解题方法
1 . 离散对数在密码学中有重要的应用.设
是素数,集合
,若
,记
为
除以
的余数,
为
除以
的余数;设
,
两两不同,若
,则称
是以
为底
的离散对数,记为
.
(1)若
,求
;
(2)对
,记
为
除以
的余数(当
能被
整除时,
).证明:
,其中
;
(3)已知
.对
,令
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05bea470ae14b90937f6f71dc9a6242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b2b0dcbc27df9950b26028e46f6c17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e5865fd0fb7c35e8a4a1d311163290b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbe6ebc6c1d1a214f5ca478ae666cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67a1f88ae28ecdb67c7f9c4ae61481b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae890dd5b6300cf23b4905e86410317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff99d1615f90ff71b56ca1dfebd626d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/420a12638f77a27c696f63ff946e8684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b0087ea124b6fd98fbbcb9bc4c2e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](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/9ce071bd0d6fa72ff4ba4e72d810d11f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac54185ed8bb89c774ceb685408156c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca7b54c31c5ab3831f260012758ffa12.png)
(2)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/099d389a1c0e5877350e62c52c4a724c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ab2ad5d8b72e3f26bef4be0697ec70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b6b09b60bf1bf8403c49bc17e365cd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ebb2233e8492cf61fe9f9bc68af470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b6b09b60bf1bf8403c49bc17e365cd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ebb2233e8492cf61fe9f9bc68af470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34fc26e532b65641a53eaa7e127aa683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4d45dbe0a914249371aed3641515123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53ace23b21d7b119ad7ac5cf877c19f0.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce071bd0d6fa72ff4ba4e72d810d11f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2793be26b839ae9f8f83cf2b5a597cd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1a6740a4f2378965bc019bc6aacd44a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f278b4fd6ed264265e3ccfac4ab7ef02.png)
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2024-01-19更新
|
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8卷引用:2024年九省联考试卷分析及真题鉴赏
2024年九省联考试卷分析及真题鉴赏2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题(已下线)2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题变式题16-19(已下线)压轴题高等数学背景下新定义题(九省联考第19题模式)讲(已下线)微考点8-1 新高考新题型19题新定义题型精选(已下线)新题型02 新高考新结构竞赛题型十五大考点汇总-2(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大核心考点)(讲义)(已下线)专题8 考前押题大猜想36-40
2 . 已知
,若函数
有且只有2个零点,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ccdc4d20e154971f184ab523a3df8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0dc76470681a49263fb2a2728d56f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
解题方法
3 . 信息熵是信息论中的一个重要概念.设随机变量X所有可能的取值为1,2,
,n,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da467b6613d9d20676bc9bddbe6f5ca.png)
,
,定义X的信息熵
,则下列判断中正确的是( )
①若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee2c054f4510895b4c526fedbe3d4f64.png)
②若
,则
;
③若
,则当
时,
取得最大值
④若
,随机变量Y所有可能的取值为1,2,
,m,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7802794b6d58c5755eb4a471f270533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da467b6613d9d20676bc9bddbe6f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85719767bc8b764fcde16731c1ea45c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c94a17b49550283be4ec1a348c8534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae49e5608e5b61ac710f93955af5798e.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba47fb63d946d478fcc51769657eeada.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee2c054f4510895b4c526fedbe3d4f64.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7947b04dfd9793eefe588ae1696f32eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e5f84b0617cbfa27da74b62ef8aae4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5790d5181783c15fd46d95bf18b796f0.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b21c7729887167e605d912861339bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5baa3c2e56ea2aca943b9b2a5b938b46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7802794b6d58c5755eb4a471f270533.png)
A.①② | B.②③ | C.①②④ | D.①②③④ |
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4 . 已知函数
.
(1)讨论函数
在
上的单调性;
(2)若
,函数
有两个极值点
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8ec7c787929d13c7161528f61f3343.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/879234adbae93aa72b7e101b3738d4e0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/050b3e1a7bf3fb787b79cf0cdbb2f2f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac1deb6fd4bb982996f4a80cb1ed221.png)
您最近一年使用:0次
名校
解题方法
5 . 已知函数
.
(1)若
的极小值为
,求实数
的值;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/430d7e3665f6e9c1e5446906f782e878.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6ddb3766b5215c115a0abf597598aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2016bd8c87171be634ebdd6fa0315ec0.png)
您最近一年使用:0次
2020-09-22更新
|
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6卷引用:中原名校2022-2023学年高三上学期质量考评一理科数学试题