名校
1 . 已知
为实数集的一个非空子集,称
是一个加法群,如果
连同其上的加法运算满足如下四条性质:
①
,
;
②
,
;
③
,
,使得
;
④
,
,使得
.
例如
是一个无限元加法群,
是一个单元素加法群.
(1)令
,
,分别判断
,
是否为加法群,并说明理由;
(2)已知非空集合
,并且
,有
,求证:
是一个加法群;
(3)已知非空集合
,并且
,有
,求证:存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd242f355d5128425429a83e4b6632c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8362f15e544684164f38ff9ad7c38ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ea5a550b5452df9abdbca776c2ff500.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509a09a7391de2cc86e5e44ccccc981b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8236622218d4d4012d8637538ac9032.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bef35ae51107e991163ea418c8dec53a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebf00e8864c86c3ce8118ea76bf69773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc118659264aca9e263cb8edc41e9c44.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebf00e8864c86c3ce8118ea76bf69773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f0119b6de9149150071fe7ed848aa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a065a5ddaa18900ee15a8b436f0fcb95.png)
例如
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/178e8cc61b87b4dc63105ab4fca8680c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7cb4e4e98b375294dc1dccbeebbd6c2.png)
(1)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/809b2e00ab8e43a0f886c7f83846d3d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b113752e4f989a338747b95a40cf386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d18f9bbb6b9feb166f7ecfb49013262d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64ee969e5c3d880e0209235bb9cfc49f.png)
(2)已知非空集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a02a810b3332821bc444f215183c9e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7d3e3d84e1fdee95574817741d731e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08152bab36dca188978d125e4b7a935a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/489ea5a5f5b5de37e238cbfbb4a01143.png)
(3)已知非空集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d28cc3165eef94c22c442b2f30c87cc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4034552829008c1daaee2701d2afe8dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e0f9ba8419972cff845bfd91f64297.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ddc4872d58eaa6bcc432b7b94939f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5eb4f6f84d264f3403eece1e7c37b7.png)
您最近一年使用:0次
2 . 已知函数
,其中
.
(1)若
在
处取得极小值,求
的值;
(2)当
时,求
在区间
上的最大值;
(3)证明:
有且只有一个极值点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7755b310ae53d9a43d427d6d9a590cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da0bf9280fa3b829628f1cfc7295ba06.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
名校
解题方法
3 . 对于集合
和常数
,定义:
为集合A相对的
的“余弦方差”.
(1)若集合
,求集合A相对
的“余弦方差”;
(2)若集合
,是否存在
,使得相对任何常数
的“余弦方差”是一个与
无关的定值?若存在,求出
的值:若不存在,则说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8368b2cc0b5ea5bcde2e386e49f57641.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c399e314ea3779046c8f1aa2e5555c16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dcd000ab235793dc4ec905c36dd2f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71b7dc3ec4bc675166b126e56c083cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82100419449370da67bf679e9dc44814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
您最近一年使用:0次
2024-03-31更新
|
246次组卷
|
2卷引用:北京市第一六一中学2023-2024学年高一下学期期中考试数学试卷
解题方法
4 .
为正实数,满足
,求
的最大值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19cb3b888b46a0c5e62ccbb09bd77ba.png)
您最近一年使用:0次
5 . 已知数列
,记集合
.
(1)若数列
为
,写出集合
;
(2)若
,是否存在
,使得
?若存在,求出一组符合条件的
;若不存在,说明理由;
(3)若
,把集合
中的元素从小到大排列,得到的新数列为
, 若
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/569e56ec73a87d19fa42045d680886c8.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/680e9ef551b325387ab31dca1f893705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9260f8989cfd0ffca5a49ffbc0668f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8f897e289555b25e8a5094c037f4d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e3bfb472f75e339198fa7415a35b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c639c7e5f1e7e7ee5d5ee2f30b155bb0.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c1ed7b10ac7ca1cd81cdd39a8fcc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e37d15cd620c5a9ae9485629354c9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25efaf1a568553b27434c71ddb447c9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-03-12更新
|
997次组卷
|
3卷引用:2024届北京市延庆区高考一模数学试题
名校
6 . 已知整数
,数列
是递增的整数数列,即
且
定义数列
的“相邻数列”为
,其中
或![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dee0bbc97117cddfdcdf148d92b5d1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a613eefdacfc611bbe69514eec2d5aa8.png)
(1)已知
,数列
,写出
的所有“相邻数列”;
(2)已知
,数列
是递增的整数数列,
,且
的所有“相邻数列”均为递增数列,求这样的数列
