1 . 如图,边长为4的正方形
中,点
分别为
的中点.将
,
分别沿
折起,使
三点重合于点
.
平面
;
(2)求三棱锥
的体积;
(3)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fe9986ebbc986fc422e514ab93a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5aed4f27de48e30e6e336aba736bf80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13668f033d00acfc366f7e47949c4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aade83af002b001a9367c2226dcfcda0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b69dd5d0374760007f4ec707a6723e0.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb3d49759594355505caaf42691e5363.png)
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2卷引用:广东省东莞市海德双语学校2023-2024学年高一下学期6月月考数学试卷
2 . 如图,在正三棱柱
中,
为
的中点.
平面
.
(2)求异面直线
与
所成角的余弦值.
(3)在
上是否存在点
,使得平面
平面
?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5362fa29dbedcdc84cda3dc5f8165c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0186d11008c7d66c85ed0d8d2e568908.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ecad355286188fd317939fa50f9555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39282bdf319f30d7bc261e2e3ab3b1e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bdc02a625fbfdd1b50c1796c1e33e95.png)
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3卷引用:广东省广州市真光中学2023-2023学年高一下学期月考数学试题
广东省广州市真光中学2023-2023学年高一下学期月考数学试题湖南省郴州市第一中学等校2023-2024学年高一下学期5月联考数学试题(已下线)贵州省贵阳市南明区部分学校2023-2024学年高一下学期6月联考数学试题
名校
3 . 在如图所示的多面体
中,四边形
是边长为
的正方形,其对角线的交点为
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b695b7f6cade157f08afee8570804e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84da16fb63c603c1a4383e83a97787f4.png)
,点
是棱
的中点.
平面
;
(2)求直线
和平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ee947130b72cccc577463e7c3d6e46f.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/3b1c2a9af60eeffad1df194e21aa08ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b695b7f6cade157f08afee8570804e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84da16fb63c603c1a4383e83a97787f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c70ba19e25c0ee0e174e72ba192834c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b61346bd4091070ba84a4046f87f365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8948ac8156d19336083987d47b0f7038.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70db40c42655327adee01caedfc9d50c.png)
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2卷引用:广东省深圳市光明区高级中学2023-2024学年高三下学期5月模拟考试数学试题
解题方法
4 . 如图,已知四棱台
的上、下底面分别是边长为2和4的正方形,
,且
底面ABCD,点P、Q分别是棱
、
的中点.
内是否存在点M,满足
平面CPQ?若存在,请说明点M的位置,若不存在,请说明理由;
(2)设平面CPQ交棱
于点T,平面CPTQ将四棱台
,分成上、下两部分,求上、下两部分的体积比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
(2)设平面CPQ交棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
您最近一年使用:0次
解题方法
5 . 如图,在长方体
中,
,
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7863ef41313423eb2247c0f9e5ad0f54.png)
A.![]() ![]() |
B.![]() ![]() ![]() |
C.![]() ![]() ![]() |
D.该长方体的外接球的表面积为![]() |
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名校
解题方法
6 . 在三棱锥
中,且
,
,
.
平面BCD.
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c9fef50a33b465aa4edc898974be7b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7daa2e5fdd2f3db55021436a884a73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95c3a9f27b8f6766aafda84ebefa736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1854ba6cc92481d7a616bd2788a47e.png)
您最近一年使用:0次
7 . 已知三棱柱
中,侧棱垂直于底面,
,点
是
的中点.正
的边长为
,
,
平面
;
(2)求三棱锥
的体积;
(3)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c90ff9402bacab8319385d3bab70dcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd597851c0db4e4de4769e10e09383b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd209cc3f91b254f5ed934e89271e0e.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d6c98b5ed325bea4a4897a60cb1c12.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a148a5584e41408fc74f8bd386b5b8.png)
您最近一年使用:0次
名校
8 . 如图,在四棱台
中,底面
为正方形,
为等边三角形,
为
的中点.
;
(2)若
,
,求直线
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be5f9ef971747d2d5bbc5823797a7a65.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/2efa092d99725fc5e9a2dcbdbf574016.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8681c1580117ed5c914c6f34cad854b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2f2241a27e42c69a2f84e44e25a5eee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
您最近一年使用:0次
2024-06-18更新
|
648次组卷
|
2卷引用:广东省湛江市第二十一中学2024届高三高考冲刺数学试题
名校
解题方法
9 . 如图,在四棱锥
中,底面
为正方形,
平面
,
,
为
中点,
为
中点,
为线段
上动点.
为
中点,求证:
平面
;
(2)证明:
平面
.
![](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/d9a4950a6e4202efd609507964af238b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19129982fd8389238b303e091bd94c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
名校
解题方法
10 . 如图,在直三棱柱
中,
,
,
为
的中点.
平面
;
(2)若二面角
的余弦值为
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d331850e91390d587ccddcb892f977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4560fa4ad459b58b723c74bd24e51ebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec2524be492bca0d1566bf848066f10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
您最近一年使用:0次
2024-06-17更新
|
1272次组卷
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4卷引用:广东省江门市开平市开侨中学2023-2024学年高二下学期期末热身模拟数学试题