名校
1 . 符号
表示不大于x的最大整数(
),例如:
,
,
.
(1)已知方程
的解集为M,方程
的解集为N,直接写出集合M、N;
(2)在(1)的条件下,设集合
,是否存在实数k使得
且
,若存在,请求出实数k的范围;若不存在,请说明理由;
(3)设函数
(
),方程
的两个实根为
和
,且满足
.若函数
在
时的函数值记为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ae4ee70c548e841fd7ceeac3250b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a6c086cd67c729ec094c21c0d45a5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c15f3d64ba357a69efe1d0c36c0d94.png)
(1)已知方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/583b10b1050c1de417cf05733d9943f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f70582a9395aec59113e8747b7f8a5.png)
(2)在(1)的条件下,设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff8515650079724b6b297689ad2e13cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1744aae300e6de013e882a9ab565d5ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8965c92d1248c68efdc1dcecea46c90c.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16faec6a9498f6d89494a565fd4ab2fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36b234ba460321e811de1729eadd4b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55cc8e31f2dd9f776d4483b8c917a1ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985354e11259c93e6cd249d87091ebe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6155e181e21ce56ea658b70f8af17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d8742c296a7949b598114a34c51f69.png)
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2 . 设集合
为非空数集,定义
.
(1)若集合
,直接写出集合
及
;
(2)若集合
且
,求证
;
(3)若集合
且
,求
中元素个数的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e32ae0e537ab483485e3dc6628b2f3a.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/265e81e52218232e16c78f57b3aa0de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b26ea9b3e6e286874c5dca1badea723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e16289945d1d1c529fb1bfd4d828f413.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77239c98c78a026cc03336edca067ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9473a5974fa9c4286f90f6a3637411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1868c8a0db983c9cc2695294fa03b1.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce46889ee6889ca41c5bd19eaf0e242f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de4d331fa6921e8ebc0b1fc4affd22ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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名校
3 . 设集合
,称坐标
在平面直角坐标系中对应的点P为A中元素a的格点.
(1)证明:若
则
.
(2)A中的元素
所对应的格点记作
(
),现将A中所有元素进行排序,使得
,在平面直角坐标系中,求以
为顶点的三角形面积.
(3)已知集合
,若
至少有2个元素,最多有5个元素,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799adb7e4c8ebf9a30182e46e56f3192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0203b006524305c3d8ee0b6c34cd872b.png)
(1)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91cc05fe570763e4af0ff4672e2d09e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae4202aa738ce97198687198555c84c.png)
(2)A中的元素
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf99487d7860d017c0747ff966edfd77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/019123b8c298384939e99ef5e37720d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c8c195da3f1e6e13cc9fc7aca43e17d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4a0c3c4114915039e38b671bb707c09.png)
(3)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63728e5600559674a6bb03a0f183007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdbfa7a63fdf5717d40c8c9a73ec160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2023-10-07更新
|
194次组卷
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2卷引用:江苏省连云港市灌南高级中学2023-2024学年高一上学期第一次月考数学试题
2023高一·全国·专题练习
名校
解题方法
4 . 在集合论中“差集”的定义是:
,且
(1)若
,
,求
;
(2)若
,
,求
;
(3)若
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f4bcaec7926363d8f77c6e773920d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b998f1e3675e0fa3b790c416a751af63.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9e6ad1166c7625e63b80e75b2fb1d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2755a85584173902f146eacf40102723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9e460c144f7a2141d2df0308b125f2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26cb7961d2d6957cfd6b4af403450e5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6846ad147da3f53658602eade09631d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9e460c144f7a2141d2df0308b125f2.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7321a9fa7a6ef6be6e40c96709763930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6846ad147da3f53658602eade09631d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfe3404ade72e644b48d19572c173c93.png)
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名校
解题方法
5 . 已知集合
为非空数集,定义:
,
(1)若集合
,直接写出集合
(无需写计算过程);
(2)若集合
,且
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1868c8a0db983c9cc2695294fa03b1.png)
(3)若集合
,记
为集合
中的元素个数,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/312ab0127457545c7bac2193505e0a6b.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e8d171c3d2d86dc5594cffb51096fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a44fa352255b81702d306cb32cf468.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77239c98c78a026cc03336edca067ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c76ad1e03a6ba59e8164e37c5e7e063e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1868c8a0db983c9cc2695294fa03b1.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df87128f2e2850f12dc88216def10cc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8279d9dd0b7750953cb9e2098b3b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8279d9dd0b7750953cb9e2098b3b90.png)
您最近一年使用:0次
2023-09-17更新
|
349次组卷
|
3卷引用:上海市高桥中学2023-2024学年高一上学期月考(一)数学试题
上海市高桥中学2023-2024学年高一上学期月考(一)数学试题(已下线)高一上学期期中考试解答题压轴题50题专练-举一反三系列北京市中央民族大学附属中学(朝阳)2023-2024学年高一上学期期中考试数学试题
解题方法
6 . 已知集合
,
.
