名校
解题方法
1 .
元向量(
)也叫
维向量,是平面向量的推广,设
为正整数,数集
中的
个元素构成的有序组
称为
上的
元向量,其中
为该向量的第
个分量.
元向量通常用希腊字母
等表示,如
上全体
元向量构成的集合记为
.对于
,记
,定义如下运算:加法法则
,模公式
,内积
,设
的夹角为
,则
.
(1)设
,解决下面问题:
①求
;
②设
与
的夹角为
,求
;
(2)对于一个
元向量
,若
,称
为
维信号向量.规定
,已知
个两两垂直的120维信号向量
满足它们的前
个分量都相同,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d617b088816e03a283123e29e4dbdca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086eb439f6a1578fdba904825340772d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efee470d0232b6b37f2fb2ab15aae0ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/948eea3409b959c7248d68a1a081819d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b1e734f151a88ccb702148615db27d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5ab6e54fc0c6b846c8d860860c087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db1cd89b86c99ce96a9336eb3b09c9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6be594c4e8c6693571d71fa7c1951796.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27a7cf91ca4cddeef99e8873ecc6fc37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05932f1afdfa963def3c811591eb62bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d69dab2a6743011b461f62448890316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c21920a0a39b1604e130601f061b056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eab8e66f785800a153d34421b2e5540.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a22804cdf4a90edff02dbb01b7481b.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23c7e4c34891b3435c39f4989470ccf.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac852f327effde190b9ebf3dd08e037c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85f7e488464e41e1a1e1eed427154aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
(2)对于一个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e363087dcbe11e11a9ec545570735c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94fcc44ac04f54d5fcc1a6154b8b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac852f327effde190b9ebf3dd08e037c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2772cf7495c2c4c70086e7d936752d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b3c80a2adf39204ce112bda7115bf40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c8af44e1a8c05007f2137fa2d1907db.png)
您最近一年使用:0次
2024-03-26更新
|
540次组卷
|
5卷引用:山西省大同市第二中学校2023-2024学年高一下学期3月月考数学试题
解题方法
2 . 已知
,若关于x的不等式
的解集是
.
(1)求a的值;
(2)设
,证明函数
在区间
上单调递增.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b48283aac275c3bd3a3f969da2608044.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2687ff35a4e89fc02d8762ab1dc2527e.png)
(1)求a的值;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd96c712e0e2afb3cd70bcbc0a8bfb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab409bb25958c2f01c73e26042c6f51e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ffd6e5f48a6f6463604ed1cc15ac36b.png)
您最近一年使用:0次
解题方法
3 . 如图1,有一个边长为4的正六边形
,将四边形
沿着
翻折到四边形
的位置,连接
,
,形成的多面体
如图2所示.
![](https://img.xkw.com/dksih/QBM/2022/5/26/2987895392780288/2989391084175360/STEM/c6b0f9b5-aef5-4abc-bda7-a2dc2fbc420d.png?resizew=304)
(1)证明:
.
(2)若
,M是线段
上的一个动点(M与C,G不重合),试问四棱锥
与
的体积之和是否为定值?若是,求出这个定值.若不是,请说明理由,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666e9462f20d4004c666654842817476.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e5016c9137ae6cac7d5b83cea41771.png)
![](https://img.xkw.com/dksih/QBM/2022/5/26/2987895392780288/2989391084175360/STEM/c6b0f9b5-aef5-4abc-bda7-a2dc2fbc420d.png?resizew=304)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a72ab9f7f6b1efc684f28e9389b9b2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466fc8155475296b15c37ed5188a47d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4117625867a74cd022584500c76deca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0d3f5c410ccce080ef25e33b11c9d5.png)
您最近一年使用:0次
名校
解题方法
4 . 若方程x2+mx+n=0(m,n∈R)有两个不相等的实数根
,且
.
(1)求证:m2=4n+4;
(2)若m≤-4,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4d57bdb85ad21a427ebc3126fab41ed.png)
(1)求证:m2=4n+4;
(2)若m≤-4,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1453e108c520c1f191668d7609dbd5fb.png)
您最近一年使用:0次
2021-11-19更新
|
297次组卷
|
4卷引用:山西省大同市2021-2022学年高一上学期期中数学试题
名校
5 . (1)试证明差角的余弦公式
:
;
(2)利用公式
推导:
①和角的余弦公式
,正弦公式
,正切公式
;
②倍角公式
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eee3f1c9130daa032e8cca82a339ad03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6276ff5468f5aa9c6eaff479c26cc7.png)
(2)利用公式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eee3f1c9130daa032e8cca82a339ad03.png)
①和角的余弦公式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3af2b192544f360cdaca81ce533b5271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e93f28dbf8ba07ea1f8fa9eece0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc799802966e0e59fcde18dc3140225.png)
②倍角公式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99d609b009b3be1329e305bd3802c4e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d849c83c4696ebf978aa99ced19c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57c9b03f86d4170819bf16623820d050.png)
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6 . 设函数
,若函数
有零点,且与函数
的零点完全相同.
(1)证明:
;
(2)求实数
的取值范围.
附:当
时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641bf261adbbe4ed33009643412666c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9e09e7b66ba97a319abd0b50200ee.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede0efb6e07b969dea99bc464b91a41b.png)
(2)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
附:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ccaa6e503b61e9ae78d8439cba2e328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2d3b81e294d777012c2fb9fb9f74fed.png)
您最近一年使用:0次
2022-02-14更新
|
314次组卷
|
2卷引用:山西省名校2021-2022学年高一上学期期末数学试题