名校
解题方法
1 . 某大学科研团队在如下图所示的长方形区域
内(包含边界)进行粒子撞击实验,科研人员在A、O两处同时释放甲、乙两颗粒子.甲粒子在A处按
方向做匀速直线运动,乙粒子在O处按
方向做匀速直线运动,两颗粒子碰撞之处记为点P,且粒子相互碰撞或触碰边界后爆炸消失.已知
长度为6分米,O为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/63a01095-e070-4050-a557-a210db24dc44.png?resizew=218)
(1)已知向量
与
的夹角为
,且
足够长.若两颗粒子成功发生碰撞,求两颗粒子运动路程之和的最大值;
(2)设向量
与向量
的夹角为
(
),向量
与向量
的夹角为
(
),甲粒子的运动速度是乙粒子运动速度的2倍.请问
的长度至少为多少分米,才能确保对任意的
,总可以通过调整甲粒子的释放角度
,使两颗粒子能成功发生碰撞?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888afd002858f23a84a8755a002bed7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c968347eabbb636d20b607a3bcfe0ac3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/63a01095-e070-4050-a557-a210db24dc44.png?resizew=218)
(1)已知向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888afd002858f23a84a8755a002bed7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c968347eabbb636d20b607a3bcfe0ac3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888afd002858f23a84a8755a002bed7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a7f004f23ec3f968d885cb111aac4e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a135466eb8ca64d002d0fad36176d1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c968347eabbb636d20b607a3bcfe0ac3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68628a408537b1cf3bf1ca2a69731b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1c6f686681d7640cd71ed82b9f07e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481e744af0f65e797a35d976c20f2dac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
2022-07-07更新
|
709次组卷
|
3卷引用:广东省汕尾市2021-2022学年高一下学期期末数学试题
名校
解题方法
2 . 已知函数
,
的最小正周期为
.
(1)求
单调递增区间;
(2)是否存在实数m满足对任意
,任意
,使
成立.若存在,求m的取值范围;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5004a7fcc043e7074ae5caae584968d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)是否存在实数m满足对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1684193bc289e50f23e5f4fcb47e714e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca5a325b00c005e99ea2dec90f84a1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b9f34804bd44921d1431aef2956932.png)
您最近一年使用:0次
2022-07-03更新
|
919次组卷
|
3卷引用:四川省巴中市2021-2022学年高一下学期期末数学理科试题
3 . 设函数
,定义集合
,集合
.
(1)若
,写出相应的集合
和
;
(2)若集合
,求出所有满足条件的
;
(3)若集合
只含有一个元素,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce5b409bb706df9ca1ccb27f893e2b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f90056bdaa86e0b862bde3dce36b53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a0c740c333f153ae2e9cdef157686b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8897aa03f96629b56ab1cc6c2398bb30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b5886cf72ed5a1073263eb9ff485c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b864bba6e36f6577c74799bb1c63303.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e76fcf1fb1bae5bfeb45951da12efb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b864bba6e36f6577c74799bb1c63303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a0bf834a9b75cdc4f9e868cd76e78e.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,在六面体
中,
是等边三角形,二面角
的平面角为30°,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/24/abf1f59c-1ce0-42f8-a29a-432634afd36b.png?resizew=215)
(1)证明:
;
(2)若点E为线段BD上一动点,求直线CE与平面
所成角的正切的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1e3a43d0fa18f6c0888ba804d5b329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f479b251fdb01bae6d16abb7f2d694a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0b3c477034d1974fecb5875c557fef6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/24/abf1f59c-1ce0-42f8-a29a-432634afd36b.png?resizew=215)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c583493109d50c9e4634c05e9042a9f.png)
(2)若点E为线段BD上一动点,求直线CE与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2022-06-23更新
|
1769次组卷
|
7卷引用:浙江省宁波市镇海中学2021-2022学年高二下学期期末数学试题
浙江省宁波市镇海中学2021-2022学年高二下学期期末数学试题第一章 空间向量与立体几何(B卷·能力提升练)-【单元测试】2022-2023学年高二数学分层训练AB卷(人教B版2019)山东省聊城市莘县第一中学2022-2023学年高二上学期第一次月考数学试题福建省南平市浦城县2022-2023学年高二上学期期中考试数学试题江苏省南京市秦淮中学2022-2023学年高二上学期期末数学试题江苏省南京市秦淮中学2022-2023学年高二下学期3月月考数学试题(已下线)第一章 空间向量与立体几何 章末测试(提升)-2023-2024学年高二数学《一隅三反》系列(人教A版2019选择性必修第一册)
名校
解题方法
5 . 已知椭圆E:
的离心率为
,
,
为其左、右焦点,左、右顶点分别为A,B,过
且斜率为k的直线l交椭圆E于M,N两点(异于A,B两点),且
的周长为8.
