名校
解题方法
1 . 如图,在多面体
中,平面
与平面
均为矩形且相互平行,
,设
.
平面
;
(2)若多面体
的体积为
:
(i)求
;
(ii)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff64de03b0302dbc12f2fc207b70d1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/336e0a8f5fbc1c44a02adab5a1fffb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc99203b785fbdbd399bb03c7556fbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
(2)若多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a391005600bdd69c96750589f9adb048.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(ii)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffee8b7eff437080a0936d837ceabe95.png)
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7日内更新
|
381次组卷
|
2卷引用:重庆市乌江新高考协作体2023-2024学年高二下学期第二阶段性学业质量联合调研抽测(5月)数学试题
名校
解题方法
2 . 如图,在体积为5的多面体ABCDPQ中,底面ABCD是平行四边形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da28d15a7c302c52990157ce5042b18.png)
为BC的中点,
.则平面PCD与平面QAB夹角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da28d15a7c302c52990157ce5042b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc32c6f379988ef94dc9fc245332ee5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf1e7f0f63d45cbf59c88d9be433a37.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
3 . 布达佩斯的伊帕姆维泽蒂博物馆收藏的达·芬奇方砖是在正六边形上画了具有视觉效果的正方体图案(如图1)把三片这样的达·芬奇方砖拼成图2的组合,这个组合再转换成图3所示的几何体.若图3中每个正方体的棱长为1,则( )
A.![]() |
B.异面直线![]() ![]() ![]() |
C.点![]() ![]() ![]() |
D.![]() ![]() ![]() |
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名校
解题方法
4 . 已知在三棱锥
中,
,
为以AC为斜边的等腰直角三角形.
平面
;
(2)设
,存在该几何体外的一点D,使得
为等边三角形,平面BCD与平面ABC所成的锐二面角的正切值为
,求AD的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbd13eeeae4d887d11685c108e462920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
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解题方法
5 . 已知正方体
的棱长为2,其外接球球心为
,点
分别是棱
的中点,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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362ef25f87ac1de47027b7d7c150a56c.png)
A.球![]() ![]() ![]() ![]() |
B.球![]() ![]() ![]() ![]() ![]() |
C.直线![]() ![]() ![]() |
D.三棱锥![]() ![]() |
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名校
6 . 在侧棱长为
的正三棱锥
中,点
为线段
上一点,且
,点M为平面
内的动点,且满足
,记直线
与直线
的所成角的余弦值的取值范围为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.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/f8aca29eb6c46838852134027cf28d99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e01ba3f329b712e87ead41125cacd34a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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名校
解题方法
7 . 如图,在直三棱柱
中,△
为边长为2的正三角形,
为
中点,点
在棱
上,且
.
时,求证
平面
;
(2)设
为底面
的中心,求直线
与平面
所成角的正弦值的最大值,并求取得最大值时
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/645b45818c7a7c68a772a30262277c8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38a1794201d5a18fe46cfb6901c7f0d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441809d6ce2df21a85b390cdce9b1112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4525c00ed908bed8ba8d353e747a858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c4c2157cf374ebe6352715ef100471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2024-06-04更新
|
664次组卷
|
2卷引用:河北省沧州市联考2023-2024学年高三下学期4月月考数学试题
8 . 在矩形
中,
,E为线段
的中点,将
沿直线
翻折成
.若M为线段
的中点,则在
从起始到结束的翻折过程中,( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c4e4a162f12d12a082b8d8fdd1aeab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a2e2a02b9fa79241ad11bbca8ca2a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac9d68b4edd4cc02f17bf8786b44086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a2e2a02b9fa79241ad11bbca8ca2a6.png)
A.存在某位置,使得![]() |
B.存在某位置,使得![]() |
C.![]() |
D.![]() ![]() ![]() |
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解题方法
9 . 在正四棱锥
中,
,
,点
满足
,其中
,
,则下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ea52361458ce2e49ed0fe99d8e6c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd3eb538f36e6e722e4ce125266b99b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ad040b00b7a307c28dd15829d00a9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79296cd4046a71e163a8f3e647a176ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/994fe2e2ccff825adfe4567a84e0fd79.png)
A.![]() ![]() |
B.当![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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10 . 如图,棱长为
的平行六面体
中,
,点
分别是棱
的中点,
与平面
交于点
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d847859a29c255d4a91679ea6c979a07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b11b45b1ae99a58e5aac679974dabcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d92178a5c6a76586292f622da298a8db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ce50ba5e349425274f05d46d120a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
A.![]() ![]() |
B.直线![]() ![]() ![]() |
C.![]() |
D.三棱锥![]() ![]() |
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