1 . 如图,已知正四面体
(所有棱长均相等的三棱锥),
,
,
分别为
,
,
上的点,
,
,分别记二面角
,
,
的平面角为
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca51f9403facfb2fe553702acc50124b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c92a3f1f4620002751549491a076c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7903ef9e9a6b57b4eacbe829fd2a0b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dae9c756fd705143ade3af93b9b4595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5fed8a3af71e3aff6124b6a449acdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2 . 已知
,
,
是三个不全相等的实数且满足
则
的值是( )
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8627e8e8d56e652abe5914f7d741b3f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae24688d4c45aad43e9af0b7bbfda6b.png)
A.1 | B.![]() | C.3 | D.6 |
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3 . 已知实数
,定义数列
如下:如果
,
,则
.
(1)求
和
(用
表示);
(2)令
,证明:
;
(3)若
,证明:对于任意正整数
,存在正整数
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a3ac83c571110d41a396d12d8eea1c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/313b65380c90e925512cf9ffa1d35623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d911bd308c26935e73225bdaa649d136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc488132d003f78ebd89c50cd5aef63a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd71bc7e6668f90f259ad0b06dd60c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7da2f386b78cdf6489efaa2f5820d3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bb119ab040107b705247d6f56d7dfa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b6423d848b3b786d6ccf0f2db220a9c.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bee2fbffbc3c3e9b40046faf9e25ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/023ceb03fb474641869492f3388a2aff.png)
您最近一年使用:0次
2024-03-31更新
|
1812次组卷
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4卷引用:辽宁省部分名校2023-2024学年高二下学期5月质检数学试题
辽宁省部分名校2023-2024学年高二下学期5月质检数学试题浙江省9+1联盟2023-2024学年高三下学期3月高考模拟数学试卷(已下线)第18题 数列新题型(高三二轮每日一题)(已下线)压轴题05数列压轴题15题型汇总-1
名校
解题方法
4 . “布朗运动”是指微小颗粒永不停息的无规则随机运动,在如图所示的试验容器中,容器由三个仓组成,某粒子作布朗运动时每次会从所在仓的通道口中随机选择一个到达相邻仓或者容器外,一旦粒子到达容器外就会被外部捕获装置所捕获,此时试验结束.已知该粒子初始位置在1号仓,则试验结束时该粒子是从1号仓到达容器外的概率为__________ .
您最近一年使用:0次
2024-02-29更新
|
4651次组卷
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12卷引用:辽宁省部分名校2023-2024学年高二下学期5月质检数学试题
辽宁省部分名校2023-2024学年高二下学期5月质检数学试题湖北省武汉市2024届高中毕业班二月调研考试数学试题(已下线)7.1.2全概率公式(分层练习,7大题型)-2023-2024学年高二数学同步精品课堂(人教A版2019选择性必修第三册)(已下线)第七章 概率初步(续)(单元重点综合测试)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)浙江省余姚中学2023-2024学年高二下学期3月质量检测试题数学试卷(已下线)第8章 概率单元综合能力测试卷-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第二册)(已下线)8.1 条件概率(七大题型)-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第二册)(已下线)高二下学期期中复习填空题压轴题十五大题型专练-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第三册)单元测试B卷——第七章 随机变量及其分布上海市交通大学附属中学2024届高三5月阶段测试数学试卷山东省菏泽第一中学八一路校区2024届高三下学期开学考试数学试题(已下线)模型1条件概率与全概率公式的应用模型(高中数学模型大归纳)
名校
5 . 半圆形量角器在第一象限内,且与
轴、
轴相切于D、E两点.设量角器直径
,圆心为
,点
为坐标系内一点.下列选项正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() ![]() | B.![]() |
C.![]() | D.若![]() ![]() |
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2023-12-27更新
|
423次组卷
|
2卷引用:辽宁省部分名校2023-2024学年高二下学期5月质检数学试题
6 . 设集合S中有10个元素,从S中每次随机选取1个元素,取出后还放回到S中,则取5次后所取出的元素有重复的概率是(保留两位有效数字)( )
A.0.50 | B.0.55 | C.0.70 | D.前三个答案都不对 |
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2023-07-31更新
|
94次组卷
|
2卷引用:辽宁省部分名校2023-2024学年高二下学期5月质检数学试题
解题方法
7 . 已知函数
满足
,且
,当
时,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918bf429ec528a5a3d8e53d1bf2cd687.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a1f42950f93ffd8c4df289dd8c56b79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b47144278d622b666fcff69aee5abc5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc0e849b72357de1cdf719a7ed5f1bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e47d77aa8a3cff15aaa7e1e893c761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918bf429ec528a5a3d8e53d1bf2cd687.png)
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解题方法
8 . 长方体
的
个顶点都在球
的表面上,
为
的中点,
,
,异面直线
与
所成角的余弦值为
,且四边形
为正方形,则球
的体积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a0268d04b9dea7629af27af9a0285a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/936d42cf8a519c51177bcbed21084783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d4548c32861ade058b139a5b2ec801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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9 . 在①
,②
的面积为
,③
这三个条件中任选一个,补充在下面的问题中,并解答问题.在
中,角
的对边分别为
, ,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5fe8aa9f26bde96eb1df14bfb42e422.png)
的外接圆的半径为4.求
的周长.
注:如果选择多个条件解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347f1001c7ef728ec091358493d3cb59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e7dc603317eb90974c75efec9f02b1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e799b8435fba6f6905895353c4d4e27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5fe8aa9f26bde96eb1df14bfb42e422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823bcda307515dbcbb0d93ba9a1b59a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
注:如果选择多个条件解答,按第一个解答计分.
您最近一年使用:0次
2020-11-15更新
|
663次组卷
|
5卷引用:辽宁省凌源市2020-2021学年下学期高二尖子生抽测数学试题
名校
解题方法
10 . 过抛物线
焦点F的直线l交抛物线于
两点,点P在线段
上运动,原点O关于点P的对称点为M,则四边形
的面积的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de6c989fd224866658230526892e2bcb.png)
A.8 | B.10 | C.14 | D.16 |
您最近一年使用:0次
2020-09-27更新
|
767次组卷
|
6卷引用:辽宁省凌源市2020-2021学年下学期高二尖子生抽测数学试题