解题方法
1 . 如图,四棱柱
的底面ABCD是正方形,O为底面中心,
平面ABCD,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/5a604142-37bc-4b3b-bc2b-68ec346570ab.png?resizew=253)
(1)证明:
平面
;
(2)求证:平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
平面
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e5981445b6f2a6c58974158d96a4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a74b4952ac58a5e3fa3f2de86024ef6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/5a604142-37bc-4b3b-bc2b-68ec346570ab.png?resizew=253)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26d8a9d64ad3c8cba28840b41ed7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4cd2b33bd983a9ed6575b9de04a46a.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86eec8526479272d15bb3b171a46de0.png)
您最近一年使用:0次
名校
解题方法
2 . 已知函数
,
(1)当
,
和
有相同的最小值,求
的值;
(2)若
有两个零点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6c66c32cf0584b8990612638fa50dd0.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b3d2315608819f8af9eeef4d3d90e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d4f313e85b97bda207222fa6e82b463.png)
您最近一年使用:0次
2023-10-21更新
|
552次组卷
|
6卷引用:四川省达州市开江县开江中学2022-2023学年高三上学期入学考试数学(理)试题
四川省达州市开江县开江中学2022-2023学年高三上学期入学考试数学(理)试题四川省成都市树德中学2022-2023学年高三上学期第一次月考模拟(理科)数学试题四川省成都市树德中学2022-2023学年高三上学期第一次月考模拟(文科)数学试题西南名校联盟2022-2023学年高三上学期11月月考数学(理)试题(已下线)专题突破卷08 极值点偏移(已下线)重难点突破05 极值点偏移问题与拐点偏移问题(七大题型)-1
解题方法
3 . 如图,在四棱锥
中,
面
,
,点
分别为
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/29/6ca73ce6-b7a7-4f56-8e8d-211729919c00.png?resizew=172)
(1)证明:直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619dc0262b1bb806dde91dd5ff428a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4762d59261265112fef9ac74d5bb9a36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f174f340eba153b73cfc03dabd0df888.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/29/6ca73ce6-b7a7-4f56-8e8d-211729919c00.png?resizew=172)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d67be899bc131ec1b9921ae9787c40d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
4 . 如图,在四棱锥
中,底面
是矩形,
是
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/91fa983f-007b-4abc-b7ca-5029591f172f.png?resizew=189)
(1)求证:平面
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7898f562dffdf08263bfb0873e0691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03bb46e45e9c26b15d53a5dc53185aca.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/91fa983f-007b-4abc-b7ca-5029591f172f.png?resizew=189)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2022-11-27更新
|
1402次组卷
|
7卷引用:四川省达州中学2022-2023学年高二上学期第三次月考理科数学试题
名校
解题方法
5 . 已知圆
和定点
,动点
在圆
上.
(1)过点
作圆
的切线,求切线方程;
(2)若满足
,求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6114947179bed8c2c86ac078e2f8497f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f9a3ea5e76e165faeabfdbc9717c287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)若满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb24e3dc219fc248249d68ac3d8ba787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
2022-11-23更新
|
965次组卷
|
6卷引用:四川省达州中学2022-2023学年高二上学期第三次月考理科数学试题
四川省达州中学2022-2023学年高二上学期第三次月考理科数学试题安徽省亳州市蒙城第一中学东校区2022-2023学年高三上学期第四次月考数学试题四川省资阳市资阳中学2022-2023学年高二上学期期中数学文科试题重庆市南开中学校2022-2023学年高一下学期第二次月考数学试题(已下线)第11讲 第二章 直线和圆的方程 章末总结(3)(已下线)专题05 直线与圆综合大题18种题型归类-【巅峰课堂】2023-2024学年高二数学上学期期中期末复习讲练测(人教A版2019选择性必修第一册)
21-22高一下·浙江·期中
6 . 已知三棱锥
中,△ABC,△ACD都是等边三角形,
,E,F分别为棱AB,棱BD的中点,G是△BCE的重心.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/30/4c768d18-52ee-428a-958c-36eeb689cbf2.png?resizew=196)
(1)求异面直线CE与BD所成角的余弦值;
(2)求证:FG
平面ADC.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b94651d11df3a469d7ac72e6ac74c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/30/4c768d18-52ee-428a-958c-36eeb689cbf2.png?resizew=196)
(1)求异面直线CE与BD所成角的余弦值;
(2)求证:FG
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
您最近一年使用:0次
名校
