名校
解题方法
1 . 已知
为坐标原点,点
在抛物线
上,过点
的直线交
于
,
两点,则下列命题正确的是________ .
(1)
的准线为
;(2)直线
与
相切;(3)
;(4)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c59f0e35b7ae5206e45878934482b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3544997cc034ed882c0d0a3bdbf5f957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cd4b5f5dfdca309903e5e3d1121d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f96ddb6b56f9ce7268b62cbc1a748d.png)
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2 . 设
,则
的最大值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a521891098b625f372ff648d110afe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d61b2953ddf211685e32116d834a9f9.png)
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7日内更新
|
634次组卷
|
3卷引用:河北省秦皇岛市青龙满族自治县第一中学2024届高三下学期5月模拟考试数学试题
名校
解题方法
3 . 设函数
,给出下列四个结论:
①当
时,函数
有三个极值点;
②当
时,函数
有三个极值点;
③
,
是函数
的极小值点;
④
,
不是函数
的极大值点.
其中,所有正确结论的序号是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e371a853510ec4256372b4aa71794f.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326ea56be82bd616fec7e6aa3c884c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7b784381c282fc5f788485316c943c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7b784381c282fc5f788485316c943c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b19c7ace2585ebedd09cd2216a83bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
其中,所有正确结论的序号是
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4 . 已知函数
,若存在实数对
满足
且
,则使得
成立的正整数
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6263576e5c3f2324a8dac311476bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef046c85a536174bec951a53d9f60b33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0470fac8658aa3c8b475059168d4a743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/576c4f7193f823f76ce654711e25e8f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33610e6e8d21945dc4c4cb8c043083a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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5 . 某班组织开展知识竞赛,抽取四名同学,分成甲、乙两组:每组两人,进行对战答题.规则如下:每次每名同学回答6道题目,其中有1道是送分题(即每名同学至少答对1题).若每次每组对的题数之和为3的倍数,则原答题组的人再继续答题;若对的题数之和不是3的倍数,就由对方组接着答题,假设每名同学每次答题之间相互独立,且每次答题顺序不作考虑,第一次由甲组开始答题,则第7次由甲组答题的概率为______ .
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2024-06-13更新
|
286次组卷
|
2卷引用:安徽省级示范高中培优联盟2023-2024学年高二下学期春季联赛数学试题
名校
解题方法
6 . 设集合
,(
,
)且A中任意两数之和不能被5整除,则n的最大值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6bd3eec1b1e189c92c2db22ea773cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
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7 . 已知函数
,若函数
的最小值恰好为0,则实数
的最小值是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1328e7d04052f002d4b3bd78d3529e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
8 . 在边长为1的正六边形
中,记以A为起点,其余顶点为终点的向量分别为
,
,
,
,
,以D为起点,其余顶点为终点的向量分别为
,
,
,
,
.记
,
为
的两个三元子集,则
的最大值为______ ;
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d344174267f996c7cefecfd6985d380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2e900404ba71110c5861ced9634646f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67dbe2e19d8960789ec873b687998b58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99184832b21db4d92cb2b162679a4948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb1edfbda49a6ef314578efd3224928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c2df57a4cdae59f1b703eff14d32b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e53874673ab14f92e915f7d4a988623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f09bac35174ec1507e3839eb54f815.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad140abd985de3f688b0bc1fa240a00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f93809be489619bb80adc4790dda4d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edbe3d8318bb799cbef82a9b829cc325.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d544b8f6fdb0865c8cb0d4c8bcc46e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f37ab30f2e841f260e46be2714954d0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c9f3889ba128190cc756a237b3c1977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b966a03263abac15ba2db3477540fc46.png)
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9 . 若函数
有且仅有两个零点,则a的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a68f2c7892f9e12d072687a124b88ab0.png)
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10 . 已知集合
,集合
满足:①每个集合都恰有4个元素;②
.集合
中元素的最大值与最小值之和称为集合
的特征数,记为
,则
的最大值与最小值的差为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b8ba1e4fc97b6aae170ba402f00a06d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fa157b4f65f3a9aa1f7f82de02e99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d343d79a12548d8e4f5b1dd6dd9bf2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed5791766a68be89ceda7f1505e4fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/977596d92064cd96041927d539b09731.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eced34833fc5ee8ad2c6817ced270988.png)
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