名校
解题方法
1 . 已知正方体
中,
、
分别为对角线
、
上的点,且
.
平面
;
(2)若
是
上的点,当
的值为多少时,能使平面
平面
?请给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77f9abe92f0cf2354ad65698bbc45c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72221ee5b504d596ff799c0b356aa0ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4da530384dd04ac90a025385e8b3c2f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/426871e39448880776fce8f032160b77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a5536e5a3ae28abfd54cc7f6bc2629.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40fd1b9b362c293683af078e30f1ce60.png)
您最近一年使用:0次
2021-09-04更新
|
1362次组卷
|
6卷引用:浙江省杭州市第四中学下沙校区2021-2022学年高一下学期期中数学试题
浙江省杭州市第四中学下沙校区2021-2022学年高一下学期期中数学试题广东实验中学2020-2021学年高一下学期期中数学试题(已下线)8.5 空间直线、平面的平行(精练)-2021-2022学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)8.5.3平面与平面平行(练案)-2021-2022学年高一数学同步备课 (人教A版2019 必修第二册)重点题型训练13:第6章平行关系、垂直关系-2020-2021学年北师大版(2019)高中数学必修第二册广东省广州市七中2023-2024学年高一下学期期中数学试题
21-22高三上·黑龙江哈尔滨·阶段练习
名校
2 . 如图,在直三棱柱
中,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98332901058e22626af97bff1b71039.png)
![](https://img.xkw.com/dksih/QBM/2021/2/19/2661504202792960/2661637481037824/STEM/62472c22-ab1a-4588-a0e1-7d5569c19892.png)
(1)证明:当
时,求证:
平面
;
(2)当
时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ad3a578f403b9e6b97fa2dc955fc11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98332901058e22626af97bff1b71039.png)
![](https://img.xkw.com/dksih/QBM/2021/2/19/2661504202792960/2661637481037824/STEM/62472c22-ab1a-4588-a0e1-7d5569c19892.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3cf0f585938ede9eca890a6eb326d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6d06903252260d31d1a9cdeb735b089.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8845fadc307f1d308410e829becedd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78ceb31247add8ca7b0853e801e1d125.png)
您最近一年使用:0次
解题方法
3 . 如图,在四棱台
中,底面
为矩形,
,
,
,
.E为
靠近D点的三等分点,平面
与直线
交于点P,连接
交
于O点.
![](https://img.xkw.com/dksih/QBM/2021/2/2/2649276907134976/2650969003556864/STEM/86dbe61cbd3c494fa29fbe655d1438aa.png?resizew=382)
(1)求证:
;
(2)若F为
的三等分点(靠近B点),请在线段
上确定一点Q,使
平面
,并证明之.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077c956ac0eb05cf120e14f17413dfa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e05c4eff7615455af8500fa211b0b071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c02ffbf0d9a3a73b896732082710c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99644f0e0881bc7bf383a88eb92c0949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/2021/2/2/2649276907134976/2650969003556864/STEM/86dbe61cbd3c494fa29fbe655d1438aa.png?resizew=382)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d31767eb718a0327eca546fe6a189cb.png)
(2)若F为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a929faf549d8b8f1cd36d7a98257ace.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc4124fd4832415701968dbec3e7499.png)
您最近一年使用:0次
4 . 已知函数f(x)=
,其中c为常数,且函数f(x)的图象过原点.
(1)求c的值,并求证:f(
)+f(x)=1;
(2)判断函数f(x)在(-1,+∞)上的单调性,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802f4adf7c33387219bf1cf370aca9db.png)
(1)求c的值,并求证:f(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95fcfaf750395f9e5b843f017aab25d9.png)
(2)判断函数f(x)在(-1,+∞)上的单调性,并证明.
您最近一年使用:0次
5 . 已知函数
的定义域是
且
,
,当
时,
.
(1)求证:
是奇函数;
(2)求
在区间![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09bce7c5de6e43a203eb98a7c23f8985.png)
)上的解析式;
(3)是否存在正整数
,使得当x∈
时,不等式
有解?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://img.xkw.com/dksih/QBM/2015/7/3/1572163784851456/1572163790241792/STEM/a51771f539164b6e9d9eead0303f5eb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cda1d250b465616dbc1fd75a2359c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c3cfe479362ebb78ff9951d1d9f083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6c48591cae0bcf7ae6c8d589527c72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc4e3775c850f1c1804f9eb7a70153a.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09bce7c5de6e43a203eb98a7c23f8985.png)
![](https://img.xkw.com/dksih/QBM/2015/7/3/1572163784851456/1572163790241792/STEM/0e39cf5721f84387a7307e4ae19b2041.png)
(3)是否存在正整数
![](https://img.xkw.com/dksih/QBM/2015/7/3/1572163784851456/1572163790241792/STEM/c0a95e15d16643a2a69d6bd21d5d9265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da7f1da7e1c7aeaf845415de9aec0bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54218478418966f351be0d622a834f07.png)
您最近一年使用:0次
2016-12-03更新
|
203次组卷
|
2卷引用:2014-2015学年浙江省东阳中学高二下学期期中考试理科数学试卷
6 . 如图所示,
为平行四边形ABCD所在平面外一点,M,N分别为AB,PC的中点,平面PAD
平面PBC=
.
