名校
解题方法
1 . 如图,已知正方体
顶点处有一质点
,点
每次会随机地沿一条棱向相邻的某个顶点移动,且向每个顶点移动的概率相同,从一个顶点沿一条棱移动到相邻顶点称为移动一次,若质点
的初始位置位于点
处,记点
移动
次后仍在底面
上的概率为
.
;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3612ef4132dfef2f8a4f5af22e89d8.png)
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解题方法
2 . 已知箱中有若干个大小相同的红球和白球,每次抽一个球,若抽到白球,则放回并再次抽球,若抽到红球,则不再抽取.设每次抽到红球的概率为p(
),记X为停止抽球时所抽取的次数,X的数学期望为
.
(1)若最多抽4次,且
,求X的分布列及数学期望;
(2)在成功概率为p(
)的伯努利试验中,记X为首次成功时所需的试验次数,X的取值为所有正整数,此时称离散型随机变量X的概率分布为几何分布.若抽球一直进行下去,则X服从几何分布.
①求恰好第k次抽到红球的概率
;
②求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c11f6c800b8e0410674a0c6d307d26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3baba074e8aeb6f3ea117865bbd1b.png)
(1)若最多抽4次,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09e5a154944cfae71a14d3da122dd08e.png)
(2)在成功概率为p(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c11f6c800b8e0410674a0c6d307d26.png)
①求恰好第k次抽到红球的概率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef133b0fd53a48310a82c18729575abd.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3baba074e8aeb6f3ea117865bbd1b.png)
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3 . 设集合
为
的非空子集,随机变量X,Y分别表示取到子集
中的最大元素和最小元素的数值.
(1)若
的概率为
,求
;
(2)若
,求
且
的概率;
(3)求随机变量
的均值
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a6a4cff8424ced7841221e2d54d95d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6c4b25a0b76fba785d5769c08714b15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ab109ec88d6f3d24b2f01ca77e7038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe08722cf9300fe188dbbb71989c06c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e32a2f594955e456f0fddad1e090bb04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8b3576b4d98a5b4ddc380ddaa0fa281.png)
(3)求随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec9f6ea6346066054b5c722763d6b026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f8506fbcb1fae930e1503065b9327a.png)
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7日内更新
|
82次组卷
|
2卷引用:河南省信阳市新县高级中学2024届高三数学考前仿真冲刺卷
4 . 11分制乒乓球比赛,每赢一球得1分,当某局打成
平后,每球交换发球权,先多得2分的一方获胜,该局比赛结束.甲、乙两位同学进行单打比赛,假设甲发球时甲得分的概率为
,乙发球时甲得分的概率为
,各球的比赛结果相互独立.在某局比赛双方打成
平后,甲先发球.
(1)求再打2球该局比赛结束的概率;
(2)两人又打了
个球该局比赛结束,求
的数学期望
;
(3)若将规则改为“打成
平后,每球交换发球权,先连得两分者获胜”,求该局比赛甲获胜的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3c3ffbae2f4ed36909dca6aecbad18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3c3ffbae2f4ed36909dca6aecbad18.png)
(1)求再打2球该局比赛结束的概率;
(2)两人又打了
![](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/5bf3baba074e8aeb6f3ea117865bbd1b.png)
(3)若将规则改为“打成
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3c3ffbae2f4ed36909dca6aecbad18.png)
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5 . 一质点在平面内每次只能向左或向右跳动1个单位,且第1次向左跳动.若前一次向左跳动,则后一次向左跳动的概率为
;若前一次向右跳动,则后一次向左跳动的概率为
.记第n次向左跳动的概率为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e948956b4ef1bb5fa3c09fbda213dee.png)
________ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f11c04103c0e5416897894d9225637b2.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffb021aa7d5a5c2f0691e337caad624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e948956b4ef1bb5fa3c09fbda213dee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f11c04103c0e5416897894d9225637b2.png)
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6 . 点列,就是将点的坐标按照一定关系进行排列.过曲线C:
上的点
作曲线C的切线
与曲线C交于
,过点
作曲线C的切线
与曲线C交于点
,依此类推,可得到点列:
,
,
,…,
,…,已知
.
(1)求数列
、
的通项公式;
(2)记点
到直线
(即直线
)的距离为
,求证:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c904567c3b3734e1eca8d042ef7a7b2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec391f08f1452fb3e0aebe7e12ba4fb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3a4422395ca20fe847419ec569e48b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eddbde5d269189fced4cc478908a6866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec391f08f1452fb3e0aebe7e12ba4fb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3a4422395ca20fe847419ec569e48b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eddbde5d269189fced4cc478908a6866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9979465ce76b8582067703b39a0bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36460040ddea4761eee10d537b14a1f6.png)
(2)记点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a5b0f908cdae073db61be5b42fbcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93f04dcabdafec74f98f4a1f4faa3fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db2da4189bf5f95ae10e6b96ee4b72e.png)
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7 . 复数
的虚部是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82d2c2dfbb02fb57313e60f3a664c6b.png)
A.1012 | B.1011 | C.![]() | D.![]() |
您最近一年使用:0次
2024-06-10更新
|
420次组卷
|
3卷引用:重庆市乌江新高考协作体2023-2024学年高二下学期第二阶段性学业质量联合调研抽测(5月)数学试题
解题方法
8 . 已知等差数列
的公差为
,数列
与数列
满足
且
.
(1)求数列
与
的通项公式;
(2)求数列
的前
项和
与数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d4886610370087259028de8f061c66c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e041e235335092ff4047a25eeb98a8.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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名校
解题方法
9 . 已知数列
为等差数列,其首项为1,公差为2,数列
为等比数列,其首项为1,公比为2,设
,
为数列
的前
项和,则当
时,
的最大值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/000f01319364c59dee948848fc4de4c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1242bce7122127c9c1ba38eab216215f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.9 | B.10 | C.11 | D.12 |
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