名校
1 . 如图,在正四棱柱
中,
,
,点
,
分别为
,
的中点,则二面角
的大小为______ ;三棱锥
的外接球的表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db57eca2a7cbd91bc57372592580a76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7be2f695260a14809dec7d84dfd6fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/580be22c91b2343e7933f8b1d925fc52.png)
您最近一年使用:0次
名校
2 . 如图,已知矩形
中,
,
,将矩形沿对角线
把
折起,使
移到
点,点
在
上,且
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/894891b7-c4cf-4903-8c21-f8ed5f324995.png?resizew=195)
(1)求证:
;
(2)求证:平面
平面
;
(3)求二面角
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc34db5860990e51ba31edc8cdd077c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e5981445b6f2a6c58974158d96a4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/894891b7-c4cf-4903-8c21-f8ed5f324995.png?resizew=195)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f752d8a27ed612c37ddc86e8b483a243.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dee56b9f36ba8f76fe67b76383636b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e18b48c0263fbc4cbf072b7662589e2.png)
您最近一年使用:0次
3 . 已知三棱锥
的所有顶点都在表面积为
的球O的球面上,AC为球O的直径,当三棱锥
的体积最大时,设二面角
的大小为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95345846d2dd4dfa042a9093c62a8b82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d294d69caac577339f11f477b2047e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/224ddd2da7f0013f0ccd1761d25370bf.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
4 . 如图,四棱锥
中,底面
为矩形,
底面
,
,点E是棱PB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/490cbe02-6b98-4f5a-8878-25d268051807.png?resizew=157)
(1)证明:
;
(2)若
,求二面角
的平面角的余弦值.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f235e99b0b55ac252c4b18cc315dc114.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/490cbe02-6b98-4f5a-8878-25d268051807.png?resizew=157)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4486d52b6e410fd7b60428121d96cef.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28f06184f021ac21d72de1c7f55b0778.png)
您最近一年使用:0次
2020-04-21更新
|
529次组卷
|
2卷引用:青海省海东市平安县第一高级中学2017-2018学年高二上学期期中考试数学(A卷)试题
5 . 在正方体
中,下列几种说法不正确的是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd694ad3a4733c7c84aaa7946aeea4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
A.![]() | B.B1C与BD所成的角为60° |
C.二面角![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
2019-01-28更新
|
907次组卷
|
4卷引用:青海省西宁市大通回族土族自治县2021-2022学年高二上学期期末考试数学(理)试题
6 . 如图,在单位正方体
中,点P在线段
上运动,给出以下四个命题:
![](https://img.xkw.com/dksih/QBM/2018/2/9/1878479938617344/1910709412995072/STEM/1c3472d8-ff47-42f5-ab12-89ae95b0caf4.png?resizew=193)
异面直线
与
间的距离为定值;
三棱锥
的体积为定值;
异面直线
与直线
所成的角为定值;
二面角
的大小为定值.
其中真命题有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd694ad3a4733c7c84aaa7946aeea4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8c72afea9fa5ab7f62401e15ca9743.png)
![](https://img.xkw.com/dksih/QBM/2018/2/9/1878479938617344/1910709412995072/STEM/1c3472d8-ff47-42f5-ab12-89ae95b0caf4.png?resizew=193)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c512c047783c07da1d4f4455a4033ef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69d591d3dfe8bd420a1fdae92a5dc6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c4ad6c77a6459a37bc398ecd5e5253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876959b9f90f2379cf3d0927a8e31005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84bff766663791e54708508919a9eec7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67773252101fb3704fdac88b5f3f1bda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7561e754058a8686dfe6e7c0a3fb73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780901c1977b08c38c6ca1e36fe667c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74269cfb503e736149e1ac3165fcbafa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7655f4296dcd6e8f7f5a9e75aebdf.png)
