2010·广东汕头·一模
名校
解题方法
1 . 如图,四棱锥
的底面是边长为1的正方形,侧棱
底面
,且
,E是侧棱
上的动点.
的体积;
(2)如果E是
的中点,求证:
平面
;
(3)是否不论点E在侧棱
的任何位置,都有
?证明你的结论.
![](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/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
(2)如果E是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb178784aa857d4d4683e650273f054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(3)是否不论点E在侧棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509d8dd6031dc0ef92075877e53fe201.png)
您最近一年使用:0次
2024-01-04更新
|
623次组卷
|
5卷引用:汕头市2009-2010学年度第二学期高三级数学综合测练题(理四)
(已下线)汕头市2009-2010学年度第二学期高三级数学综合测练题(理四)广东省2024年1月高中合格性学业水平考试模拟测试数学试题(三)2017届北京市海淀区高三3月适应性考试(零模)文科数学试卷(已下线)第13讲 8.6.2直线与平面垂直的性质定理 (第2课时)-【帮课堂】(人教A版2019必修第二册)陕西省西安市西安中学2023-2024学年高二学考仿真考试数学试题
名校
解题方法
2 . 已知函数
.
(1)求证:
是奇函数;
(2)判断
在
上的单调性,并证明;
(3)已知关于
的不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47024cb8062925596b0b902917d3a779.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(3)已知关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa6024d1514f7598e197ad3d7f8d720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2023-11-09更新
|
941次组卷
|
2卷引用:广东省广州市育才中学2023-2024学年高一上学期期中数学试题
名校
解题方法
3 . (1)已知函数
,
,若
,都有
,求证:
为奇函数.
(2)设函数
定义在
上,证明:
是偶函数,
是奇函数.
(3)已知
是定义在
上的函数,设
,
,试判断
与
的奇偶性;根据
,
与
的关系,你能猜想出什么样的结论?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41c7798e8266916b8501e3837194407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e36e45821cc161584ad64043772227a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90c3cfb21d60dc4bea0083dbbba146c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1836fe79a57e10d585d267c50d67d421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8625e475c73bdfd992254680dc7d6b7f.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63c9abee0619dcc5cd3bf7f40c4edadd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca2ea8a2a6013eb18b53ea3aeb6ef56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
2023-08-20更新
|
252次组卷
|
2卷引用:广东省广雅中学2023-2024学年高一上学期期中数学试题
4 . 已知数列
的前n项和为
,且满足
.
(1)证明:数列
是等比数列;
(2)记
,数列
的前n项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/694469ac77ae7c840a2f206dc2b5da89.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e764296a62a7def78e39370f746b4663.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da72309d2507e2f5e5ed88d8cc08963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cf49305249eb983fb10c95c2287d1ee.png)
您最近一年使用:0次
2023-08-18更新
|
1601次组卷
|
4卷引用:广东省揭阳市普宁市第二中学2023-2024学年高三上学期第一次月考数学试题
广东省揭阳市普宁市第二中学2023-2024学年高三上学期第一次月考数学试题四川省2023届高三诊断性检测文科数学试题四川省仁寿县铧强中学2024届高三上学期9月诊断性考试理科数学试题(已下线)第二篇 “搞定”解答题前3个 专题2 数列解答题【练】高三逆袭之路突破90分
解题方法
5 . 已知函数
.
(1)当
为何值时,
为偶函数,说明理由;
(2)若
,证明:
;
(3)若
,求证:
有两个不相等的实数根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caef851640adfb3514851b0225e7114b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9b896371aa9ee32182684a06d72cf63.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa6e9df5ed46e9a0ddba84d4b82813b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
您最近一年使用:0次
2023-08-06更新
|
153次组卷
|
2卷引用:广东省佛山市南海区2022-2023学年高一上学期期中数学试题
名校
解题方法
6 . 如图,在棱长为2的正方体
中,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/15/87bb0b53-3cb0-414f-ac51-d843ae06f1fe.png?resizew=154)
(1)求证:
平面
;
(2)证明:
;
(3)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/15/87bb0b53-3cb0-414f-ac51-d843ae06f1fe.png?resizew=154)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5830646a912c3a916beac4f88c116b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4fcf607b0710d12aaabd17fd053d83.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
您最近一年使用:0次
7 . 如图所示,在四棱锥
中,
是正方形,
平面
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/2023/11/20/3371845519507456/3372278063579136/STEM/d8991f00258b43fab4e2b29949b3fa3a.png?resizew=153)
(1)求证:平面
平面
;
(2)证明:平面
平面
.
![](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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64fca8e84d5429615acbec07521bee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e3a25299c121dbb883fd3c7918d566d.png)
![](https://img.xkw.com/dksih/QBM/2023/11/20/3371845519507456/3372278063579136/STEM/d8991f00258b43fab4e2b29949b3fa3a.png?resizew=153)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67aca4db7d67c75ce68fe6912d17053d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5394d00a80a5900d7fd7d9961868bd22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
解题方法
8 . 如图,在四棱锥
中,底面ABCD为正方形,
平面ABCD,
,E为PB中点,M为AD中点,F为线段BC上动点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
平面AEF;
(2)证明:平面
平面PBC.
![](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/d9a4950a6e4202efd609507964af238b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6501f1c913a4ef64957a2f01ab5baa15.png)
您最近一年使用:0次
2023-07-07更新
|
412次组卷
|
2卷引用:广东省江门市2022-2023学年高一下学期期末数学试题
23-24高二上·上海·期末
名校
9 . 定义:对于任意大于零的自然数n,满足条件
且
(M是与n无关的常数)的无穷数列
称为M数列.
(1)若等差数列
的前n项和为
,且
,
,判断数列
是否是M数列,并说明理由;
(2)若各项为正数的等比数列
的前n项和为
,且
,证明:数列
是M数列;
(3)设数列
是各项均为正整数的M数列,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68f165a34038d89623948dbe0a669df0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5612ce06759d0f77ca029d10083f7d1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb8cf8df82fd05e5549ce9c1a6f3524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4818548de2563bc81198611cf3468f13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若各项为正数的等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c8a7aaf355cf3ea778c73eea8ae635.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de777c4e44546bcfe26ad5b6bb418052.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/292852a3aa9790d661862ff0b67c8971.png)
您最近一年使用:0次
2024-01-14更新
|
1330次组卷
|
8卷引用:广东2024届高三数学新改革适应性训练三(九省联考题型)
广东2024届高三数学新改革适应性训练三(九省联考题型)(已下线)期末真题必刷压轴60题(22个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)安徽省六安第二中学2023-2024学年高二上学期期末统考数学试卷(已下线)第4章 数列(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)湖北省荆州市沙市中学2023-2024学年高二下学期3月月考数学试题(已下线)模块五 专题5 全真拔高模拟5(北师大高二期中)(已下线)模块三专题2 数列的综合问题 【高二下人教B版】(已下线)模块三 专题4 数列的综合问题 【高二下北师大版】
10 . 已知数列
满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060c880252326cb449d8253539d92aff.png)
(1)判断数列
是否是等比数列?若是,给出证明;否则,请说明理由;
(2)若数列
的前10项和为361,记
,数列
的前n项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390636a89883bd64bf8da9bf8654aff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060c880252326cb449d8253539d92aff.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf33b2a94eae16760d746f9b4b8dbc.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04053ecf80b3bb9179c8baab47bf8dae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc0cf1f0a00718b95a2a4fffd11dd32.png)
您最近一年使用:0次
2023-08-20更新
|
2549次组卷
|
9卷引用:广东省南澳县南澳中学2024届高三上学期校一模数学试题