1 . 已知集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb666f694add11464df52978d2c5c8da.png)
,
表示和
中所有不同值的个数.则
的最小值是.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb666f694add11464df52978d2c5c8da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ca7644adddf2eacc949fc219328552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f287eeb047884b44460a1c8e73726d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc77fb90f486489496e78acede64561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f287eeb047884b44460a1c8e73726d5.png)
A.2008 | B.2013 |
C.4013 | D.4016 |
您最近一年使用:0次
名校
2 . 设
、
、
是两个两两不相等的正整数.若
,则
的最小值是( )
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b8429214f1f47081172e867a215f18c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dd4067a19eeb07474557fe7b2508880.png)
A.2007 | B.1949 | C.1297 | D.1000 |
您最近一年使用:0次
2018-12-27更新
|
400次组卷
|
4卷引用:数学奥林匹克高中训练题_101
数学奥林匹克高中训练题_101上海市南洋模范中学2022-2023学年高一上学期开学考试数学试题(已下线)第09讲 函数的基本性质(7大考点)-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)北京市第八十中学2023-2024学年高一上学期(10月月考)阶段测评数学试题
3 . 给定三个非空数集
,
,
,满足“若
,则
”.求实数
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1f8f6377df6ec052c181dba2ea30ba3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a87f8b6e8b3b79ff59b4bc94df89f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da6f7bb0a452a7b82c944f657645a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/582ad43edf388c096e7704d92340bf75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6fcd8c080cd267741fd19e7612a251c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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4 . 设
是20个两两不同的正整数,且集合
中有201个不同的元素.求集合
中不同元素个数的最小可能值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cddcc224ef4ac220c316d8a67c7fd74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a6c7c317022791a2a54ae2572006e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1a21dd5955f3672144cccf31ca03bd.png)
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5 . 设
是由整数组成的集合,满足:(1)对一切
、
,
,均有
;(2)存在
、
,使
.请问,
中是否必有元素0?
是否必定为无穷集合?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95d24952c1772d8db28522e5daff31e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22404ecc9b3ef48f2674c905008521bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a54f16c896d289d7cbe1dc6f9fa81898.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95d24952c1772d8db28522e5daff31e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c27dd7d52809f198bec7854492661aa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e063f9c4e38ecae6d149c4b1c95dfc31.png)
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6 . 给定正整数
,集合
,
,且
,其中,
满足
是7的倍数
.求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cadff4f1f0e22210065c67f00b971e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e022f1250e19fe4514c0c67a15ebfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1368a045ba80f97383f3d9d7fcdc8f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90c998886b1483221a5b4941f6e874c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eba64ebd3a3d1f626ea8249aa390385.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed59dd55a0ff43f08a1a501623ad634a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49823a74ab0237a20a538e4db432c9cf.png)
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7 . 已知一个正整数集合
,其元素之和为2009,试求其元素之积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c9526d6b90914ec17fdda5040ceeda7.png)
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8 . 已知从有限个平面向量构成的集合
中任取三个元素,其中总存在两个元素
,使得
.试求
中元素个数的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64fa2fcefaf3d8868da0cb52877c5247.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a8e7376a9f393a3a1c7109e43b1b6c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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9 . 已知集合
,
,若
,则以
、
、
为三边.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d70b8eb37faf17ac997272bf1c881d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d861cfbc354ea7cd62650dc0c9b738b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8d40e257f9c446b8e30fa841b74bbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce22731a412796fe2925e01f765d5976.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ccefdce953ac4ac08b5fc0191b85dbd.png)
A.一定构成锐角三角形 | B.一定构成直角三角形 |
C.一定构成钝角三角形 | D.可能不构成三角形 |
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10 . 已知
、
、
,集合
,且
为
的
个不同的
元子集.证明:存在集合
、
满足下列条件:
(1)
,
;
(2)在
,
这
个集合中至多有
个为空集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e636dc36f3c4ebc07af69afdf9004d35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876bf8f1423e57be124a4f780f53ee17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0173fb7b171deab443795a36fc0557bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1019d4ad2e3fb4a7abb66e0e9e55b556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eea9af1af88f5432a3f174641211711.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f366f44e4a10f96daf4a28f8ef4055e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a897d586e4bc1160675e3e0490e082b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b6af0d30e50bf74d26d00bc37a846f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aadf9ab510510120699c5eee39ab18b.png)
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