名校
解题方法
1 . 设
,若非空集合
同时满足以下4个条件,则称
是“
无和划分”:
①
;
②
;
③
,且
中的最小元素大于
中的最小元素;
④
,必有
.
(1)若
,判断
是否是“
无和划分”,并说明理由.
(2)已知
是“
无和划分”(
).
①证明:对于任意
,都有
;
②若存在
,使得
,记
,证明:
中的所有奇数都属于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c8559db5cec89fb0ed29e8be8fdb0b1.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03710ecc47ca36cb01c337a71d300974.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b6e72a98cbc82cb24cb85aa3ab837f5.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35a2410ce34b36954ed4923e600d42f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e006283149b3d1662205b5271dd69db2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58f045d0c3275b992d4a4f90dcd20e63.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/408f3365f7c6767cd3f006022ee22413.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da92a00c5e0121accc325e50f6492fe.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c8559db5cec89fb0ed29e8be8fdb0b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
①证明:对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb6b675fa03f7268b8cbd1f1d91bd27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4003dc977c4cacda932927eed9c9d10.png)
②若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8457b5be40500d437a83bb12e488b5eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09bd7ed301e00171b88549a8deb65035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5203c10c41f8b8aaa4c9cc90f1f3271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2024-06-10更新
|
132次组卷
|
2卷引用:北京市丰台区2023-2024学年高一上学期期末练习数学试卷
2 . 已知集合A为非空数集.定义:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d0e7221341950bd4e1f93a803b9801.png)
(1)若集合
,直接写出集合S,T;
(2)若集合
且
.求证:
;
(3)若集合
记
为集合A中元素的个数,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d0e7221341950bd4e1f93a803b9801.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90f0e502a03ff4b6a9f6fd29b8034992.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6b5e47c9f736eabab184039643c34ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c76ad1e03a6ba59e8164e37c5e7e063e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de5a7e700e4c1d41bb3bb8be9f55580b.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa47f7e9136938b09be369fce567669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b5214a796412b3df9f716da0bf339b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b5214a796412b3df9f716da0bf339b.png)
您最近一年使用:0次
名校
3 . 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.
您最近一年使用:0次
2024-02-23更新
|
280次组卷
|
2卷引用:北京市通州区2023-2024学年高一上学期期末质量检测数学试卷
4 . 已知集合
,若
中元素的个数为
,且存在
,使得
,则称
是
的
子集.
(1)若
,写出
的所有
子集;
(2)若
为
的
子集,且对任意的
,存在
,使得
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/946ca6ef235e10f31fe03cc2737dfcc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1071ac8657ef1c4e1ea7e0530196298d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/496549fb22714bf0d5719538c7a52cd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/477caa6a1198bc26f4199e75aadf445f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f12af2f56950da618a53de06aaf0eee4.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c414a10d73f453fc1109e5b2243d2369.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f12af2f56950da618a53de06aaf0eee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09219fd705c1aa88b3453e1d4d7ccc67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1484a3c8a21bcd584d5ac2cd1e8bb7b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbae3b57b2ba8226b77919686f5886c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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5 . 对于正整数集合
(
,
)如果去掉其中任意一个元素.
之后,剩余的所有元素组成的集合都能分为两个交集为空集的集合,且这两个集合的所有元素之和相等,就称集合
为“和谐集”.
(1)判断集合
是否是“和谐集”,并说明理由;
(2)求证:若集合
是“和谐集”.则集合
中元素个数为奇数;
(3)若集合
是“和谐集”,求集合
中元素个数的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcbde10b7bc82536072ca38f32b2f8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca1d86c9f078347773f700fee49d1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701281aafdb6f984a3bcbc1418e46ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f37ab30f2e841f260e46be2714954d0e.png)
(2)求证:若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
名校
6 . 已知
是各项均为正整数的无穷递增数列,对于
,定义集合
,设
为集合
中的元素个数,若
时,规定
.
