名校
解题方法
1 . 某
(应用软件)举行推广活动,新用户注册前7天内,每天登录可获得1元红包,前7天连续登录的新用户,还可进入抽奖活动页面领取红包,每位用户随机点击4个红包中的1个领取(领取前不知道红包金额),领取后看1分钟广告,可再次从剩余3个红包中领取1个,4个红包的金额分别为
元、
元、
元、
元
.
(1)若前7天连续登录且抽奖活动页面看1分钟广告的新用户获得的所有红包金额之和
(单位:元)的期望值为70元,求
的值;
(2)该
推广活动进行一个月后,对新用户登录方案进行了调整,调整为:新用户注册前7天内,连续登录第
天,当天可获得
元红包,中间中断再登录重新计算连续天数,若新注册用户甲前4天已经连续登录该
,后3天每天登录的概率均为
,求该用户前7天内通过登录获得红包金额之和
(单位:元)的分布列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba5bb5088efb59d57c36b919197126e.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/878e89b6eca35e34c863e832a2c661db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9878a063abcb6098d10560f2bf2d4b71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/073bd7cec3f5d4d0107a2b6affcf59c2.png)
(1)若前7天连续登录且抽奖活动页面看1分钟广告的新用户获得的所有红包金额之和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)该
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba5bb5088efb59d57c36b919197126e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba5bb5088efb59d57c36b919197126e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
您最近一年使用:0次
名校
2 . 某学校组织游戏活动,规则是学生从盒子中有放回的摸球且每次只能摸取1个球,每次摸球结果相互独立,盒中有1分和2分的球若干,摸到1分球的概率为
,摸到2分球的概率为
.
(1)若学生甲摸球2次,其总得分记为
,求随机变量
的分布列与期望;
(2)学生甲、乙各摸5次球,最终得分若相同,则都不获得奖励;若不同,则得分多者获得奖励.已知甲前3次摸球得了6分,求乙获得奖励的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
(1)若学生甲摸球2次,其总得分记为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)学生甲、乙各摸5次球,最终得分若相同,则都不获得奖励;若不同,则得分多者获得奖励.已知甲前3次摸球得了6分,求乙获得奖励的概率.
您最近一年使用:0次
2024-06-10更新
|
1289次组卷
|
4卷引用:广西南宁市第三中学2024届高三下学期校二模数学试题
名校
解题方法
3 . 已知函数
.
(1)当
时,求
的最小值;
(2)①求证:
有且仅有一个极值点;
②当
时,设
的极值点为
,若
.求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2efe2b4b78548b27554a16f30cbbda8.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c04c105ef35ea19d5a74738079e758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ae1942a92849b7de5cf879777bf5868.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0821dd73cd58f5b7dc26dbea4b7eed29.png)
您最近一年使用:0次
2024-06-08更新
|
657次组卷
|
3卷引用:广西南宁市第三中学2024届高三下学期校二模数学试题
4 . 2023年10月7日,杭州第19届亚运会女子排球中国队以3:0战胜日本队夺得冠军,这也是中国女排第9个亚运冠军,她们用汗水诠释了几代女排人不屈不挠、不断拼搏的女排精神,某校甲、乙、丙等7名女生深受女排精神鼓舞,组建了一支女子排球队,其中主攻手2人,副攻手2人,接应手1人,二传手1人,自由人1人.现从这7人中随机抽取3人参与传球训练
(1)求抽到甲参与传球训练的概率;
(2)记主攻手和自由人被抽到的总人数为
,求
的分布列及期望;
(3)若恰好抽到甲,乙,丙3人参与传球训练,先从甲开始,甲传给乙、丙的概率均为
,当乙接到球时,乙传给甲、丙的概率分别为
,当丙接到球时,丙传给甲、乙的概率分别为
,假设球一直没有掉地上,求经过n次传球后甲接到球的概率.
(1)求抽到甲参与传球训练的概率;
(2)记主攻手和自由人被抽到的总人数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
(3)若恰好抽到甲,乙,丙3人参与传球训练,先从甲开始,甲传给乙、丙的概率均为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d02b811bb9c27723442c470a4bcd6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d02b811bb9c27723442c470a4bcd6e.png)
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名校
解题方法
5 . 现定义“
维形态复数
”:
,其中
为虚数单位,
,
.
