1 . 如图,
中,
两点分别是线段
的中点,现将
沿
折成直二面角
.
(Ⅰ)求证:
; (Ⅱ)求直线
与平面
所成角的正切值.
![](https://img.xkw.com/dksih/QBM/2014/9/12/1571852923830272/1571852929409024/STEM/521eaf5e2a3a4681b4a2d18ed1557b3e.png?resizew=162)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://img.xkw.com/dksih/QBM/2014/9/29/1571869383196672/1571869389103104/STEM/96e8e9ad0e5c4192892346e5762715c4.png?resizew=209)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d54431bbb28ebd98db5c1dc6083a75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/370148e9147aa25c60a07ab4ad46e83d.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde8d73a600160afef8bb0b127d58fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://img.xkw.com/dksih/QBM/2014/9/12/1571852923830272/1571852929409024/STEM/521eaf5e2a3a4681b4a2d18ed1557b3e.png?resizew=162)
![](https://img.xkw.com/dksih/QBM/2014/9/12/1571852923830272/1571852929409024/STEM/00d6cd1c57eb4e31a7f9184c1536ff58.png?resizew=224)
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2014·湖南益阳·三模
名校
2 . 已知椭圆
(
)的短轴长为2,离心率为
.过点M(2,0)的直线
与椭圆
相交于
、
两点,
为坐标原点.
(1)求椭圆
的方程;
(2)求
的取值范围;
(3)若
点关于
轴的对称点是
,证明:直线
恒过一定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/658aa70a197c830aa765f2f7ea4c86c5.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
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|
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|
3卷引用:2014届湖南省益阳市高三模拟考试理科数学试卷
真题
名校
3 . 已知抛物线
的顶点为原点,其焦点
到直线
的距离为
.设
为直线
上的点,过点
作抛物线
的两条切线
,其中
为切点.
(1) 求抛物线
的方程;
(2) 当点
为直线
上的定点时,求直线
的方程;
(3) 当点
在直线
上移动时,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0753fd52355cd4de8e764bf5b0a2cad5.png)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571289657753600/1571289663455232/STEM/39046aa731724ec0a5a505dbb84ff932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7116071164cdc45f5d312a437c68bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1) 求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2) 当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc26262f7a1603369462c7c2f2197a42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3) 当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d7183f8ff3a9ad590ae4229df386708.png)
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2016-12-02更新
|
5275次组卷
|
20卷引用:湖南省长沙市2018届高三第一次模拟数学(理科)试题
湖南省长沙市2018届高三第一次模拟数学(理科)试题湖南省长沙市长郡中学2018-2019学年高二下学期入学考试数学(理)试题2013年全国普通高等学校招生统一考试理科数学(广东卷)2013年全国普通高等学校招生统一考试文科数学(广东卷)(已下线)2014届人教版高考数学文科二轮专题复习提分训练16练习卷(已下线)2014届甘肃省兰州一中高考模拟三文科数学试卷2015-2016学年河北省武邑中学高二4月月考理科数学试卷2015-2016学年河北省武邑中学高二4月月考文科数学试卷【全国百强校】贵州省铜仁市第一中学2019届高三上学期第二次月考数学(理)试题上海市七宝中学2018-2019学年高三上学期12月月考数学试题重庆市巴蜀中学2018-2019学年高二上学期期末复习模拟题(1)(文科)数学试题2019届重庆市合川瑞山中学高三下学期模拟训练(文)数学试题西藏自治区拉萨市拉萨中学2021届高三第二次月考数学(理)试题西藏自治区拉萨市拉萨中学2021届高三第二次月考数学(文)试题(已下线)专题12 解析几何中的定值、定点和定线问题 第一篇 热点、难点突破篇(练)-2021年高考数学二轮复习讲练测(浙江专用)广东实验中学2022届高三上学期11月阶段性考试数学试题(已下线)专题14 圆锥曲线切线方程 微点2 圆锥曲线切线方程的常用结论及其应用河南省驻马店市确山县第一高级中学2022-2023学年高二上学期数学竞赛试题上海市交通大学附属中学2023届高三下学期开学考试数学试题(已下线)四川省成都外国语学校2024届高考模拟文科数学试题(三)
2010·湖南·二模
4 . 如图,
为圆
的直径,点
、
在圆
上,
,矩形
所在的平面和圆
所在的平面互相垂直,且
,
.
(1)求证:
平面
;
(2)设
的中点为
,求证:
平面
;
(3)设平面
将几何体
分成的两个锥体的体积分别为
,
,求![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/1ed8e20d200d4839a93618d2498ca4c3.png)
.
