2022高三·全国·专题练习
1 . 在如图所示的几何体中,
平面
,
平面
,
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/0370cf55-b102-4527-bb65-8323f4096abd.png?resizew=147)
(1)求证:
;
(2)求
与平面
所成角的大小;
(3)求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed04b01505bbd8a4ac0bc12e46f23bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c5ae16a7145a28a91d45ef950a07c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0134a8463eec67424af096f369777557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/0370cf55-b102-4527-bb65-8323f4096abd.png?resizew=147)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/785546906851d56da452b46052eeb8a0.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383ec3453527947ed7a5960e9a8fbe0b.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
您最近一年使用:0次
名校
2 . 如图,在四棱锥
中,平面
平面
,四边形
是边长为2的菱形,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/17/7a27efab-0905-47af-8083-aef2eba0e679.png?resizew=163)
(1)求证:
;
(2)若
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/17/7a27efab-0905-47af-8083-aef2eba0e679.png?resizew=163)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ccd5c41c921836b50f8e18abfdc5df3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ec435aa1401dbce7863b531bf2f3e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
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2022-07-12更新
|
1235次组卷
|
2卷引用:新疆维吾尔自治区乌鲁木齐市第101中学2022-2023学年高二上学期12月月考数学试题
名校
3 . 如图,四边形
为菱形,
,将
沿
折起,得到三棱锥
,点M,N分别为
和
的重心.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/15/532c4dbc-6d2b-450b-a7b4-3af6a6222db2.png?resizew=296)
(1)证明:
∥平面
;
(2)当三棱锥
的体积最大时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f9b0e2a09c7cddb40cea36cbade9b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/15/532c4dbc-6d2b-450b-a7b4-3af6a6222db2.png?resizew=296)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212a67f115d1cbe69f100b489babe5f8.png)
(2)当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6230ec526fcab9f2e73901cca0a5a5f0.png)
您最近一年使用:0次
2022-06-14更新
|
791次组卷
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6卷引用:新疆维吾尔自治区乌鲁木齐市第101中学2024届高三上学期8月月考数学(理)试题
新疆维吾尔自治区乌鲁木齐市第101中学2024届高三上学期8月月考数学(理)试题福建省三明市第一中学2022届高三5月质量检测数学试题河南省濮阳市第一高级中学2021-2022学年高三上学期第一次质量检测理科数学试题(已下线)第4讲 空间向量的应用 (3)(已下线)第07讲 空间向量的应用 (2)理科数学-【名校面对面】河南省三甲名校2023届高三校内模拟试题(六)
名校
4 . 四棱锥
中,四边形
为梯形,其中
,
,
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/8/106276a8-c69e-4e1a-b856-c610539f41a2.png?resizew=132)
(1)证明:
;
(2)若
,且
与平面
所成角的正弦值为
,点
在线段
上且满足
,求二面角
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/68d31600cba2d5256c7e78b6122d6755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec2d5ab801f2a84b78139b0ea2c5032b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ec435aa1401dbce7863b531bf2f3e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/8/106276a8-c69e-4e1a-b856-c610539f41a2.png?resizew=132)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9104a1941e557a85fd1496bc2b9be297.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d0710321d97361e5782124bbf7f0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d9662368fd788afb77b79035cdd268b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fdc0a6c51f53d6845deec5edd6a200f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26bd9e6b1ef5ea610e0e9a2a4eff4a94.png)
您最近一年使用:0次
2022-09-08更新
|
889次组卷
|
4卷引用:新疆克拉玛依市第十三中学2024届高三上学期12月月考数学试题
名校
5 . 如图,四边形ABCD是圆柱的轴截面,
,O分别是上、下底面圆的圆心,EF是底面圆的一条直径,DE=DF.
