真题
1 . 如图,在三棱锥
中,
,点O、D分别是
的中点,
底面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/127ccddf-3220-46bd-a33c-29318a99553d.png?resizew=194)
(1)求证:
平面
;
(2)求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3458ac2f57ca59ad8052807621cf0ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d207c42271921326f7cdcce3e2569665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc6f007dbf1c1a36eb031e520608403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/127ccddf-3220-46bd-a33c-29318a99553d.png?resizew=194)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6072ec6dfc0203cabb1fe289a5ddc8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
真题
解题方法
2 . 如图,在四棱锥
中,底面为直角梯形,
,
底面
,且
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/517cfa72-c952-43e0-bd34-1e4ac98a7cd9.png?resizew=156)
(1)求证:
;
(2)求
与平面
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4465d6a588e4d4eb3d93b153ec6fb81a.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/5857b03445433bfe181ea446ecc4b51b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829a1a887ceba13dd8551b1e3604bf6f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/517cfa72-c952-43e0-bd34-1e4ac98a7cd9.png?resizew=156)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/962515007ca98ad2d36557b60a42ad6f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a406f24b5131eb7da9127750319e52.png)
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真题
解题方法
3 . 如图,椭圆
与过点
的直线只有一个公共点
,且椭圆的离心率
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/d606e492-88c2-4dfd-989c-76def5786589.png?resizew=206)
(1)求椭圆方程;
(2)设
分别为椭圆的左、右焦点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589b8f644f09ce16191577f2441e86c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/d606e492-88c2-4dfd-989c-76def5786589.png?resizew=206)
(1)求椭圆方程;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df5a24bc02c90e73cacb03b97add0c5.png)
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4 . 如图,在四棱锥
中,底面为直角梯形,
,
底面
,且
分别为
的中点.
;
(2)求
与平面
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25cf1949a53a014c451ee56801800f3.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/5857b03445433bfe181ea446ecc4b51b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829a1a887ceba13dd8551b1e3604bf6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/962515007ca98ad2d36557b60a42ad6f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a406f24b5131eb7da9127750319e52.png)
您最近一年使用:0次
2022-11-09更新
|
1166次组卷
|
5卷引用:2006年普通高等学校招生考试数学(文)试题(浙江卷)
2006年普通高等学校招生考试数学(文)试题(浙江卷)(已下线)易错31题专练(沪教版2020必修三全部内容)-2022-2023学年高二数学考试满分全攻略(沪教版2020必修三)内蒙古自治区赤峰市赤峰红旗中学2022-2023学年高一下学期期末数学试题黑龙江省大庆市东风中学2023-2024学年高二上学期开学考试数学试题专题05 空间直线、平面的垂直-《期末真题分类汇编》(新高考专用)
真题
名校
5 . 设
,若
,求证:
(1)方程
有实根;
(2)
;
(3)设
是方程
的两个实根,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412d06553744fabe8eadbf9ef17e8518.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d382878db7c1087f64bddc73bda2f20.png)
(1)方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3047d4ab078dafc06c047bcbf0a6ffaf.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e0852599fd15f0648eb8137b098c8da.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3047d4ab078dafc06c047bcbf0a6ffaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2240a1ffe507ac47aa66729d7cc6be53.png)
您最近一年使用:0次
2022-11-09更新
|
400次组卷
|
2卷引用:2006年普通高等学校招生考试数学(文)试题(浙江卷)
真题
6 . 如图,已知正方形ABCD和矩形ACEF所在的平面互相垂直,
,M是线段EF的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/d513db97-63a3-41c9-a9fd-8c3a74c7399c.png?resizew=172)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
平面BDE;
(2)求证:
平面BDF;
(3)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f32456ccb324ca898b27d3e024fe7de9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/d513db97-63a3-41c9-a9fd-8c3a74c7399c.png?resizew=172)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4019805fed3b6cca619f4035e7618cd0.png)
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7 . 已知数列
中的相邻两项
,
是关于x的方程
的两个根,且
.
(1)求
及
(不必证明);
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7b6ecfdff9d2b29ef64d2a6f3343f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39773a450e3c30c72ead226d84e54563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17fd2e41fc78ca4be731f145ddfd4de6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/000b5bec9ba47981b959ea4ea3d78d23.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b8f3b8dff8e8fa0331f1e9e59f084cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a559f141b44fd26bc509f7d767983e1.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
您最近一年使用:0次
2022-11-09更新
|
572次组卷
|
2卷引用:2007年普通高等学校招生考试数学(文)试题(浙江卷)
真题
8 . 如图,椭圆
与过点
的直线有且只有一个公共点T,且椭圆的离心率
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/a4dad4bc-ae4a-4d06-9d6a-8d8f5723268e.png?resizew=212)
(1)求椭圆方程;
(2)设
分别为椭圆的左、右焦点,M为线段
的中点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589b8f644f09ce16191577f2441e86c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/a4dad4bc-ae4a-4d06-9d6a-8d8f5723268e.png?resizew=212)
(1)求椭圆方程;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72404eb522c6cc692757b0855c2df865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42f080c04382a1a2337f863fc00ffe66.png)
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真题
解题方法
9 . 如图,
的在个顶点坐标分别为
,设
为线段BC的中点,
为线段CO的中点,
为线段
的中点,对于每一个正整数n,
为线段
的中点,令
的坐标为
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/16ccea36-95c1-4c6d-9915-d555ea137a23.png?resizew=145)
(1)求
及
;
(2)证明
;
(3)若记
,证明
是等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebb49c1fd097c5aafc0c9080449f5fc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5ac4fc58a2fb27dff627ded546cb01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1652145a4785b50fa22fdd8c63f724b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7be4892a56cae353323a90026dcbf517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5968bd8d9b7fceea8f0793a3e4e158e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92abae836b8026511113ad8c3ea23028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7184ccefde0f04b2f1cfff0ff6c1492e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/16ccea36-95c1-4c6d-9915-d555ea137a23.png?resizew=145)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c14d9ae06f864498048d55088ff4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0910dd96fbf663d41b57f7df65bedc3b.png)
(3)若记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39c96c23c0597908084a7091e5c6ceea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
您最近一年使用:0次
真题
10 . 设点
和抛物线
,其中
,
由以下方法得到:
,点
在抛物线
上,点
到
的距离是
到
上点的最短距离,……,点
在抛物线
上,点
到
的距离是
到
上点的最短距离.
(1)求
及
的方程.
(2)证明
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ddf358a5bd45285693963081eb45534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4165af644315776a4ca477ff04e1537a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eb213494d7551a41dc5153de3bfc850.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec71037a96b7a4bb1653de301369cbd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921fcafcfe1ab0a10af0ed484afa5d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa6b09f39af8d61f60a430cbcadc6027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f536611d68bd7e72f580602902ebdd40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ec8d169ca3965aa240cdaad351482a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb07a9ee7fa07fcec6a679c9bee53a01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c15016fc7de1cd5971b7d38c70071e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
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