其中真命题有
A.1个 | B.2个 | C.3个 | D.4个 |
您最近一年使用:0次
2018-03-26更新
|
6796次组卷
|
15卷引用:青海省湟川中学2019-2020学年高二上学期期末考试数学(理)试题
青海省湟川中学2019-2020学年高二上学期期末考试数学(理)试题江西省南昌市第三中学2017-2018学年度上学期高二期末考试数学(理)试题重庆市渝北区松树桥中学校2019-2020学年高二上学期第一次段考考数学试题黑龙江省大庆市铁人中学2019-2020学年高二下学期第一次月考学数学(理)试题安徽省阜阳市太和第一中学2020-2021学年高二(奥赛班)上学期开学考试数学试题黑龙江省大庆中学2021-2022学年高二上学期开学考试数学试题(已下线)卷02 空间向量与立体几何-单元检测(中)-2021-2022学年高二数学单元卷模拟(易中难)(2019人教A版选择性必修第一册+第二册)黑龙江省大庆市让胡路区大庆中学2021-2022学年高二上学期数学开学考试试题四川省雅安市芦山县芦山中学2020-2021学年高二下学期期中数学理科试题四川省泸州市泸县第一中学2022-2023学年高二下学期开学考试数学(理)试题四川省宜宾市叙州区第一中学校2022-2023学年高二下学期4月月考数学(理)试题【全国百强校】郑州外国语学校2018届高三第十五次调研考试(文)试题(已下线)专题4.3 立体几何的动态问题-玩转压轴题,进军满分之2021高考数学选择题填空题(已下线)专题05 押全国卷(理科)7,9小题 立体几何(已下线)第二章 立体几何中的计算 专题六 空间定值问题 微点1 立体几何中的定值问题综述及定长、定距问题【培优版】
7 . A是锐二面角α-l-β的α内一点,AB⊥β于点B,AB=
,A到l的距离为2,则二面角α-l-β的平面角大小为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3f8c3ba00c59e0634ed10fa85289de.png)
您最近一年使用:0次
2017-12-03更新
|
592次组卷
|
3卷引用:青海省西宁市第十四中学2019-2020学年高二上学期期中数学(文)试题
12-13高一上·福建·期末
8 . 如图,已知正方体
,则二面角
的正切值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd190b5a26dfb45a06c1d6ee86dd82d9.png)
![](https://img.xkw.com/dksih/QBM/2017/4/14/1665420759760896/1666346901176320/STEM/28cbba81dbf04fcc89e98fee48491d62.png?resizew=101)
您最近一年使用:0次
2017-04-15更新
|
570次组卷
|
6卷引用:青海省大通回族土族自治县第一完全中学2019-2020学年高二上学期期中考试数学试题
青海省大通回族土族自治县第一完全中学2019-2020学年高二上学期期中考试数学试题2016-2017学年湖南省醴陵二中、醴陵四中高二下学期期中联考数学(文)试卷人教版 全能练习 必修2 第一章 滚动习题(二)(已下线)2011-2012学年福建省八县一中高一上学期期末考试数学(已下线)2011-2012学年福建省厦门六中高一下学期期中数学试卷2015-2016学年福建省师大附中高一上学期期末数学试卷
9 . 如图,在圆锥
中,已知
的直径
的中点.
![](https://img.xkw.com/dksih/QBM/2014/5/22/1571734572580864/1571734578470912/STEM/b2a6ed50-3f10-4f9e-9beb-2867593916fc.png?resizew=238)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adec05260cb32350463ec97607b9d0a1.png)
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7648f049cc17a82fe816f5de3d9693c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5c6af2604ff0f121c696eb2876f023f.png)
![](https://img.xkw.com/dksih/QBM/2014/5/22/1571734572580864/1571734578470912/STEM/b2a6ed50-3f10-4f9e-9beb-2867593916fc.png?resizew=238)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adec05260cb32350463ec97607b9d0a1.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a4bddf1ea3c5d37f2233a4821909e9.png)
您最近一年使用:0次
2016-12-03更新
|
3406次组卷
|
4卷引用:青海省西宁市城西区青海湟川中学2020-2021学年高二上学期期中数学试题
10 . 如图,
与
都是边长为2的正三角形,平面
平面
,
平面
,
.
(1)求直线
与平面
所成的角的大小;
(2)求平面
与平面
所成的二面角的正弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/14/1b33781a-322d-457a-a9ca-b38ea92942f6.png?resizew=150)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df6d51738ac1bc8b9530ea4a55745c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13fd8dabc5a9c5f42aa21044007c7bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c72b92177ddfe056e6f90af4f37e64d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077c956ac0eb05cf120e14f17413dfa2.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/14/1b33781a-322d-457a-a9ca-b38ea92942f6.png?resizew=150)
您最近一年使用:0次
2016-11-30更新
|
4428次组卷
|
9卷引用:青海省湟川中学2019-2020学年高二上学期期末考试数学(理)试题
青海省湟川中学2019-2020学年高二上学期期末考试数学(理)试题福建省泉州市晋江市南侨中学2019-2020学年高二上学期11月月考数学试题陕西省商洛市商丹高新学校2019-2020学年高二上学期11月质量检测数学(理)试题广东省广州市广州大学附属中学2021-2022学年高二上学期9月入学考试数学试题重庆市石柱中学校2021-2022学年高二上学期第一次月考数学试题2010年普通高等学校招生全国统一考试(江西卷)数学(文科)(已下线)考点21 直线、平面垂直的判定及其性质-备战2022年高考数学(文)一轮复习考点微专题(已下线)专题8.7 立体几何中的向量方法(练)- 2022年高考数学一轮复习讲练测(新教材新高考)(已下线)考向24空间向量与立体几何-备战2022年高考数学一轮复习考点微专题(上海专用)