1 . 如图,在五棱锥
中,
平面
,
,
,
,
,
,
.
(1)求证:平面
平面
;
(2)已知直线
与平面
所成的角为
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be89b9d1709d7974a108142c5fa2ccec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d54224e81a15a8cae082c8a3c121df2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86b2c0468bc8a7ca5f3bba74dd0b86c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99e43ede64da9df1d6d38f7e0f7fc3fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42fcb730e00ae46399217ad27718d49.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/51405a06-61e5-4bbc-89d8-c48397b6656b.png?resizew=194)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2 . 已知椭圆
(
)的离心率为
,左、右焦点分别为
,
.过
的直线交椭圆于
,
两点,过
的直线交椭圆于
,
两点,且
,垂足为
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/a5001eba-90d9-482d-82f3-61b7959295f4.png?resizew=163)
(1)求椭圆的标准方程;
(2)求四边形
的面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc1f76257275ab4b04f9bc913535670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59d0a70a96b10b60cd69ffe26bf155b6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/a5001eba-90d9-482d-82f3-61b7959295f4.png?resizew=163)
(1)求椭圆的标准方程;
(2)求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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解题方法
3 . 如图,在三棱锥
中,
⊥平面
,点P,M分别是
和
的中点,已知
,
,直线
与平面
所成的角为30°.
![](https://img.xkw.com/dksih/QBM/2024/1/25/3418618703503360/3419700500963328/STEM/a80e7a64126240678692ba1918391b49.png?resizew=185)
(1)求证:平面
⊥平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbc5ea3b02aa149ab24f9faa04339744.png)
(2)求二面角
的正切值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2823bdb03fbdacb513498a41ac63b3d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5c9ca3af3eb8bc486f7b3f29f5065eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787ac5e13622afab5e9f8603afe42356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5c9ca3af3eb8bc486f7b3f29f5065eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ff6089095a8b825eeb8002b6996929e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a6fc026d474b8327e834ca0650b72be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daadcd54ede70b183d92857bc85cebf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1165830b314a0dab65ea267e82bd3f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787ac5e13622afab5e9f8603afe42356.png)
![](https://img.xkw.com/dksih/QBM/2024/1/25/3418618703503360/3419700500963328/STEM/a80e7a64126240678692ba1918391b49.png?resizew=185)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f26293ff841043aaf9e67c39f1fea6d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbc5ea3b02aa149ab24f9faa04339744.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a6b0b4cd6c9052a2afea4c897c1c5aa.png)
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4 . 如图,多面体
,四边形
是矩形,梯形
平面
,
为
中点,
.
![](https://img.xkw.com/dksih/QBM/2024/1/15/3411850336886784/3412267611127808/STEM/170c424651404fa3865b5c884abf2ab2.png?resizew=166)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
平面
;
(2)求平面
和平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a685fd7539b94dcede33055ef3b0e340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1953be42cd629684fea9a22a423ecb2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e50b2e53c74dba074cc314b6e6b7890b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4079b8e3e53b0de4fe767379147028bb.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/8b0c05e82af84e3d87046555342208fd.png)
![](https://img.xkw.com/dksih/QBM/2024/1/15/3411850336886784/3412267611127808/STEM/170c424651404fa3865b5c884abf2ab2.png?resizew=166)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df21b7b7a47318ef2bb069450c39f1cd.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588690c4a218025937357ffab8d63c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82cb18c10820d927ecd53326f58aaf8f.png)
您最近一年使用:0次
5 . 如图,在长方形
中,
为
中点,
.以
为折痕将四边形
折起,使
,
分别达到
,
,当异面直线
,
成角为
时,异面直线
,
成角余弦值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/2ae8cd16-0fa0-46f5-b9d0-8d651558fae1.png?resizew=221)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/1b929269c53a44907dba8ee298a0a522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f1158eaa2e338f564eb18de5bef1d25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926d1308d5db144e31b4d0211c63ef52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/2ae8cd16-0fa0-46f5-b9d0-8d651558fae1.png?resizew=221)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
6 . 如图,在四棱锥
中,
平面
,
,
为
中点,且
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/33275e30-5435-486d-bbdd-67b988a90feb.png?resizew=164)
(1)求二面角
的余弦值;
(2)若
在线段
上,直线
与平面
所成角的正弦值为
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1ac2e11788860424508ea9e80cf89d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/33275e30-5435-486d-bbdd-67b988a90feb.png?resizew=164)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e867e5c7ef4da37d8985ce82022060e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b045689b0f5e75ddc88774d02b4f734d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8948ac8156d19336083987d47b0f7038.png)
您最近一年使用:0次
7 . 在空间直角坐标系中,已知点
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57cf4881ebb11e41972186ed6b55ad43.png)
A.![]() |
B.![]() |
C.异面直线![]() ![]() ![]() |
D.![]() ![]() ![]() |
您最近一年使用:0次
8 . 如图,斜三棱柱
中,
,
,
,
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/235dec1b-b4b2-45e7-9790-5dabe808ad60.png?resizew=235)
(1)证明
;
(2)求
与平面
成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd8f940b796af67206b3f9dd410a407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07e87f191a0b670956b03927318dfd28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/235dec1b-b4b2-45e7-9790-5dabe808ad60.png?resizew=235)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eacc0e7474802ce634de6f55a3287115.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61dc0fec2de4694075281e882d3c5ac.png)
您最近一年使用:0次
解题方法
9 . 已知双曲线
的左焦点为F,过F作双曲线C的一条渐近线的垂线,垂足为A,并与双曲线C交于点B,且有
,则双曲线C的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0dddff208cedff93a55f1a2da24c4c.png)
A.![]() | B.2 | C.![]() | D.![]() |
您最近一年使用:0次
2024-01-29更新
|
469次组卷
|
2卷引用:辽宁省大连市2023-2024学年高二上学期期末数学试题
名校
解题方法
10 . 设抛物线
的焦点为
,动直线
交抛物线于
,
两点,当直线
过焦点且
的中点
的横坐标为2时
.
(1)求抛物线
的方程;
(2)已知点
,当焦点为
为
的垂心时,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0907a673d52825cd7df84b400972d4b9.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae02f139fdf785ced96e3980f1a6c57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7ad41b36674fd6e90176ee24cdefbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2024-01-29更新
|
244次组卷
|
2卷引用:辽宁省葫芦岛市2023-2024学年高二上学期1月普通高中学业质量监测考试数学试题