名校
解题方法
1 . 无穷等比数列
的前n项和为
,且
,则首项
的取值范围是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3a1491985bc04a1ac7b37e80ad0a06c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c0b1ee965332e7575c046a0966a89c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
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2022-11-20更新
|
446次组卷
|
5卷引用:上海交通大学附属中学2022-2023学年高一下学期期末数学试题
上海交通大学附属中学2022-2023学年高一下学期期末数学试题上海市市西中学2023-2024学年高一下学期期末复习数学试卷上海市黄浦区2021届高三下学期二模数学试题(已下线)课时24 数列的极限与无穷等比数列各项的和-2022年高考数学一轮复习小题多维练(上海专用)(已下线)上海市华东师范大学第二附属中学2022-2023学年高二上学期10月月考数学试题
名校
解题方法
2 . 设
.
(1)求不等式
的解集
;
(2)若函数
在
上最小值为
,求实数
的值;
(3)若对任意的正实数
,存在
,使得
,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c2ae6aee8491f0529137bd4fc415abd.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40a1783a95ef17b28034ff496c6e811b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30842ff3466f4037a64c33366eee2719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若对任意的正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36ad23d93c0e20425a3a7f3a8605a61d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/691d1f53d989eb13e2599fedfc746c01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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3 . 设复数
为虚数单位,
.
(1)若
,且
,试确定虚数q的值,使得
,并计算
的值;
(2)若数列
是各项均为正数的等比数列,
,
,
,求
的值;
(3)若
,且
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a036e9ee70ced65188b33599f9c5cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22214f48085c06e62521bf96c27191b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a58dcdbc4ba66c058b9c2ea0b66c78d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cf89ab7d054f735048e3f2de3790952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e958699ed7f4ec14624af584b08869c.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a19c1b64ab0b0ddcf2392cdc57b3772.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0dd3fb6af23def773e1b0032a4f3c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d308b3a2305c0a30cd95d08e6b039986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621c88d8efebb14c021243cf153046bb.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4638a75e65012bebf3684a34212a2ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93fb330f2c2ee620c57204e75f439e99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900298ea19e2fd2d1c99e9744484b0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4914cce8e01442532dbcee3564708e85.png)
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解题方法
4 . 已知
是数列
的前
项和,对任意
,都有
;
(1)若
,求证:数列
是等差数列,并求此时数列
的通项公式;
(2)若
,是否存在正整数
,使得
成等差数列?若存在,求出所有
的值;若不存在,请说明理由;
(3)设
,若
,求实数
的取值范围.
![](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/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b01b45fbdee2d58311040c1ef69336d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711b21672fd907c5c92fee1d649e7003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46db680bc60929939e0f09990c03583e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711b21672fd907c5c92fee1d649e7003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040e97f0892f327f38d2814f3c0e9985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adbf3a9f127d49fc85888d6101c6d86d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77eccbe1f09eb53db3446352ff7be5f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75330ac9e51cdef4bc61012551e1d00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
5 . 已知O是四边形ABCD所在平面上一点,并且这五点,任意三点不共线,若存在一组正实数
、
、
、
使得
,则关于这四个角
、
、
、
的判断,一定正确的是______ .
①一定存在钝角 ②可能有两个钝角 ③可能四个角都是钝角 ④可能没有钝角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b5dc876d7dcd3c971b36d26668b1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7345f310975ddb40dca94b5135c35dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061baa765d2939a416300de14c45b8ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf97cb5e2fa09745dbb21b9bcfe9e6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d9a08cf5fee968d97f92555b8bd61ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22df2977de56cc69be0c1e847653d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed66570f697459aba9daa2eaf9460bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f51d0f39a59c3b7d6d8422c802fee1.png)
①一定存在钝角 ②可能有两个钝角 ③可能四个角都是钝角 ④可能没有钝角
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解题方法
6 . 著名数学家欧拉提出了如下定理:三角形的外心、重心、垂心依次位于同一直线上,且重心到外心的距离是重心到垂心距离的一半,此直线被称为三角形的欧拉线,该定理被称为欧拉线定理.已知
的外心为O,重心为G,垂心为H,M为BC中点,且
,
,则下列各式正确的有______ .
①
②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d13a088bc184bfefd8414284501aec4.png)
③
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e4139319479a982d1a34187d00b0ba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d13a088bc184bfefd8414284501aec4.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ef5de81202c50e6a5f52b955af24722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f0c94583a65e896b2b246a4cd7c5c9e.png)
您最近一年使用:0次
2022-04-26更新
|
677次组卷
|
3卷引用:上海交通大学附属中学2021-2022学年高一下学期线上教学反馈数学试题
名校
解题方法
7 . 关于任意平面向量可实施以下6种变换,包括2种v变换和4种w变换
:模变为原来的
倍,同时逆时针旋转90°;
:模变为原来的
倍,同时顺时针旋转90°;
:模变为原来的
倍,同时逆时针旋转45°;
:模变为原来的
倍,同时顺时针旋转45°;
:模变为原来的
倍,同时逆时针旋转135°;
:模变为原来的
倍,同时顺时针旋转135°.
