解题方法
1 . 已知正方体
,
分别是边
上(含端点)的点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1405380585b52d7fc8640f179cceec9.png)
A.当![]() ![]() |
B.当![]() ![]() |
C.当![]() ![]() ![]() |
D.当平面![]() ![]() ![]() |
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解题方法
2 . 设
均为单位向量,且
可按一定顺序成等比数列,写出一个符合条件的
的值_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8002bd93f0d69a81ed5564c10d44571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854e16eb319ee454088f5b527cf6c4d5.png)
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3 . 复数
满足
,复数
,若
在复平面上对应的点在第四象限,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed98359cf005d2b49ec68f55d1f87c6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0417be0e1cfafb231b652e20221eecef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4822de5a98d756d98fad5feff9343dc1.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
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解题方法
4 . 某批农产品的质量(单位:千克)服从正态分布,且其中质量大于0.7的数量等于质量小于0.4的数量,则下列四部分中( )
A.质量小于0.4的农产品数量最多 | B.质量大于1.09的农产品数量最多 |
C.质量大于0.7的农产品数量最多 | D.质量小于0.55的农产品数量最多 |
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5 . 指示函数是一个重要的数学函数,通常用来表示某个条件的成立情况.已知
为全集且元素个数有限,对于
的任意一个子集
,定义集合
的指示函数
若
,则( )
注:
表示
中所有元素
所对应的函数值
之和(其中
是
定义域的子集).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.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/c37959331f824e0153871d62a13cb30e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85325300b6ce106910cc9e758b56e6b.png)
注:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2059b60ca47a69612f16e1a3f63d8cf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
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2024-04-18更新
|
1199次组卷
|
3卷引用:福建省安溪第八中学2024届高三下学期5月份质量检测数学试题
名校
解题方法
6 . 4月19日是中国传统二十四节气之一的“谷雨”,联合国将这天定为“联合国中文日”,以纪念“中华文字始祖”仓颉[jié]造字的贡献,旨在庆祝多种语言以及文化多样性,促进联合国六种官方语言平等使用.某大学面向在校留学生举办中文知识竞赛,每位留学生随机抽取问题并依次作答,其中每个问题的回答相互独立.若答对一题记2分,答错一题记1分,已知甲留学生答对每个问题的概率为
,答错的概率为
.
(1)甲留学生随机抽取
题,记总得分为
,求
的分布列与数学期望;
(2)(ⅰ)若甲留学生随机抽取
道题,记总得分恰为
分的概率为
,求数列
的前
项和;
(ⅱ)记甲留学生已答过的题累计得分恰为
分的概率为
,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
(1)甲留学生随机抽取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)(ⅰ)若甲留学生随机抽取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad491e5b5e14c49ef8b7004ebcfcef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fb9b392b1c516e66242727dd9c055f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/539e3e51e18372f6f4dd743e1f006cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(ⅱ)记甲留学生已答过的题累计得分恰为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21c72eb6ab46e9f3ffe71cdf050e5666.png)
您最近一年使用:0次
2024-04-11更新
|
772次组卷
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2卷引用:福建省泉州第五中学2024届高三下学期适应性监测(一)数学试题
名校
解题方法
7 . 定义:若对
恒成立,则称数列
为“上凸数列”.
(1)若
,判断
是否为“上凸数列”,如果是,给出证明;如果不是,请说明理由.
(2)若
为“上凸数列”,则当
时,
.
(ⅰ)若数列
为
的前
项和,证明:
;
(ⅱ)对于任意正整数序列
(
为常数且
),若
恒成立,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9e587fa47050e45101bbfbfe129fa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3adcc926ce1056eefbad88408820424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48407f815d07eb8b5dfa8d34b724512e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede85acd5056e2907a48131e71c45411.png)
(ⅰ)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](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/0a62e059e03eda6884da213547097ed9.png)
(ⅱ)对于任意正整数序列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6f1287d0218a833f34a97a9db24cef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e988e0b43c5730e1c104004514801d9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c9507d571eb0de009f16f1837579f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2024-04-10更新
|
693次组卷
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4卷引用:福建省漳州市龙文区2024届高三6月模拟预测数学试题
福建省漳州市龙文区2024届高三6月模拟预测数学试题安徽省池州市第一中学2024届高三第一次模拟联合检测数学试题山东师范大学附属中学2024届高三下学期考前适应性测试数学试题(已下线)压轴题05数列压轴题15题型汇总-1
名校
8 . 2023年12月19日至20日,中央农村工作会议在北京召开,习近平主席对“三农”工作作出指示.某地区为响应习近平主席的号召,积极发展特色农业,建设蔬菜大棚.如图所示的七面体
是一个放置在地面上的蔬菜大棚钢架,四边形ABCD是矩形,
m,
m,
m,且ED,CF都垂直于平面ABCD,
m,
,平面
平面ABCD.
(2)求平面BFHG与平面AGHE所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b09030a47bf268b6ea0c341ca76c2358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb8fe3b14007e4be4c99c85e5b9610a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d824078abdd94782c09ccc39ddb539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f43ee6bef36a3a67b497cb2e67f4df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a17980426cd9d489706fdc45b81b9f92.png)
(2)求平面BFHG与平面AGHE所成锐二面角的余弦值.
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2024-04-02更新
|
787次组卷
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4卷引用:福建省安溪第八中学2024届高三下学期5月份质量检测数学试题
解题方法
9 . 在数字通信中,信号是由数字0和1组成的序列,发送每个信号数字之间相互独立.由于随机因素的干扰,发送的信号0或1有可能被错误地接收为1或0.
(1)记发送信号变量为
,接收信号变量为
,且满足
,
,
,求
;
(2)当发送信号0时,接收为0的概率为
,定义随机变量
的“有效值”为
(其中
是
的所有可能的取值,
),发送信号“000”的接收信号为“
”,记
为
,
,
三个数字之和,求
的“有效值”.(
,
)
(1)记发送信号变量为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d1e02a486fb356d9c69702ff770c251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be45d49ded3a7346716f8d1a2280101.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c770b5658e0a1ebbcfd04126b744cca9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3b5f4c0d268103afcf9cf90ab115a6.png)
(2)当发送信号0时,接收为0的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c1116ce7f5a1a7b57517276d5092fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8452ce8ad440b05c39487f58c3bd752a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c1116ce7f5a1a7b57517276d5092fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab46d077ba3d6e13fa1f6a5aaa0ce6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d928f7dfae47fb4e159e01868f6df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9314bd1d7a6e070f4f2428f9a321804e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab1cb23df1e01a5120207dbfb4ae6c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f4d8318aba2dd01bfdc4c6b77c6121.png)
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名校
解题方法
10 . 已知中心在原点、焦点在x轴上的圆锥曲线E的离心率为2,过E的右焦点F作垂直于x轴的直线,该直线被E截得的弦长为6.
(1)求E的方程;
(2)若面积为3的
的三个顶点均在E上,边
过F,边
过原点,求直线
的方程:
(3)已知
,过点
的直线l与E在y轴的右侧交于不同的两点P,Q,l上是否存在点S满足
,且
?若存在,求点S的横坐标的取值范围,若不存在,请说明理由.
(1)求E的方程;
(2)若面积为3的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a29ba49963134a7232fa8574105fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d196dfa1217d0db795705c28eb988c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f25d2d5078ac5925c12ddbbb57eb67d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a137073216d1de26f3923e08614306f9.png)
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2024-03-26更新
|
1137次组卷
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2卷引用:福建省泉州市2024届高三质量监测(三)数学试题