(1)若
,均有
,求实数
的取值范围;
(2)若
,设
,
,求证:
是
成立的必要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbdd554d014590a23cfac06de3bda440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac39d8afe38aca6b52b43641a274ea54.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd170c506a8ce70f550f5751ae016ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/653bcf7b627c3b87fcb310732313d9b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79df3000f987277819847391e0548c3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ba27566052abbb25340b6499ae3044a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7848c89302a41e9576530313fc3e61b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db40961f2dcdf88ac84a8f739317b191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
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2022-11-24更新
|
236次组卷
|
5卷引用:江西省名校2022-2023学年高一上学期第三次大联考数学试题(三)
7 . 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,我们就称集合
为“和谐集”
(1)判断集合
是否是“和谐集”,并说明理由.
(2)判断集合
是否是“和谐集”,并说明理由.
(3)求证:集合
不是和谐集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8a2094e3909dbce5d966776a5cb847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2613279bffd089060f0d05e48eabd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42c015b7ebebf921e559369b98bc98d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcb62f10c9971d5aafff76dc4dfb4732.png)
(2)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b91f2f906face10cd95d22d83921abc.png)
(3)求证:集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032b0be0be95b689ebcf3ccdfd059652.png)
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8 . 若集合
,其中
为非空集合,
,则称集合
为集合A的一个n划分.
(1)写出集合
的所有不同的2划分;
(2)设
为有理数集Q的一个2划分,且满足对任意
,任意
,都有
.则下列四种情况哪些可能成立,哪些不可能成立?可能成立的情况请举出一个例子,不能成立的情况请说明理由;
①
中的元素存在最大值,
中的元素不存在最小值;
②
中的元素不存在最大值,
中的元素存在最小值;
③
中的元素不存在最大值,
中的元素不存在最小值;
④
中的元素存在最大值,
中的元素存在最小值.
(3)设集合
,对于集合A的任意一个3划分
,证明:存在
,存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e887bc41e7c72b69482b7cb153b9f40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c7bb3662baf8ab4da46099adc0180a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d16c5b1cefd28f020a899803181867be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a111d44296a6d4c373e33e0267baeb8.png)
(1)写出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbefb4190e6d31cf43ce5258ebf325c3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b064529d4274a25ea70cec901689595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16c303b55101c9d049947443d85bd3d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b31852ebf26c81693dc084facc76a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a5abe56c019ac914e1fcde1865a747.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a99ef56247036a98e53aa8c16c3e02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48ec13d90542aaca7af71224a3d8ea1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2199afe5dd5ad25962537abfa209b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f351ce8d2e5f2160bf2f771642f6dca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92916a0ce7c44bbd09a54a9aedd2e8ac.png)
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2022-07-08更新
|
1219次组卷
|
6卷引用:北京市第一七一中学2023-2024学年高一上学期12月调研数学试题
北京市第一七一中学2023-2024学年高一上学期12月调研数学试题北京市朝阳区2021-2022学年高一下学期期末质量检测数学试题(已下线)第1章 集合与常用逻辑用语(基础、典型、新文化、压轴)分类专项训练-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)(已下线)高一上学期期末【压轴60题考点专练】-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)北京市海淀区首都师范大学附属中学2023-2024学年高一上学期10月期中练习数学试题(已下线)第1章 集合与常用逻辑用语-【优化数学】单元测试能力卷(人教B版2019)
名校
9 . 已知集合
为非空数集,定义:
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e092a46bd0eb089045217e1b13ccbb65.png)
(1)若集合
,直接写出集合
,
.
(2)若集合
,
,且
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1868c8a0db983c9cc2695294fa03b1.png)
(3)若集合
,
,
,记
为集合
中元素的个数,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0d6adf2d45f344e1ca24c4cf0e4884c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e092a46bd0eb089045217e1b13ccbb65.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa9c26b45f6947550f7c40cbfdecbba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faaa2c9b8bc8ee534a517d6a108a66d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3604274ad6707a906eba371a9e884144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c76ad1e03a6ba59e8164e37c5e7e063e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1868c8a0db983c9cc2695294fa03b1.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b408aeda05ba8f05babea6251dcab2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a6a3d1be93cf6d16ee6e0ce0497f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650aa72fd4034517f9f981e382c1e50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650aa72fd4034517f9f981e382c1e50.png)
您最近一年使用:0次
2020-11-15更新
|
2481次组卷
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21卷引用:湖南省长沙市湖南师大附中2020-2021学年高一上学期第一次大练习数学试题
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10 . (1)已知m是实数,集合
,
.求证:“
”是“
”的充要条件.
(2)设
.证明:若
是奇数,则n也是奇数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0274ba49bbad8b3179d628e3d7025cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6e153c5b9e2e807125326fd904644c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed39f5aca78934fb383402433fe549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e851796d98eb47a8d17f4e1b4cea196.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f02d5c8eec434a3f90348d770a2e2b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
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2020-10-27更新
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