的个数;
(3)已知
,数列
是递增的整数数列,
,且存在
的一个“相邻数列”
,对任意的
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d474360f3650b435422b925c7de7c0ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b07b8019e3b1561635042ea589126b15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f846d93390223b563770b676ee30b06c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4b177a056b806e6389db9397891963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5ca042f30e8814ad6f3dfc820eb2100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dee0bbc97117cddfdcdf148d92b5d1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a613eefdacfc611bbe69514eec2d5aa8.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee34bed3d3cbcbe9f351c2fbe1f08e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe08722cf9300fe188dbbb71989c06c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5906e621de4f31a011d9696f19c5a03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51128198ebf849b706e1df99d71a2fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fafbc94594b8c877de8883dea10e374c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00d1ddad8dfcef0761c6e645ececa2a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d64548546547314a555333fd07b1aa.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/ec51ee00b796b08a2aef72d661c73966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066bed69d03aee63a37e1259f6599e55.png)
您最近一年使用:0次
2024-02-04更新
|
532次组卷
|
4卷引用:北京市清华附中高22级2023-2024学年高二上学期期末数学试题
北京市清华附中高22级2023-2024学年高二上学期期末数学试题北京市清华大学附中2023-2024学年高二上学期期末数学试题北京市陈经纶中学2023-2024学年高二下学期4月期中诊断数学试卷(已下线)压轴题数列新定义题(九省联考第19题模式)讲
名校
7 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8dda8e0f05f65226b95a71bc0d75bc9.png)
(1)当
时,求函数
的极值;
(2)求函数
的单调区间;
(3)若对任意的实数
,函数
与直线
总相切,则称函数
为“恒切函数”.当
时,若函数
是“恒切函数”,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8dda8e0f05f65226b95a71bc0d75bc9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若对任意的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceee0ff5c929d67de3c294e027c9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a60550d48fcf76d109f426149d8185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0780bba5832fe480a5fddd87bd1af36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6077c98670d416a38f736c11f3591966.png)
您最近一年使用:0次
2023-12-20更新
|
599次组卷
|
4卷引用:北京市海淀区中关村中学2024届高三上学期12月月考数学试题
名校
8 . 某学校组织竞赛,有A,B两类问题可供选择,其中A问题答对可得5分,答错0分,B问题答对只可得3分,但答错有2分,现小明与小红参加此竞赛,小红答对2种问题的概率均为0.5,小明答对A,B问题的概率分别为0.3,0.7
(1)小红一共参与回答了2题,记X为小红的累计得分,求X的分布列
(2)小明也参与回答了2道问题,记Y为小明的累计得分,求该如何选择问题,使得E[Y]最大.
(1)小红一共参与回答了2题,记X为小红的累计得分,求X的分布列
(2)小明也参与回答了2道问题,记Y为小明的累计得分,求该如何选择问题,使得E[Y]最大.
您最近一年使用:0次
2023-12-20更新
|
1071次组卷
|
5卷引用:2024年北京高考数学真题平行卷(提升)
(已下线)2024年北京高考数学真题平行卷(提升)上海市普陀区长征中学2024届高三上学期10月月考数学试题7.3.1离散型随机变量的均值练习(已下线)考点12 离散型随机变量的期望和方差 2024届高考数学考点总动员【练】江西省赣州市南康中学2024届高三上学期七省联考考前数学猜题卷(二)
解题方法
9 . 已知椭圆
过点
,且离心率
.
(1)求椭圆
的方程;
(2)设点
为椭圆
的左焦点,点
,过点
作
的垂线交椭圆
于点
,连接
与
交于点
.求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b836d2b043c465ccb0207ad6ca78b1c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceb0ef5e6c3771175aff1b8fc9e17110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/234e7679481ec0d01c915b7fbb71891d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b70a820c1dae7a9395a62bc50459480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963111aff6952322dfaca75ae069873c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be99fa94a1f3e4964fcc13a14fab9ba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5808b2b9ddb2001b5294a96e7fc835d.png)
您最近一年使用:0次
10 . 在平面直角坐标系xOy中,定义
,
两点间的“直角距离”为
.
(1)填空:(直接写出结论)
①若
, 则
;
②到坐标原点的“直角距离”等于1的动点的轨迹方程是 ;
③记到M(-1,0),N(1,0)两点的“直角距离”之和为4的动点的轨迹为曲线G,则曲线G所围成的封闭图形的面积的值为 ;
(2)设点A(1,0), 点B是直线
上的动点,求ρ(A,B)的最小值及取得最小值时点B的坐标;
(3)对平面上给定的两个不同的点
,
,是否存在点C(x,y), 同时满足下列两个条件:
①
;
②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2466d223bbf22896a350f2c46eee3c5.png)
若存在,求出所有符合条件的点的集合;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a97b49a5539ea7c791da1beb0a83c49.png)
(1)填空:(直接写出结论)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca1d2645ca6fd82a0483e6bc962eb14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daca6e9e7f98d284cadef013e413ca23.png)
②到坐标原点的“直角距离”等于1的动点的轨迹方程是 ;
③记到M(-1,0),N(1,0)两点的“直角距离”之和为4的动点的轨迹为曲线G,则曲线G所围成的封闭图形的面积的值为 ;
(2)设点A(1,0), 点B是直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4349a46e3c054b326644f2aafd312536.png)
(3)对平面上给定的两个不同的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9361963efd6a9027e8dc91edf9aa7b8b.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2466d223bbf22896a350f2c46eee3c5.png)
若存在,求出所有符合条件的点的集合;若不存在,请说明理由.
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2023-10-29更新
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6卷引用:北京市昌平区第一中学2023-2024学年高二上学期期中考试数学试题
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