解题方法
1 . 如图,在平面四边形
中,
为正三角形,设
的中点为
.
![](https://img.xkw.com/dksih/QBM/2023/12/29/3399731396272128/3399821954179072/STEM/97dd858fe2844991b8c68ba314f47da2.png?resizew=138)
(1)求证:
的面积为定值,并求出该值;
(2)求
的正切值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fc779c4d22f15d835b51b2277c94e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/2023/12/29/3399731396272128/3399821954179072/STEM/97dd858fe2844991b8c68ba314f47da2.png?resizew=138)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2281cb6df0c3c518ce5ed19a02b57e.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76bc8e50eeccced1d7f3bc52e09a7d03.png)
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2 . 设集合
,
的所有子集构成的集合记为集合
,则集合
的非空真子集一共有__________ 个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78a96152c480ec21462f47f3728ed0e.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/7f9e8449aad35c5d840a3395ea86df6d.png)
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3 . 若直线
与函数
的图像交于
两点,且
中点的坐标为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2776f2aca0d2a9e2b6875d1c93ed5cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dda1d7b3982b398ffa32f3dbfdfe787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
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解题方法
4 . 已知三棱锥
的三条侧棱两两垂直,且
,则该三棱锥的内切球的半径为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a94d59dee2d5a8f0425b64b2083825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/341cbaa8d3149beaaf75487ab7f5e734.png)
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5 . ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18430f9877b7e142b9de481824cb29da.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18430f9877b7e142b9de481824cb29da.png)
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解题方法
6 . 设实数
,函数
.
(1)若
的最小正周期是
,求
在
上的最大值与最小值;
(2)若
在
上有且仅有2个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eaa6cbe72e34aab6c31a1f651a51397.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad1dfb10a0ad4195a890223f40a2147.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137d6a66a015ddd2a8076f35ed191927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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2023-12-29更新
|
981次组卷
|
2卷引用:广东省佛山市顺德区2020-2021学年高一下学期竞赛数学试题
解题方法
7 . 如图,在正方体
中,
分别为棱
的中点.
的截面.(只需写出作图过程,不用证明)
(2)请求出截面分正方体上下两部分的体积之比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ae536809b1161fd4e83fdc7f42be96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/548d64146122e344b7d30bf0dbedb374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba446c8c4a5f93fa23dc21acd4cb1920.png)
(2)请求出截面分正方体上下两部分的体积之比.
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解题方法
8 . 设复数
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e0aeeb125cfb42e33094594d4381f5.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e54e87a90b22379756ce056697726bf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e0aeeb125cfb42e33094594d4381f5.png)
您最近一年使用:0次
2023-12-29更新
|
637次组卷
|
6卷引用:广东省佛山市顺德区2020-2021学年高一下学期竞赛数学试题
广东省佛山市顺德区2020-2021学年高一下学期竞赛数学试题(已下线)专题06 复数的四则运算(六大考点)-【寒假自学课】(人教A版2019)(已下线)第七章:复数-高一数学同步精品课堂(人教A版2019必修第二册)(已下线)第02讲 复数的四则运算-《知识解读·题型专练》(人教A版2019必修第二册)云南省昭通市水富市第一中学等三校联考2023-2024学年高二下学期开学考试数学试卷(已下线)第七章 复数(知识归纳+题型突破)-单元速记·巧练(人教A版2019必修第二册)
解题方法
9 . 已知
中,
分别为边
上的点,且
,
.
与
的交点为
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5266f8ab2016b96ddaef54c0e9e2e0bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21370b099839b61e81cd4cf7ef7e3818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bea3ed0cfe4b0bb079c98d1dd26dad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
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10 . 在一个圆心角为
,半径为1米的扇形铁板中按如图方式截出一块矩形,则该矩形的面积的最大值为__________ 平方米.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/35775a7c-ce74-4f0e-ac92-5dd210550021.png?resizew=141)
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