1 . 设
且
,集合
的所有
个元素的子集记为
.
(1)当
时,求集合
中所有元素之和
;
(2)记
为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
中最小元素与最大元素之和,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/110cb59a3406578a01263b76e5325273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44417455b9cc30693d09cbcfe4ed97c3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44417455b9cc30693d09cbcfe4ed97c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a584b6ad5577ab3e2d22caf23e3c32b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835e8c3900cb61bc8ddc313d5ce2253d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bac6aad5d92e36b11607f1c9c9640bd.png)
您最近一年使用:0次
2018-12-13更新
|
1315次组卷
|
5卷引用:【校级联考】江苏省南京市六校联合体2019届高三12月联考数学试题
名校
2 . 已知关于
的方程
的两根为
,方程
的两根为
,如果
互不相等,设集合
,作集合
;
;若已知
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74457dc76d16897775a5021da7e3a3a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/704099a3426479f387b9b1b01f3e438e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4224b6c936b438df381a89eda0accf89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf8a57d75adab52e9ee310b4e49a9f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c47ec46c08894af0e0c70ddb4443bb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83b98f5281444344305d38b65b052148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a237c4bc661667d3b3b98d926fe4843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b909ee3789b879f30d1fe2cdad60393.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
您最近一年使用:0次
2018-09-06更新
|
1128次组卷
|
7卷引用:江苏省常州市前黄高级中学2020-2021学年高一上学期第一次阶段检测数学试题
江苏省常州市前黄高级中学2020-2021学年高一上学期第一次阶段检测数学试题(已下线)知识点03 交集、并集-2021-2022学年高一数学同步精品课堂讲+例+测(苏教版2019必修第一册)(已下线)1.3 交集、并集(课堂培优)-2021-2022学年高一数学课后培优练(苏教版2019必修第一册)上海市杨浦高级中学2017-2018学年高一上学期第一次月考数学试题【全国百强校】广西南宁市第三中学2018-2019学年高一上学期第一次月考数学试题人教A版(2019) 必修第一册 逆袭之路 第一章 集合与常用逻辑用语 本章整合提升(已下线)1.1.3 集合的基本运算(第2课时)-高一数学同步精品课堂(人教B版2019必修第一册)
名校
3 . 设
,
,在集合
的所有元素个数为2的子集中,把每个子集的较大元素相加,和记为
,较小元素之和记为
.
(1)当
时,求
,
的值;
(2)求证:为任意的
,
,
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1534b035eca39010118a83486de8904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8c29b297e3ec337c3139c2a1ebed1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/330a768883271ebe0b692f6c226867a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6862dd3c43647ce7d7935a7d205b54d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)求证:为任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1534b035eca39010118a83486de8904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8c29b297e3ec337c3139c2a1ebed1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f563f31a226905e5b38ca81078a1af35.png)
您最近一年使用:0次
2018-06-23更新
|
1103次组卷
|
2卷引用:【全国百强校】江苏省泰州中学2017-2018学年高二6月月考数学(理)试题
名校
4 . 设集合
是非空集合
的两个不同子集.
(1)若
,且
是
的子集,求所有有序集合对
的个数;
(2)若
,且
的元素个数比
的元素个数少,求所有有序集合对
的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a518060a86e8bb366d103ccb0b956be3.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/41be4f4fbf21555f325caf280c392c00.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/541e580c3d6f81c223f79400e738af6b.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/41be4f4fbf21555f325caf280c392c00.png)
您最近一年使用:0次
5 . 已知等差数列
与等比数列
是非常数的实数列,设
.
(1)请举出一对数列
与
,使集合
中有三个元素;
(2)问集合
中最多有多少个元素?并证明你的结论;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b45ed42bacc8c561a88b41d2db90a88.png)
(1)请举出一对数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)问集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
名校
6 . 设集合
是非空集合
的两个不同子集.
(1)若
,且
是
的子集,求所有有序集合对
的个数;
(2)若
,且
的元素个数比
的元素个数少,求所有有序集合对
的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520eeac333d308b57ad3b899e24e5fa6.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)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dc61971e3389bb5c43be486b865a2b4.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)
您最近一年使用:0次
名校
7 . 对于函数
,若存在实数对(
),使得等式
对定义域中的每一个
都成立,则称函数
是“(
)型函数”.
