名校
1 . 如图,三棱锥
的底面
和侧面
都是边长为2的等边三角形,
分别是
的中点,
.
平面
;
(2)求直线
与平面
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.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/114328e2c6128710608977e7927c7a0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963a91995abd4927d75406d16e10a81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e6629d0e1a4ce3fe4f0345f6961473.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c157ff302a881c17514534903c575f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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名校
2 . 如图,
平面ABCD,
,
,
,
,点E,F,M分别为AP,CD,BQ的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/27/bca75ace-88ac-4178-b096-546857c004e1.png?resizew=156)
(1)求证:
平面CPM;
(2)求平面QPM与平面CPM夹角的大小;
(3)若N为线段CQ上的点,且直线DN与平面QPM所成的角为
,求N到平面CPM的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0657604c530cc1e6d741e4f3e8efa169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdf7ab831f4d2053cbd4a6d63ad7ac5d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/27/bca75ace-88ac-4178-b096-546857c004e1.png?resizew=156)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
(2)求平面QPM与平面CPM夹角的大小;
(3)若N为线段CQ上的点,且直线DN与平面QPM所成的角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
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2023-02-22更新
|
2238次组卷
|
6卷引用:天津市双菱中学2022届高三下学期开学考试数学试题
解题方法
3 . 已知数列
的前
项和
和通项
满足
.
(1)求数列
的通项公式;
(2)求证:
;
(3)设函数
,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.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/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8580be5d491f0743244648329dcc46.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1f5d407c0e99344ed5f0f5926c5d22.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02443719c9dab7d4fdcfa927855c2d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfff315899c6b590435df2ad5b14f9a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699b338d62ac06d8d12b030912edf094.png)
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4 . 已知函数
(
).
(1)当
时,求
的图象在
处的切线方程;
(2)若函数
的图象与
轴有两个不同的交点
,
(
),求证:
(其中
为
的导函数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede5b40ccf27062aacd525e17fc7fff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da989240786ef7c3e2d903f30caf59e3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f5cd8f5dd05a04331f43a2ba55953b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f399b1f59ee66176b4038e91a3eb1bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56cd6c2b238f22b97be9df377a10ed56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/624568f386214e6f79fd02bba24bb120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1cbfdc87849f6cbbbb72f1d5e933c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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5 . 如图,正方形
所在的平面与平面
垂直,
是
和
的交点,
,且
.
![](https://img.xkw.com/dksih/QBM/2016/4/7/1572569174687744/1572569181011968/STEM/187bdabeb7494bf2b1ec70e588669f9a.png)
(1)求证:
平面
;
(2)求直线
与平面
所成的角的大小;
(3)求二面角
的大小.
(4)你认为求二面角常用的方法有哪些?请按应用的重要程度写出3种,并就其中一种方法谈谈它的应用条件.
![](https://img.xkw.com/dksih/QBM/2016/4/7/1572569174687744/1572569181011968/STEM/9cc9e426190d4299a3c77583223a99d0.png)
![](https://img.xkw.com/dksih/QBM/2016/4/7/1572569174687744/1572569181011968/STEM/5497423b6c234073bc464df1ef34b96e.png)
![](https://img.xkw.com/dksih/QBM/2016/4/7/1572569174687744/1572569181011968/STEM/d11eab10b64743cea50e9d77303ac95e.png)
![](https://img.xkw.com/dksih/QBM/2016/4/7/1572569174687744/1572569181011968/STEM/12cf2174077d4cd3b2965f92918f7f2f.png)
![](https://img.xkw.com/dksih/QBM/2016/4/7/1572569174687744/1572569181011968/STEM/ce7593be1f0649ffb308a56f0512c45d.png)
![](https://img.xkw.com/dksih/QBM/2016/4/7/1572569174687744/1572569181011968/STEM/3562b0659cca408c9f3a7fa8c6cfbf92.png)
![](https://img.xkw.com/dksih/QBM/2016/4/7/1572569174687744/1572569181011968/STEM/702809205e184c59a5b1cfa7286ccc12.png)
![](https://img.xkw.com/dksih/QBM/2016/4/7/1572569174687744/1572569181011968/STEM/187bdabeb7494bf2b1ec70e588669f9a.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/4/7/1572569174687744/1572569181011968/STEM/de8ee198420d43bb9beb951aad2c323c.png)
![](https://img.xkw.com/dksih/QBM/2016/4/7/1572569174687744/1572569181011968/STEM/164bc8b2f7c14ae9bfcee0d0f7088280.png)
(2)求直线
![](https://img.xkw.com/dksih/QBM/2016/4/7/1572569174687744/1572569181011968/STEM/c479c66934934175bdd23fcdef1f585a.png)
![](https://img.xkw.com/dksih/QBM/2016/4/7/1572569174687744/1572569181011968/STEM/164bc8b2f7c14ae9bfcee0d0f7088280.png)
(3)求二面角
![](https://img.xkw.com/dksih/QBM/2016/4/7/1572569174687744/1572569181011968/STEM/37b4dba301674268b26de3fd4db73661.png)
(4)你认为求二面角常用的方法有哪些?请按应用的重要程度写出3种,并就其中一种方法谈谈它的应用条件.
您最近一年使用:0次