1 . 已知双曲线
,点
在
上,
为常数,
.按照如下方式依次构造点
:过
作斜率为
的直线与
的左支交于点
,令
为
关于
轴的对称点,记
的坐标为
.
(1)若
,求
;
(2)证明:数列
是公比为
的等比数列;
(3)设
为
的面积,证明:对任意正整数
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a3771d89c653798f5164c8dcfc94137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7680911a1cc664a88db0a4260c4849c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffbb4e6b92463a41bd9460dac6b1ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85def4eebc99aecdc878cd7c4180b8b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb90a2118db1e9945d7b5997bf2482a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6192139c2fa8ac2dcf92c777c93b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6192139c2fa8ac2dcf92c777c93b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28c66751ff7fe93ebc69986088141e8c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a2a34b4317deffa40ba34e269c2b81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c788875fe76212a7c59d0a9cee345d7.png)
(2)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f33eb7bcdb380fa633771537843b525.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/968a2a65734098f665e104786ec7a990.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f14afef14d8198491b9c43b1b5a0192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b306ea5e1ebbb1c2ec9450b3aedb74.png)
您最近一年使用:0次
7日内更新
|
5281次组卷
|
7卷引用:福建省泉州市安溪铭选中学2023-2024学年高二下学期6月份质量检测数学试题
福建省泉州市安溪铭选中学2023-2024学年高二下学期6月份质量检测数学试题2024年新课标全国Ⅱ卷数学真题专题08平面解析几何(已下线)2024年新课标全国Ⅱ卷数学真题变式题16-19专题08[2837] 平面解析几何(已下线)平面解析几何-综合测试卷B卷(已下线)2024年高考数学真题完全解读(新高考Ⅱ卷)
名校
2 . 某市联考后从全体考生中随机抽取42名,获取他们本次考试的数学成绩
和物理成绩
,绘制成如图散点图:
与
之间有线性相关关系,但图中有两个异常点
.经调查得知,
考生由于重感冒导致物理考试发挥失常,
考生因故未能参加物理考试.为了使分析结果更科学准确,剔除这两组数据后,对剩下的数据作处理,得到一些统计的值:
,其中
,
分别表示这40名同学的数学成绩、物理成绩,
与
的相关系数
.
(1)若不剔除
两名考生的数据,用42组数据作回归分析,设此时
与
的相关系数为
.试判断
与
的大小关系,并说明理由;
(2)求
关于
的线性回归方程,并估计如果
考生参加了这次物理考试(已知
考生的数学成绩为126分),物理成绩是多少?
(3)从概率统计规律看,本次考试该市的物理成绩
服从正态分布
,以剔除后的物理成绩作为样本,用样本平均数
作为
的估计值,用样本方差
作为
的估计值.试求该市共40000名考生中,物理成绩位于区间
的人数
的数学期望.
附:①回归方程
中:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446c21b8025405469a473aa0b32f9373.png)
②若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754a89032ac17e6f6afae4888fdc12dd.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c2719fc8914037d61e5bac0e1c5980.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d649a4ddb20c4242160669dd2c3aeedd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/54712c3a7d07b9d319432ba79ea7cfe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de122ae929b1acaff321dec137622ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cc10faaf971fee2258a5cf3620743e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa363608f5f5ea1de6be403fae7fec6.png)
(1)若不剔除
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2833ddbe58a6f4e7585c69c698f0d2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2833ddbe58a6f4e7585c69c698f0d2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(3)从概率统计规律看,本次考试该市的物理成绩
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29bcc248a7770a16fa10fc4602d71e0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923d80da4a6cb5f102be334006d875a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671f43c79d612c93a6d160335e86e177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742d3e642d52e01899f66df411100838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c103ffa4e14fe8ed4c45fc5bb3d3c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
附:①回归方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9cf74bbdee085c44778ac6191e5016b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446c21b8025405469a473aa0b32f9373.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c1ed67167078ea4f5f1ee53ee14164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754a89032ac17e6f6afae4888fdc12dd.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/327ad12594450986c1635f073e122b6a.png)
您最近一年使用:0次
名校
3 . 已知函数
,其导函数为
,集合
,
,若A B,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/153a430f99c4004a94325ab49d84dc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dd6895df6cb633f5d9de2bd8cf1c29c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d450142eb4c0dd50187307ebe90e631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
4 . 已知函数
,
,若函数
与
的图象在
上恰有2个交点
,
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed3aec19f4ad1dac8a1710b888d2dd17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/391e64453fa47903c5b71260069670bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ad9a4881ebe1a4a566d0fab96d71baa.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5 . 无穷数列
,
,…,
,…的定义如下:如果n是偶数,就对n尽可能多次地除以2,直到得出一个奇数,这个奇数就是
﹔如果n是奇数,就对
尽可能多次地除以2,直到得出一个奇数,这个奇数就是
.
