解题方法
1 . 为提升学生用数学知识解决现实生活或其他学科领域中的问题的能力,发展学生数学建模素养,某市面向全市高中学生开展数学建模论文征文活动.对于参加征文活动的每篇论文,由两位评委独立评分,取两位评委评分的平均数作为该篇论文的初评得分.从评委甲和评委乙负责评审的论文中随机抽取10篇,这10篇论文的评分情况如下表所示.
(1)从这
篇论文中随机抽取1篇,求甲、乙两位评委的评分之差的绝对值不超过
的概率;
(2)从这
篇论文中随机抽取3篇,甲、乙两位评委对同一篇论文的评分之差的绝对值不超过
的篇数记为
,求
的分布列及数学期望;
(3)对于序号为
的论文,设评委甲的评分为
,评委乙的评分为
,分别记甲、乙两位评委对这10篇论文评分的平均数为
,
,标准差为
,
,以
作为序号为
的论文的标准化得分.对这10篇论文按照初评得分与标准化得分分别从高到低进行排名,判断序号为2的论文的两种排名结果是否相同?(结论不要求证明)
序号 | 评委甲评分 | 评委乙评分 | 初评得分 |
1 | 67 | 82 | 74.5 |
2 | 80 | 86 | 83 |
3 | 61 | 76 | 68.5 |
4 | 78 | 84 | 81 |
5 | 70 | 85 | 77.5 |
6 | 81 | 83 | 82 |
7 | 84 | 86 | 85 |
8 | 68 | 74 | 71 |
9 | 66 | 77 | 71.5 |
10 | 64 | 82 | 73 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
(2)从这
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(3)对于序号为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2968ea9d16fcf1181908c9790c423336.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f95e54a9b7c66c97dc6ee6161a25c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc00379c7af113543302417b685c7d6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80746e5e22851a0f1075374a3c3280ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab7a1a659607d4d81c81f4f6545df241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02526771dc5a6d66fb9029bff5eac3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4bf6d5a546594c4176867be0ec896b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356a0eecfd01ef9b7fec91cf600603ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
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解题方法
2 . 已知函数
,函数
的最小值记为
,给出下面四个结论:
①
的最小值为0;
②
的最大值为3;
③若
在
上单调递减,则
的取值范围为
;
④若存在
,对于任意的
,
,则
的可能值共有4 个;
则全部正确命题的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efee94d8d161b6471d4c6e89a153af7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a239d924a26dbc7f33052c63a20a327a.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a239d924a26dbc7f33052c63a20a327a.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a239d924a26dbc7f33052c63a20a327a.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c82644f77c5455ceb7f94950e94273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/573490ed07601c52a92d4a374db57d95.png)
④若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ccecaf28ac8d62d16577082832dab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
则全部正确命题的序号为
您最近一年使用:0次
2023-03-07更新
|
1325次组卷
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5卷引用:北京中央民族大学附属中学2023届高三零模数学试题
北京中央民族大学附属中学2023届高三零模数学试题(已下线)北京市中央民族大学附属中学2023届高三零模数学试题山东师范大学附属中学幸福柳分校2023-2024学年高一上学期期中考试数学试题(已下线)第三章 函数的概念与性质-【优化数学】单元测试能力卷(人教A版2019)(已下线)专题6 绝对值函数中参数问题(每日一题)
3 . 两个数互素是指两个正整数之间除了1之外没有其他公约数.欧拉函数
(
)的函数值等于所有不超过正整数n,且与n互素的正整数的个数,例如
,
.
关于欧拉函数给出下面四个结论:
①
;
②
,恒有
;
③若m,n(
)都是素数,则
;
④若
(
),其中
为素数,则
.
(注:素数是指除了1和它本身以外不再有其他因数,且大于1的正整数.)
则所有正确结论的序号为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc89a53c03cb86fb653bb82128f6cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9edd29e22f6a7f4d14d9f8d2684d47e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39de1bc04496b97dcf401c669e6ab44e.png)
关于欧拉函数给出下面四个结论:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bb88141edd6ddf3efbede1cb9b9051.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b78297a65e7fad69635b19928ecc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2eb229ae25851eae3cf941fd46eca4.png)
③若m,n(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d9712c3b25f3030e166e136d3a4686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b8178596507fe45cea77096a53d6395.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ae00da0e4adace07489880ab64d391.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ef0a61e3c701a7cb3a9f9ca3c8dd37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bced1fbb4e3bde1437f4fb2821d81a9.png)
(注:素数是指除了1和它本身以外不再有其他因数,且大于1的正整数.)
则所有正确结论的序号为
您最近一年使用:0次
名校
4 . 对于定义域为
的函数
,设关于
的方程
,对任意的实数
总有有限个根,记根的个数为
,给出下列命题:
①存在函数
满足:
,且
有最小值;
②设
,若
,则
;
③若
,则
为单调函数;
④设
,则
.
其中所有正确命题的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20e258c0598cc43a382cce8bab8260a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b6bd51117f63f7482ee9782fb9889b.png)
①存在函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c34c1508ab9af5b2e5986652ba68da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc67984ac4e76c6f95b3fc885948fb29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/138fa4ed39079099fcc80e10b5df6712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85187c85826beeca12137805293fff77.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc75ca9fbb27f0066677deb5d8f7220d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
④设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71595f31b25fcd5879783d89ab9b9bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4990c48f7ef2a3c9141679809307bbad.png)
其中所有正确命题的序号为
您最近一年使用:0次
2021-05-08更新
|
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4卷引用:北京市东城区2021届高三下学期二模数学试题