(1)当
时,证明:“2维形态复数”与“1维形态复数”之间存在平方关系;
(2)若“2维形态复数”与“3维形态复数”相等,求
的值;
(3)若正整数
,
,满足
,
,证明:存在有理数
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9dc4e868a310c371ff88075d8a966a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef9d830212489b316bb052455098108e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc8299790d98621b87e73212a2ebb91.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905dd10639c9fef5ef8d66a124756140.png)
(2)若“2维形态复数”与“3维形态复数”相等,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c136aaf9b5dedec254a92ce302f4a70c.png)
(3)若正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94742ebbb028c50d7a58e3e8f4ab329c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35490c12e57ecd91af9934cb17b5c927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ed110fbfeb14003270a1039ba174d0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f02f2606180ffeda602ff9ae747af6f.png)
您最近一年使用:0次
2024-05-11更新
|
638次组卷
|
3卷引用:广西南宁市第二中学2023-2024学年高一下学期5月月考数学试卷
解题方法
6 . 有两个盒子,其中1号盒子中有3个红球,2个白球;2号盒子中有4个红球,6个白球,这些球除颜色外完全相同.
(1)先等可能地选择一个盒子,再从此盒中摸出2个球.若摸出球的结果是一红一白,求这2个球出自1号盒子的概率;
(2)如果从两个盒子中摸出3个球,其中从1号盒子摸1个球,从2号盒子摸两个球,规定摸到红球得2分,摸到白球得1分,用
表示这3个球的得分之和,求
的分布列及数学期望.
(1)先等可能地选择一个盒子,再从此盒中摸出2个球.若摸出球的结果是一红一白,求这2个球出自1号盒子的概率;
(2)如果从两个盒子中摸出3个球,其中从1号盒子摸1个球,从2号盒子摸两个球,规定摸到红球得2分,摸到白球得1分,用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
您最近一年使用:0次
名校
解题方法
7 . 已知曲线.
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3da570b85be54e1194ca485d4751abfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed983f366396f988a3090fbf14ce696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1642eec556eb252de9c1ab7bb5ca90b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
①试问是否为定值?若是,求出该定值;若不是,请说明理由.
②若直线与
轴分别交于点
,证明:
.
您最近一年使用:0次
8 . 若无穷数列满足
,则称数列
为
数列,若
数列
同时满足
,则称数列
为
数列.
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b12e5ecd81639f10f291240e384ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8b5274263f066a66515cca40ca6af24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a24dc73f12d72a1a01e693f7f11814c.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8321dab9d32a7adeb315561309d1d8cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd7db94da6a1d4a0b1ee0cac227e4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4acfdca1f3bb06d2b56b57339eabef5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
您最近一年使用:0次
名校
解题方法
9 . 若各项为正的无穷数列
满足:对于
,
,其中
为非零常数,则称数列
为
数列.记
.
(1)判断无穷数列
和
是否是
数列,并说明理由;
(2)若
是
数列,证明:数列
中存在小于1的项;
(3)若
是
数列,证明:存在正整数
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f8365233f341451598eb50525a1557a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/782fdf6345302a3d8814acf96f6b3acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5653b60d16ec4e653518f0562680250.png)
(1)判断无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93068e5f0dedec981ec828ffa4458c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4b5779873cb3f4366dbfdb983dec81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446e8a7985d4d3dd95c70dc4aad67861.png)
您最近一年使用:0次
2024-01-04更新
|
1520次组卷
|
3卷引用:广西南宁市第二中学2023-2024学年高二下学期开学考试数学试卷
名校
10 . 设
是定义在
上的函数,若存在区间
和
,使得
在
上严格减,在
上严格增,则称
为“含谷函数”,
为“谷点”,
称为
的一个“含谷区间”.
(1)判断下列函数中,哪些是含谷函数?若是,请指出谷点;若不是,请说明理由:
(i)
,(ii)
;
(2)已知实数
,
是含谷函数,且
是它的一个含谷区间,求
的取值范围;
(3)设
,
.设函数
是含谷函数,
是它的一个含谷区间,并记
的最大值为
.若
,且
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1486d2ae6c7e7904ab47b909039ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adadc4c82ed03710cb917d552ac6e1c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd33dd2e1b404daf7c1cbbf147ab7f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)判断下列函数中,哪些是含谷函数?若是,请指出谷点;若不是,请说明理由:
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65ecb5b1f957213346a78a229314e73f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2323ed90e5321507ae65763db9594b9.png)
(2)已知实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2739d1d7a587d0a327c5b75fcaba9d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7242b2ab643f9470da77e29d043b893.png)
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5卷引用:广西南宁市第二中学2023-2024学年高三下学期5月月考数学试题
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