真题
解题方法
1 . 已知
,
,其中
,设
,
.
(1)写出
;
(2)证明:对任意的
,恒有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0201063518911954b565c33f4e6922b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ef9a5c965598ea0f492ade8bf01f85c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dbc206aad9e1a0edfb2504e513d3a9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1497c9cb334ca9a1d7b817abb8034735.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f0ca536621ec8db02707ba65917029.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6645a5979b3436efdf7d76210d060b7.png)
(2)证明:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05adfa1f46f8d2eb486991e61b727f27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9653a00340ce6cfb8d273cc36b1c01d8.png)
您最近一年使用:0次
真题
2 . 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
|
1612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
3 . 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
解题方法
4 . 如图,在棱长为1的正方体
中,
,截面
,截面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/e833ef3a-fc93-4942-a35a-ee78b5819b83.png?resizew=158)
(1)证明:平面
和平面
互相垂直;
(2)证明:截面
和截面
面积之和是定值,并求出这个值;
(3)若
与平面
所成的角为
,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e720d4370f3b33ce080af9823c2a6f3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75ef43979ba61665c72085f9ad8cb25a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39695b69fea8beeecc3c6cfce00fbcb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/e833ef3a-fc93-4942-a35a-ee78b5819b83.png?resizew=158)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3534df651f0a681bc905795b26833107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856c8fca99cfb17d4ac1e84a9a6f0f15.png)
(2)证明:截面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3534df651f0a681bc905795b26833107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856c8fca99cfb17d4ac1e84a9a6f0f15.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f611f5bb08a66cae8fe411e59a1c08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3534df651f0a681bc905795b26833107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f611f5bb08a66cae8fe411e59a1c08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856c8fca99cfb17d4ac1e84a9a6f0f15.png)
您最近一年使用:0次
真题
解题方法
5 . 设
为常数,且
.
(1)证明对任意
;
(2)假设对任意
,有
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c6ad6e390596d22fb7e13402067d0c8.png)
(1)证明对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/376e07b940161b91bc48d2d9984af567.png)
(2)假设对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd3e65f0f4bf3e5fb6570df7fb60510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
您最近一年使用:0次
2022-11-09更新
|
756次组卷
|
4卷引用:2003 年普通高等学校招生考试数学试题(辽宁卷)
2003 年普通高等学校招生考试数学试题(辽宁卷)2003 年普通高等学校招生考试数学试题(广东卷)2003 年普通高等学校招生考试数学(理)试题(天津卷)(已下线)专题1 数列的单调性 微点9 数列单调性的判断方法(九)——数列单调性的应用
6 . 已知正四棱柱
,E为
中点,F为
中点.
为
与
的公垂线;
(2)求点
到面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35435fa442f3474e7d312c2360b28fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
您最近一年使用:0次
2022-11-09更新
|
926次组卷
|
8卷引用:2003 年普通高等学校招生考试数学试题(辽宁卷)
2003 年普通高等学校招生考试数学试题(辽宁卷)2003 年普通高等学校招生考试数学试题(广东卷)2003 年普通高等学校招生考试数学(文)试题(全国卷)2003 年普通高等学校招生考试数学(文)试题(天津卷)内蒙古包头市第四中学2022-2023学年高二上学期期末考试数学(理)试题(已下线)考点11 空间距离 2024届高考数学考点总动员 【讲】广东省汕头市潮阳黄图盛中学2023-2024学年高二上学期期中数学试题(已下线)第33题 空间距离解法笃定,向量方法建系第一(优质好题一题多解)
真题
解题方法
7 . 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
真题
解题方法
8 . 函数y=f(x)在区间(0,+∞)内可导,导函数
是减函数,且
.设x0∈(0,+∞),
是曲线y=f(x)在点(x0,f(x0))的切线方程,并设函数
.
(1)用
表示m;
(2)证明:当x0∈(0,+∞)时,
;
(3)若关于x的不等式
在[0,+∞)上恒成立,其中a,b为实数,求b的取值范围及a与b所满足的关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e808873b814cf720131eeed83e88bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0195b09df4650c8e818131f4608000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46240f61b85f15c0ef80b30b599c9772.png)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba09c544777391218919e9146d45ad2.png)
(2)证明:当x0∈(0,+∞)时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e653994b245fbdc2ac3458429c65e69e.png)
(3)若关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c070bd52b36f70fe52b7d5187de1163.png)
您最近一年使用:0次
2021-12-09更新
|
424次组卷
|
3卷引用:2005年普通高等学校招生考试数学试题(辽宁卷)
2005年普通高等学校招生考试数学试题(辽宁卷)天津市南开区南大奥宇培训学校2020-2021学年高三上学期第一次月考数学试题(已下线)考点20 导数的应用--不等式问题 2024届高考数学考点总动员【练】
真题
解题方法
9 . 已知函数
的最大值不大于
,又当
时,
.
(1)求a的值;
(2)设
,
,
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72d0f4934c4c5a75403a65fd455eeede.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6486784415f3537c9a13556c05d893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/072c49a32e8d537004c2b14bc0403539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7f52bd491c313f2db4b89b3794c6e58.png)
(1)求a的值;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b93de100d473ce4b0ae2119361bf075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cfb19f0c37a72b33083ae9319f11a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6190b53b3c2362929b165929427a535c.png)
您最近一年使用:0次
2021-09-25更新
|
164次组卷
|
4卷引用:2004年普通高等学校招生考试数学试题(辽宁卷)
真题
解题方法
10 . 已知点
,
是抛物线
上的两个动点,
是坐标原点,向量
,
满足
.设圆
的方程为
.
(1)证明线段
是圆
的直径;
(2)当圆
的圆心到直线
的距离的最小值为
时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75893f778061c3a7270f02db57fba2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588414d07bcedbf1e7d46d0d028e269d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5773af927ab0caa208eef1adf9e87aee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbfd7bfa201296e1797635f02240835b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7dd85a205ad4f52154f0141f45b8f6c.png)
(1)证明线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f52cb58b6bc5d71030463ba7e28134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
您最近一年使用:0次
2020-06-26更新
|
367次组卷
|
3卷引用:2006 年普通高等学校招生考试数学(文)试题(辽宁卷)