(1)写出这个数列的前7项;
(2)如果
且
,求m,n的值;
(3)记
,
,求一个正整数n,满足
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0e19f7bfb0ee59fc93e6e822a0658af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)写出这个数列的前7项;
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/564e60383b05d2e0ee94a733742ae424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb93a77f1677e8eb0e6e3d419d3217f.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/695950fe16f7972182bd2d0864e12feb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0317b77cd356da2676220a79762c11dd.png)
您最近一年使用:0次
2024-05-20更新
|
2591次组卷
|
3卷引用:单元测试A卷——第四章 数列
6 . 某学校数学实践小组为该校一块长方形空地设计种树方案,在坐标纸上设计如下:第
棵树种在点
处,其中
,当
时,
,[
]表示不大于x的最大整数,按此设计方案,第3株树种植点的坐标为___________ ;第2025棵树种植点的坐标为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a9ea0c17c1c1576541f981a202701b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e93eb05e988d2fd48fac631e479b3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c972cbd63decec197aec1bdc306de67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7437284d09b06a4e911be5feaf83dd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2024-05-11更新
|
217次组卷
|
2卷引用:山东省潍坊市2023-2024学年高二下学期期中质量监测数学试题
名校
解题方法
7 . 假设视网膜为一个平面,光在空气中不折射,眼球的成像原理为小孔成像. 思考如下成像原理: 如图,地面内有圆
,其圆心在线段
上,且与线段
交于不与
重合的点
,
地面,且
,
点为人眼所在处,视网膜平面与直线
垂直. 过
点作平面
平行于视网膜平面. 科学家已经证明,这种情况下圆
上任意一点到
点的直线与平面
交点的轨迹(令为曲线
)为椭圆或圆,且由于小孔成像,曲线
与圆
在视网膜平面上的影像是相似的,则当视网膜平面上的圆
的影像为圆时,圆
的半径
为____________ . 当圆
的半径
满足
时,视网膜平面上的圆
的影像的离心率的取值范围为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137d33c8575602cb3480ba3825dece9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7442b64b37f685bc3ae88ff450c1a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e92e4810c9461c39fae1acde95e489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3dc6893e52bbca0d011ac46845334d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
您最近一年使用:0次
2024-05-09更新
|
98次组卷
|
2卷引用:四川省成都市实验外国语学校2023-2024学年高二上学期期末能力测评数学试题
8 . 已知向量
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e78f6720046711719447650c97c351c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1260fbfccb2c549ded380c494dce0f33.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
23-24高二下·全国·课前预习
9 . 知识点一 函数最值的定义
1、一般地,如果在区间[a,b]上函数y=f(x)的图象是一条_____ 的曲线,那么它必有最大值和最小值.
2、对于函数f(x),给定区间I,若对任意x∈I,存在x0∈I,使得f(x)_____ f(x0),则称f(x0)为函数f(x)在区间I上的最小值;若对任意x∈I,存在x0∈I,使得f(x) _____ f(x0),则称f(x0)为函数f(x)在区间I上的最大值.
1、一般地,如果在区间[a,b]上函数y=f(x)的图象是一条
2、对于函数f(x),给定区间I,若对任意x∈I,存在x0∈I,使得f(x)
您最近一年使用:0次
名校
解题方法
10 . 某学校有
、
两家餐厅,王同学第1天午餐时随机选择一家餐厅用餐,如果第1天去
餐厅,那么第2天去
餐厅的概率为0.6;如果第1天去
餐厅,那么第2天去
餐厅的概率为0.8.
(1)求王同学第2天去
餐厅用餐的概率;
(2)如果王同学第2天去
餐厅用餐,求他第1天在
餐厅用餐的概率;
(3)
餐厅对就餐环境、菜品种类与品质等方面进行了改造与提升.改造提升后,
餐厅对就餐满意程度进行了调查,统计了100名学生的数据,如下表(单位:人).
依据小概率值
的独立性检验,能否认为学生对于
餐厅的就餐满意程度与餐厅的改造提升有关联?如果有关联,请分析两者的影响规律.
附:
,其中
.
![](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/5963abe8f421bd99a2aaa94831a951e9.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/5963abe8f421bd99a2aaa94831a951e9.png)
(1)求王同学第2天去
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)如果王同学第2天去
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
就餐满意程度 |
| 合计 | |
改造提升前 | 改造提升后 | ||
满意 | 28 | 57 | 85 |
不满意 | 12 | 3 | 15 |
合计 | 40 | 60 | 100 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0255cd2084765f7019367ff6e575b9d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8a6d141688731d46a6ef75b1d438534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
0.1 | 0.05 | 0.01 | 0.005 | |
2.706 | 3.841 | 6.635 | 7.879 |
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