名校
解题方法
1 . 已知平行四边形如图甲,
,
,沿
将
折起,使点
到达点
位置,且
,连接
得三棱锥
,如图乙.
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e9ac46aabe38e5ea1a8cb0febc98af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5ec70bc9d4f8f5df312e2f09ee3bcb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd088fbf960bc8d04067b6128c8cba20.png)
您最近一年使用:0次
2024-01-11更新
|
1639次组卷
|
4卷引用:云南省昆明市西山区2023-2024学年高二上学期1月期末考试数学试题
名校
解题方法
2 . 如图,在直三棱柱
中,
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/ffe773bf-791b-4c5b-aa07-0b073c4dacb4.png?resizew=157)
(1)求异面直线
与
所成角的余弦值;
(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/cc56304fc1ad830df3f5372f323657d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/ffe773bf-791b-4c5b-aa07-0b073c4dacb4.png?resizew=157)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4997d1354f13e6074018ab1aa3927507.png)
您最近一年使用:0次
2024-01-10更新
|
245次组卷
|
3卷引用:云南省昆明市官渡区云南大学附属中学呈贡中学2023-2024学年高二下学期3月月考数学试卷
名校
3 . 已知在直三棱柱
中,侧面
为正方形,
,E,F分别为
和
的中点,
.
(1)证明:
;
(2)设D为棱
上的点,当
为何值时,平面
与平面
夹角的正弦值最小?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0023280949eda97787964f0a9d41ed2e.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
(2)设D为棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af6c9a36e2ef7189317ae652c56e49c8.png)
您最近一年使用:0次
名校
解题方法
4 . 已知椭圆C:
的一个焦点为
,且过点
.
(1)求椭圆C的方程;
(2)直线l:
(
)与椭圆C交于M,N两点,求
(O为坐标原点)面积的最大值及此时t的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/580afba2dd40c59442fcab57e4bb7591.png)
(1)求椭圆C的方程;
(2)直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59662505ce1e4177673fb158f6f1402e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823ab696d27d40920c39b8c910789380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
您最近一年使用:0次
名校
解题方法
5 . 已知椭圆C:
(
)的左、右焦点分别为
,
,过
的直线l与C交于P,Q两点,若
,则( )
![](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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f4e4cc1d4653db0404bd69da61335f.png)
A.![]() | B.![]() ![]() |
C.直线l的斜率为![]() | D.C的离心率等于![]() |
您最近一年使用:0次
名校
解题方法
6 . 已知双曲线C:
(
,
)的左、右焦点分别为
,
,O为坐标原点,以
为直径的圆与C在第二象限内相交于点A,与C的渐近线在第一象限内相交于点M,且
,则C的离心率为____________ ;若
的面积为8,则C的方程为____________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.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/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af7f3fe900b463a9a9feb2c2436bb43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dd8b1b47853312648efc2aacd12436.png)
您最近一年使用:0次
名校
解题方法
7 . 如图甲,在矩形
中,
,
,
,
为边
上的点,且
.将
沿
翻折,使得点
到
,满足平面
平面
,连接
,
,如图乙.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/d16fb04f-4ba0-4a7b-850d-b6448a610225.png?resizew=352)
(1)求证:平面
平面
;
(2)求二面角
的正弦值的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1364213f546b37f8764ddcb59e36ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dee56b9f36ba8f76fe67b76383636b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f233b375753611ffa7a93c2c12ef5e28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/d16fb04f-4ba0-4a7b-850d-b6448a610225.png?resizew=352)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c44c1843ff6150ebc6aad3e34e477d2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1d934590b10316fed6ee4114481f7a.png)
您最近一年使用:0次
名校
解题方法
8 . 已知过抛物线
的焦点
的直线
与抛物线相交于
,
两点,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108c18cb76d7d34b05c991a644c8b136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354cf8fe61ca8994f29f12602d0263cc.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/2e3b791319189ef84780f7bfa0a2c7cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d103d683d2fd06b6fa9ec5523c2ea0c9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
9 . 由伦敦著名建筑事务所Steyn Studio设计的南非双曲线大教堂惊艳世界,该建筑是数学与建筑完美结合造就的艺术品.若将如图1甲、乙所示的大教堂外形弧线的一段近似看成双曲线
下支的一部分,且此双曲线的下焦点到渐近线的距离为4,离心率为2,则该双曲线的方程为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/4/8894ab4f-56eb-4b4e-a5cd-377684fc94d7.png?resizew=324)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/965017ac28701e1bc9afe7668c751950.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/4/8894ab4f-56eb-4b4e-a5cd-377684fc94d7.png?resizew=324)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
10 . 如图,在三棱锥
中,
平面
,点
,
分别是
和
的中点,设
,
,直线
与直线
所成的角为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/4/da20ea5a-6fa1-4c93-8ee6-e8cff6e2ddd2.png?resizew=167)
(1)求
的长;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6deecf9ccb7b7879455050633219e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8318fac197efd590ebbe81c475605866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed8f7d3d7043d4b1eb98fc5c4e2fcd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/4/da20ea5a-6fa1-4c93-8ee6-e8cff6e2ddd2.png?resizew=167)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faa23fa14f624ad8212bda55d321362f.png)
您最近一年使用:0次