名校
解题方法
1 .
年九省联考后很多省份宣布高考数学采用新的结构,多选题由
道减少到
道,分值变为一题
分,多选题每个小题给出的四个选项中有两项或三项是正确的,全部选对得
分,有错选或全不选的得
分
若正确答案是“两项”的,则选对
个得
分
若正确答案是“三项”的,则选对
个得
分,选对
个得
分
某数学兴趣小组研究答案规律发现,多选题正确答案是两个选项的概率为
,正确答案是三个选项的概率为
其中
.
(1)在一次模拟考试中,学生甲对某个多选题完全不会,决定随机选择一个选项,若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
,求学生甲该题得
分的概率![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e1d918e7fb74176679d526cdfc8fa16.png)
(2)针对某道多选题,学生甲完全不会,此时他有三种答题方案:
Ⅰ
随机选一个选项
Ⅱ
随机选两个选项
Ⅲ
随机选三个选项.
若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
,且学生甲选择方案Ⅰ,求本题得分的数学期望![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e1d918e7fb74176679d526cdfc8fa16.png)
以本题得分的数学期望为决策依据,
的取值在什么范围内唯独选择方案Ⅰ最好
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0474a66dcdf88bde5beabc5adbd58402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e1d918e7fb74176679d526cdfc8fa16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a15a5ae975912f37b876cbf8c546fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c27aefc2917776f72f95c675b638d20.png)
(1)在一次模拟考试中,学生甲对某个多选题完全不会,决定随机选择一个选项,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e1d918e7fb74176679d526cdfc8fa16.png)
(2)针对某道多选题,学生甲完全不会,此时他有三种答题方案:
Ⅰ
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3493090ac9f2ba0670c837f08154da0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e1d918e7fb74176679d526cdfc8fa16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3493090ac9f2ba0670c837f08154da0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e1d918e7fb74176679d526cdfc8fa16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3493090ac9f2ba0670c837f08154da0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3067f0f3fe2606168b402a956e73d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e1d918e7fb74176679d526cdfc8fa16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1756e209e9538fc4348d9cab8caac438.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82bbee662e242611afdbdae4b8a36a7c.png)
您最近一年使用:0次
今日更新
|
982次组卷
|
6卷引用:江西省宜春市樟树中学2024届高三下学期高考数学仿真模拟试卷
江西省宜春市樟树中学2024届高三下学期高考数学仿真模拟试卷福建省南安市侨光中学2023-2024学年高二下学期第2次阶段考试(5月月考)数学试题重庆市求精中学校2023-2024学年高二下学期第二阶段考试数学试题(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)山东省淄博实验中学2023-2024学年高二下学期第二次诊断考试(6月月考)数学试题山东省淄博市张店区淄博实验中学2023-2024学年高二下学期6月月考数学试题
解题方法
2 . 如图是一个各棱长均为1米的正四棱锥
,现有一只电子蛐蛐在棱上爬行,每次从一个顶点开始,等可能地沿棱爬到相邻顶点,已知电子蛐蛐初始从顶点
出发,再次回到顶点
时停止爬行.
的概率;
(2)在电子蛐蛐停止爬行时爬行长度不超过4米的条件下,记爬行长度为
,求
的分布列及其数学期望
;
(3)设电子蛐蛐爬行
米后恰好停止爬行(首次回到顶点
)的概率记为
,求
(用
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(2)在电子蛐蛐停止爬行时爬行长度不超过4米的条件下,记爬行长度为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0f9be682a12c517e6f1e293d94eb1cb.png)
(3)设电子蛐蛐爬行
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e3273deabbf8c7d700d340b71ca2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
3 . 为提高学生对航天科技的兴趣,培养学生良好的科学素养,某学校组织学生参加航天科普知识挑战赛,比赛共设置A,B,C三个问题,规则如下:①每位参加者计分器的初始分均为50分,答对问题A,B,C分别加10分,20分,30分,答错任一题减10分;②每回答一题,计分器显示累计分数,当累计分数小于40分或答完三题时累计分数不足80分,答题结束,挑战失败;当累计分数大于或等于80分时,答题结束,挑战成功;③每位参加者按问题A,B,C顺序作答,直至挑战结束.设甲同学能正确回答出问题A,B,C的概率分别为
,
,
,且回答各题正确与否互不影响.
