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解题方法
1 . 在下面两个条件中任选一个,补充到下面的问题中,并对其求解.
条件①:
;条件②:
.
问题:已知
,若__________.
(1)求实数
的值;
(2)求
的值.
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e375fc24463eb3f06d73f52a6c96d55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2b531ad9d5d3486641d65575d74e86d.png)
问题:已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c439cb5fa460215a1194d66031eb81bb.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a998364a96daaec729167c82f9954f1.png)
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2 . 已知事件
和
相互独立,
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de68170f9ef4c6ba7531579b247ea63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0807c6d71228f0dc0291953647f8e9c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d4a36ecf4af580800f761e6f3727e78.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 正十二边形的对角线的条数是( )
A.56 | B.54 | C.48 | D.44 |
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2024-06-04更新
|
248次组卷
|
2卷引用:江苏省泰州中学2023-2024学年高二下学期期中考试数学试题
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4 . 已知函数
,其中
,
.
(1)若n=8,
,求
的最大值;
(2)若
,求
;(用n表示)
(3)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53d2b110c5f66893e0a264dacd9ce2cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e87088da41685cc8d433fbbe0e18d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
(1)若n=8,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44e7f35951f719ea517964e451a65e9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c450e67915ca03156ebdc0357cfc05c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2f2d7c81cb44416bcdf59419637682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b09a4a450878fcc078372bbb9ad9e6d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c9c39efc53af82fec6d9cf76db5afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99f1f0df4e581e025fd9934a88e36d0.png)
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5 . 有一个益智类的古堡探险闯关游戏,玩家每局都有甲、乙两座不同的古堡可供选择.已知某玩家古堡甲闯关成功的概率为
,古堡乙闯关成功的概率为
.若该玩家第一局选择古堡甲闯关的概率为
,前一局选择了古堡甲闯关,则继续选择古堡甲闯关的概率为
;前一局选择了古堡乙闯关,则继续选择古堡乙闯关的概率为
.
(1)求该玩家第一局闯关成功的概率;
(2)记该玩家第
局选择古堡甲闯关的概率为
,第
局闯关成功的概率为
.
(i)求
和
的表达式;
(ii)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求该玩家第一局闯关成功的概率;
(2)记该玩家第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
(ii)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b147ff9c39062ae2364cbacc3fe973a.png)
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解题方法
6 . 已知随机变量
,则下列说法一定正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a3bc0f34bd55c43cf3bbb6bff4f9d9.png)
A.![]() |
B.若![]() ![]() |
C.![]() |
D.若![]() ![]() |
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7 . 已知直线
的方向向量为
,平面
的法向量为
,若
,则实数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af7c77efa7d61a474ff7cd61c54e4939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59cf6c916e9b41d3139de56ca66f84dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1754786a3367aca3da18ee3316e5b968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 已知集合
,记集合
的元素个数为
.当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/056d6e45df3b36b7ace1c1e0d3f16d8d.png)
__________ (用数字表示);当
(
且
)时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/056d6e45df3b36b7ace1c1e0d3f16d8d.png)
__________ .(用含有
的式子表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2590bb37cb7630923a429d4a1d847efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8b3217efbef2d705f5beedb40c1fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ddbd996153d8fa0640bae56e0328c04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/056d6e45df3b36b7ace1c1e0d3f16d8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98de99e0441b45f322a34566393e022f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/056d6e45df3b36b7ace1c1e0d3f16d8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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9 . 在棱长均为1的三棱柱
中,
,点
满足
,其中
,则下列说法一定正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b11a79894447b31c2ca1163bc304871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d051546c15ec453fc53a6de2774b414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1ccdad989ebe7c7087be45cd0683a3.png)
A.当点![]() ![]() ![]() |
B.当![]() ![]() ![]() |
C.当点![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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10 . 小明想邀请8位朋友中的5位参加自己的生日宴会,其中甲、乙不能同时邀请,甲、丙要么都邀请,要么都不邀请,则不同的邀请方法种数为__________ .
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