名校
解题方法
1 . 已知集合
中含有
个元素,集合
是
的非空子集,且
,则不同的集合对
有______ 个.(用含
的代数式表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4f27f84764f1cca89ce3d93fc1cf603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.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/a95d247ffb2774bb7e22708b25daf7f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
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2 . 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)
您最近一年使用:0次
2023-12-20更新
|
407次组卷
|
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(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
解题方法
3 . 已知集合
是由某些正整数组成的集合,且满足:若
,则当且仅当
其中
且
,或
其中
且
.现有如下两个命题: ①
;②集合
.则下列选项中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09256752badab8d69ae679796896ed97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d69ad2e6fb245dd796a90069cdecf5bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4e2c7d495c75424714210323455d9ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb4e301bb40ce2f30a10cd44ddb5a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f44754f1a3fb7f49c2f1bc8d55a78d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e6e9364f9bff37c962556537a0a7a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0908dc92cc1b6c38fa8114c0e122c4eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d00c07c7865e822c502ffb72ae0406d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b29af0b42059c645d2164532cd286c.png)
A.①是真命题, ②是真命题; | B.①是真命题, ②是假命题 |
C.①是假命题, ②是真命题; | D.①是假命题, ②是假命题. |
您最近一年使用:0次
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4 . 对于平面上点
和曲线
,任取
上一点
,若线段
的长度存在最小值,则称该值为点
到曲线
的距离,记作
.下列结论中正确的个数为( )
①若曲线
是一个点,则点集
所表示的图形的面积为
;
②若曲线
是一个半径为
的圆,则点集
所表示的图形的面积为
;
③若曲线
是一个长度为
的线段,则点集
所表示的图形的面积为
;
④若曲线
是边长为
的等边三角形,则点集
所表示的图形的面积为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a421e5d3b3752b9e1f04c30799bace.png)
①若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26bee18b0b9fdb657956eaeb43023288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b3a91ccf6028608cd03df7072f6536.png)
②若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d079a36153052a0fbdf35b2a2bd3b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e95a79288fcb7e47fba4410722e2bc6.png)
③若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d079a36153052a0fbdf35b2a2bd3b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7b0c7fb6244310e468d5092cf0dba4f.png)
④若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d02ea8c4988c5c28ab93f0d70fb55a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d079a36153052a0fbdf35b2a2bd3b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebceb91a9f116f8f5308bcad3020bae4.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
2023-11-23更新
|
436次组卷
|
6卷引用:浙江省湖州市第二中学2024届高三上学期期中数学试题
浙江省湖州市第二中学2024届高三上学期期中数学试题北京市陈经纶中学2023-2024学年高二上学期期中考试数学试卷(已下线)考点3 与集合相关的新定义问题 --2024届高考数学考点总动员【练】(已下线)专题1 直线与圆的位置关系【练】(压轴小题大全)(已下线)专题02 直线和圆的方程(5)(已下线)2.1.4 圆与圆的位置关系(十大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
23-24高三上·北京·期中
名校
5 . 已知集合
,集合
,且满足,
,
与
恰有一个成立.对于
定义
,以及
,其中
.
例如
.
(1)若
,
,求
的值及
的最大值;
(2)从
中任意删去两个数,记剩下的数的和为
,求
的最小值(用
表示);
(3)对于满足
的每一个集合
,集合
中是否都存在三个不同的元素
,
,
,使得
恒成立?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d7759d382dfd33b5a08fa4592b5178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0b8b719c20b1888fe2cb3d454419ee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b18a24af2916239dfd649c37cf27770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9501ed9d84c443aee21eb55f5ce385f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1322ce3a3343914627e90d26e39e40f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0179662fc6cf8112ec0c42c8f6cdf53a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6288cc5be15de868fe6c1f6fef6a309.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b0e3b00fe47801afb53ec56706c21a.png)
例如
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63af360678d1ba9333fcb05dc46b08b9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0ea63a47001e23b4d244777be6d2719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3ab6dd619d6d614608a2087dff6186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c11ec2069caa7f0d750971ff67fe1288.png)
(2)从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/726c816d07c8c3adc7fa610e3d0335e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)对于满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f5178625a53061308733d7f0393199.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276509f01529d982ab21e479a4619268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbd1d5178f23e7be5a3da0399a770404.png)
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23-24高三上·上海浦东新·期中
名校
6 .
是正整数集的子集,满足:
,并有如下性质:若
、
,则
,其中
表示不超过实数
的最大整数,则
的非空子集个数为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/793b9b22f06177785864b283ff38d61e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab92728b35ed5798e07a2b0095bfcc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b958eb9d7d286a1c6daf4711f304b9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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解题方法
7 . 已知
元正整数集合
满足:
,且对任意
,都有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/453e81d3dacb5e2e527b8daebcf19fc9.png)
(1)若
,写出所有满足条件的集合
;
(2)若
恰有
个正约数,求证:
;
(3)求证:对任意的
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5fcfc55b56f04ac530871067e5ce71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b5ba5a3d48da1d7f3952c013a5ee0de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/139ae1c18e2cded6d04808a3aa24c6bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26c7cb34e9b5c1ecd75ff1966e882ae7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/453e81d3dacb5e2e527b8daebcf19fc9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7334c46af837676ada9575630a48d60f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7979eac1b85b681ba94bf8d833c5c6e7.png)
(3)求证:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa673986cef1873a421a572abf9ed71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57cee7a77f2f4592cb5c96245ff025f8.png)
您最近一年使用:0次
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解题方法
8 . 设集合
,其中
.若集合
满足对于任意的两个非空集合
,都有集合
的所有元素之和与集合
的元素之和不相等,则称集合
具有性质
.
(1)判断集合
是否具有性质
,并说明理由;
(2)若集合
具有性质
,求证:
;
(3)若集合
具有性质
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d7759d382dfd33b5a08fa4592b5178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d267c89385033926ef80e9b65f45a15b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1100967c4704ee3f4eddc759f565a75.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/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baccb9bfcf79366c4605055b9ce5c2fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af8e17568e91b25776648c078886ee07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f95d6428ee9a829917262324c03ab4.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83dfa7b5f718ed24cde77b169b3d76f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/706182007fed7b3cf14e78cbb47fda42.png)
您最近一年使用:0次
解题方法
9 . 从集合
的非空子集中随机取出两个不同的集合
,则在
的条件下,
恰有1个元素的概率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cea90e212e75cde4ac6baf48eac94ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7dcbd7f44645b8c707627ab0795e18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdbfa7a63fdf5717d40c8c9a73ec160.png)
您最近一年使用:0次
2023-10-01更新
|
444次组卷
|
2卷引用:浙江省金华十校2023-2024学年高三上学期11月模拟考试预演数学试题
名校
10 . 设m是实数,已知集合
,集合
,且
,则m的取值范围是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc088345fb1d4cfdda89d068dd0f93d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104668ced17a26db2ae1862b9f0b23c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e63128a77392afc5f8b873b7a67f2b5f.png)
您最近一年使用:0次
2023-09-11更新
|
767次组卷
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4卷引用:上海市敬业中学2024届高三上学期开学考试数学试题
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