7 . 如图,在四棱锥
中,
为等腰梯形,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/7/7b3cec59-b3ad-4bbb-bc5d-0d3c5aba87d1.png?resizew=146)
(1)证明:
平面
;
(2)求平面
和平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790e1f26a6b7010bab031c5bfc655c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b64b03bdd6fe567c99c15220aebbd63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16aad38b43462ca7a8fb9bc9484ad3a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5204ad2a40c7bb60751d92f64409742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71826134c3080aa75becc655a9089855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e0b64d25ddd18454f88e40c45d7d8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/712f7375b4ede5f75c0d81870c0f86af.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/7/7b3cec59-b3ad-4bbb-bc5d-0d3c5aba87d1.png?resizew=146)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b64b03bdd6fe567c99c15220aebbd63.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab594531ac1e4439b351dabf9f21d92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2022-09-06更新
|
488次组卷
|
2卷引用:四川省达州市开江县开江中学2022-2023学年高三上学期入学考试数学(理)试题
名校
8 . 如图,在四棱锥
中,
面
,
,
,点
分别为
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/71654a21-d300-4c81-a8f2-9f2d03018911.png?resizew=176)
(1)证明:直线
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4762d59261265112fef9ac74d5bb9a36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c3ca1c27bdc0102bf2c6b306ddd1d95.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/71654a21-d300-4c81-a8f2-9f2d03018911.png?resizew=176)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc6bc85b019e9d158ca1d92feed796e.png)
您最近一年使用:0次
2023-01-15更新
|
1360次组卷
|
11卷引用:四川省达州市2022-2023学年高二上学期期末监测数学(理科)试题
四川省达州市2022-2023学年高二上学期期末监测数学(理科)试题(已下线)第8章 立体几何初步 重难点归纳总结-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)专题2 求二面角的夹角(1)(已下线)上海市华东师范大学第二附属中学2023届高三下学期2月月考数学试题(已下线)8.6.3 平面与平面垂直(1)-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(人教A版2019必修第二册)(已下线)专题8.16 空间角大题专项训练(30道)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)(已下线)上海市华东师范大学第二附属中学2023届高三最后一模数学试题上海市嘉定区第一中学2024届高三上学期10月月考数学试题上海市同济大学第二附属中学2024届高三上学期期中数学试题海南省琼海市海桂中学2023-2024学年高二上学期期中考试数学试题(B卷)陕西省兴平市南郊高级中学2023-2024学年高二上学期第三次质量检测数学试题
名校
解题方法
9 . 已知
,且
.
(1)求证:
;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67784e0c5b774a658b3c12fe05800df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b40b1544e62be8b9e9f4dc9f2c0c74.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c557ed60aaee8b22ef705124462bfc45.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7b3a4f314fca607b3e9f7b67e1298.png)
您最近一年使用:0次
2022-09-06更新
|
2082次组卷
|
6卷引用:四川省达州市开江县开江中学2022-2023学年高三上学期入学考试数学(文)试题
名校
解题方法
10 . 在四棱锥
中,
为等腰梯形,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/7/fe0102e5-8a2d-4c94-b4ce-b9d4295d4860.png?resizew=122)
(1)证明:
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790e1f26a6b7010bab031c5bfc655c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b64b03bdd6fe567c99c15220aebbd63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6285e439ffea5fc8fc4de67c022849e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cf468cf2761c5c0eaffca51815e5724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33b7121462070532bdd8a2147f2fb90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7101f450b804c558db69846b042f8e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15d94f47a77447c0607d22e4e5e18369.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/7/fe0102e5-8a2d-4c94-b4ce-b9d4295d4860.png?resizew=122)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca997e4c7c92a066655ff0714c2046a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b64b03bdd6fe567c99c15220aebbd63.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9e54073845d1ddb3526c9887524c197.png)
您最近一年使用:0次