记集合
,若每次从集合S中随机抽取一种变换.经过n次抽取,依次将第i次抽取的变换记为
,即可得到一个n维有序变换序列,记为
,则以下判断中正确的序号是______ .
①单位向量
经过2022次v变换后所得向量一定与向量
垂直;
②单位向量
经过2022次w变换后所得向量一定与向量
平行;
③单位向量
经过
变换后得到向量
,则
中有且只有2个v变换;
④单位向量
经过
变换后不可能得到向量
;
⑤存在n,使得单位向量
经过
次变换后,得到
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f44c235d8b49207ad3f2d77dc5d6cf20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/814f55724f7ee57bd395eb3b95393c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c3871a062c5e0a4e009b01aa47afb48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a14b56f7f7bb23cd4bf9041e440a46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43801f9d9826f8e3646803c915f70e8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd028b19c0cbdb7f6f8a6390f7b7fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
记集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ef6e24288a68823a7d3143eb547a72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ebdb675dac2dc1d7cfeb8e6882b288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e45ec2967e63500678755d5d5dbfb1f.png)
①单位向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deab0dd26dbb0badb5f6006722f8514a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc1a0171524ed73b7a52a9f96ecde272.png)
②单位向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deab0dd26dbb0badb5f6006722f8514a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc1a0171524ed73b7a52a9f96ecde272.png)
③单位向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deab0dd26dbb0badb5f6006722f8514a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24cb1319a55351f60be7045aa860eb38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137e0222430eda79fff5ff9fae699581.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24cb1319a55351f60be7045aa860eb38.png)
④单位向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deab0dd26dbb0badb5f6006722f8514a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca1f45a8716bdab6cad8261af16aa10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24b06ffa0ec8b3f73dab0eee6e3f89a3.png)
⑤存在n,使得单位向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deab0dd26dbb0badb5f6006722f8514a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9445875e1d2f78a79c38a04897435418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbdd31e5732b68aca509f55e69578fb9.png)
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名校
8 . 已知复数
,
满足
,
,
,则
在复平面所对应的点组成的图形的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b670aca396b96eaf2c553b1ca84486dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56bd60194534e5488f4a2fb2dd34d63d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9126857a18d59d73edabe16cbe835aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a67a742d2a43e907fb1c3a1bdf1d6a9.png)
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2022-04-25更新
|
952次组卷
|
7卷引用:上海交通大学附属中学2021-2022学年高一下学期期中数学试题
上海交通大学附属中学2021-2022学年高一下学期期中数学试题(已下线)7.2 复数的四则运算(精练)-【题型分类归纳】2022-2023学年高一数学同步讲与练(人教A版2019必修第二册)(已下线)专题06 复数的四则运算(六大考点)-【寒假自学课】(人教A版2019)(已下线)第03讲 7.2.1 复数的加、减运算及其几何意义-【帮课堂】(人教A版2019必修第二册)(已下线)第15题 复数的几何意义和复数减法的几何意义(高一期末每日一题)(已下线)模块一 情境5 以复数为背景(已下线)第六章 复数与平面向量 专题2 有关复数的几何意义
名校
解题方法
9 . 已知
,存在实数
,使得对任意
,
总成立,则
的最小值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e162d1739982517c1a337606c0e26573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6daa3514d49ca92dd7835326bd2f92d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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|
353次组卷
|
2卷引用:上海交通大学附属中学2021-2022学年高一下学期期中数学试题
名校
10 . 定理(三角不等式),对于任意的
、
,恒有
.定义:已知
且
,对于有序数组
、
、
、
,称
为有序数组
、
、
、
的波动距离,记作
,即
,请根据上述俼息解决以下几个问题:
(1)求函数
的最小值,并指出函数取到最小值时
的取值范围;
(2)①求有序数组
、
、
、
的波动距离
;
②求证:若
、
、
、
且
,则
;题(注:该命题无需证明,需要时可直接使用).设两两不相等的四个实数
、
、
、
,求有序数组
、
、
、
的波动距离
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49506c61cf5c61605f1cf90a440348cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](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/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec475a4298eab592d6589aab8915276.png)
![](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/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef141315bf951ddcd300f0743a16897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7cfd590897d8d908066c781c63a812d.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d3b887215cd1514d3e2e79063729a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)①求有序数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7330e52932883877de428cfe91962b96.png)
②求证:若
![](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/7a876ecb804eb0553c246e5fcc40b708.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73abfe4bc26b1ded680d7abb1a2cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/effb89a4bffb74028211ecfe671b79d1.png)
![](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/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46944e1594eec140cacd7b454342561.png)
![](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/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc0ce632fa217dc77f6c92afd311815.png)
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2022-08-22更新
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7卷引用:上海市吴淞中学2023-2024学年高一上学期期中数学试题
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