(1)若
,写出
及
的值;
(2)若数列
是等差数列,求数列
的通项公式;
(3)设集合
,求证:
且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/542b4acf7b25b750fbe7205fd179b978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/857369257ea1b23ef40ce7e3a0f058af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233427826eb2233641fc3a9805f6d206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1202d58cd3ad66e7b23f01024566705b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cc57d8a4f67a040435d8b206d3254bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6510d0816033afa001c130342bb7cda.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4b5779873cb3f4366dbfdb983dec81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b6f99a33b14f53fb398a195aa2ec3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac648580405ecaa29e91d45738a08af7.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b54e4701d4cb8d0133ad2044a7e0f52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1479e28bf6a8cb64ec7df77cd295f99d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a6a3d1be93cf6d16ee6e0ce0497f46.png)
您最近一年使用:0次
2024-01-21更新
|
1356次组卷
|
7卷引用:北京市朝阳区2024届高三上学期期末数学试题
北京市朝阳区2024届高三上学期期末数学试题(已下线)2024年高考数学二轮复习测试卷(北京专用)(已下线)专题1 集合新定义题(九省联考第19题模式)讲(已下线)黄金卷01(2024新题型)(已下线)微考点4-1 新高考新试卷结构压轴题新定义数列试题分类汇编广东省江门市开平市忠源纪念中学2024届高三下学期高考冲刺考试(一)数学试卷江苏省常州市华罗庚中学2024届高三下学期4月二模训练数学试卷
名校
解题方法
7 . 定义集合
的“长度”是
,其中a,
R.已如集合
,
,且M,N都是集合
的子集,则集合
的“长度”的最小值是_____ ;若
,集合
的“长度”大于
,则n的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3296f5d3fbd7177849bbd7bd30fbd3a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13502d46b8563c54c09b29b20b3006a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd7701d084d2b153bbea08cfbf63413a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2532b1aa9a6b334d7395fc020bf0a6be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2512da0056b913e36a72419c91a5d8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/640f4732df2e4b84c5e98b47e37d4e65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c81919684bc4047d376c7e57dc6c8f1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc8032a17aee665217899ed88652375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83ae18508906c21d3e1199f231b1a9a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
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名校
解题方法
8 . 给定正整数
,设集合
.对于集合
中的任意元素
和
,记
.设
,且集合
,对于
中任意元素
,若
则称
具有性质
.
(1)判断集合
是否具有性质
?说明理由;
(2)判断是否存在具有性质
的集合
,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5f57a82532efc3493710a2ff44fefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94a6d1701e8172b86bc880c24d0bc58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8eb800ed1a7e5e22e3947e6bd30c87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35e477c52dfbfb80f1fc315143c8b06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1368a045ba80f97383f3d9d7fcdc8f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ae454efa6255bf3bb1c43e845746088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9855cb665c7f3785a17718be10538af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a2f08194bb663f1a086fa2f555ebf43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5651757f34e9de2462ccdc056f04ab4.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2fbba9715be4e3cb0886973e3d3ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25c874d4ce0667f3acfe8d26d2a5b6f.png)
(2)判断是否存在具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d0e79b3bb773de1ebea52199754c01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2024-01-25更新
|
312次组卷
|
4卷引用:北京市海淀区北京交通大学附属中学2023-2024学年高二上学期期中练习数学试题
北京市海淀区北京交通大学附属中学2023-2024学年高二上学期期中练习数学试题北京市延庆区2023-2024学年高二上学期期末考试数学试卷(已下线)专题04 分类讨论型【讲】【北京版】2(已下线)专题1 集合新定义题(九省联考第19题模式)练
名校
9 . 设正整数
,若由实数组成的集合
满足如下性质,则称
为
集合:对
中任意四个不同的元素
,均有
.
(1)判断集合
和
是否为
集合,说明理由;
(2)若集合
为
集合,求
中大于1的元素的可能个数;
(3)若集合
为
集合,求证:
中元素不能全为正实数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ead6fe08a80379f496eab2129655bd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be0f5b704e46d64481197273b2e2557.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85ccef0bee54b52b069616251fbea584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9cba4a6e473e359492361f51d8556a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def70b21b73d0d0156f8ffb526413d97.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37fb28a9d01dfd12b13bce4ac4c3c5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def70b21b73d0d0156f8ffb526413d97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ead6fe08a80379f496eab2129655bd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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2024-01-19更新
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215次组卷
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2卷引用:北京市朝阳区2023-2024学年高二上学期期末质量检测数学试题
名校
10 . 已知数集
具有性质
:对任意
,
与
两数中至少有一个属于
.
(1)分别判断数集
与
是否具有性质
;
(2)求证:
;
(3)给定正整数
,求证:
,
,
,
组成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e7cdd844688e7a1b08f8ed3792760a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29bcdd8c05cd04f46c6f4ba8aa3cb1d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c981868188750ab216366b8272d4b35f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3541598c0e0e6d5050c5a562515c430e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13ee542834ccbb57fcc55b1680ca9db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4489d9b83072184c0e1d6b09be50ca.png)
(1)分别判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edd14cb27cbdb43c432f7493c34575c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ec8506f11fb704c94772de34e05381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29bcdd8c05cd04f46c6f4ba8aa3cb1d0.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e6fc2c0740f9ff797037bcd1409768.png)
(3)给定正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0fee7283a714563ad255f3ef9ac1a30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
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2023-12-20更新
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4卷引用:北京市海淀区中央民族大学附中2024届高三上学期12月月考数学试题
北京市海淀区中央民族大学附中2024届高三上学期12月月考数学试题北京市北京师范大学燕化附属中学2023-2024学年高二下学期期中考试数学试卷(已下线)专题1 集合新定义题(九省联考第19题模式)练(已下线)微考点4-1 新高考新试卷结构压轴题新定义数列试题分类汇编