1 . 已知数列
为等差数列,
的前
项和为
.
(1)求数列
的通项公式;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71a2df2c37d2f8dcdfd42af8c3d50606.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c8c2d17624dca14c2a6fcc229965d9.png)
您最近一年使用:0次
2024-01-18更新
|
374次组卷
|
2卷引用:重庆市渝中区巴蜀中学校2023-2024学年高二上学期期末数学试题
名校
解题方法
2 . 如图1所示,
为等腰直角三角形,
分别为
中点,将
沿直线
翻折,使得
,如图2所示.
(1)求证:平面
平面
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a305db42ca2851c5065dd3556083b1a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e675a92cad72c65aa4071b9d9e226090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff39c7aa648afd1080206c8080ff79e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/869c343a4b0c14a89ed8e688cfe6f7e4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/dfafd27d-c1b0-4498-a3f0-378e9a26b99c.png?resizew=322)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a46fbde58e12b1edc038ae9e921722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
您最近一年使用:0次
2024-01-16更新
|
750次组卷
|
4卷引用:重庆市渝中区巴蜀中学校2023-2024学年高二上学期期末数学试题
名校
3 . 如图,在四棱锥
中,
平面
,且
,点
为棱
上一点(不与
重合),平面
交棱
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/31d997fd-1915-4538-8483-49468c3a44f9.png?resizew=166)
(1)求证:
:
(2)若
为
中点,求平面
与平面
夹角的余弦值.
![](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/ed2297710e4816494ee24270513fe8d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05740f0c6071846227dc0ec177ad15e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc793a6afea747370cae351b53efd46e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/31d997fd-1915-4538-8483-49468c3a44f9.png?resizew=166)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba46f9fceccff74b15e6dad269412cd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
2023-10-13更新
|
668次组卷
|
3卷引用:重庆市巴蜀中学校2023-2024学年高二上学期10月月考数学试题
重庆市巴蜀中学校2023-2024学年高二上学期10月月考数学试题(已下线)高二数学上学期期中模拟卷02(空间向量与立体几何+直线与圆的方程+椭圆+双曲线)(原卷版)山东省滕州市第五中学2023-2024学年高二上学期第二次单元检测(1月)数学试题
名校
解题方法
4 . 如图,四棱柱
为平行六面体,
为
的中点.
(1)若点
满足
,求证:
四点共面;
(2)若
为正方体,求直线
平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/7/3119f3de-5e6a-44db-83b7-8d3080e4bd44.png?resizew=177)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7115ad722348fd88428fe9febf7f2442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a328378487c776ac0fe6482ac4309c9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fed2f706801662432b68797e72647c6e.png)
您最近一年使用:0次
名校
解题方法
5 . (1)不等式
对任意的
恒成立,求m的取值范围;
(2)当
,求证:
.
(参考数据:
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c03b1b7812bd364bbcfc6acea45f9182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882b660047bb6ded500cedba57958e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69ef0632493b910258a1f59c8a29aa1e.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70559d4c1408ed986b4ba646d045d023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c6338466609519ed240407ebe9959af.png)
您最近一年使用:0次
名校
解题方法
6 . 如图,在四棱锥
中,
为平行四边形,
,平面
平面
,
,
,
.
(1)求证:平面
平面
;
(2)若
与平面
所成角为
,E为
的中点,求锐二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e4d19bf237a6fca67e0d01a9ddb726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e4dbea6a5faecdd8f6c06cf9fd43a90.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/23/698a287e-212f-4962-b78f-0c126aa67a3a.png?resizew=209)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aad963ee7cdc7ff35a8dd23685589d1.png)
您最近一年使用:0次
名校
7 . 如图,在圆柱
中,
是圆柱的一条母线,
是底面圆
的内接四边形,
是圆
的直径,
为
上一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/20/910f5a91-6323-4dc9-8ea8-71bb5558d7e7.png?resizew=153)
(1)求证:
;
(2)若
是
的中点,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/400f22a89679edab146f86964fd45a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/20/910f5a91-6323-4dc9-8ea8-71bb5558d7e7.png?resizew=153)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b92bdf778aa32f238bad820d72d62f0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba73af162663a8907ff69e9cf179cf31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5102c216393e133fa25dba98cd78535.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,在四棱锥
中,
是以
为斜边的等腰直角三角形,
为
的中点.
(1)证明:
平面
;
(2)求直线
与平面
间的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e4e188783b4e9382b1772031de17036.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/23/a33ca21c-d3e7-4e03-ada0-4f4e98099454.png?resizew=161)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932a04304f2d4975955d4baabb2deeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2023-08-22更新
|
557次组卷
|
12卷引用:重庆市第二十九中学2023-2024学年高二上学期10月月考数学试题
重庆市第二十九中学2023-2024学年高二上学期10月月考数学试题天津市第五十五中学2020-2021学年高二(上)第一次月考数学试题吉林省东北师大附中2021-2022学年高二上学期大练习(一)数学试题江西省泰和中学2021-2022学年高二上学期第一次段考数学(理)试题山东省烟台市招远市第二中学2022-2023学年高二上学期10月月考数学试题山东省潍坊市寿光市第一中学2021-2022学年高二上学期期末数学试题山东省淄博市淄博第五中学2022-2023学年高二上学期期末数学试题贵州省贵阳市清华中学2022-2023学年高二上学期11月月考数学试题浙江省杭州第十四中学2023-2024学年高二上学期10月阶段性监测数学试题(已下线)每日一题 第6题 空间距离 要用向量(高二)(已下线)专题07 利用空间向量计算空间中距离的8种常见考法归类 - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)(已下线)第34讲 利用坐标法解决立体几何的角度与距离问题-2022年新高考数学二轮专题突破精练
9 . 如图,椭圆
的左顶点
,点
都在椭圆上不与顶点重合且关于坐标原点
对称,其中点
在第一象限,线段
的中点是
,点
在
轴上的投影是
,直线
交椭圆C于另一交点
.直线
的斜率分别是
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/8/d3d1e34d-1b34-4e04-b1bb-389423c75a7e.png?resizew=189)
(1)求证:
是定值并求出该定值;
(2)求证:
;
(3)求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9bf37fb661ccc2fdd67407269708df4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2790947716b1cfa9c5e7a65db4093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5671fb25040a712a49e8c8148d67d300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/8/d3d1e34d-1b34-4e04-b1bb-389423c75a7e.png?resizew=189)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b881044b5c73db6fcce110525741b02.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbe870e7477244aab08cc0fd8de24971.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17277a306d4d0a0a0cf293f87802cf66.png)
您最近一年使用:0次
2023-02-07更新
|
796次组卷
|
3卷引用:重庆市巴蜀中学校2022-2023学年高二上学期期末数学试题
名校
解题方法
10 . 如图,在三棱柱
中,
.
(1)证明:
;
(2)若
,且
,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d680dee3f8f4cf06ec8d8e7fe9eac0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/23/bcf9f731-db4a-47fa-872d-835b1ad64dc4.png?resizew=184)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5431bb5f4e7e2e10568077996707348f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4666b10f919aba3f891a661a868494f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c43dee42d93175967c4d33a4b59cf95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec7a5e032e61a0b576ef6468714ab4a8.png)
您最近一年使用:0次
2023-05-19更新
|
991次组卷
|
4卷引用:重庆市巴蜀中学校2022-2023学年高二下学期期中数学试题