2012高三·湖北·竞赛
1 . 设集合
,
是
的子集,且满足
,
.则满足条件的子集
的个数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6ee46190eb71b8df0136983ab79678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d020cd453031ae9eede7961ec78f21a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29719d33af813b84dae0191ae5c92a00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82468a8ceda9d0573e58b98a3c866dcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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2012高三·湖北·竞赛
2 . 设
表示不超过实数
的最大整数.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969ce30f7953cac3c102e2e7d0b495a9.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969ce30f7953cac3c102e2e7d0b495a9.png)
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2012高三·湖北·竞赛
3 . 已知数列
满足
若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/469384028013368be6aa82c79d7cbb48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6e1f53b8629c599143966ca7b49be65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
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4 . 已知数列
满足:
,
,
.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc00c62f5dda3fb46d69c9f1a8027de4.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f966272f7781790ff27e40db6b525253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d983de2be935fe91d013e7e0cac54123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc00c62f5dda3fb46d69c9f1a8027de4.png)
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5 . 设集合
.若方程
至少有一个根
,则称该方程为“合格方程”.那么,合格方程的个数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63446d9ae9fdbdcf80a2fbaeabe828a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9569c69c6444fe7f58048da2f0736c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcf45c1228d917a80907cbb22b2cd33.png)
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2011高三·湖北·竞赛
6 . 设
是模为
的复数.则
的最大值与最小值的和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd49d374aeb8e3aa003b628a93a7c1e.png)
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2011高三·湖北·竞赛
7 . 已知椭圆
:
,过点
而不过点
的动直线
与椭圆
交于
、
两点.
(1)求
;
(2)记
的面积为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d80b861ba40387cb2bcd04945f5a371a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e656a08a82bcccddf0facd8d8cff9446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02b3a9a7b97b1a58c6d15bc11e147204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c7bbe0ac1c88c9d35978a7184ba553.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1ddff9c93c234562c44d1808831bc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cbf55c52a95f6c4f036036d78822742.png)
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8 . 已知数列
满足
,
.证明:对这一切
,有
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75f96d18755cfc571e47e24684bdb33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d5ec9ad92f37e64eccce922ab1b14e.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a03580918dd4526cb5729bff4c0bcca.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4106b4c67eb711b3f7782f8ac812f1a1.png)
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9 . 已知
是
所在平面上一点,满足
.则
与
的面积之比为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/253b1cbcf52de4b40e8455eb47b31796.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2694c32ca1e120e988012b7ecd74f625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
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2011高三·湖北·竞赛
10 . 对一切满足
的实数
、
,不等式
恒成立.则实数
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4edf2e906d4bbfdb6d02e13597236ac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be073f77137d537c1d1926d2e42d2ace.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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