://static.xuejinqu.com/qimg/1c1/1c1fc79529545e2c0921f12fb6653cda.png)
![](http://static.xuejinqu.com/qimg/ca0/ca0117ba97dcc5c90fb296197e73aaac.png)
![](http://static.xuejinqu.com/qimg/2ad/2ad8bafcedadbaec921904ce79cb212d.png)
23.
已知数列
与
满足
,
.
(1)若
,且
,求数列
的通项公式;
(2)设
的第
项是最大项,即
,求证:数列
的第
项是最大项;
(3)设
,![](//static.xuejinqu.com/qimg/f2e/f2ead8bbe9609982816c3b4f22c80ed9.png)
,求
的取值范围,使得对任意
,
,
,且
.
已知数列
![](http://static.xuejinqu.com/qimg/cee/cee2f22ae55d884b760bc525ef55f519.png)
![](http://static.xuejinqu.com/qimg/74d/74dff9f63e99a6176f2d607cc96aea07.png)
![](http://static.xuejinqu.com/qimg/9c0/9c0e599b46f2d275edca2d870632257e.png)
![](http://static.xuejinqu.com/qimg/89f/89fd03c553160df4546eb648ecf9deac.png)
(1)若
![](http://static.xuejinqu.com/qimg/8e0/8e02eb239a43702017dada5f05f8d3a0.png)
![](http://static.xuejinqu.com/qimg/835/83563f4f1dba65b21bdbd6f81c2150e4.png)
![](http://static.xuejinqu.com/qimg/cee/cee2f22ae55d884b760bc525ef55f519.png)
(2)设
![](http://static.xuejinqu.com/qimg/cee/cee2f22ae55d884b760bc525ef55f519.png)
![](http://static.xuejinqu.com/qimg/210/210802a54b37d4720f56cf62d670754b.png)
![](http://static.xuejinqu.com/qimg/c59/c597a32714fb6657fb42a24f4125ffc7.png)
![](http://static.xuejinqu.com/qimg/74d/74dff9f63e99a6176f2d607cc96aea07.png)
![](http://static.xuejinqu.com/qimg/210/210802a54b37d4720f56cf62d670754b.png)
(3)设
![](http://static.xuejinqu.com/qimg/161/161b252bded090f652d79ffadfb55b93.png)
![](http://static.xuejinqu.com/qimg/f2e/f2ead8bbe9609982816c3b4f22c80ed9.png)
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