(1) 判断函数
是否为 “(
)型函数”,并说明理由;
(2) 若函数
是“(
)型函数”,求出满足条件的一组实数对
;
(3)已知函数
是“(
)型函数”,对应的实数对
为(1,4).当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681d6d27b23b1c41834d7516122f73f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e34c5eb4ca05084c4c6f55565fb7ec.png)
,若当
时,都有
,试求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c974dafd7f992c28eb67787daa6387b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f00386d48a305ca42d0a391beb59b8a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c974dafd7f992c28eb67787daa6387b.png)
(1) 判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b43539708e9663f5aa0b9336076936e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c974dafd7f992c28eb67787daa6387b.png)
(2) 若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf44ef8807abfa79ffe1fb2919e9309e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c974dafd7f992c28eb67787daa6387b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503b2dce4a732fc1f7c856251a6794b8.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c974dafd7f992c28eb67787daa6387b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503b2dce4a732fc1f7c856251a6794b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1376168658dbe7f5b7f4d75fb1db545a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681d6d27b23b1c41834d7516122f73f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e34c5eb4ca05084c4c6f55565fb7ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bcaceadc00d891e292c8bdff9e4ce64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbb01a7f5e9861aa185c6c63fcd58c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b6ee958612051792de2e49fff0abf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
8 . 选修4-5:不等式选讲
已知集合![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787364352/STEM/ff930142bf4b4d9baee798f35a5075e3.png?resizew=92)
,对于集合
的两个非空子集
,
,若
,则称
为集合
的一组“互斥子集”.记集合
的所有“互斥子集”的组数为
(视
与
为同一组“互斥子集”).
(1)写出
,
,
的值;
(2)求
.
已知集合
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787364352/STEM/ff930142bf4b4d9baee798f35a5075e3.png?resizew=92)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787364352/STEM/9d817a611a9b4c85906b5478d4574c5f.png?resizew=97)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787364352/STEM/3814caf869ff42c68550761692d6bd6a.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787364352/STEM/656513f66f24446a80c4e5c369a7d49f.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787364352/STEM/f565d7f8551d4fbdb225fb43209616e3.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787364352/STEM/1483627c95a940feb90a52428a992ad1.png?resizew=71)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787364352/STEM/13f74a4aaccf432a8beca88981c3934c.png?resizew=43)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787364352/STEM/3814caf869ff42c68550761692d6bd6a.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787364352/STEM/3814caf869ff42c68550761692d6bd6a.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787364352/STEM/df5e4553940b43d2abdde22f6df01f5b.png?resizew=36)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787364352/STEM/13f74a4aaccf432a8beca88981c3934c.png?resizew=43)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787364352/STEM/ef344fc7a29343a6985791307bb1af77.png?resizew=43)
(1)写出
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787364352/STEM/f10a8f2024224424a4b1ee3be6694f70.png?resizew=36)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787364352/STEM/73adced74b8c49eda13f141ccfd20d35.png?resizew=35)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787364352/STEM/2c0595c66057400797c166305a338c01.png?resizew=36)
(2)求
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787364352/STEM/df5e4553940b43d2abdde22f6df01f5b.png?resizew=36)
您最近一年使用:0次
11-12高一上·山东济宁·期末
名校
解题方法
9 . 已知
|
,
|
,且B⊆A,求实数
组成的集合C
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b6a190672edaf8102870e69d657eaa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b977a41d1cedfed81ce1f35d3f80d9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc69947847486808e7119761f2c3527e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27147bf23ad4ec3444dc1a98e685ed74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2018-10-31更新
|
2859次组卷
|
14卷引用:江苏省徐州市菁华高级中学2021-2022学年高一上学期12月月考数学试题
江苏省徐州市菁华高级中学2021-2022学年高一上学期12月月考数学试题(已下线)2011年山东省兖州市高一上学期期末考试数学试卷2016-2017学年北京昌平临川育人学校等高一上月考一数学试卷苏教版2017-2018学年必修一检测第一单元章末过关检测数学试题黑龙江省哈尔滨师范大学青冈实验中学校2017-2018学年高一上学期期中考试数学试题【校级联考】辽宁省辽阳市辽阳县2017-2018学年高一上学期期末考试数学试题黑龙江省黑河市嫩江县高级中学2019-2020学年高一第一次月考数学试题(已下线)1.2+集合间的基本关系-2020-2021学年高一数学新教材配套学案(人教A版必修第一册)四川省泸州市泸县第二中学2020-2021学年高一上学期第一次月考数学试题1.2 集合间的基本关系(学案)-2021-2022学年高一数学教材配套学案+练习(人教A版2019必修第一册)辽宁省抚顺市抚顺县高级中学校2021-2022学年高一上学期10月月考数学试题江西省修水中等专业学校2023届高三上学期第1次段考数学试题人教A版(2019) 必修第一册 数学奇书 学业评价(三) 集合间的基本关系(已下线)1.2集合间的基本关系(导学案)-【上好课】
名校
解题方法
10 . 设集合
是
的两个非空子集,且满足集合
中的最大数小于集合
中的最小数,记满足条件的集合对
的个数为
.
(1)求
的值;
(2)求
的表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c0edf87f1f5e5cd72dce579196e63e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.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/41be4f4fbf21555f325caf280c392c00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be56ba2c0be4776fa76fde419d707d0.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
您最近一年使用:0次
2016-12-03更新
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1317次组卷
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2卷引用:2015届江苏省南京市、盐城市高三第一次模拟考试理科数学试卷