名校
解题方法
1 . 如图所示,在直三棱柱
中,若
,
,则下列说法中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6c02338caa8ea2a27a5a37226a8a472.png)
A.三棱锥![]() ![]() |
B.点![]() ![]() ![]() ![]() |
C.![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.点![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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2 . 刻画空间的弯曲性是几何研究的重要内容,用曲率刻画空间的弯曲性,规定:多面体顶点的曲率等于2π与多面体在该点的面角之和的差,其中多面体的面的内角叫做多面体的面角,角度用弧度制.例如:正四面体每个顶点均有3个面角,每个面角均为
,故其各个顶点的曲率均为
.如图,在直三棱柱
中,点A的曲率为
,N,M分别为AB,
的中点,且
.
平面
.
(2)证明:平面
平面
.
(3)若
,求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7b2dd83fcacead6b6c7733503dfcee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e79fd1a2ba4245c902b45bf9fc5c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0211da37e92f915e781691296578ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00c25c4259d935d6e6fabe5c3fc1f43c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0b52ab4b32b650e57f9233c1b9bd30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c5282bc1ea20767a6c092c22c761ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95c6dbe3dde6e5b84a240b2baf87201.png)
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名校
解题方法
3 . 在圆锥
中,C是母线
上靠近点S的三等分点,
,底面圆的半径为r,圆锥
的侧面积为
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e5ef91fb27dd684a27ae7f1993cfba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ddaa2c8b030ac1dd8029a2413b166c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e5ef91fb27dd684a27ae7f1993cfba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9c018281fcaaf52863e1f83d9dad0.png)
A.当![]() ![]() |
B.当![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() ![]() |
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4 . 在三棱锥
中,已知
是边长为2的正三角形,且
.若
和
的面积之积为
,且二面角
的余弦值为
,则该三棱锥外接球的表面积为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e4d19bf237a6fca67e0d01a9ddb726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d294d69caac577339f11f477b2047e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
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5 . 如图,在五边形
中,四边形
为正方形,
,
,F为AB中点,现将
沿
折起到面
位置,使得
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ff27eea7545bb06f9472f91290c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddbb52f9b226b1db3f6f9f055948bd38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66a6eb75c2bc5a47ec8c8d83d79fd431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db6ff4159947ed2dc47d82fa3bcab9a.png)
A.平面![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.折起过程中,![]() ![]() |
D.三棱锥![]() ![]() |
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名校
解题方法
6 . 已知矩形
,其中
,
,点D沿着对角线
进行翻折,形成三棱锥
,如图所示,则下列说法正确的是__________ (填写序号即可).
①点D在翻折过程中存在
的情况;
②三棱锥
可以四个面都是直角三角形;
③点D在翻折过程中,三棱锥
的表面积不变;
④点D在翻折过程中,三棱锥
的外接球的体积不变.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c586b72a984e1fd9082b9f02ef7f3e91.png)
①点D在翻折过程中存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc9aabd9a42a97a1108149fafca8a919.png)
②三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c586b72a984e1fd9082b9f02ef7f3e91.png)
③点D在翻折过程中,三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c586b72a984e1fd9082b9f02ef7f3e91.png)
④点D在翻折过程中,三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c586b72a984e1fd9082b9f02ef7f3e91.png)
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解题方法
7 . 如图所示,在棱长为
的正方体
中,点
是平面
内的动点,满足
,则直线
与平面
所成角正切值的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](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/9e975f6c9fafab8fd7639dc0cd0f70a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd59db010066332804a06b9290ad6580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c798204bbe306b3efd5bc9eae594c171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e975f6c9fafab8fd7639dc0cd0f70a4.png)
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吉林省长春市第二中学2023-2024学年高一下学期第二次学程考试(6月)数学试题浙江省杭州第二中学2023-2024学年高一下学期期中考试数学试卷(已下线)6.5.1直线与平面垂直-【帮课堂】(北师大版2019必修第二册)(已下线)专题04 第八章 立体几何初步(2)-期末考点大串讲(人教A版2019必修第二册)(已下线)专题01 高一下期末真题精选(2)-期末考点大串讲(人教A版2019必修第二册)安徽省安庆市第一中学2023-2024学年高一下学期5月同步测试数学试卷
名校
8 . 已知
是直线
上的动点,
为坐标原点,过
作圆
的两条切线,切点分别为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980737863d238e24e443230ff19d9bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
A.当点![]() ![]() ![]() ![]() ![]() |
B.当![]() ![]() ![]() |
C.![]() ![]() |
D.![]() ![]() |
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2卷引用:吉林省通化市梅河口市第五中学2024届高三下学期一模数学试题
解题方法
9 . 如图,在多面体
中,底面
是边长为
的正方形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f1b071579d7562d63aef9fc1a49b260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
平面
,动点
在线段
上,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/8ee0dd40-162e-4c2e-88c3-35abdcd2a35e.png?resizew=172)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f1b071579d7562d63aef9fc1a49b260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5d971c5140d79006ca2d066c2eaa81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/8ee0dd40-162e-4c2e-88c3-35abdcd2a35e.png?resizew=172)
A.![]() |
B.存在点![]() ![]() ![]() ![]() |
C.三棱锥![]() ![]() ![]() |
D.当动点![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
10 . 已知圆
,直线
过点
,且交圆
于B,C两点,点
为线段
的中点,点
为圆
上任意一点,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4c60a4ff9461122d351735ba44a071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a26e951d6d2369e8da79a793a93a66a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5374caaa0cb83b1781af1beab7adcfa5.png)
A.若圆![]() ![]() ![]() ![]() ![]() |
B.使![]() ![]() |
C.若直线![]() ![]() ![]() |
D.![]() ![]() |
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