名校
1 . 已知有
个连续正整数元素的有限集合
(
,
),记有序数对
,若对任意
,
,
,
且
,A同时满足下列条件,则称
为
元完备数对.
条件①:
;
条件②:
.
(1)试判断是否存在3元完备数对和4元完备数对,并说明理由;
(2)试证明不存在8元完备数对.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/244a73e2cab2b626e12058164680d7cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6526915197667b48dc2e6c1ff413bcf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4a8ca987823fe459fafc1c4fd057d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa9458be5eac5e4b7fbd28850e43d96f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba54a91d651db38d3a13a461252223e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a205f096c854a2f7cd71255056f9f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9169084fc046cdf9b9831f4030f58217.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f34affbf06b09098b13a5b89c0989fb8.png)
(1)试判断是否存在3元完备数对和4元完备数对,并说明理由;
(2)试证明不存在8元完备数对.
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2024-02-23更新
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2卷引用:重庆市乌江新高考协作体2023-2024学年高一下学期开学学业质量联合调研抽测数学试题
名校
2 . 已知有限集合
,定义集合
中的元素个数为集合
的“容量”,记为
.若集合
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aacb0cef0b4732cd149dbf81db44835d.png)
__________ ;若集合
,且
,则正整数
的值是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb9e56ab45ddf991ae24983027e04b08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30502b549c09cd1094e061090e64e866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e20929ac73a0217b33cd41f6aa86cf29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ebc3da55cca67bac55ace85a5f4c556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aacb0cef0b4732cd149dbf81db44835d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc0e7c8479f8f57d2b4d29dbab700753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6532556ff662731db6be89bee77a8b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2023-09-19更新
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293次组卷
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2卷引用:重庆市南开中学校2023-2024学年高一上学期开学考试数学试题
名校
3 . 设集合
为
元数集,若
的2个非空子集
满足:
,则称
为
的一个二阶划分.记
中所有元素之和为
中所有元素之和为
.
(1)若
,求
的一个二阶划分,使得
;
(2)若
.求证:不存在
的二阶划分
满足
;
(3)若
为
的一个二阶划分,满足:①若
,则
;②若
,则
.记
为符合条件的
的个数,求
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e05aa7f57c4914f5248f44b09def2c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.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/20106a23af649dffb3571082e5a9cfdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09f78031a7d18c8f8ddf04bffd1871.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca717c6a55e786238e64f7ebd69b9b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43de850d8546d0933b37846a84f90bc5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f76be59eef5f019579f1f5b936b98b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41212f1139ba1b062d7f40ec7120a9bf.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f12f339b0f68f0739fdfcb39ec4f7eb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10732f3fb10019cb15c3c46d118f7da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3eb5935678e432e6f1f3180bfdb3175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f19c9afadbf80e1e6b5b3a673e6270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
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2023-07-17更新
|
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5卷引用:重庆市南开中学校2023-2024学年高一上学期开学考试数学试题
重庆市南开中学校2023-2024学年高一上学期开学考试数学试题北京市顺义区2022-2023学年高一下学期期末质量监测数学试题(已下线)难关必刷01集合的综合问题(3种题型40题专项训练)-【满分全攻略】(人教A版2019必修第一册)(已下线)第三章 函数的概念与性质-【优化数学】单元测试能力卷(人教A版2019)(已下线)专题03 函数的概念与性质3-2024年高一数学寒假作业单元合订本
名校
解题方法
4 . 有三支股票
位股民的持有情况如下:每位股民至少持有其中一支股票.在不持有
股票的人中,持有
股票的人数是持有
股票的人数的2倍.在持有
股票的人中,只持有
股票的人数比除了持有
股票外,同时还持有其它股票的人数多1.在只持有一支股票的人中,有一半持有
股票.则只持有
股票的股民人数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c81a0ea59d9b9ab49a07a7e4f9c4796.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.7 | B.6 | C.5 | D.4 |
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17卷引用:重庆市南开中学校2023-2024学年高一上学期开学考试数学试题
重庆市南开中学校2023-2024学年高一上学期开学考试数学试题重庆市乌江新高考协作体2023-2024学年高一下学期开学学业质量联合调研抽测数学试题北京市西城区2017届高三二模数学理科试题北京市西城区2017届高三5月模拟测试(二模)数学理试卷(已下线)专题01 集合的运算-2018年高考数学(理)母题题源系列(北京专版)(已下线)专题01 集合的运算-2018年高考数学(文)母题题源系列(北京专版)北京市人民大学附属中学2019-2020学年高一10月数学阶段性练习试题北京市人大附中2019-2020学年高一(10月份)段考数学试题(一)北京市人大附中2020-2021学年高一(10月份)段考数学试题(一)(已下线)专题03 集合中的压轴题(一)-【尖子生专用】2021-2022学年高一数学考点培优训练(人教A版2019必修第一册)(已下线)专题05 集合与常用逻辑用语压轴题型汇总-2021-2022学年高一《新题速递·数学》(人教A版2019)(已下线)专题1-1 集合题型归类-2(已下线)北京市第四中学2023届高三数学保温测试试题(已下线)第06讲 第一章集合与常用逻辑用语章末题型大总结(2) -【帮课堂】(已下线)1.3 集合的基本运算(精讲)-《一隅三反》(已下线)专题01 集合及其运算-2023-2024学年高一数学上学期期中考点大串讲(人教A版2019必修第一册)(已下线)模块二 专题1 集合,简易逻辑与不等式 单元检测篇 B提升卷