2024·全国·模拟预测
名校
1 . 已知平面
平面
,且均与球
相交,得截面圆
与截面圆
为线段
的中点,且
,线段
与
分别为圆
与圆
的直径,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414844edd458857bdfc80bffa61cbf9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32987e12782f888f4a6db40c5c3d13ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2892d380f9370caecf6ac7370b3a0737.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/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
A.若![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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2 . 如图所示,四边形
为梯形,
,
,
,以
为一条边作矩形
,且
,平面
平面
.
;
(2)甲同学研究发现并证明了这样一个结论:如果两个平面所成的二面角为
,其中一个平面内的图形
在另一个平面上的正投影为
,它们的面积分别记为
和
,则
.乙同学利用甲的这个结论,发现在线段
上存在点
,使得
.请你对乙同学发现的结论进行证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a75b1354b8b783a65ee5e3bc596a976.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbc56d42b003cbcb1fbe5c50e55b26b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3362a45b72536c714c5107b0ae94f1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c0db1f4f666a9be9ede868065a50997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31025539da369c563e8633f375146593.png)
(2)甲同学研究发现并证明了这样一个结论:如果两个平面所成的二面角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c5a434a89f3f689db2a4623efbc74a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81722445de00f3cfcc3cb97e45b0d8dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27e50f80b7bf7025a049692b17abcd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbce6d96030ceae48cfef1634085c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3effb95a6c4422798440cd8a2a110636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8c820f511d3b23ffebae3822f19589.png)
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解题方法
3 . 正方体的棱长为
,平面展开图为图①.
、
分别为棱与面对角线中点.则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() ![]() |
B.![]() |
C.![]() ![]() ![]() |
D.三棱锥![]() |
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名校
解题方法
4 . 空间四边形
中
分别为
的点(不含端点).四边形
为平面四边形且其法向量为
.下列论述错误项为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c2d86d8daea5e652d99fe1c6bc3f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0898551729a5c3d2c69d40ba58a7c9b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37564ec4e9e92485f1769e8ffaac31d.png)
A.![]() ![]() ![]() |
B.![]() ![]() ![]() |
C.![]() ![]() |
D.![]() ![]() |
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5 . 如图,正方体
的棱长为2,在正方形
的内切圆上任取一点
,在正方形
的内切圆上任取一点
,在正方形
的内切圆上任取一点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/3/aab1b163-e061-424a-be58-377ca9a334d1.png?resizew=160)
(1)若
分别是棱
的中点,,求棱
和平面
所成角的余弦值;
(2)求
的最小值与最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4c7d46046bee57490a3e57cbb1d2fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c6d456e2adab93eabc931b3227bb79f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d85d8c1f8add55bdc8c393be3ba2ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acda1869fac2cc90e784fba183bbcc15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac64da7f096fea95c25cfe54fe83d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c89029e1d782dbf6a0bda8605a7c5ad4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9d7cb07ff7f2c4da5f7b33c5484c09.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/3/aab1b163-e061-424a-be58-377ca9a334d1.png?resizew=160)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99cc3fb30df78f02d680e281d7056dc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e6deeea89bf3591f0e272310f3d47a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade8909fc5354a7b5391213fbc5304ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef32166670d0745cd341ec21a6338cad.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14c5f98aafaae4bd386e8d9701187e70.png)
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2024-03-02更新
|
1137次组卷
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2卷引用:湖南省湖南省长沙市第一中学2024届高三下学期高考适应性演练(一)数学试题
名校
6 . 如图所示,圆台的上、下底面圆半径分别为
和
为圆台的两条不同的母线.
分别为圆台的上、下底面圆的圆心,且
为等边三角形.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/d1ec33ef-6414-439c-8a01-5fe56fdfd595.png?resizew=153)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
;
(2)截面
与下底面所成的夹角大小为
,求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c78d0ab561d0c9bb9099772c596af8bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7d791489abcbe5a60c359093981fe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cef469b1ee29d124cfd6f62423724cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/d1ec33ef-6414-439c-8a01-5fe56fdfd595.png?resizew=153)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)截面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2d57c8c293377c6dd5d5aadd5e22b33.png)
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2024-01-24更新
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名校
解题方法
7 . 苏州博物馆(图一)是地方历史艺术性博物馆,建筑物的顶端可抽象为如图二所示的上、下两层等高的几何体,其中上层是正四棱柱,下层底面
是边长为4的正方形,
在底面
的投影分别为
的中点,若
,则下列结论正确的有( )
A.该几何体的表面积为![]() |
B.将该几何体放置在一个球体内,则该球体体积的最小值为![]() |
C.直线![]() ![]() ![]() |
D.点![]() ![]() ![]() |
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2023-11-10更新
|
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10卷引用:湖南省常德市部分学校2023-2024学年高二上学期11月联考数学试题
湖南省常德市部分学校2023-2024学年高二上学期11月联考数学试题湖南省湘潭市湘潭县第四中学2023-2024学年高二上学期期中数学试题河北省部分高中2023-2024学年高二上学期期中数学试题河北省邢台市五岳联盟2023-2024学年高二上学期期中数学试题湖北省荆州中学2023-2024学年高二上学期期中数学试题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河北省沧州市沧县中学等校2023-2024学年高二上学期期中联考数学试题河北省石家庄市第十八中学2023-2024学年高二上学期期中数学试题(已下线)黄金卷02(已下线)第四章 立体几何解题通法 专题三 参数法 微点3 参数法综合训练【培优版】
名校
解题方法
8 . 如图所示的空间直角坐标系中,
,
,M是BC上的一个靠近B的三等分点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52705567101a48893de582656ef41527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40d398e31d27052f0b689bb30706faac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/10/f49a40a5-05ca-48f2-9211-87b303b8b652.png?resizew=150)
A.![]() |
B.存在实数x,y,使得![]() |
C.点C到AM的距离为![]() |
D.![]() |
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2023-10-09更新
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解题方法
9 . 如图1,《卢卡•帕乔利肖像》是意大利画师的作品.图1中左上方悬着的是一个水晶多面体,其表面由18个全等的正方形和8个全等的正三角形构成,该水晶多面体的所有顶点都在同一个正方体的表面上,如图2.若
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/056c2272e0d10d6dd9706e6324d8e62d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/7/e2766f47-dfba-470c-a91c-9c5dd8604653.png?resizew=354)
A.![]() |
B.该水晶多面体外接球的表面积为![]() |
C.直线![]() ![]() ![]() |
D.点![]() ![]() ![]() |
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2023-08-03更新
|
589次组卷
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4卷引用:湖南省湘潭市湘潭县第一中学等2022-2023学年高二下学期期末联考数学试题
10 . 如图,圆柱的轴截面
是边长
,
的矩形,点
在上底面圆
内,且
(
,
,
三点不在一条直线上).下底面圆
的一条弦
交
于点
,其中
,平面
平面
.
(1)证明:
平面
;
(2)若二面角
的正切值为
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49437f474e5805688dff21ded2d1fd7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9ba35b3357bff9ec2801b955b6ccc63.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f4da89257f9bb399d8b9cd874b222b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0955685db9fa79c29b1211805662c247.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40d2f4252121bc0b97333b34d1d8eeab.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/2/bc80ed13-cd42-49ec-a899-923206f4906f.png?resizew=130)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9df740160690029ac1e730c85f20347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb32b4f2ac4e9c29c3e437439f75bd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
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