13-14高三·全国·课后作业
名校
解题方法
1 . 如图所示,四边形ABCD是边长为3的正方形,
平面ABCD,
,
,BE与平面ABCD所成角为60°.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/8f5b1f87-0212-4f87-942f-5de747eb65b6.png?resizew=187)
(1)求证:
平面BDE;
(2)求二面角
的余弦值;
(3)设点M是线段BD上的一个动点,试确定点M的位置,使得
平面BEF,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8139d9fd5c670c91aa7dc485366dd1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c5624c7941eb3cca11d8efbe76d9af5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/8f5b1f87-0212-4f87-942f-5de747eb65b6.png?resizew=187)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f717b7d4d0978eec7330afec554c078.png)
(3)设点M是线段BD上的一个动点,试确定点M的位置,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f33fa5152ba27f7b8a28890cefca219.png)
您最近一年使用:0次
2021-11-11更新
|
1832次组卷
|
27卷引用:福建省南平市浦城县2021届高三上学期期中测试数学试题
福建省南平市浦城县2021届高三上学期期中测试数学试题(已下线)2015高考数学(理)一轮配套特训:7-7立体几何中的向量方法北京市朝阳区第80中学2017届高三上12月月考数学试题北京市朝阳区80中学2017届高三上学期12月月考数学(理)试题【全国百强校】2018年天津市南开中学高三模拟考试数学(理)【全国百强校】天津市南开中学2018-2019学年高三(下)第四次月考数学试题(理科)(2月份)(已下线)考点52 空间向量在立体几何中的运用-备战2022年高考数学一轮复习考点帮(新高考地区专用)【学科网名师堂】北京市西城区北京师范大学第二附属中学2022届高三上学期期中数学试题(已下线)考点31 直线、平面平行与垂直的判定与性质-备战2022年高考数学典型试题解读与变式(已下线)重难点03 空间向量与立体几何-2022年高考数学【热点·重点·难点】专练(新高考专用)江苏省苏州第十中学2022届高三下学期3月阶段检测数学试题(已下线)一轮巩固卷02-【赢在高考·黄金20卷】备战2022年高考数学模拟卷(新高考专用)(已下线)2022年高考考前20天终极冲刺攻略(三)【理科数学】 (5月27日)北京东城171中2016-2017学年高二上期中数学(理)试题辽宁省丹东市2017-2018学年高二数学理科上学期期末考试试题河北省衡水市阜城中学2017-2018学年高二上学期第五次月考数学(理)试题2018-2019人教A版高中数学选修2-1第三章 空间向量与立体几何 章末评估验收(三)(已下线)第01章+章末复习课(重点练)-2020-2021学年高二数学十分钟同步课堂专练(人教A版选择性必修第一册)山东省滕州市第一中学2020-2021学年高二9月开学收心考试数学试题人教B版(2019) 选择性必修第一册 过关斩将 第一章 空间向量与立体几何 本章复习提升(已下线)3.5 章末复习课(重点练)-2020-2021学年高二数学(理)十分钟同步课堂专练(人教A版选修2-1)重庆十八中两江实验中学2020-2021学年高二上学期12月月考数学试题云南省大理下关第一中学教育集团2021-2022学年高二上学期段考数学试卷(一)试题北京市海淀区北京理工大学附属中学2020-2021学年高二上学期期中考试数学试题河北省邢台市第一中学2021-2022学年高二上学期第三次月考数学试题宁夏育才中学2022-2023学年高二下学期开学考试理科数学试题北京市第一七一中学2023-2024学年高二上学期期中调研数学试题
解题方法
2 . 若数列
共有
项,对任意
都有
(
为常数,且
),则称数列
是
关于
的一个积对称数列.已知数列
是
关于
的一个积对称数列.
(1)若
,
,
,求
的值;
(2)已知数列
是公差为
的等差数列,
,若
,
,求
和
的值;
(3)若数列
是各项均为正整数的单调递增数列,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a2ba64bfc61ec78a65944fb8247a937.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c11950e41ac5d26b212a972cc58a3d6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c876f7c64d581afb4d1bb6063c48f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fe8fabd6b7f3547c18062c8781dbd45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bfe21c96489cb30c544d49ddb4c1c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b13bd7807908887b854773a4901da0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42dc22436b2a4edf3d6e15e1e5a15343.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de06482cf6ed8f6c8bc13de27e736fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c95a5133241ba22e1c805480c1b02a.png)
您最近一年使用:0次
解题方法
3 . 如图,在四棱锥
中,
平面
,
,
,
.
,
分别为棱
,
上的动点(与端点不重合),且
.