(1)求甲同学挑战成功的概率;
(2)用X表示甲同学答题结束时答对问题的个数,求X的分布列和数学期望
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7294f5ae2a24ff42e84cd9773b2a7287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求甲同学挑战成功的概率;
(2)用X表示甲同学答题结束时答对问题的个数,求X的分布列和数学期望
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3baba074e8aeb6f3ea117865bbd1b.png)
您最近一年使用:0次
名校
4 . 如图,在四棱锥
中,四边形
为正方形,
平面
,且
.E,F分别是PA,PD的中点,平面
与PB,PC分别交于M,N两点.
;
(2)若平面
平面
,求平面
与平面
所成锐二面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f4248e8021130ab60365e3d2e9a694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d685b2138e6499686474bb2d131a2234.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6330fd7da754a65cc0328dfdba3169f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f4248e8021130ab60365e3d2e9a694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
5 . 我市开展了“暖冬计划”活动,为高海拔地区学校加装供暖器.按供暖器的达标规定:学校供暖器的噪声不能超过50分贝、热效率不能低于
某地采购了一批符合达标要求的供暖器,经抽样检测,这批供暖器的噪声
单位:分贝
和热效率的频率分布直方图如图所示:
(1)求a,b的值;
(2)如果供暖器的噪声与热效率是独立的,从这批供暖器中随机抽2件,求恰有1件噪声不超过25分贝且热效率不低于
的概率;
(3)当
,设供暖器的噪声不超过
(分贝)的概率为
,供暖器的热效率不低于
的概率为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238e94eef445570873d15db2d04d1782.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
(1)求a,b的值;
(2)如果供暖器的噪声与热效率是独立的,从这批供暖器中随机抽2件,求恰有1件噪声不超过25分贝且热效率不低于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c4bf61e073c899494b2fb3b767b108.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13620684da9724432d33a2489c63bedb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b30c7c297a88106f7380440c113f7a91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be646cd52d7f2f1714e7542e75810f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cf7b4e54130938f457d00a45977586e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adad9633b73dfbbb3d84b4f15979e99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca4b2f545d6cfd6764ad19c7bc2c2f8.png)
您最近一年使用:0次
6 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc80f38b6d55c82cabe23189b34bd1c9.png)
(1)当
时,求
在点
处的切线方程;
(2)若
在区间
上单调递增,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc80f38b6d55c82cabe23189b34bd1c9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
您最近一年使用:0次
7 . 已知函数
的最小正周期为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
(1)求函数
的单调递增区间;
(2)已知
的三边长分别为a,b,c,其所对应的角为A,B,C,且
,
,
,求该三角形的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f7a080cc7738a3c11acbc19fecd9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95f2d59590aa4817f957ccf6dc23f4d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/468aa4abb9d9f7c3617068fc1cfd6f08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1225fd03e8e8730dac8487dae5387635.png)
您最近一年使用:0次
名校
8 . 已知函数
,
是函数
的一个极值点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9c1fce9fa39cabf241d72fee10dd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
A.![]() | B.函数![]() ![]() |
C.过点![]() ![]() | D.函数![]() |
您最近一年使用:0次
9 . 已知随机变量
,若
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b8d5cafb2d0e7708747735454aa7cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e548813dce120689b9b962b7260128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42ad7282e8eeeb70fb4ffb07ebc6a4fd.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
10 . 已知函数
的极值点为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd328b299019b8427c74c39bac0235a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdbc03249f9d6d092d0e4fa59fc65ad0.png)
A.![]() | B.2 | C.![]() | D.1 |
您最近一年使用:0次