1 . 如图,在四面体
中,
平面
,
,点
为
上一点,且
,连接
.
.
(2)求点
到平面
的距离;
(3)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34b7f2f1f988d3c64932006f1ace80c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c90da0cd2708481057fe19acebf2ec7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeef1db30212433062b3297569a7aafd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c19575ff7d42ffcccaba961deb5ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33fd089cdee8bb2aaa65a4cd2597398d.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17c5ef850e256c98ca4f033999e61311.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a8e0c5bcf2d86726cd9f561b8ff5fe.png)
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2卷引用:广西来宾市忻城县高级中学2023-2024学年高一下学期5月月考数学试卷
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2 . 忻城县环境优美,准备在泮水生态公园建造一个四边形的露营基地,如图
所示.为考虑露营客人娱乐休闲的需求,在四边形
区域中,将三角形
区域设立成花卉观赏区,三角形
区域设立成烧烤区,边
修建观赏步道,边
修建隔离防护栏,其中
米,
米,
.
米,求烧烤区的面积?
(2)考虑到烧烤区的安全性,在规划四边形
区域时,首先保证烧烤区的占地面积最大,再使得花卉观赏区的面积尽可能大,则应如何设计隔离防护栏以及观赏步道?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b589ca985b32e60ea2e39fe58d4ac9d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2dcf2debb4c733c88061662bd22a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68e7cdc183f6e2f163aa1e4caeb485e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c3a1f1a37e69b2dc06bf0affd58f22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bbabd6229d1bbd4736b776b2e111318.png)
(2)考虑到烧烤区的安全性,在规划四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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3 . 忻城县高级中学有1100名高一学生,1000名高二学生,1200名高三学生,高一数学兴趣小组欲采用分层抽样的方法在全校抽取33名学生进行某项调查,则下列说法正确的是( )
A.高三每一个学生被抽到的概率最大 | B.高三每一个学生被抽到的概率最小 |
C.高一每一个学生被抽到的概率最大 | D.每位学生被抽到的概率相等 |
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4 . 若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aa549c975f7596748b32b6160368bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e0aeeb125cfb42e33094594d4381f5.png)
A.1 | B.![]() | C.![]() | D.3 |
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2024-06-11更新
|
448次组卷
|
3卷引用:广西来宾市忻城县高级中学2023-2024学年高一下学期5月月考数学试卷
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解题方法
5 . 记
的内角
的对边分别为
,已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c32540dd35e216215b44ce3e03d8368.png)
(1)试判断
的形状;
(2)若
,求
周长的最大值.
![](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/8c32540dd35e216215b44ce3e03d8368.png)
(1)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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5卷引用:广西来宾市忻城县高级中学2023-2024学年高一下学期5月月考数学试卷
6 . 某艺术吊灯如图1所示,图2是其几何结构图.底座
是边长为
的正方形,垂直于底座且长度为6的四根吊挂线
,
,
,
一头连着底座端点,另一头都连在球
的表面上(底座厚度忽略不计),若该艺术吊灯总高度为14,则球
的体积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:广西来宾市忻城县高级中学2023-2024学年高一下学期5月月考数学试卷
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解题方法
7 .
的内角
,
,
的对边分别为
,
,
,
为
平分线,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734e4bdd3d2a5d489dd863b17687e61.png)
;
(2)若
,
上存在点
,使得
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734e4bdd3d2a5d489dd863b17687e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0b5b7c4ecfb428a6a7bb52fbcdcaba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab268845d3dbdbc9ef05e8b721e59c16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907a78dce0556d07572d9fd12112ca9a.png)
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解题方法
8 . 设
、
、
为非零向量,若
,则
的最大值与最小值的差为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7328473182f501a7d331662c02f7ddb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9963fe377bb415d71d1fe599eee188ce.png)
A.0 | B.1 | C.2 | D.3 |
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9 . 已知
,且
,记随机变量X为x,y,z中的最小值,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223770da09feb2fc824764188e924d7e.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960430a95fa214ab71f3bab114c22080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb603414e6b47ce46dbbcd3f955a424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223770da09feb2fc824764188e924d7e.png)
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10 . 机械学家莱洛发现的莱洛三角形给人以对称的美感.莱洛三角形的画法:先画等边三角形ABC,再分别以点A,B,C为圆心,线段AB长为半径画圆弧,便得到莱洛三角形.若线段AB长为1,则莱洛三角形的周长是( )
A.![]() | B.![]() | C.![]() | D.![]() |
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