名校
解题方法
1 . 设
,
.如果存在
使得
,那么就说
可被
整除(或
整除
),记做
且称
是
的倍数,
是
的约数(也可称为除数、因数).
不能被
整除就记做
.由整除的定义,不难得出整除的下面几条性质:①若
,
,则
;②
,
互质,若
,
,则
;③若
,则
,其中
.
(1)若数列
满足,
,其前
项和为
,证明:
;
(2)若
为奇数,求证:
能被
整除;
(3)对于整数
与
,
,求证:
可整除
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b72ea8ec0d9f8b1cfc4de834b8bfb608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87803b7cee18366b89d51799250df510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6705dba65746e1d4cac6a268b3c806ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.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/020e12ff4f028aba3a205a95e650d72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.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/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79bda3d07c2fef4d6af4a13ade4c743e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020e12ff4f028aba3a205a95e650d72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4d6df2a57b7e5be32c05c10257ea6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91638bacbf4d15736d26713ba90e0fc4.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/91638bacbf4d15736d26713ba90e0fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4d6df2a57b7e5be32c05c10257ea6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0601879ae4ca9592246d135bfa48658c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383eb235f8e0ceda13367b16d29e0180.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503618b9bfb53a06f0ec6a5e427dcdbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0da20edf2714109dcfded7e212ec44a.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e12059d1dac926a235ccd40c3b61b1b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed9dbd8ed61db4f1c14f6b0e5f071200.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1e4de97f8490fddcff16afe8583266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
(3)对于整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b96cdd9e003120b6102d927dbf53e39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5009ce2d56180d31204f77c871fb375c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b326965628b5d967aafe9e696fdc07.png)
您最近一年使用:0次
2024-05-19更新
|
538次组卷
|
2卷引用:河南省驻马店市新蔡县第一高级中学2023-2024学年高二下学期6月月考数学试题
2 . (1)设
、
,
,求证:
;
(2)请利用二项式定理证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7870c36161f465fc992534b5fc3777f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec7e58f57ee4e8667499e3ff9a00ab11.png)
(2)请利用二项式定理证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b4fad9318b8c34e067afb27e6cefcc9.png)
您最近一年使用:0次
2020-07-16更新
|
744次组卷
|
8卷引用:上海市复旦大学附属中学青浦分校2022-2023学年高二下学期3月月考数学试题
上海市复旦大学附属中学青浦分校2022-2023学年高二下学期3月月考数学试题上海市静安区2019-2020学年高二下学期期末数学试题(已下线)对点练69 二项式定理-2020-2021年新高考高中数学一轮复习对点练(已下线)专题2.6 排列组合和二项式定理【章节复习专项训练】-2020-2021学年高二数学下学期期末专项复习(沪教版)(已下线)考向38 二项式定理全归纳(十五大经典题型)-3(已下线)拓展二:二项式定理15种常见考法归类 -【帮课堂】2022-2023学年高二数学同步精品讲义(人教A版2019选择性必修第三册)(已下线)高二下期末真题精选(易错60题45个考点专练)(高中全部内容)(原卷版)(已下线)第03讲 二项式定理(十五大题型)(讲义)-3
名校
解题方法
3 . 若
,
是样本空间
上的两个离散型随机变量,则称
是
上的二维离散型随机变量或二维随机向量.设
的一切可能取值为
,
,记
表示
在
中出现的概率,其中
.
(1)将三个相同的小球等可能地放入编号为1,2,3的三个盒子中,记1号盒子中的小球个数为
,2号盒子中的小球个数为
,则
是一个二维随机变量.