平面
;
(2)若
,设平面
与平面
所成的角为
,求
的最大值.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada414c44eda3553b2b8bd070511b965.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da3b18adacdc2379dff16946537ea0ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bff03bfdc11e703c0e8fd99133552fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4c26f3f4d96117f087400a0f32ece8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cdd1acd5353365eb41cfc2cabad999.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4c26f3f4d96117f087400a0f32ece8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a282d19bf2c827a98d4443330f7ca1.png)
您最近一年使用:0次
解题方法
4 . 已知
,
,直线
,
相交于点
,且它们的斜率之积是4,记点
的轨迹为曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
的方程;
(2)不过
,
的直线
与
交于
,
两点,直线
与
交于点
,点
在直线
上,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d07a71ea5e77168d101526bd081433.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12387f16bfc90abd7581d9f0f8d7a804.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc48974114e23f5a801843710c7ae21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)不过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe61d39d080872caa8973a70a3b4955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a439c8a01a6626d7a3f53af31ef0bcae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
解题方法
5 . 如图,在四棱锥
中,
,
.
平面
;
(2)在棱
上是否存在点
,使得平面
与平面
夹角的正弦值为
?若存在,求
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cbb6e60e8fe0d8c5a463827e6f4ae5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e405331d1a798d8f5b46631864d35d31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4a6b8ef3e79b4482388c3391d8b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642a7dd471434c923f76809dfa5ee183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bb9d82f939a1ed231721e1ec2ae70e.png)
您最近一年使用:0次
2024-05-14更新
|
1676次组卷
|
5卷引用:福建省南平市建阳区2023-2024学年高三预测绝密卷模拟预测数学试题
福建省南平市建阳区2023-2024学年高三预测绝密卷模拟预测数学试题山东省泰安市2024届高三下学期高考模拟((三模))数学试题山东省菏泽市2024届高三下学期模拟预测数学试题(三)(已下线)模块5 三模重组卷 第1套 全真模拟卷(已下线)易错点4 忽视法向量夹角与二面角的关系
名校
6 . 已知函数
,其中
为自然对数的底数.
(1)讨论
的单调性;
(2)若方程
有两个不同的根
.
(i)求
的取值范围;
(ii)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ca6a47d8e2b8ff86f955f401ed47acc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28638f8c054a7bb4d9b46fde330bc76f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04133adb6f1562d859510c9771b2e545.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,在三棱锥
中,
平面
,
,
,
是
的中点,
为
上的动点.
(1)证明:平面
平面
;
(2)
平面
时,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a94d59dee2d5a8f0425b64b2083825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c439e4e4e48b17e19e666d892216fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d38c12844d5897c9edd650ce16bff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95226c64f0afdaa10b95ec097a0720ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/27/da0bff03-fd71-4c7e-9ce8-4709c2f36e15.png?resizew=134)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c9831963e3d8ca278fbf96908b0075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af57d63e83ef0e183add10cd6beec65b.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c7534cbe3ee2be8d10597cbc465c07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2023-09-26更新
|
644次组卷
|
5卷引用:福建省南平市邵武市邵武一中2023-2024学年高三上学期10月月考数学试题
名校
8 . 已知函数
.
(1)求
的单调区间;
(2)若
有两个零点,记较小零点为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7baac46881798c16564d0e59e94afbe.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11a5876a83f57158550b206800dab275.png)
您最近一年使用:0次
2023-08-20更新
|
777次组卷
|
5卷引用:福建省南平市建阳第二中学2024届高三上学期第二次月考数学试题
福建省南平市建阳第二中学2024届高三上学期第二次月考数学试题海南省陵水黎族自治县陵水中学2024届高三上学期第一次模拟考试数学试题福建省莆田锦江中学2024届高三上学期第一次阶段(开学考)考试数学试题山东省威海市乳山市银滩高级中学2023-2024学年高三上学期9月月考数学试题(已下线)考点19 导数的应用--函数零点问题 2024届高考数学考点总动员【练】
9 . 记
为数列
的前
项和,
为数列
的前
项和,若
且
.
(1)证明:数列
是等比数列;
(2)若
成立,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8251ae667250fb36ce4c0d75228317.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34f86e5aaea193d51fa06c58abb3898b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c364305551ca3312dfb6bd3dc3a6de2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2023-10-02更新
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3卷引用:福建省南平市建阳第二中学2024届高三上学期第二次月考数学试题
10 . 已知
,
,
都是正数,且
.
(1)若
,求函数
的最小值;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b05d3b8f5c9df891ef6fbcaf12f43207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e2b7ec0abbdc79dc6a9c4be71c5de9.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a3cfe361051dc5e9a3a36b2818db0.png)
您最近一年使用:0次
2022-11-20更新
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2卷引用:福建省南平市浦城县第三中学2023届高三上学期期中测试数学模拟卷试题(2)