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/5107dc9b0d26403588b53dd4853891ba.png)
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/f4bba79db2254a7caceaf19fcceebe47.png)
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/740b73c7dd74478d92befd2219da5f24.png)
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/ae549fb8729141909aa723475dd41c66.png)
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/f4bba79db2254a7caceaf19fcceebe47.png)
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/779b72e206c642da8792216095b0a4be.png)
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/39c4e95dcf1045d29f9b3ef1a8ae14ad.png)
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/f4bba79db2254a7caceaf19fcceebe47.png)
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/005b25333d0b4c279192d7a328923bd6.png)
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/92384b8434aa4bac92d76e50e29e1b8b.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/b7fb95aaa5644f02bea5464f6e4748c6.png)
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/e87634a30f4443fcbeb73c4f4afb8472.png)
(2)设
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/a1a4245f8be64551b2c9fb8b34a18e16.png)
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/a549af7b865345139ec00689dd67e6b7.png)
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/3b0e88dc00a64a84ac0d3ce96a2bf954.png)
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/65f873eeb5674aac95442ae9ccdb11f5.png)
(3)设平面
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/e87634a30f4443fcbeb73c4f4afb8472.png)
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/f256e4e38987423b9cd0ab607ec9b096.png)
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/1ed8e20d200d4839a93618d2498ca4c3.png)
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/a03bc08de16b45eb9bc1d0644432e3eb.png)
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/1ed8e20d200d4839a93618d2498ca4c3.png)
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/548991055efd499abecba636668ffa8d.png)
![](https://img.xkw.com/dksih/QBM/2010/5/21/1569739460681728/1569739465646080/STEM/c1a9bb58f8a74fcc89d998fad4092af3.png)
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12-13高三·福建泉州·阶段练习
名校
5 . 如图,
是以
为直径的半圆上异于点
的点,矩形
所在的平面垂直于该半圆所在平面,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dd0fcd2321affac19e79366ee260b8.png)
![](https://img.xkw.com/dksih/QBM/2014/1/6/1571461553094656/1571461558452224/STEM/106d04c0b27b43dd9bc4e0d6d05bc837.png?resizew=239)
(1)求证:
;
(2)设平面
与半圆弧的另一个交点为
,
①求证:
//
;
②若
,求三棱锥E-ADF的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dd0fcd2321affac19e79366ee260b8.png)
![](https://img.xkw.com/dksih/QBM/2014/1/6/1571461553094656/1571461558452224/STEM/106d04c0b27b43dd9bc4e0d6d05bc837.png?resizew=239)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2014/1/6/1571461553094656/1571461558452224/STEM/9f22cd7c391748e7955bd7cf3c0ca308.png?resizew=64)
(2)设平面
![](https://img.xkw.com/dksih/QBM/2014/1/6/1571461553094656/1571461558452224/STEM/b627cede330e4a56bb6bba3368360dfc.png?resizew=37)
![](https://img.xkw.com/dksih/QBM/2014/1/6/1571461553094656/1571461558452224/STEM/5e9cfe3be6c449d5bf27c5ea43eea7ab.png?resizew=17)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
②若
![](https://img.xkw.com/dksih/QBM/2014/1/6/1571461553094656/1571461558452224/STEM/82c95f601a5547d0ac0906e6e2c5f0b6.png?resizew=48)
您最近一年使用:0次
2016-12-02更新
|
906次组卷
|
10卷引用:【全国百强校】湖南省长沙市长郡中学2019届高三上学期第三次调研考试数学(文科)试题
【全国百强校】湖南省长沙市长郡中学2019届高三上学期第三次调研考试数学(文科)试题(已下线)2013届福建省泉州市普通中学高三毕业班质量检查文科数学试卷(已下线)2012-2013学年福建省泉州一中高二下学期期中考试文科数学试卷(已下线)2014届安徽省淮南二中高三上学期第三次月考文科数学试卷(已下线)2014届安徽池州第一中学高三上学期第三次月考文科数学试卷(已下线)2014届吉林省长春市高中毕业班第一次调研测试文科试卷2015-2016学年山东省滕州市二中高一12月月考数学试卷2017届福建福州外国语学校高三上月考一数学(理)试卷2017届福建福州外国语学校高三文上月考一数学试卷山东省昌乐第一中学2018-2019学年高二下学期第二次段考数学试题
6 . 如图,在四棱锥
中,底面
是直角梯形,
∥
,
,
⊥平面SAD,点
是
的中点,且
,
.
![](https://img.xkw.com/dksih/QBM/2012/8/15/1570971190861824/1570971196096512/STEM/2d1d0290f21843ae878c1fea24ca345c.png?resizew=208)
(1)求四棱锥
的体积;
(2)求证:
∥平面
;
(3)求直线
和平面
所成的角的正弦值.