(1)求椭圆C的方程;
(2)若P为椭圆上一点,O为坐标原点,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5585a42c8f07ad90b94ace9db3d78994.png)
(1)求椭圆C的方程;
(2)若P为椭圆上一点,O为坐标原点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c922f835c095ce76ccef75e396b1cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e6453bd1dd6184452f8df1ec70ae59.png)
您最近一年使用:0次
2022-05-14更新
|
971次组卷
|
5卷引用:河南省好教育联盟2022届普通高校招生全国统一考试猜题压轴卷(AA)高三理科数学试题
河南省好教育联盟2022届普通高校招生全国统一考试猜题压轴卷(AA)高三理科数学试题宁夏银川一中2022届高三第四次模拟考试数学(理)试题宁夏银川一中2022届高三第四次模拟考试数学(文)试题(已下线)重难点12五种椭圆解题方法-1(已下线)专题29 弦长问题及长度和、差、商、积问题-1
名校
6 . 已知函数
(
,
)是奇函数.
(1)若
,对任意
有
恒成立,求实数
的取值范围;
(2)设
(
,
),若
,问是否存在实数
使函数
在
上的最大值为0?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fa28501b76696dd6e1ab8ad83b33d64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ad8c8165036178e5ca51d0a7c2b3a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3993391fe16e7315c4d92af28c03fa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305c82799c4a08c2c6b1aac3aa5c9423.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7e2fc9cebff67c6d256cc75ce86dd60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060e7930731eddbcfac592b808e9b698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0e5e3f3477931e7c15cf609b422410.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6602b172fa321eacd584c338dee7bef8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
解题方法
7 . 已知函数
,
,且
在
上单调递增.
(1)若
恒成立,求
的值;
(2)在(1)的条件下,若当
时,总有
使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5ffc29095607e86d6cd2f55a79e7193.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57d91a4ab67a4edb4b62f4e36ea89035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3aae9c8988f4a48db69cad3308942c9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98d3196f675600803cdc74c72470d32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(2)在(1)的条件下,若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4361b7baf57ec27b60ac4aa637e16a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00fff2634ce3999c544b19d011924df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-04-01更新
|
1225次组卷
|
3卷引用:河南省南阳市六校2021-2022学年高一下学期第一次联考数学试题
名校
8 . 已知
,若方程
有四个不同的实数根
,
,
,
,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38cf09c172661244bf42742c295f8939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ad597ac16a5478e29bfa6760618fa45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365b38a7689a8eede6820cd6f1fe952b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a3d41be26be9622d0cbc9825778b362.png)
A.(3,4) | B.(2,4) | C.[0,4) | D.[3,4) |
您最近一年使用:0次
2022-03-28更新
|
1784次组卷
|
8卷引用:内蒙古赤峰二中2021-2022学年高一上学期期末考试数学(文科)试题
内蒙古赤峰二中2021-2022学年高一上学期期末考试数学(文科)试题(已下线)江苏省南通市如皋市2021-2022学年高二下学期期中模拟数学试题江西省上饶市横峰中学2022-2023学年高二上学期开学考试数学试题广东省清远市四校2022-2023学年高一上学期联合学业质量检测数学试题云南省2022-2023学年高一上学期期末数学模拟试题云南省临沧市临翔区第一中学2022-2023学年高一下学期3月月考数学试题(已下线)第二章 函数的概念与性质 第四节 二次函数(B素养提升卷)云南省北京教能教育集团(昆明艺卓中学)2023-2024学年高二上学期12月月考数学试题
名校
9 . 若函数
对定义域内的每一个值
,在其定义域内都存在唯一的
,使
成立,则称该函数为“依赖函数”.
(1)判断函数
是否为“依赖函数”,并说明理由;
(2)若函数
在定义域
上为“依赖函数”,求
的取值范围;
(3)已知函数
在定义域
上为“依赖函数”,若存在实数:
,使得对任意的
,不等式
都成立,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92365662df7a3badcfaa2bcd0b54bffe.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c86ec4ffba69df637d15be893deb46e.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da5bf1fbb7d7339058beb960a4c6ae5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67417af99db3ea6103a47cc3ca888069.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1019d4ad2e3fb4a7abb66e0e9e55b556.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc23f8d012aeaf9ee20a2fe375ccc1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851ba83b36dc51cbe6711b4dfaf1781e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69ef8712fdc2c58083c0d9844d8f5c89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eaaf57bdb80bd7cfe4abe1cf06a369c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
您最近一年使用:0次
名校
解题方法
10 . 已知二次函数
.
(1)若
,且
在
上的最大值为
,求
的值;
(2)若对任意实数
,在区间
上总存在两实数
,
,使得
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d7763547284c85fc773fe2c4a5bc32e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f22fec5a381ae8aca93d876e54c79de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7570c77bd375f4dfdffee64fce8d1a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e43c4ba99bf7f402ae720f7f7a2136e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d5d83ab1a353c993aa2711c88c269c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
2022-02-23更新
|
345次组卷
|
2卷引用:浙江省名校协作体2021-2022学年高二下学期开学考试数学试题