名校
解题方法
1 . 如图,在四棱锥
中,
底面
,底面
是矩形,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/25/655e8c62-2ec0-469f-8277-19bb2945eaff.png?resizew=154)
(1)证明:
.
(2)求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466deee706eb335b7d05b35bfc9319b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/25/655e8c62-2ec0-469f-8277-19bb2945eaff.png?resizew=154)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186e5e7efe51fd25b9e38dc0fa23de9d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1269599d8f29c769773c8288e91b831.png)
您最近一年使用:0次
2023-03-24更新
|
1011次组卷
|
4卷引用:甘肃省白银市会宁县会宁县第四中学2022-2023学年高二下学期期中数学试题
2 . 如图,在正方体
中,
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/27/67171837-067e-461a-8467-46043d6ff75f.png?resizew=335)
(1)试判断直线
与平面
的位置关系,并说明理由;
(2)求证:直线
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
(3)若正方体
的棱长为2,求点
到平面
的距离
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/27/67171837-067e-461a-8467-46043d6ff75f.png?resizew=335)
(1)试判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4645450a006f2c20087486d0833afbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
(3)若正方体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
的定义域为
,且对一切
都有
,当
时,
.
(1)判断
的单调性并加以证明;
(2)若
,解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a9344f4fca7b9779ca7720e5277ea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25bea6d14c16f7c06e4e028f36131360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec8d82fe0dd2eb26609e6b27168dcdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d466dfe4e72daa47c395135c24c0d641.png)
您最近一年使用:0次
2023-04-11更新
|
748次组卷
|
6卷引用:甘肃省兰州市城关区兰州第一中学2023-2024学年高一上学期期中数学试题
4 . 求证:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b4d876f05652bbbdedb7af34be6ac68.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab928f0aed5ba99269d5732f49e918a3.png)
您最近一年使用:0次
2023-05-02更新
|
499次组卷
|
4卷引用:甘肃省甘南藏族自治州卓尼县柳林中学2022-2023学年高一下学期期中数学试题
甘肃省甘南藏族自治州卓尼县柳林中学2022-2023学年高一下学期期中数学试题(已下线)5.5 三角恒等变换(精讲)-《一隅三反》系列(已下线)专题5-5 三角函数综合大题归类(1) - 【巅峰课堂】题型归纳与培优练2.2 二倍角的三角函数
5 . 问题:设公差不为零的等差数列
的前
项和为
,且
, .
下列三个条件:①
成等比数列;②
;③
.从上述三个条件中,任选一个补充在上面的问题中,并解答.
(1)求数列
的通项公式;
(2)若
,数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36183db0759eec0e108274d229fcd00b.png)
下列三个条件:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29b1b845916a4b6a18cdfbcd308d09c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f9b2392bd67dc2427bf0654ec0d7857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cecb36665ae97f385fa4ce5726d8aa8f.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82ecbca314a76a2cc7ba40066813296.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae6358af7332d7609bf8d18467487d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca91cc521bd5796cac29169a3ca79d5a.png)
您最近一年使用:0次
2023-03-27更新
|
266次组卷
|
3卷引用:甘肃省民乐县第一中学2023-2024学年高三上学期第二次诊断考试数学试题
解题方法
6 . 已知正方体
的棱长为1,如图以
为原点,
为单位正交基底,建立空间直角坐标系
.
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/27/e0a36205-ce29-4724-b743-0fb7367f5ba2.png?resizew=174)
(1)求直线
的一个方向向量;
(2)证明:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95628327dc58037e5368f4404c05ec39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e4a743dc54bc087773cb27e6f676a60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3648c864f9f58da1dbb166fee84cfeaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50fe3d30308fe2320c9a81aed199616.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/27/e0a36205-ce29-4724-b743-0fb7367f5ba2.png?resizew=174)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c643d1581b072f4b61a2211828eb0569.png)
您最近一年使用:0次
2023-01-08更新
|
291次组卷
|
2卷引用:甘肃省武威市凉州区2022-2023学年高二下学期期中考试数学试题
名校
解题方法
7 . 在四棱锥
中,
底面
,底面
是边长为2的菱形,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/25/46f6f48b-a926-440d-9334-c6c4faf33ea1.png?resizew=159)
(1)求证:平面
平面
;
(2)直线
与平面
所成角为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/25/46f6f48b-a926-440d-9334-c6c4faf33ea1.png?resizew=159)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a26a7784c7419d8359fb119c8ecc03d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/334b0be972ebf5a46333c0c4369aa90a.png)
您最近一年使用:0次
2023-02-24更新
|
777次组卷
|
8卷引用:甘肃省兰州第一中学2022-2023学年高二下学期期中数学试题
名校
8 . 如图,
平面ABCD,四边形ABCD是正方形,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/8/3c66657b-ce06-4bb3-9774-84ae96f0ca75.png?resizew=168)
(1)证明:AB垂直平面PDE;
(2)求直线
与平面DCE所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8429790ba9382464cf29244da6f1c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e975fa87eb6a9c2fe19a943cefee808.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/8/3c66657b-ce06-4bb3-9774-84ae96f0ca75.png?resizew=168)
(1)证明:AB垂直平面PDE;
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
您最近一年使用:0次
9 . 已知正四面体
的棱长为2,点
是
的重心,点
是线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/16/ae13c046-a84b-4004-8346-0ba0cf9a66c8.png?resizew=180)
(1)用
表示
,并求出
;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebcc52a06d806fde891e09a0a389fcd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/16/ae13c046-a84b-4004-8346-0ba0cf9a66c8.png?resizew=180)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12043fbdfadbf715bbc7969cdf71a907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6799b234237333b0efa331d98f0374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac86fb41def60231a763706fb644cda.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a89efb10e95245a41f6c7a80189528.png)
您最近一年使用:0次
2022-10-13更新
|
364次组卷
|
5卷引用:甘肃省武威市天祝一中、民勤一中、古浪一中2022-2023学年高二下学期期中数学试题
甘肃省武威市天祝一中、民勤一中、古浪一中2022-2023学年高二下学期期中数学试题(已下线)期中押题预测卷(考试范围:选择性必修第一册)(提升卷)-【单元测试】2022-2023学年高二数学分层训练AB卷(人教B版2019)(已下线)6.1.2 空间向量的数量积(练习)-2022-2023学年高二数学同步精品课堂(苏教版2019选择性必修第二册)(已下线)第02讲 1.1.2空间向量的数量积运算(7类热点题型讲练)-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第一册)河南省洛阳市强基联盟大联考2022-2023学年高二上学期10月数学试题
名校
解题方法
10 . 已知函数
.
(1)判断函数
的单调性,并用定义法证明;
(2)当
时,求函数
在区间
上的最大值和最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73be0a77b439bce4d8d472ac469be50a.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff3fefc0b55e0e5719c0ab45c359df21.png)
您最近一年使用:0次
2022-11-07更新
|
207次组卷
|
6卷引用:甘肃省武威市天祝一中、民勤一中、古浪一中等四校联考2023-2024学年高一上学期11月期中数学试题