①写出该二维离散型随机变量
的所有可能取值;
②若
是①中的值,求
(结果用
,
表示);
(2)
称为二维离散型随机变量
关于
的边缘分布律或边际分布律,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c1116ce7f5a1a7b57517276d5092fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4d15d2e2dc5b64da00f2f90613f6b73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4d15d2e2dc5b64da00f2f90613f6b73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fadab9bb02100d7e9f12989b89721482.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66ae8920473eb5e860b0d625d0fe07eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8038ba89dea0aa5c0e760bb5ed5f8561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fadab9bb02100d7e9f12989b89721482.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e2fc8dcdb957351e81bd926db46ef9.png)
(1)将三个相同的小球等可能地放入编号为1,2,3的三个盒子中,记1号盒子中的小球个数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c1116ce7f5a1a7b57517276d5092fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4d15d2e2dc5b64da00f2f90613f6b73.png)
①写出该二维离散型随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4d15d2e2dc5b64da00f2f90613f6b73.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64d924836b4292239d9726c6473d7f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a061d6375056092d2d831bd7cae6988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbefad0c67ac64be204e45c95b2dc35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4d15d2e2dc5b64da00f2f90613f6b73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe4cecc21cb09b200a771b8ec5cea0f.png)
您最近一年使用:0次
2024-03-29更新
|
2032次组卷
|
4卷引用:山东省烟台市龙口第一中学东校2023-2024学年高二下学期第一次质量检测(3月)数学试题
4 . 某高中学校有室内、室外两个运动场.假设同学们可以任意选择其中一个运动场锻炼,也可选择不锻炼,一天最多锻炼一次,一次只能选择一个运动场.若同学们每次锻炼选择去室内、室外运动场的概率均为0.5,每次选择相互独立.设
同学三天内去运动场锻炼的次数为
,已知
的分布列如下:(其中
)
(1)记事件
表示
同学三天内去运动场锻炼
次
;事件
表示
同学在这三天内去室内运动场锻炼的次数大于去室外运动场锻炼的次数.当
时,试根据全概率公式求
的值;
(2)是否存在实数
,使得
?若存在,求
的值;若不存在,请说明理由;
(3)记
表示事件“室外运动场举办集体锻炼活动”,
表示事件“王同学去室外运动场锻炼”,
.已知
同学在室外运动场举办集体锻炼活动的情况下去室外运动场锻炼的概率,比不举办集体锻炼活动的情况下去室外运动场锻炼的概率大,试比较
与
的大小,并证明之.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e362ab25e6f8719efd1b515094b69561.png)
![]() | 0 | 1 | 2 | 3 |
![]() | ![]() | ![]() | ![]() | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eef5855dd54b607a61027e0b212cd61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f970f380a12c843bb4a74ff34a15b2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108ab49f370919e730e3567070deee65.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667df0f959f5626681d6d9aecaf05be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6efafab9402e42c2212489d7b9408c4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697e2bfec979c21b2ba96569f82dba64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/519abef903d663a9633f5ac89bc45fe0.png)
您最近一年使用:0次
名校
解题方法
5 . 设离散型随机变量X,Y的取值分别为
,
.定义X关于事件“
”
的条件数学期望为
,已知条件数学期望满足全期望公式
.解决如下问题:为了研究某药物对于微生物A生存状况的影响,某实验室计划进行生物实验.在第1天上午,实验人员向培养皿中加入10个A的个体.从第1天开始,实验人员在每天下午向培养皿中加入该种药物.当加入药物时,A的每个个体立即产生1次如下的生理反应(设A的每个个体在当天的其他时刻均不发生变化,不同个体的生理反应相互独立):①直接死亡;②分裂为2个个体,且这两种生理反应是等可能的.
设第n天上午培养皿中A的个体数量为
.规定
,
.
(1)求
,
;
(2)证明
;
(3)已知
,求
,并结合(2)说明其实际含义.
附:对于随机变量X,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4c5ef7cc433f6d83d5dace3007d81e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12044571bb321a077e62fe3d24921d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dfe778b3e0bbd2220de99c382ec323b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d94932ae5d8a1772b36b5268a234a046.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8baaca444be2d6b341f0310d17ba5558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7af49ca40f22b61efbda45d7632da572.png)
设第n天上午培养皿中A的个体数量为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d0f3799612b81e85b87241ec8eee68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f93ddfb6148d7377a0d659b2429706a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843b0b9191cabb7c63a406e37650a96a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7af337627e78cece1daf3a8cf11a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c7173930e7a13eb63e18f901f7772.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d6030f60e25c6344f62d900167a604.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8218c7894f6caad3396a4eab9e6094a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58664d4fcfe5b765ccc1f86d7c29ce1c.png)
附:对于随机变量X,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83507976fbfb5685fd79058bc438f0a.png)
您最近一年使用:0次
7日内更新
|
214次组卷
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2卷引用:2024届福建省莆田市第一中学高三下学期5月模拟考试数学试题
名校
解题方法
6 . 已知某系统由一个电源和并联的
三个元件组成,在电源电压正常的情况下,至少一个元件正常工作才可保证系统正常运行,电源及各元件之间工作相互独立.
(1)电源电压
(单位:
)服从正态分布
,且
的累积分布函数为
,求
.
(2)在统计中,指数分布常用于描述事件发生的时间间隔.已知随机变量
(单位:天)表示某元件的使用寿命,
服从指数分布,其累积分布函数为
.