![](https://img.xkw.com/dksih/QBM/2022/3/24/2943275657469952/2943887327248384/STEM/6733c25cd9b3432e834d1091d18c5e34.png?resizew=254)
(1)证明:EF⊥AB;
(2)若
,求平面BCF与平面CDE所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://img.xkw.com/dksih/QBM/2022/3/24/2943275657469952/2943887327248384/STEM/6733c25cd9b3432e834d1091d18c5e34.png?resizew=254)
(1)证明:EF⊥AB;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb37765c3d5d6b74791358200a834a67.png)
您最近一年使用:0次
2022-03-25更新
|
1021次组卷
|
5卷引用:新疆昌吉学联体2022届高三下学期第三次高考适应性联考数学(理)试题
名校
6 . 如图所示等腰梯形ABCD中,
,
,
,点E为CD的中点,沿AE将△DAE折起,使得点D到达F位置.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/96529d3a-60d0-44a3-88e8-48672a4363ce.png?resizew=222)
(1)当
时,求证:
平面AFC;
(2)当
时,求二面角B-EF-C的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21da760ad4567cbf991f70dca72f60d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e918b70b02a73685e3c536c7f380e2c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/96529d3a-60d0-44a3-88e8-48672a4363ce.png?resizew=222)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2f0d6b7c46fd8152fc6f7bfc70ae54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662698361c6b3ddaf0c28a3c87be53e0.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246403a89c5e6795ef2ac6eb19928ced.png)
您最近一年使用:0次
2022-03-02更新
|
256次组卷
|
2卷引用:新疆维吾尔自治区乌鲁木齐市第十二中学2024届高三下学期2月月考数学试题
名校
7 . 如图,在四棱锥
中,平面
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/e17d9f5d-b9de-4052-a288-c1ec4859c9df.png?resizew=201)
(1)求证:
平面
;
(2)若直线
与底面
所成的角的正切值为
,求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5799e67a7f6ef3e0e1ec46aa0ee4c0c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7856b06682c9058d76120982fdbc91c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/e17d9f5d-b9de-4052-a288-c1ec4859c9df.png?resizew=201)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/290a37874cd284fb1a8c864769ce50c9.png)
您最近一年使用:0次
2022-02-08更新
|
474次组卷
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8卷引用:新疆维吾尔自治区伊宁市第三中学2024届高三下学期3月月考数学试题
新疆维吾尔自治区伊宁市第三中学2024届高三下学期3月月考数学试题湖北省郧阳中学,恩施高中,随州二中,襄阳三中,十堰一中2021届高三下学期4月联考数学试题(已下线)专题2.7 空间向量与立体几何-2021年高考数学解答题挑战满分专项训练(新高考地区专用)湖南省长沙市长郡中学2021-2022学年高二上学期期中数学试题安徽省亳州市第一中学2021-2022学年高二上学期11月教学检测数学试题辽宁省葫芦岛市四校2022-2023学年高二上学期期中联考数学试题福建省泉州市泉港区第一中学、厦门外国语学校石狮分校2023-2024学年高二上学期期中联考数学试题湖南省长沙外国语学校2023-2024学年高二下学期3月月考数学试题
名校
8 . 如图,在四棱锥
中,底面
是直角梯形,
,
,平面
平面
,E是
的中点,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/20/e8bec57e-7de7-4700-8617-11ff05d793a9.png?resizew=220)
(1)证明:
;
(2)求平面
与平面
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/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2726a625945b21b63804e07dd12c920c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae79b7d1fc4131ae3b9de76e2fa45e5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58fc6a5e71fa379d613ac1ef1cdf1048.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/20/e8bec57e-7de7-4700-8617-11ff05d793a9.png?resizew=220)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfa54114f04a75b8c96165b3718ed7f.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb31601464364be2baf4aa87404bcd.png)
您最近一年使用:0次
2022-06-25更新
|
1171次组卷
|
5卷引用:新疆维吾尔自治区乌鲁木齐市第十二中学2024届高三上学期9月月考数学(理)试题
新疆维吾尔自治区乌鲁木齐市第十二中学2024届高三上学期9月月考数学(理)试题浙江省嘉兴市2021-2022学年高二下学期期末数学试题四川省内江市威远中学校2022-2023学年高三下学期第一次月考数学(理)试题江西省部分学校2022-2023学年高一下学期期末检测数学试题(已下线)第一章 空间向量与立体几何(基础、典型、新文化、压轴)分类专项训练-2022-2023学年高二数学考试满分全攻略(人教A版2019选择性必修第一册)
名校
解题方法
9 . 如图,在多面体
中,
为正方形,
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/1/14/2894203289747456/2895176848891904/STEM/54939ee7-0352-4531-94f2-2104ea035dd9.png?resizew=196)
(1)求证:
;
(2)求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1019c0405370c673e37b46c066eba839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1100a56e918f75ed6d955a802050f9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7a63258b68e472bedca08381d47630.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e0346a3f335e7734772d32d9903f2cc.png)
![](https://img.xkw.com/dksih/QBM/2022/1/14/2894203289747456/2895176848891904/STEM/54939ee7-0352-4531-94f2-2104ea035dd9.png?resizew=196)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2187a6bf82f1d5e534274e12f96594be.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00d4825584cf2a3f381de72c179e22.png)
您最近一年使用:0次
2022-01-15更新
|
418次组卷
|
5卷引用:新疆乌苏市第一中学2022-2023学年高二上学期线上第二次月考数学试题
名校
10 . 在正三角形ABC中,E、F、P分别是AB、AC、BC边上的点,满足
(如图1).将
沿EF折起到
的位置,使二面角
成直二面角,连接A1B、A1P(如图2)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/e2179bba-35a2-4e7a-812a-f03e1a2c7f25.png?resizew=314)
(1)求证:
平面BEP;
(2)求直线A1E与平面A1BP所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67cdda05f0fab4c742a89d6214f0cd5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb2d555062f34d5a74f6d47da4ea8888.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc14ed237a4bcc35cbd1f5f1321b3718.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/e2179bba-35a2-4e7a-812a-f03e1a2c7f25.png?resizew=314)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4525c00ed908bed8ba8d353e747a858.png)
(2)求直线A1E与平面A1BP所成角的大小.
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