名校
1 . 已知X为包含v个元素的集合(
,
).设A为由X的一些三元子集(含有三个元素的子集)组成的集合,使得X中的任意两个不同的元素,都恰好同时包含在唯一的一个三元子集中,则称
组成一个v阶的Steiner三元系.若
为一个7阶的Steiner三元系,则集合A中元素的个数为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe0953f915a38732687056d9e2dee04c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6ce9503fa100664e4aa127f513a167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8721733e3975550483a89a78203dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8721733e3975550483a89a78203dd.png)
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2023-04-19更新
|
3241次组卷
|
10卷引用:湖北省2023届高三下学期四月调研考试数学试题
湖北省2023届高三下学期四月调研考试数学试题江苏省南通市新高考2024届高三适应性测试数学模拟试题河南省信阳市新县高级中学2024届高三考前第三次适应性考试数学试题专题01集合与常用逻辑用语(已下线)高一上学期第一次月考填空题压轴题50题专练-举一反三系列(已下线)第01讲 集合(七大题型)(讲义)(已下线)高一上学期期末考试填空题压轴题50题专练-举一反三系列(已下线)集合及其运算(已下线)新题型01 新高考新结构二十一大考点汇总-1湖北省武汉市第十一中学2023-2024学年高二下学期6月考数学试题
名校
解题方法
2 . 定义两个点集S、T之间的距离集为
,其中
表示两点P、Q之间的距离,已知k、
,
,
,若
,则t的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc583b7bb3ab41850a8a2447a7abaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e7033cdfb9fb5770ca833f2c83ecb3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450f84739e8a2d21b374ccedc8972605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d56d22586bc5fb71fe1b442ee7580268.png)
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2023-03-02更新
|
2202次组卷
|
9卷引用:河北省部分学校2024届高三上学期摸底考试数学试题
解题方法
3 . 已知集合
,其中
且
,函数
,且对任意
,都有
,则
的值是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc0d2590f22b0507223d880e983d9ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84dededf0bca6907ca47d7ab4d8a154a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10609768b6708e5ed47d2fdf2ce48ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b61608d785aa5aab652b78217b1708.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eceec5a0e6d5eb97f7d411d6213d8988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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4 . 已知非空集合A,B满足:
,
,函数
对于下列结论:
①不存在非空集合对
,使得
为偶函数;
②存在唯一非空集合对
,使得
为奇函数;
③存在无穷多非空集合对
,使得方程
无解.
其中正确结论的序号为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d7f14bf7f60fe19b509223284455f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/114a7e4139f39bd366cdd221e86bea0e.png)
①不存在非空集合对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a95d247ffb2774bb7e22708b25daf7f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②存在唯一非空集合对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a95d247ffb2774bb7e22708b25daf7f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
③存在无穷多非空集合对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a95d247ffb2774bb7e22708b25daf7f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
其中正确结论的序号为
您最近一年使用:0次
5 . 设
是集合
,且
(其中
为自然对数的底数)中所有的数从小到大排成的数列,若
,则
的最大值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a8085f0d2e4ce70976bcf530a9e68c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd7ef95943c51fcd2c41bd1732381c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a84f32b1e0493e7e36a1da48ce40a2ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
6 . 向量集合
,对于任意
,以及任意
,都有
,则称S为“C类集”,现有四个命题:
①若S为“C类集”,则集合
也是“C类集";
②若S,T都是“C类集”,则集合
也是“C类集”;
③若
,
都是“C类集”,则
也是“C类集”;
④若
,
都是“C类集”,且交集非空,
,也是“C类集”.
其中正确的命题有____________________ (填所有正确命题的序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41bbea48a9e8cdc6e591bdc85ef6cdda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2cd5b73e6422370539a64e009edb741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb6bf23a5a12e1ba5413594d7b1a57c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e756357aaab202398e6cded445f9caeb.png)
①若S为“C类集”,则集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8ade2d8330ac61c4192cfd1df19fc0.png)
②若S,T都是“C类集”,则集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194bad922d5bc98b6a7e51ae35f67d54.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2646f41226f24960a6186dc7860ef45.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b76d26b78e63683dfacf10d3da6d74d.png)
其中正确的命题有
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7 . 如图所示,平面中两条直线
与
相交于点
,对于平面上任意一点
,若
,
分别是
到直线
与
的距离,则称有序非负实数对
是点
的“距离坐标”,给出下列四个命题:
![](https://img.xkw.com/dksih/QBM/2021/4/23/2706077913825280/2707664354615296/STEM/9e15335e-6124-48a7-8b6a-2816d5519936.png)
①“距离坐标”为
的两点间距离为2;
②若
,则点
的轨迹是一条过
点的直线;
③若
,则“距离坐标”为
的点有且仅有4个;
④若直线
与
的夹角是60°,则
或
.
