名校
1 . 如图,在正四棱锥
中,E,F分别为
的中点,
.
(1)证明:B,E,G,F四点共面.
(2)记四棱锥
的体积为
,四棱锥
的体积为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1443bfe022f648f813fb1e15b2d78b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9fed9241141f03f50a109ff718a8cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/1/7c55d54f-f787-4c6a-922d-e23a594a6325.png?resizew=152)
(1)证明:B,E,G,F四点共面.
(2)记四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83ddaa4ddb1938c804299f54f2f8ff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737b04ce09bc7e1ed86dc9b3c85203b.png)
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2023-11-10更新
|
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8卷引用:广西贵港市部分学校2023-2024学年高二上学期期中联考数学试题
名校
解题方法
2 . 如图,已知
,
分别是双曲线E:
的左、右焦点,
是E上一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/2/57d19132-b2a4-4803-adf4-46d435dda95c.png?resizew=204)
(1)求E的方程.
(2)过直线l:
上任意一点T作直线
,
与E的左、右两支相交于A,B两点,直线
关于直线l对称的直线为
(与
不重合),
与E的左、右两支相交于C,D两点.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c7bcdcd135d4e537a1952f622eb1ecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5df6fcdb019f3743b26127ef5576c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f2bd968d77544b90a81cde792a28e76.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/2/57d19132-b2a4-4803-adf4-46d435dda95c.png?resizew=204)
(1)求E的方程.
(2)过直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c1016bc9ef1c728bccf070a6e4a532f.png)
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2023-11-10更新
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6卷引用:广西贵港市部分学校2023-2024学年高二上学期期中联考数学试题
3 . 如图,在正四棱柱
中,
,E为
的中点.
(1)证明:
平面
.
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c5282bc1ea20767a6c092c22c761ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/c9a34271-75c0-4207-a4d1-228fee8594f0.png?resizew=130)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923d409630f5331cf8e85fb6c584e31b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
您最近一年使用:0次
2023-11-11更新
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88次组卷
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2卷引用:广西贵港市部分学校2023-2024学年高二上学期期中联考数学试题
解题方法
4 . 已知
是定义域为R的奇函数,当
时,
.
(1)求
的解析式;
(2)判断
在
上的单调性,并用定义证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea79854761a898f4b2be21dd23e5bb29.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
您最近一年使用:0次
2022-11-13更新
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123次组卷
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2卷引用:广西贵港市2022-2023学年高一上学期期中教学质量检测数学试题
解题方法
5 . 已知函数
的定义域为
,且
,
,
.
(1)求
和
值;
(2)判断
的奇偶性,并证明;
(3)若
,则
,求
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac04d918a37edd0bc68dbe9632c03a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6593a700bf3e89107556454666b787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e63c91626ffa91e590925e6f206c3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a26a5485711386aa0cc3a06cc480656.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6155e181e21ce56ea658b70f8af17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a32822a106d217ffdec43557a236f786.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca542e78b7d77d008c9c4752afa91a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e279ff4d60f7d07dec30d6950e25e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6131d1c0a13d57596a0c56e82588887c.png)
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名校
解题方法
6 . 图,在正三棱柱
中,O为
与
的交点,M为
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/967cb39e-51f9-4598-8df3-d77f92111cbc.png?resizew=191)
(1)证明:
平面
;
(2)若G为线段FC上一动点,在平面
上是否存在一点N,使得
平面
恒成立?若存在,请找出点N位置并证明
平面
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a9ad711b25c36dae0c2a2cedff9954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/393ebfea258a58906706888f0d6f2582.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/967cb39e-51f9-4598-8df3-d77f92111cbc.png?resizew=191)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa1211fdbcc2a4a36e24b4e6c5c920bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
(2)若G为线段FC上一动点,在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e6c97d975d4b04061715c41c00e1e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b14cf4977ee2dac0bd5b0fca4dadc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e6c97d975d4b04061715c41c00e1e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b14cf4977ee2dac0bd5b0fca4dadc3.png)
您最近一年使用:0次
2022-05-13更新
|
1016次组卷
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5卷引用:广西桂平市麻垌中学2021-2022学年高一下学期期中考试数学试题
广西桂平市麻垌中学2021-2022学年高一下学期期中考试数学试题福建省龙岩市非一级达标校2021-2022学年高一下学期期中联考数学试题福建省厦门外国语学校2021-2022学年高一下学期期中考试数学试题河北省邢台市南和区第一中学2021-2022学年高一下学期第三次月考数学试题(已下线)第一章 点线面位置关系 专题一 空间平行关系的判定与证明 微点1 空间平行关系的判定与证明【培优版】
名校
7 . 如图,菱形
的边长为2,
,E为AB的中点.将
沿DE折起,使A到达
,连接
,
,得到四棱锥
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/9257abca-364c-4f0e-99a8-cb7cc21ed349.png?resizew=284)
(1)证明:
;
(2)当二面角
在
内变化时,求直线
与平面
所成角的正弦值的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e663220a66eff19da6a71e46b397db2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb97aff0960e2640314888a38e7169c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be7527d873655c33ebcd1f2b14a9315c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/9257abca-364c-4f0e-99a8-cb7cc21ed349.png?resizew=284)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb50274e8907ba8ba624755c9f3462d3.png)
(2)当二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/413057311afa5daa3815d4afd08dd3a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b5e354bb26ff35ea03241c4fdff96b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb97aff0960e2640314888a38e7169c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c87014fbb5c656a4f1892dbd88f242.png)
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2022-11-09更新
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10卷引用:广西桂平市浔州高级中学2022-2023学年高二上学期贵港地区统考段考数学试题
广西桂平市浔州高级中学2022-2023学年高二上学期贵港地区统考段考数学试题湖南省多所学校2022-2023学年高二上学期期中联考数学试题辽宁省县级重点高中联合体2022-2023学年高二上学期期中考试数学试题山西省部分名校2022-2023学年高二上学期期中联考数学试题金太阳2022-2023学年高二上学期期中数学试题辽宁省抚顺市六校协作体2022-2023学年高三上学期期中考试数学试题辽宁省实验中学2023-2024学年高二上学期10月月考数学试题江西省南昌市铁路第一中学2023-2024学年高二上学期10月月考数学试题重庆市重点中学2023-2024学年高二上学期10月月考数学试题福建省福州市闽侯县第一中学2023-2024学年高二上学期10月月考数学试题