1 . 如图,在长方体木料
中,
,
为棱
的中点,要过点
和棱
将木料锯开.
![](https://img.xkw.com/dksih/QBM/2021/7/6/2758350145085440/2778947132907520/STEM/7ed2088e90e942a3a5b83e7714aaf7e1.png?resizew=206)
(1)在木料表面画出符合要求的线,写出作图过程并说明理由;
(2)写出切割后体积较大的几何体的名称,并求出它的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f7ad41c55fab640a159a08a12c6b03c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2021/7/6/2758350145085440/2778947132907520/STEM/7ed2088e90e942a3a5b83e7714aaf7e1.png?resizew=206)
(1)在木料表面画出符合要求的线,写出作图过程并说明理由;
(2)写出切割后体积较大的几何体的名称,并求出它的体积.
您最近一年使用:0次
解题方法
2 . 如图,已知多面体
的底面
是边长为2的正方形,
底面
,
,且
.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712476293095424/2799521670234112/STEM/77ffa5cb-3f4b-459d-ae04-204c542de695.png?resizew=209)
(1)求证:
平面
;
(2)记线段
的中点为K,在平面
内过点K作一条直线与平面
平行,要求保留作图痕迹,但不要求证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a325f7220b9d63033befaa589646e802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed04b01505bbd8a4ac0bc12e46f23bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a060f4fc2c8034b08c77c065f9e125d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba1316f4183e8854d38283b716e2ba1b.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712476293095424/2799521670234112/STEM/77ffa5cb-3f4b-459d-ae04-204c542de695.png?resizew=209)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/111da2c687a67fd089c365090908eb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
(2)记线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f636f76d550dfb593a25eb680cff556.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,四边形
是正方形,
平面
,
,
,
在线段
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/dee0013d-4a39-4b68-af36-65913fee0109.png?resizew=141)
(1)若
平面
,请在图中画出点
,保留作图痕迹,并说明理由.
(2)是否存在点
,使得
与平面
所成角的正弦值为
,若存在,求出
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed04b01505bbd8a4ac0bc12e46f23bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/180868535d96d800625148a03a33e9d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bcf55cb4ea16c17f20e02190ffdff07.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/2022/12/26/dee0013d-4a39-4b68-af36-65913fee0109.png?resizew=141)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d30788a482598e638aea779ac14da12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df5935c893580c77ab6fa6eb0a70bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83303d3784492506fc44f2b4d6b07bc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383c681f398877a4589a389d19a0f2e6.png)
您最近一年使用:0次
名校
解题方法
4 . 已知正方体
中的棱长为2,
是
中点.则一定有__________.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/021fc76b-8880-4246-abc3-6ccc0e032d6e.png?resizew=164)
(1)在下面三个选项中选取一个正确的序号填写在横线上,并说明理由 .
①
面
②
与平面
相交 ③
面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4294ffdba16ae69fd03b13959d682aba.png)
(2)设
的中点为
,过
、
、
作一截面,交
于点
,求截面
面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/021fc76b-8880-4246-abc3-6ccc0e032d6e.png?resizew=164)
(1)在下面三个选项中选取一个正确的序号填写在横线上,并
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b40182088e5367922bce35c1e346e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4294ffdba16ae69fd03b13959d682aba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cee51552e3c12bc27cf8ab1777bf191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4294ffdba16ae69fd03b13959d682aba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8e17c564112659044ca3d4759e3923e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4294ffdba16ae69fd03b13959d682aba.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f882d03e5de46c3ad4c2620ca2200c5.png)
您最近一年使用:0次
2020-10-31更新
|
300次组卷
|
2卷引用:福建省厦门市湖滨中学2020-2021学年高一下学期期中考试数学试题