其中所有正确命题的序号为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e257b2b02bcd57c116841807979bbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/2021/4/23/2706077913825280/2707664354615296/STEM/9e15335e-6124-48a7-8b6a-2816d5519936.png)
①“距离坐标”为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72583e4cbf9e64cf692ecf600983fdee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6c0ae5144fcc033002b54006a9cfdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e257b2b02bcd57c116841807979bbc.png)
④若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441347596788bcbd19dd6bbfb2ce7b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61a87cc610f1c8796f6c477c9fce58ec.png)
其中所有正确命题的序号为
您最近一年使用:0次
2021-04-25更新
|
568次组卷
|
2卷引用:山东省聊城市2021届高三二模联考数学试题
8 . 已知集合M={x∈N|1≤x≤21},集合A1,A2,A3满足①每个集合都恰有7个元素; ②A1∪A2∪A3=M.集合Ai中元素的最大值与最小值之和称为集合Ai的特征数,记为Xi(i=1,2,3),则X1+X2+X3的最大值与最小值的和为___ .
您最近一年使用:0次
2021-09-19更新
|
1208次组卷
|
11卷引用:【区级联考】北京延庆区2019届高三一模数学(理)试题
【区级联考】北京延庆区2019届高三一模数学(理)试题(已下线)专题1.1 集合-(练)【理】-《2020年高考一轮复习讲练测》(已下线)专题01 集合-2022年高考数学一轮复习小题多维练(新高考版)(已下线)专题8.3 临界知识问题 玩转压轴题-玩转压轴题,进军满分之2021高考数学选择题填空题福建省泉州科技中学2021-2022学年高一上学期第一次月考数学试题(已下线)专题02 集合与常用逻辑用语常考压轴题型-2021-2022学年高一《新题速递·数学》(人教A版2019)(已下线)第01节 集合(好题帮)(已下线)专题1-1 集合及集合思想应用(讲+练)-3(已下线)高一上学期第一次月考填空题压轴题50题专练-举一反三系列(已下线)高一上学期期中考试填空题压轴题50题专练-举一反三系列湖南省长沙市明德中学2023-2024学年高二下学期3月阶段测试数学试卷
2012·四川·一模
名校
9 . 已知集合
,对任意
、
、
,规定运算“
”满足如下性质:
(1)
;(2)
;(3)
;
给出下列命题:①
;
②若
,则
;
③若
,且
,则
;
④若
、
、
,且
,
,则
.
其中所有正确命题的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc487556ec9fca7872e6fdbbe16136d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac385ec112e6d61b90d953e3f106ee85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3c2f679d53b91088ba6eb14c16cbc0.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c7be7c38e798904fbd8bd25f701e7f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef893afdedb510db45601b997ef8679.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcde01eca1201caef258f60fe0a86c30.png)
给出下列命题:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2faf3937abcb6a59071c17bc6bb10f6.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35a2410ce34b36954ed4923e600d42f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22b86625e97b1fda21b92123cdf5eb04.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78fb280705068e78205b9be5027784c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac385ec112e6d61b90d953e3f106ee85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78fb280705068e78205b9be5027784c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d18d7bf1aaf5cf38599b5629120311f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/759b29a7b2b3735306f1a650355a7858.png)
其中所有正确命题的序号是
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解题方法
10 . 关于下列两个命题:设
是定义在
上的偶函数,且当
时,
单调,则方程
的所有根之和为______ ;对于
有性质
:“对
时,必有
.现给定①
;②
;现与
对比,①中
、②中
同样也有性质
的序号为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50ab9a7e0459170b74091235ed37155c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b49e0a5e0946955251b7a2f3bfc21ed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d206c6853cb138f3d8db4f9acc9b99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b03422c87acca23dcc4e51e40221e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04cf321d8cf6a9c7adff9900857732b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6667b1e60410178985f7ee42e161abab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/b1010846eeec6c9da29640f5aa3f8738.png)
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