1 . 考查等式:
(*),其中
,
且
.某同学用概率论方法证明等式(*)如下:设一批产品共有
件,其中
件是次品,其余为正品.现从中随机取出
件产品,记事件
{取到的
件产品中恰有
件次品},则
,
,1,2,…,
.显然
,
,…,
为互斥事件,且
(必然事件),因此
,所以
,即等式(*)成立.对此,有的同学认为上述证明是正确的,体现了偶然性与必然性的统一;但有的同学对上述证明方法的科学性与严谨性提出质疑.现有以下四个判断:①等式(*)成立,②等式(*)不成立,③证明正确,④证明不正确,试写出所有正确判断的序号___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb037e045b5418574fe43786d011b870.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4a0d69abd7440e8c12a1cc1473a97a8.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/845198f8baea2e38597b647c25c9f80d.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a724f29764aa9f60eae054bc085cd3c1.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd55ae46a41a37f90a3d745b9e8f879.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb037e045b5418574fe43786d011b870.png)
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2 . 设正数
不全相等,
,函数
.关于说法
①对任意
都为偶函数,
②对任意
在
上严格单调递增,
以下判断正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56667aabbe787eb1c3189d487d203e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d74781f2fcb2c572de65c4f702d5457.png)
①对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75c03244f2565ccad815ed9305655b4.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75c03244f2565ccad815ed9305655b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d720165be8b61db4a8b305ad47c7f2a0.png)
以下判断正确的是( )
A.①、②都正确 | B.①正确、②错误 | C.①错误、②正确 | D.①、②都错误 |
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3 . 已知四边形
是椭圆
的内接四边形,其对角线
和
交于原点
,且斜率之积为
.给出下列四个结论:
①四边形
是平行四边形;
②存在四边形
是菱形;
③存在四边形
使得
;
④存在四边形
使得
.
其中所有正确结论的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caeb11677994ba487096958b1ad82ea1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30d314a642667fef559032264647366.png)
①四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
②存在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
③存在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e84f14a77c27b015b6b1cf0896228b1.png)
④存在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d8d582c0bf83314b19df67e1bd2740.png)
其中所有正确结论的序号为
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4卷引用:2.2.2 椭圆的性质(十八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
(已下线)2.2.2 椭圆的性质(十八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)北京市海淀区2023-2024学年高二上学期期末练习数学试卷北京市人大附中2023-2024学年高二上学期期末数学试题北京市第五十七中学2023-2024学年高一1+3下学期期中考试数学试卷
名校
解题方法
4 . 已知函数
给出下列四个结论:
①若
有最小值,则
的取值范围是
;
②当
时,若
无实根,则
的取值范围是
;
③当
时,不等式
的解集为
;
④当
时,若存在
,满足
,则
.
其中,所有正确结论的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ff4e0cfa86f6d91ff0b3cdb3251393b.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c6cc71d0c988d725b25c55c2672919c.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976d18a5396ba232f0aa38d136f1d749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da1606791e5eeefbf298210543e01dd4.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e5bcfb3bafe8373dd907e0e55d08f8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168fef6477a494abceae56fb6c2e4c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b61bb7cb94b4d06f0090df1e365667.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ede78fd7ac619ea597856254bb5d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/339de01d9636343c484391b421c31301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ec808ad60dbf016632ec816eaca1df.png)
其中,所有正确结论的序号为
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5卷引用:上海市实验学校2023-2024学年高三下学期四模数学试题
5 . 设集合
,点P的坐标为
,满足“对任意
,都有
”的点P构成的图形为
,满足“存在
,使得
”的点P构成的图形为
.对于下述两个结论:①
为正方形以及该正方形内部区域;②
的面积大于32.以下说法正确的为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03cd04b82dda9c0d2dd0957ffc407d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9712a0071f6d0d78d17ce18f6084cad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3693b84b83679c30b1035750d9b4f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deebd2c36a5e644a566f1980091359bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9712a0071f6d0d78d17ce18f6084cad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3693b84b83679c30b1035750d9b4f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e32039addb008103a2a8344225214a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deebd2c36a5e644a566f1980091359bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e32039addb008103a2a8344225214a.png)
A.①、②都正确 | B.①正确,②不正确 |
C.①不正确,②正确 | D.①、②都不正确 |
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6 . 平面上的向量
、
满足:
,
,
.定义该平面上的向量集合
.给出如下两个结论:
①对任意
,存在该平面的向量
,满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092597e9907aab9a47d6e23057c8d274.png)
②对任意
,存在该平面向量
,满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092597e9907aab9a47d6e23057c8d274.png)
则下面判断正确的为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6316d995f00623f05fc3d56a6cbe5f00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/407538138dd68ab917925c2063cc98e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bf21fef3026cfe445a855c94cab5c84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30f758f45abc258acfe2c619a901dd4.png)
①对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f878c229fc3898c45a76727eee75370d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0c5dcc6c7cbc617957931d8b8b4b09f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092597e9907aab9a47d6e23057c8d274.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f878c229fc3898c45a76727eee75370d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e8b56ab93d5122afcddb46d502012ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092597e9907aab9a47d6e23057c8d274.png)
则下面判断正确的为( )
A.①正确,②错误 | B.①错误,②正确 | C.①正确,②正确 | D.①错误,②错误 |
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7 . 已知
,集合
,
,
. 关于下列两个命题的判断,说法正确的是( )
命题①:集合
表示的平面图形是中心对称图形;
命题②:集合
表示的平面图形的面积不大于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923078510697d5f7f9ea392eb76dd9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01a037f86b6fbf91b8e112ae8613ad4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28d2f35fefd24f3cb607b9771ea69951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a41a4507d85c446a8f3324de736dc778.png)
命题①:集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
命题②:集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c79cff5cd16432d03d1c38e2ea800a38.png)
A.①真命题;②假命题 | B.①假命题;②真命题 |
C.①真命题;②真命题 | D.①假命题;②假命题 |
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|
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3卷引用:上海市闵行区2024届高三下学期学业质量调研(二模)数学试卷
名校
解题方法
8 . 已知函数
的导函数为
,
,且
在R上为严格增函数,关于下列两个命题的判断,说法正确的是( )
①“
”是“
”的充要条件;
②“对任意
都有
”是“
在R上为严格增函数”的充要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d0c99ddd028f0bc3b1d64924ff0f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d0c99ddd028f0bc3b1d64924ff0f61.png)
①“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2210f152080d9a68a97c805f5c1cde96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc1a317e2e6f1caf1e67bf4073cf789.png)
②“对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e702d87b7d70bf870bc04ef6df889d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
A.①真命题;②假命题 | B.①假命题;②真命题 |
C.①真命题;②真命题 | D.①假命题;②假命题 |
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2023-12-12更新
|
765次组卷
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7卷引用:上海市闵行区2024届高三上学期学业质量调研(一模)数学试卷
上海市闵行区2024届高三上学期学业质量调研(一模)数学试卷(已下线)专题09 导数(三大类型题)15区新题速递(已下线)专题01 集合(15区真题速递)(已下线)上海市高二下学期期末真题必刷03(常考题)--高二期末考点大串讲(沪教版2020选修)江西省上饶市广丰一中2024届高三上学期12月月考数学试题湖南省衡阳市第八中学2024届高三上学期第五次月考数学试题广东省广州市第二中学2023-2024学年高二下学期期中考试数学试题