名校
1 . 记集合
.对任意
,
,记
,对于非空集合
,定义集合
.
(1)当
时,写出集合
;对于
,写出
;
(2)当
时,如果
,求
的最小值;
(3)求证:
.
(注:本题中,
表示有限集合A中的元素的个数.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a89f895a14b4f202dfe6b19224857c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c86c0b2a71ee538df6ab1eab3c8b2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd58ba2338450bd94bc2a1ec0a0a51ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/120df58b92e747fc3091f1a3aeff228d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13342dd73eb34ca37aaca5b521706442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ca324ae5ead82dd03b6cb5afac67a5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4469a0542c773e329e8cc42e14a84169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0ca0b9e99203ec575c46cdbf2d4ef0d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8839c83b988c42da1fce4a96787583eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c045c7a097a2908732932f4c0c170693.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25376e139f40d0df5ada2c9ebb1da2e4.png)
(注:本题中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c045c7a097a2908732932f4c0c170693.png)
您最近一年使用:0次
名校
解题方法
2 . 设集合
为满足
,
,
的空间向量
,
,
中可能出现的两两共线的向量组数组成的数集,集合
,若
,则
的取值范围为______ ,当
最小时,
的取值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ee0b48b17112965d224bd169314f5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42725bfd7040b47a57faa633f163b856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbd4c620c5f6235adcb1c148cad15080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e61c7d643455ec2d0d4fdbc4ee4dd1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eac19737d882225c903054eb4863501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-02-21更新
|
536次组卷
|
2卷引用:广东省广州市华南师范大学附属中学2024届高三上学期数学周测试题(12)
名校
解题方法
3 . 对非空整数集合M及
,定义
,对于非空整数集合A,B,定义
.
(1)设
,请直接写出集合
;
(2)设
,
,求出非空整数集合B的元素个数的最小值;
(3)对三个非空整数集合A,B,C,若
且
,求
所有可能取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef96396caccbf2f959e9d233f060317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff97e9f30e667709fc602b8dcc7523e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ef9a7e4979cb5c0e8f4ff92af351dc.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679a7e0835c8200dc4975baf3e89d058.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048b9f7e0aa69227773cb9d9b7bb6244.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2463f83ca63b14937787c99fcd1958d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e79b6edfd5f5bb3866599fcb2aa6f3.png)
(3)对三个非空整数集合A,B,C,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22fcff4bcf7a1e6652774a5aee4519c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72944e6acd452acaa213f6ae23ae9a2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a6e825795c828f8281e93607d0e1b1.png)
您最近一年使用:0次
2023-11-05更新
|
1341次组卷
|
4卷引用:2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题变式题16-19
(已下线)2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题变式题16-19(已下线)专题1 集合新定义题(九省联考第19题模式)讲江苏省徐州市沛县第二中学2024届高三下学期期初测试数学试题北京市清华大学附属中学2023-2024学年高一上学期期中考试数学试题
名校
解题方法
4 . 函数的最大值记为M,最小值记为m,其中
为负常数,若
,则
您最近一年使用:0次
2023-10-30更新
|
441次组卷
|
3卷引用:第1题 集合关系与运算,转化化归渡难关
名校
5 . 已知全集
,非空集合
. 若在平面直角坐标系
中,对
中的任意点
,与
关于
轴、
轴以及直线
对称的点也均在
中,则以下命题:
①若
,则
;
②若
,则S中至少有8个元素;
③若
,则S中元素的个数可以为奇数;
④若
,则
.
