1 . 有两个相同的直三棱柱,高为
,底面三角形的三边长分别为
,
,
,用它们拼成一个三棱柱或四棱柱,在所有可能的情形中,全面积最小的是一个三棱柱,则
的取值范围是__ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbfe017e21d1a4e5cf7b1fbf44fcc0ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9878a063abcb6098d10560f2bf2d4b71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d2a7b13d95229e2e938514739054541.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/182841875763d3ce72c6ad0bc7183869.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-02-28更新
|
1354次组卷
|
17卷引用:2005年普通高等学校招生考试数学(文)试题(上海卷)
2005年普通高等学校招生考试数学(文)试题(上海卷)2005年普通高等学校招生考试数学(理)试题(上海卷)(已下线)2014-2015学年浙江省嘉兴市一中高二上学期第一次阶段测试数学试卷上海市曹杨第二中学2018-2019学年高二上学期期末复习试卷1数学试题上海市金山区亭林中学2020-2021学年高二下学期期末数学试题沪教版(2020) 必修第三册 新课改一课一练 期中测试A上海市崇明区2021-2022学年高二上学期期末数学试题上海市第六十中学2021-2022学年高二上学期期中数学试题上海市向明中学2021-2022学年高二上学期期中数学试题(已下线)第23练 几何体的体积与表面积(已下线)上海高二下学期期末真题精选(压轴60题35个考点专练)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)山东省菏泽市定陶区明德学校(山大附中实验学校)2022-2023学年高一(创新部)下学期6月月考数学试题(已下线)11.1 柱体(第2课时)(五大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)(已下线)期中真题必刷压轴50题专练-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)上海市闵行(文琦)中学2023-2024学年高二下学期3月月考数学试题(已下线)8.3简单几何体的表面积与体积【第三课】“上好三节课,做好三套题“高中数学素养晋级之路(已下线)8.3.1 棱柱、棱锥、棱台的表面积和体积-同步精品课堂(人教A版2019必修第二册)
真题
解题方法
2 . 已知函数
,
.
(1)证明:当
时,
在
上是增函数;
(2)对于给定的闭区间
,试说明存在实数k,当
时,
在闭区间
上是减函数;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3c267c46b3e503a97cf11a08cd5cd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0dc3a93128cc0bbf6d36e42e2eff454.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f19bb8718ccb46af2fe8aa22759d69a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(2)对于给定的闭区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4318dc1a6f86b65714ac6b762de0a4b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a3275978bc2d7766a62f96ae4fdccbe.png)
您最近一年使用:0次
真题
3 . 设函数
(
,且
,
)
(1)当
时,求
的展开式中二项式系数最大的项;
(2)对任意的实数
,证明
(
是
的导函数);
(3)是否存在
,使得
恒成立?若存在,试证明你的结论并求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f69438543e3a9928c1f2295262f6579c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e468312d09c6563c9094b710a35a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54c50fb5615e36df436d747356b00d78.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39cc033406da2cdd342308972c6701f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f71935797074e889f15a62ac370a9c1.png)
(2)对任意的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a0ffe57e983469b590914f5ce06d88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c38f3baf9a34265fbdb5c65dd1664d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b5fb0bc5207a915464ef8a5f40f5e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
4 . 已知函数
,设曲线
在点
处的切线与x轴的交点为
,其中
为正实数.
(1)用
表示
;
(2)求证:对一切正整数n,
的充要条件是
;
(3)若
,记
证明数列
成等比数列,并求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7b0deaff280ebbee0f91be5acd20d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641fec779880f75fa8ee6782f3350402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edeb4aa8a3ca0261e0161fd7fa8bde97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3002f56900c2924bfd79fc3865b0a02e.png)
(2)求证:对一切正整数n,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0b3c80e774501722f46f97800f1d400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3fd5fd833041ae95d8b7f8d2897e35.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4223bd6ee8f82d59d244371fbcddc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dfe65f891c54780bcf1ed6a9f8a0f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
您最近一年使用:0次
2022-11-23更新
|
1068次组卷
|
3卷引用:2007年普通高等学校招生考试数学(理)试题(四川卷)
真题
5 . 已知正方形
,E、F分别是边
的中点,将
沿
折起,如图所示,记二面角
的大小为
.