![](https://img.xkw.com/dksih/QBM/2013/4/3/1571173404172288/1571173409808384/STEM/f85c11167abc4c27a05212a6d345d89e.png?resizew=69)
![](https://img.xkw.com/dksih/QBM/2013/4/3/1571173404172288/1571173409808384/STEM/54602f6be0484bcc94b52476a4556e5e.png?resizew=45)
![](https://img.xkw.com/dksih/QBM/2013/4/3/1571173404172288/1571173409808384/STEM/e6cf148bcca0470e9880adeb848a6a4f.png?resizew=27)
![](https://img.xkw.com/dksih/QBM/2013/4/3/1571173404172288/1571173409808384/STEM/dcd795dbc29d4eceaf8bcf0fb1a9a07e.png?resizew=25)
![](https://img.xkw.com/dksih/QBM/2013/4/3/1571173404172288/1571173409808384/STEM/d0dbee6170c14143a5570ab36f47ce69.png?resizew=59)
![](https://img.xkw.com/dksih/QBM/2013/4/3/1571173404172288/1571173409808384/STEM/9408ea9070ef4a4aa2cc06c04ac5037a.png?resizew=25)
![](https://img.xkw.com/dksih/QBM/2013/4/3/1571173404172288/1571173409808384/STEM/57858b4cd8434e228cd773e48dcdbe79.png?resizew=20)
![](https://img.xkw.com/dksih/QBM/2013/4/3/1571173404172288/1571173409808384/STEM/da28b34b3c1c4b77af3e578ca81ff022.png?resizew=24)
![](https://img.xkw.com/dksih/QBM/2013/4/3/1571173404172288/1571173409808384/STEM/905bdf4d930d4da180a04fc16b796da7.png?resizew=113)
![](https://img.xkw.com/dksih/QBM/2013/4/3/1571173404172288/1571173409808384/STEM/1dc771bc35ce44de9458dfa4ed9444f9.png?resizew=51)
![](https://img.xkw.com/dksih/QBM/2012/8/15/1570971190861824/1570971196096512/STEM/2d1d0290f21843ae878c1fea24ca345c.png?resizew=208)
(1)求四棱锥
![](https://img.xkw.com/dksih/QBM/2013/4/3/1571173404172288/1571173409808384/STEM/f85c11167abc4c27a05212a6d345d89e.png?resizew=69)
(2)求证:
![](https://img.xkw.com/dksih/QBM/2013/4/3/1571173404172288/1571173409808384/STEM/c0b908389d584cae9584851299696168.png?resizew=29)
![](https://img.xkw.com/dksih/QBM/2013/4/3/1571173404172288/1571173409808384/STEM/6afa0f5d15514e0bbef5798725ea2dcc.png?resizew=33)
(3)求直线
![](https://img.xkw.com/dksih/QBM/2013/4/3/1571173404172288/1571173409808384/STEM/da28b34b3c1c4b77af3e578ca81ff022.png?resizew=24)
![](https://img.xkw.com/dksih/QBM/2013/4/3/1571173404172288/1571173409808384/STEM/6afa0f5d15514e0bbef5798725ea2dcc.png?resizew=33)
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7 . 一个四棱锥的三视图如图所示,E为侧棱PC上一动点.
![](https://img.xkw.com/dksih/QBM/2012/2/27/1570778392223744/1570778397515776/STEM/3826b97bd73143faae65a79d512f3cb5.png?resizew=264)
(1)画出该四棱锥的直观图,并指出几何体的主要特征(高、底等).
(2)点
在何处时,PC
面EBD,并求出此时二面角A-BE-C平面角的余弦值
![](https://img.xkw.com/dksih/QBM/2012/2/27/1570778392223744/1570778397515776/STEM/3826b97bd73143faae65a79d512f3cb5.png?resizew=264)
(1)画出该四棱锥的直观图,并指出几何体的主要特征(高、底等).
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252053b853152bd294a8315debd00b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a1eaafdbeb79a0006580b02b8074056.png)
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9-10高三·北京·阶段练习
解题方法
8 . 如图,在四棱锥P—ABCD中,PA⊥平面ABCD,底面ABCD为直角梯形,∠ABC=
∠BAD=90°,AD>BC,E,F分别为棱AB,PC的中点.
(I)求证:PE⊥BC;
(II)求证:EF//平面PAD.
∠BAD=90°,AD>BC,E,F分别为棱AB,PC的中点.
(I)求证:PE⊥BC;
(II)求证:EF//平面PAD.
![](https://img.xkw.com/dksih/QBM/2010/4/8/1569695110791168/1569695167635456/STEM/68dbb74cfabd404cbe7c13e7986403bd.png?resizew=196)
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