其中正确命题的序号为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad79f30410cb52f68d9dba9c5c5b7ce2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7d5e33f296db5c92f103ec5b8d851d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aada9a837b764c886a451003c590d65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46dee9a7ce99bbcba531c2ef1d6f154.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2070176ac1c57ba86235db68f1be3ddd.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91c45170b5d2c3a31ce773de80e727c.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dddb2d01c331c86930972e4d6918e288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6be5b2a6c8d41a82f0b0c11e0d9d1df9.png)
其中正确命题的序号为
您最近一年使用:0次
2023-05-05更新
|
838次组卷
|
5卷引用:上海市东华大学附属奉贤致远中学2024届高三上学期10月教学评估数学试题
上海市东华大学附属奉贤致远中学2024届高三上学期10月教学评估数学试题北京市陈经纶中学2022-2023学年高二下学期数学期中诊断试题(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-举一反三系列北京市清华志清中学2023-2024学年高一上学期第一次月考练习数学试题
名校
解题方法
6 . 设
.若对任意
,都存在
,使得
,则
可以是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7f9b35017daa8b524c5717a355834a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e639d3988cf151c19aa1295aa8ea11a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47177d53ef4acf85cb9b9d9b79a350cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47e5ebc9785fa6449f427a9344175af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-05-02更新
|
769次组卷
|
4卷引用:专题17 三角值域问题
(已下线)专题17 三角值域问题上海市曹杨第二中学2022-2023学年高一下学期期中数学试题江西省湖口中学2022-2023学年高一下学期5月期中考试数学试题(已下线)7.1 正弦函数的图像与性质-高一数学同步精品课堂(沪教版2020必修第二册)
名校
7 . 已知
且
,若集合
,
,且
,则实数a的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/321846a971dff65f9fe62f289a98b975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde61e26e97b0226209d795d66b29d92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-04-01更新
|
1037次组卷
|
3卷引用:中学生标准学术能力诊断性测试2023届高三下学期3月测试数学试题
8 . 已知函数
.
(1)当
时,求
的单调递增区间;
(2)设直线l为曲线
的切线,当
时,记直线l的斜率的最小值为
,求
的最小值;
(3)当
时,设
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd8f2f805576e3cbaff4b1d0f8c9a503.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设直线l为曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a7bfd399a358e122c8add5530a8e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1a0c9f001e9509422a9be2c198a88e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec74068a5a9efcdb7f7813f03db53a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
名校
解题方法
9 . 已知函数
.
(1)若方程
有三个不等实根,求实数
的取值范围;
(2)若
,且对
,总
,使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/283178de54cebd86f7867d1519566119.png)
(1)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb101c5df08aa35ae24a6416840b199b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/259e10b808fa4b7aaf7d26fc72a017b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5560bffff313447919d7a24d2a2a5b53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db37a30cc9c01c37f6f14ba27c898f22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-02-19更新
|
699次组卷
|
4卷引用:江西省贵溪市实验中学2024届高三上学期总复习双向达标月考调研(二)(10月)数学试题
名校
10 . 已知集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99dd46e001c117104353b2e41867994e.png)
,
,
,对任意
,定义
.若存在正整数
,使得对任意![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff430dfb9275eed8c6e0cbe671a2798.png)
,都有
,则称集合
具有性质
.如集合
、
都具有性质
.记
是集合
中的最大值.
(1)判断集合
和集合
是否具有性质
(直接写出结论);
(2)若集合
具有性质
,求证:
和
;
(3)若集合
具有性质
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99dd46e001c117104353b2e41867994e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ef42f964d02549eec898b0d3f0588e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20e326e8f60f19e64e32c584ccfc40c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a703c80c9a9624b08ada02523257b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff430dfb9275eed8c6e0cbe671a2798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66ff43ffdcc8b03787a1faa6509d79c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff430dfb9275eed8c6e0cbe671a2798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db67bc808e5b3a6ba3f7691a50d20957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20362ac95ee78ef94caeb0579bb40bfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1baf30f84a1797c8e345c624e6cab1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36cd2052417ccb1650cc533f62273aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e10cda3e056f1db8777f3c322165bb05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287adcb739a4890d108dd974358345fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b87cd94fef6e528d0913bb1b7b53de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1be13762bee8c87a904b93379c76ac8b.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb6d9e9e68d8fa416188fe9c5efafae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2309c5526d918b1e6d456a999ab88c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287adcb739a4890d108dd974358345fa.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57e296d9adecd44ddd36ec145dcf9dc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f80a1f6a8c236559e2fa55feb9ee1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923eed4cf08e8bef3e7a61ce3ba48d62.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f3b97c217370c2b3d22e6738006cc2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d5ade4406641db15a62630f06e4201.png)
您最近一年使用:0次
2022-12-26更新
|
424次组卷
|
4卷引用:广西名校2024届高三高考模拟猜题试卷
广西名校2024届高三高考模拟猜题试卷上海市曹杨第二中学2021-2022学年高一上学期期中数学试题(已下线)第1章 集合与逻辑 单元测试(单元重点)--高一数学同步精品课堂(沪教版2020必修第一册)上海师范大学附属中学闵行分校2023-2024学年高一上学期期中数学试题