平面
;
(2)若
为正三角形,试判断点A在平面
内的射影G是否在直线
上,证明你的结论,并求角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28d2790a97390935125aa897417f970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e231505648333857565accb0c3c898.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/798cdca7d20743e0197fe422f09fcbfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8ccd4181f956f6e0140bf0ab8f0716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
您最近一年使用:0次
2022-11-23更新
|
1602次组卷
|
6卷引用:2006 年普通高等学校招生考试数学(文)试题(辽宁卷)
2006 年普通高等学校招生考试数学(文)试题(辽宁卷)2006 年普通高等学校招生考试数学(理)试题(辽宁卷)(已下线)专题46 空间向量与立体几何大题解题模板-2021年高考一轮数学(理)单元复习一遍过(已下线)专题17 空间向量与立体几何大题专项练习(已下线)第四章 立体几何解题通法 专题四 投影变换法 微点1 投影变换法(一)【培优版】(已下线)8.5.2 直线与平面平行【第三课】“上好三节课,做好三套题“高中数学素养晋级之路
真题
解题方法
6 . 已知函数
.设数列
满足
,
,数列
满足
,
.
(1)用数学归纳法证明:
;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cc3b27e71b72f2b49753a222d7c4b96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cfb19f0c37a72b33083ae9319f11a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6edd52cb8d2c6a209590b59c61de68d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af75c5fc07fdedd4f3399413f7c4c44e.png)
(1)用数学归纳法证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b431dd05fdb0a36bbb29c8f1959b9ea.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2e4bf053d2425d369f7c6d1cf78a68.png)
您最近一年使用:0次
7 . 已知中心在原点的双曲线
的一个焦点是
,一条渐近线的方程是
.
(1)求双曲线
的方程;
(2)若以
为斜率的直线
与双曲线
相交于两个不同的点M,N,线段MN的垂直平分线与两坐标轴围成的三角形的面积为
,求k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ef1ff0b6addca3494d762c7602c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86100c8c8396373d55cd05c08452a00e.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bcb166b53a49e393871bcb14a528792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac3d9e689f2f9c38e8fd2385e68479a.png)
您最近一年使用:0次
2022-11-13更新
|
1326次组卷
|
2卷引用:2008年普通高等学校招生考试数学(理)试题(天津卷)
真题
8 . 已知数列
(n是正整数),与数列
(n是正整数).记
.
(1)若
,求r的值;
(2)求证:当n是正整数时,
;
(3)已知
,且存在正整数m,使得在
中有4项为100,求r的值,并指出哪4项为100.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d19a154d898e9a75558de47eda6984d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b49b65b373b80ab90ade7ee4e1c63b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b94cc670751592bc9f8ba1371f7f412.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e507b7fdc9a2266d4288f83d646da43.png)
(2)求证:当n是正整数时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b3c97ee691113146a95188a631b1230.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba6b6aa6c3f9faba6b03bc193a6e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c74020889304c77a09413413a7039a2b.png)
您最近一年使用:0次
真题
解题方法
9 . 如图,
和
是平面上的两点,动点P满足:
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/85201825-e007-4a67-94f7-cc8088ce75a6.png?resizew=200)
(1)求点P的轨迹方程;
(2)若
,求点P的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/accf35598ee054f1bf8b6584641d6d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4b2bb30137f92479d11827ee769f001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e74c84de9ea091cc6dbe1e5e1f85c107.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/85201825-e007-4a67-94f7-cc8088ce75a6.png?resizew=200)
(1)求点P的轨迹方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aef3f4dd5f295dd69e7792c28adda7a.png)
您最近一年使用:0次
真题
解题方法
10 . 已知函数
.
(1)若
,则
的定义域是___________ ;
(2)若
在区间
上是减函数,则实数a的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f43b312904eaaed95921a2121468b36a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf87d9d48c3de0a5e9f1a70e51a0bef.png)
您最近一年使用:0次