(ⅰ)设
,证明:
;
(ⅱ)若第
天只有元件
发生故障,求第
天系统正常运行的条件概率.
附:若随机变量
服从正态分布
,则
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
(1)电源电压
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/515c70580e9f247fe27b2f0c964bc5ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166b72040b0aa1e70564fa174b91f6b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb8c83d6dd000e7c0180d91ed146a90.png)
(2)在统计中,指数分布常用于描述事件发生的时间间隔.已知随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d377090d1f35e2b0f2061052e238a8.png)
(ⅰ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f9a9793d0ce6ccb20dc7972d59e73f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c7ac9cc03bbbb308beaa88f424fc1dc.png)
(ⅱ)若第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
附:若随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34f77553716bd8b2f4680893d6d496b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbd61d3462563f0964a9fde5537eaef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42373c7a83e1e876aa12d7e6ac028a17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28613181e6953c9858da252bfd62c569.png)
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7 . “四平方和定理”最早由欧拉提出,后被拉格朗日等数学家证明.“四平方和定理”的内容是:任意正整数都可以表示为不超过四个自然数的平方和,例如正整数
.设
,其中
均为自然数,则满足条件的有序数组
的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19e9edd49b95d101473211fa54acfcdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6f5f4751622b599216b655a679cdd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5e4be004a34cfce346c12feea0a696.png)
A.26 | B.28 | C.29 | D.30 |
您最近一年使用:0次
名校
8 . 在活动中,初始的袋子中有5个除颜色外其余都相同的小球,其中3个白球,2个红球.每次随机抽取一个小球后放回.规则如下:若抽到白球,放回后把袋中的一个白球替换为红球;若抽到红球,则把该红球放回袋中.记经过
次抽取后,袋中红球的个数为
.
(1)求
的分布列与期望;
(2)证明
为等比数列,并求
关于
的表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8dfeb1a37fe9ebefefd522a7c582e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d0f3799612b81e85b87241ec8eee68.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5031a3a951c4a1d1c5e9f80a5e26513.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46931d3b33e64b09805b43b4d0da253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685a18e8694ab2c3243133d8a1988e68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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7日内更新
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623次组卷
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9卷引用:江西省部分学校2023-2024学年高二下学期第二次月考(5月联考)数学试题
江西省部分学校2023-2024学年高二下学期第二次月考(5月联考)数学试题河南省创新发展联盟2023-2024学年高二下学期5月月考数学试题河北省秦皇岛市卢龙县2023-2024学年高二下学期5月考试数学试题云南省部分校2023-2024学年高二下学期月考联考数学试题内蒙古开鲁县第一中学、和林格尔县第三中学等2023-2024学年高二下学期5月月考数学试题湖北省荆州市沙市中学2023-2024学年高二下学期6月月考数学试题内蒙古名校联盟2023-2024学年高二下学期教学质量检测数学试题河北省保定市部分学校2023-2024学年高二下学期5月期中考试数学试题(已下线)专题04 随机变量及其分布类常考题型归类--高二期末考点大串讲(人教B版2019选择性必修第二册)
解题方法
9 . 若一个两位正整数
的个位数为6,则称
为“幸运数”.
(1)对任意“幸运数”
,证明:
能被6整除;
(2)已知集合
.
①若
,证明:
;
②若“幸运数”
,则称数对
为“亲密数对”,规定:
,求小于50的“幸运数”中,所有“亲密数对”的
的所有值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)对任意“幸运数”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b044c1df8d6021eccebd4e9120f232.png)
(2)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e5dc7f66a23728165409821aaca1b3.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf58d3883bcd6273dc624a0abef69f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d783f369011a6d18f3b14c8d8ed171fb.png)
②若“幸运数”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0ac8b620b5eca9daa7276712935ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698c4d4e50062b4a7dd70fe1b4ab4fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e0d26b41dcdbe19680eade8702c0a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f884759486947e0215402e45ed0a2e.png)
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解题方法
10 . (1)在
的展开式中,求形如
(
,
)的所有项的系数之和.
(2)证明:
展开式中的常数项为
.
(3)设
的小数部分为
,比较
与1的大小
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a94cee4761bbe64fbeabd6011a07ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c908a876be601f54c1af6cf77a445685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9a9067fce21d7f9e6108766dd7067a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09ab55bbc2761abe6b82ccf9456881b4.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/487aaa5d6a92b34f9019a6531258d17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eb1855504bc8be2becec8d259e7f199.png)
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183次组卷
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3卷引用:山西省忻州市2023-2024学年高二下学期5月联考数学试题