名校
1 . 在三棱柱
中,侧面
平面
,
,侧面
为菱形,且
为
中点.
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df00cdf77ed39ca5a0b305861a693142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65220a73f2926dd73e083627524af97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/269c684310d0f7b5b9bf0a291e7ee748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a0bebcc9e80bbe35943d42f0e00d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4890e58791814622b87c4d60ea971f54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd9ed960d92cd08e368ed56651fe6632.png)
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解题方法
2 . 在棱长为2的正方体
中,
为
的中点,以
为原点,OB,OD,OO1所在直线分别为
轴、
轴、
轴,建立如何所示空间直角坐标系.若该正方体内一动点
,满足
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a20b689283cc8b311eddae4c8c4242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49ea83a384f056dadaacfa349cc84130.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bfcaf2a345411411cf94422703e9269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e588cb555e36f28c5db66d213ef064d4.png)
A.点![]() ![]() | B.![]() ![]() |
C.![]() | D.三棱锥![]() ![]() |
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3 . 如图所示,多面体
,底面
是正方形,点
为底面的中心,点
为
的中点,侧面
与
是全等的等腰梯形,
,其余棱长均为2.
平面
;
(2)若点
在棱
上,直线
与平面
所成角的正弦值为
,求
.
![](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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b312dab930cbbb9a4bb1a99f044dab73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/613dedf2d90e58591b7ac4a250ac7b5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab8a2ca644d9d7cdb4784a4fd28d3904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3653ada76ba0c8afe9d57c8e7832c6ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f44fc60c0b360e1b0708a249e4ce0643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f541f7ae7c39082d202efd28805c54e.png)
您最近一年使用:0次
4 . 如图1,在
中,
是
的中位线,沿
将
进行翻折,连接
得到四棱锥
(如图2),点
为
的中点,在翻折过程中,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/525cf9256d5dcd7bfc4b555fdcdd7009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e7cedc39297d66dbb177f2a1f6bee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.直线![]() ![]() |
B.直线![]() ![]() |
C.平面![]() ![]() ![]() |
D.平面![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
5 . 泉州花灯技艺源于唐朝中期从形式上有人物灯、宫物灯、宫灯,绣房灯、走马灯、拉提灯、锡雕元宵灯等多种款式.在2024年元宵节,小明制做了一个半正多面体形状的花灯,他将正方体沿交于一顶点的三条棱的中点截去一个三棱锥,共截去八个三棱锥,得到一个有十四个面的半正多面体,如图所示.已知该半正多面体的体积为
,M为
的中心,过M截该半正多面体的外接球的截面面积为S,则S的最大值与最小值之比( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d754c4ad51e4482e12a615d20a13fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.![]() | B.![]() | C.3 | D.9 |
您最近一年使用:0次
6 . 如图所示,点
为正方体形木料
上底面的动点,则下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
A.三棱锥![]() |
B.存在点![]() ![]() ![]() |
C.不存在点![]() ![]() ![]() |
D.经过点![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
解题方法
7 . 在四面体
中,平面
平面
,
是直角三角形,
,则二面角
的正切值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b027ed57b9c6f24e27ec0ae282c76efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae054a3f7c399dc5125ed094fd464dee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a438393ddfc7da1804baf4932442bb35.png)
您最近一年使用:0次
解题方法
8 . 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)
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名校
9 . 如图,在直三棱柱
中,
,
,
,
.
时,求证:
平面
;
(2)设二面角
的大小为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42da806a6bd2472459f6c4ad1dab7b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b360c98bd3fd209525fd8fece4246590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c3ea872a20fdc1843cb5ffce8a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b190c8d3d7d7d0e6e959e8a52eae90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
(2)设二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306681bd5aaa51e9c63ab3002e23dec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
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昨日更新
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123次组卷
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3卷引用:山东师范大学附属中学2024届高三下学期考前适应性测试数学试题
10 . 在四棱锥P-ABCD中,
底面
,四边形
是矩形,且
,点
是棱
上的动点(包括端点),则满足
的
点有( )
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b929269c53a44907dba8ee298a0a522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/248ddfad39864ab0e183e01f82859e72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
A.0个 | B.1个 | C.2个 | D.3个 |
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