(1)求证:BC∥
;
(2)MN与平面PAD是否平行?试证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a66854bb5784c29a27075e884e10e392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/14/399c27b2-a665-4662-b01f-b2b094c376ce.png?resizew=123)
(1)求证:BC∥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)MN与平面PAD是否平行?试证明你的结论.
您最近一年使用:0次
2016-12-03更新
|
2275次组卷
|
22卷引用:【新东方】高中数学20210527-022【2021】【高一下】
(已下线)【新东方】高中数学20210527-022【2021】【高一下】(已下线)2014-2015学年江苏省高邮市第二中学高二学情检测数学试卷【全国百强校】陕西省西安市长安区第一中学2018-2019学年高一上学期第二次月考数学试题人教B版(2019) 必修第四册 逆袭之路 第十一章 立体几何初步 11.3.2 直线与平面平行天津市静海县第一中学2017-2018学年高一4月学生学业能力调研测试数学试题陕西省榆林市绥德中学2019-2020学年高一上学期第三次阶段性考试数学试题(已下线)【新教材精创】11.3.2直线与平面平行(第1课时)练习(1)四川省眉山市仁寿一中北校区2020-2021学年高二(上)期中数学试题云南省大理下关一中教育集团2020-2021学年高一下学期期中考试数学试题福建省龙岩市长汀县三级达标校2020-2021学年高一下学期期中考试数学试题江苏省南京师范大学附属实验学校2019-2020学年高一下学期第二次月考数学试题(已下线)第十一章 立体几何初步 11.3 空间中的平行关系 11.3.2 直线与平面平行人教A版高中数学必修二2.2.2平面与平面平行的判定2云南省保山市昌宁县2021-2022学年高一下学期期中考试数学试题(已下线)9.3 空间点、直线、平面之间的位置关系甘肃省定西市临洮县临洮中学2022-2023学年高一下学期期中数学试题2023版 湘教版(2019) 必修第二册 过关斩将 第4章 4.3 直线与直线、直线与平面的位置关系 4.3.2 空间中直线与平面的位置关系 第1课时 直线与平面平行第 10 章 空间直线与平面 “四基”单元测试云南省昭通市绥江县第一中学2020-2021学年高一下学期期中考试数学试题新疆维吾尔自治区2023年普通高中学业水平考试数学模拟试卷(四)河南省焦作市第十一中学2022-2023学年高一下学期4月月考数学试题(已下线)第十三章 立体几何初步(压轴题专练)-单元速记·巧练(苏教版2019必修第二册)
7 . 已知四棱锥
,
⊥面
,底面
为正方形,
,
为
的中点.
面
;
(2)求直线
与面
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.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/a93767331e9bac06a564973a9f4fc663.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defa5b53043ae802bb1af7d14374406d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b5e290c6b2c5508a3bf6117afbf7e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
您最近一年使用:0次
8 . 如图,四棱锥
中,底面
为正方形,
平面
,点
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/c37383f1-7423-4c39-8b4b-ca5b300aabbe.png?resizew=166)
(1)求证:
;
(2)求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b55fce0a4716058fe0ad64b01eccc66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e3a25299c121dbb883fd3c7918d566d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/c37383f1-7423-4c39-8b4b-ca5b300aabbe.png?resizew=166)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc6269077b8e6b063efb583c91a564d.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05479863cf9f41e2ad9f843ea740a3c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
您最近一年使用:0次
解题方法
9 . 如图,在四棱锥
中,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/adcb658e-3739-475d-ab40-db553701daba.png?resizew=144)
(1)求证:
;
(2)若四棱锥
的体积为12,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3ed4f6bc8c7f08e80b194b867b0092d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f72c935697ef9ceb633a15b90b19ebc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eee296a7d9fba487f1485c61580196f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/adcb658e-3739-475d-ab40-db553701daba.png?resizew=144)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44f4120c94cb7176dc31fcac387b32e.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2024-01-25更新
|
394次组卷
|
2卷引用:浙江省宁波市慈溪市2024届高三上学期期末测试数学试题
名校
解题方法
10 . 正方体
中,
,
分别是
,
的中点.
与
所成角;
(2)求证:
平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2024-05-08更新
|
3427次组卷
|
4卷引用:浙江省杭州外国语学校2023-2024学年高一下学期期中考试数学试卷
浙江省杭州外国语学校2023-2024学年高一下学期期中考试数学试卷(已下线)6.4.2平面与平面平行-【帮课堂】(北师大版2019必修第二册)(已下线)6.4 .1 直线与平面平行-同步精品课堂(北师大版2019必修第二册)广西来宾市忻城县高级中学2023-2024学年高一下学期5月月考数学试卷