名校
1 . 如图,已知
平面ABC,
,
,
,
,
,点
为
的中点
平面
;
(2)求直线
与平面
所成角的大小;
(3)若点
为
的中点,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa742d9b84b537be10034553776400e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4f0c1c9cca0555906d8a53e1a6803d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/133760237c0ccf2d6a83786925b6d23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ab527e1b5f124429b532804ef3f870f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4eaac4ba87386eca79a4f8b5d99ec38.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/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7f072f0834ebdf155abc5dcc9c8d99.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7f072f0834ebdf155abc5dcc9c8d99.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
您最近一年使用:0次
昨日更新
|
654次组卷
|
3卷引用:吉林省长春外国语学校2023-2024学年高一下学期5月期中考试数学试题
名校
解题方法
2 . 如图,在正方体
中,
是
的中点,
分别是
的中点. ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
平面
;
(2)若正方体棱长为1,过
三点作正方体的截面,画出截面与正方体的交线,并求出截面的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c7b255eaafe00d925cf7284b573c01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bf9ef324f1289e205e29fed105c38e.png)
(2)若正方体棱长为1,过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92a643637f6ac4c594c1665be42b6184.png)
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3 . 如图,在四面体
中,
,
,
为
的中点,
为
上一点.
平面BDF;
(2)若
,
,
.
(ⅰ)求二面角
的余弦值;
(ⅱ)求直线
与平面
所成角的正弦值的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ad8d16722f5b9e7fd2602f14d5ffbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc6db50a9709c3f4d84eee7bdf1250.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3bbe4cdd2c154bd9a8073b0d4cecb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8726e6a11ad400cfd860b09debe475be.png)
(ⅰ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1854ba6cc92481d7a616bd2788a47e.png)
(ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,已知正方体
的棱长为
.
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4645450a006f2c20087486d0833afbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239198e40085b7dcffbe747c9c265a05.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239198e40085b7dcffbe747c9c265a05.png)
您最近一年使用:0次
名校
解题方法
5 . 如图,在正方形
中,E,F分别是BC,CD的中点,现在沿AE,AF及EF把这个正方形折成一个空间图形,使B,C,D三点重合,重合后的点记为G,且取EF中点为O,则在这个空间图形中必有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
6 . 如图,AB是⊙O的直径,PA垂直于⊙O所在的平面,C是圆周上不同于A,B的一动点.
是直角三角形;
(2)若
,
,求直线AB与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71807a35b3170fce28ee6edf4c00d083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2024-06-17更新
|
818次组卷
|
2卷引用:吉林省长春市第二实验中学2023-2024学年高一下学期期中考试数学试题
名校
解题方法
7 . 已知三棱柱
的各棱长均相等,且侧棱垂直于底面,点
是侧面
的中心,则
与平面
所成的角为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
8 . 已知正四棱柱
中,
,
,点
分别是棱
的中点,过
三点的截面为
.
(保留作图痕迹);
(2)设截面
与平面
交于直线
,且截面
把该正四棱柱分割成两部分,记体积分别为
.
(ⅰ)求证:
;
(ⅱ)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f3327964cfd3ad40d603b0ba7f6973.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3472985d11e56d62b88cc8c5ac25fd82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(2)设截面
![](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/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76a8c0b40531e187a2774a01588a0e9.png)
(ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455757b1ac1fb4779265335d21004c23.png)
(ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737b04ce09bc7e1ed86dc9b3c85203b.png)
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名校
解题方法
9 . 已知
为两个不同的平面,
为两条不同的直线,下列说法正确的是______ .
①
,
,
②
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f1b7081da6d7ef0998eccb9cd36b1d.png)
③
,
,
④
,
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fbc714c63815dad9a27418f6492f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4d6a7aec04e1d5768ef830b534460a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0136ff034377d0109923e845dbd27dfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/675f1e09eb033dab8ef96d1f1c349150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f1b7081da6d7ef0998eccb9cd36b1d.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/542a1572078188c8fbe82ebddf8af3ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72d2a947e3fdc214d40a7d3f54679a73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb82a0d764e8301607285c7cdaefd53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f747152f006301e03b643afb80195c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/675f1e09eb033dab8ef96d1f1c349150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a557a5746706ff11213e3c33add965ef.png)
您最近一年使用:0次
名校
解题方法
10 . 四棱台
中,
底面
,
是直线
上的两个动点,两个底面是正方形,
,
,
,
,则下列叙述正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](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/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54638dd4ebf19815a1333d84e42f927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4901a7eda97d6a307db76c4fb196ba3d.png)
A.侧棱![]() ![]() |
B.侧面![]() |
C.该棱台的全面积是![]() |
D.三棱锥![]() |
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