1 . 设12元实数集合
满足:可将其划分为两个6元子集
和
,使得对每个
,均有
,则这样的
可以是______ .(写出一个即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab68ee11734bd89733c3064af16cea50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe342a96adffebbb5d59c5fcfd138e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fde1b1e2b446a4db8650c9fdab83766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff197132463fd76db478b76ed2cf653c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/908fbdc652b3cafc1f4d0b2e3ae2a094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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2 . 设双曲线Γ:
,
,B,C在Γ上且直线
经过A.设
分别为Γ在B,C处的切线,点D满足
,则D的轨迹方程是___________ ;若D的横纵坐标均为正整数,且二者之和大于2024,则D可以是_____ .(写出1个即可).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af3674d64026a371b001453280477ba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40630a669f4eedf626bc24851df10c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86de0e038b0304e34ca8c9b117fec917.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e6aa92080d4e1f43a1ac2f9c2965fe.png)
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解题方法
3 . 已知正四面体
棱长为2,点
分别是
,
,
内切圆上的动点,现有下列四个命题:
①对于任意点
,都存在点
,使
;
②存在
,使直线
平面
;
③当
最小时,三棱锥
的体积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0467b0675c3ecfb282cc88255284d3e1.png)
④当
最大时,顶点
到平面
的距离的最大值为
.
其中正确的有___________ .(填选正确的序号即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7807638578edd712265463a7a5eab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
①对于任意点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c89d54457ad06f095a8643cf3c77923.png)
②存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5425108c557f0f21474c045334f97d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e39cbda9b51329928487a7462cb550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b9ffc9d4fbb08792f487b787c71c8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d919276bf6174bdf850673cd38284cda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0467b0675c3ecfb282cc88255284d3e1.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b9ffc9d4fbb08792f487b787c71c8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56448a74c1b8430c425d79d626764f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839c7616cd0d90265f4b2c9c021254fe.png)
其中正确的有
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2024-06-05更新
|
373次组卷
|
2卷引用:辽宁省部分高中2023-2024学年高三下学期第三次模拟考试数学试题
4 . 已知有限集
(
).如果A中的元素
(
)满足
,就称A为“复活集”,给出下列结论:
①集合
是“复活集”; ②若
,且
是“复活集”,则
;
③若
,则
不可能是“复活集”;④若
,则“复活集”A有且只有一个,且
.
其中正确的结论是__________ .(填上你认为所有正确的结论序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f3f090142bfa3bcb90ecdb3ee904e88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b0e3b00fe47801afb53ec56706c21a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5deeed8d5eefca600669724369678a27.png)
①集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc508cedd135c79cd3d0c5232de772cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faaab33de7a473d72438f99e0814711c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ed17b083fe22b6f302ee13b7d181d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd2995bc6100a2ba0ff45d28dea41b9.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b92442e3a390779ed8f0e849e65517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ed17b083fe22b6f302ee13b7d181d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65f477bb468a7cd2e854d8f9ad848a72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
其中正确的结论是
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5 . 已知有限集合
,定义如下操作过程
:从
中任取两个元素
、
,由
中除了
、以外的元素构成的集合记为
;①若
,则令
;②若
,则
;这样得到新集合
,例如集合
经过一次操作后得到的集合可能是
也可能得到
等,可继续对取定的
实施操作过程
,得到的新集合记作
,……,如此经过
次操作后得到的新集合记作
,设
,对于
,反复进行上述操作过程,当所得集合
只有一个元素时,则所有可能的集合
为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91cad2d17a76b59c35e5568ae94bbab4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e74a53b443fe1b4e68f15517fe615e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f52783e7a39f438adf08ef7d05d8c78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9553cec51b508143a367c4a9daa17c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/682b374037dd56ab53d9308f44230068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50e57a5236bd0563182511bf0f2902a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ad06aef621f76cd7761dcf224af0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/150c00670642d60bb4459bf6d2ca1ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6904797da5330bab047b695df7ba11d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533293cde0852cf1dfdb649412c452b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7f2c72ab559a0615db4c51327b78d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f538b5f31197347d360938a5e535506e.png)
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
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6 . 某校高二年级共有10个班级,5位教学教师,每位教师教两个班级,其中姜老师一定教1班,张老师一定教3班,王老师一定教8班,秋老师至少教9班和10班中的一个班,曲老师不教2班和6班,王老师不教5班,则不同的排课方法种数______ .
您最近一年使用:0次
2021-03-22更新
|
3217次组卷
|
7卷引用:黑龙江省哈尔滨市第三中学2020-2021学年度上学期高二学年第二模块考试(理科)数学试题
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