1 . 已知
,
,…,
是集合
的n个非空子集,如果对于任意的i,
,均有
,则n的最大值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9721059d158853671eaf19e39769b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8db4b168ddbcba90ac9b31d36a0432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64e11e77f3276edde5c0a9f2057beb44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a42daf2970136f21f3e5b3b2f96fe44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac30abcc83eecff9e2cb8dabc1d10ac8.png)
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2 . 如图,P为长方体
的对角线
上一点,平面
平面
,若
,则二面角P-AB-C的正切值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7ddbb49c644bf06ccbad885ba2c84a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6392ebb67310d3a4cd0332c06c70390b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d8d008397ca32c5094fe9e7a28dd46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f85b73cdc1d447a2c516644bcb836c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65674c041e5b46bcc6de4e7b0df2db2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/beeff07a-31f1-4208-a090-e5be3c1baf76.png?resizew=184)
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3 . 已知双曲线C:
的离心率为
,
、
分别为C的左、右焦点,过
的直线l交C于A、B两点(点A在第一象限),且
若
的面积为
,则
内切圆半径为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31f8f7e40ba386c0a9675896b52752d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e82fe25db889399bb3ca4ffd5dd5db84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61d572ecf27dc02fcbd588f24647b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61d572ecf27dc02fcbd588f24647b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35c18ad167885ce5fd21176665d6a6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7351556b6a4cf148007c3db422023d08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/031661aa4b14c3b9954ec444ad5b6f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ff8a5886e42095da57422c8777c10d.png)
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4 . 已知各项均为正数的等比数列
中,
,
.数列
满足:对任意正整数n,有
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/277b017e9e3ee7c44e4f5ff779777d59.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0391da6e1057ac401356adfab040e182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8647d69f70675bbb51832daae63c5a5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195431ccf2756a0db26f14b7b91a32a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3fde30beb51cd8d499f308050caf21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/277b017e9e3ee7c44e4f5ff779777d59.png)
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5 . 如图,点M、N分别在△ABC的边AB、AC上,且
,
,D为线段BC的中点,G为线段MN与AD的交点.若
,则
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/637ead8ff2c33546dc4b7ae439d3cffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e73df9bd672a72bd945449a606cbd27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3235f0f3c3faa679c2e9420d298a1f58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2be5e24170427caed4175e2863995aa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/66865588-9b96-4f15-8040-cab6d1f93f20.png?resizew=176)
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6 . 已知
,
,
,且
,则
的最大值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4aa0e79f03404207ee3da7262922f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a32c9bb7fe249c8054979b97fe032eb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5122f4a3ce9717386f47796b1193adde.png)
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7 . 某校数学兴趣小组有14位同学,他们组成了n个不同的课题组.每个课题组有6位同学,每位同学至少参加2个课题组,且任意两个课题组至多有2位共同的同学,求n的最大值.
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8 . 如图,
、
分别是△ABC、△ACD的重心,
的外接圆与直线BD相交于点P,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc71c35d851ff74646c728756b24efb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/951d73cefe3fed1c5e70210ce71ae2fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5035afd29380c8912a02ac79a7db19b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7a69a73f2044f45086374c2e068b548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3269cf61861183004455d640aac8ccf0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/ada6f890-0c6f-474f-a6a8-d92f18e4566a.jpg?resizew=193)
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9 .
的末三位数是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce59b1cb2c7c9978fbf1450dcca76e95.png)
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10 . 已知函数
.
(1)若
恒成立,求a的最小值;
(2)若
存在最大值,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083ad02d1a6ec52d79cee9321938a762.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fce85097fee1cbceeace9d1873fa71a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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