名校
解题方法
1 . 在棱长均相等的四面体
中,
为棱
(不含端点)上的动点,过点
的平面
与平面
平行.若平面
与平面
,平面
的交线分别为
,则
所成角的正弦值的最大值为________ .
![](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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
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名校
解题方法
2 . 在棱长为1的正方体
中,E,F分别为
和
的中点,
是侧面
内一点,若
平面
,则线段
长度的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183d4a4db2be531d09a180b36515ff75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5563473602e1b17d582a165b7b7b6b2.png)
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名校
解题方法
3 . 《九章算术》是我国古代数学名著,它在几何学中的研究比西方早
多年,在《九章算术》中,将底面为直角三角形且侧棱垂直于底面的三棱柱称为堑堵,将底面为矩形且一侧棱垂直于底面的四棱锥称为阳马,将四个面均为直角三角形的四面体称为鳖臑.如图在堑堵
中,
,
,
,
分别为棱
,
的中点,则下列说法正确的是______ .(只填序号)
①四面体
为鳖臑
②
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
③若
,则
与
所成角的正弦值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa42621cd6793e7f3673fdb49bc3123.png)
④三棱锥
的外接球的体积为定值![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30821635432b069b6c2bf74fa09552f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dadc63e6e33743ce590ed968948a5a58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30dbd22b0cbb47c914c42a4355e3ca98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
①四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/861d61d2b7b16e12fd97f870fb3fa522.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa42621cd6793e7f3673fdb49bc3123.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/861d61d2b7b16e12fd97f870fb3fa522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30821635432b069b6c2bf74fa09552f.png)
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名校
解题方法
4 . 在直四棱柱
中,所有棱长均为2,
,
为
的中点,点
在四边形
内(包括边界)运动,下列结论中正确的是_____ (填序号)
在线段
上运动时,四面体
的体积为定值
②若
面
,则
的最小值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
③若
的外心为M,则
为定值2
④若
,则点
的轨迹长度为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71a46dc0bb5d8fa33583817e530a5d21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b54387f870ae37f7951b253665d64f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd91ef047f2591dc1406bc0e39934fe6.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea3bcade880af77158e0dc1a6af2980.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be61fee6829cb6e6fe17808c1a8fe197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4996e2ab0b3cdb7d3406e038e5a46c5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497ad8ec00e4751a797d755753c8e760.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e077661d6c2faacf4a12f6cfba099f88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
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2024-06-11更新
|
405次组卷
|
2卷引用:江苏省扬州市第一中学2023-2024学年高一下学期5月教学质量调研评估数学试题
名校
5 . 下列命题正确的是__________ .(填序号)
①若一条直线平行于两个相交平面,则这条直线与这两个平面的交线平行;
②垂直于同一条直线的两直线平行;
③两个平面互相垂直,过一个平面内任意一点作交线的垂线,必垂直与另一个平面;
④过两个点与已知平面的垂直的平面可能不存在;
⑤过两条异面直线外任一点有且只有一条直线与这两条异面直线都垂直;
⑥到一个四面体的四个顶点的距离都相等的平面有7个.
①若一条直线平行于两个相交平面,则这条直线与这两个平面的交线平行;
②垂直于同一条直线的两直线平行;
③两个平面互相垂直,过一个平面内任意一点作交线的垂线,必垂直与另一个平面;
④过两个点与已知平面的垂直的平面可能不存在;
⑤过两条异面直线外任一点有且只有一条直线与这两条异面直线都垂直;
⑥到一个四面体的四个顶点的距离都相等的平面有7个.
您最近一年使用:0次
6 . 在棱长为1的正方体
中,P为正方形ABCD内(包括边界)的一动点,E,F分为别为棱AB,BC的中点,若直线
与平面
无公共点,则线段
的长度范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c798204bbe306b3efd5bc9eae594c171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1f68454096da710903e9693c7f2015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c798204bbe306b3efd5bc9eae594c171.png)
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2024高一下·全国·专题练习
解题方法
7 . 如图,已知四面体ABCD的各条棱长均等于4,E,F分别是棱AD、BC的中点.若用一个与直线EF垂直,且与四面体的每一个面都相交的平面
去截该四面体,由此得到一个多边形截面,则该多边形截面面积最大值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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解题方法
8 . 在棱长为1的正方体
中,过面对角线
的平面记为
,以下四个命题:
,使
;
②若平面
与平面
的交线为
,则存在直线
,使
;
③若平面
截正方体所得的截面为三角形,则该截面三角形面积的最大值为
;
④若平面
过点
,点
在线段
上运动,则点
到平面
的距离为
.
其中真命题的序号为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b239e234d9ae31814af54bf27b7056ba.png)
②若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d0c6947783608bd8f6dc7fdaadad2cb.png)
③若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
④若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b78c047642924fe864028c81b1f49d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
其中真命题的序号为
您最近一年使用:0次
解题方法
9 . 在
中,
是边
的中点,
是边
上的动点(不与
重合),过点
作
的平行线交
于点
,将
沿
折起,点
折起后的位置记为点
,得到四棱锥
,如图所示,给出下列四个结论:正确的是_______ .
不可能为等腰三角形;
②
平面
;
③对任意点
,都有平面
;
④存在点
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e8a02a7f28add9b9f32e836fd8a55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2ea13010e2399194be2a681310543e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57650963051ccb44a3cfb24f08228405.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f9596850884048064a3ec8bd48c4762.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f81fa367ec317fe2a30142e1c30cce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
③对任意点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30802944c1ea7d005c392e9a54eabedc.png)
④存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666e81326945f168fc30291f1bb2fc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9986e9390b44ddde72b54779f5825bb6.png)
您最近一年使用:0次
10 . 如图,在长方体
中,
,
,M,N分别为BC,
的中点,点P在矩形
内运动(包括边界),若
平面AMN,则
取最小值时,三棱锥
的体积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5213d6ac74fb6044cab6927a3d2acaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f86e2d69b11402d9d6cbb06e057778a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d88755289c4e9a6fd25b181c82bf8057.png)
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