名校
1 . “物不知数”是中国古代著名算题,原载于《孙子算经》卷下第二十六题:“今有物不知其数,三三数之剩二:五五数之剩三;七七数之剩二.问物几何?”问题的意思是,一个数被3除余2,被5除余3,被7除余2,那么这个数是多少?若一个数
被
除余
,我们可以写作
.它的系统解法是秦九韶在《数书九章》大衍求一术中给出的.大衍求一术(也称作“中国剩余定理”)是中国古算中最有独创性的成就之一,现将满足上述条件的正整数从小到大依次排序.中国剩余定理:假设整数
,
,…,
两两互质,则对任意的整数:
,
,…,
方程组
一定有解,并且通解为
,其中
为任意整数,
,
,
为整数,且满足
.
(1)求出满足条件的最小正整数,并写出第
个满足条件的正整数;
(2)在不超过4200的正整数中,求所有满足条件的数的和.(提示:可以用首尾进行相加).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bfa96cf7f45afec8a40d3fe7e24f509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ab1256702aef4e9f1a5eb6c12ecc96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fbd67f60f04c278bdd867fdb3979dfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a625b91e0eba33b107550ee2a1e2f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2858005b9ae89ae080d83dcc13cf8e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3e95410f3b4fcb0cba425b521d1f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a135cb036833400f3fa1edc92d5ce410.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2e034e96fafe12d9aadca06c029ee87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc0d6dc164a597aa467bc2a82d09719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c462cd0fa26921b316bc436f4e6ea1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d4b9cf64ea7a6171db43eec4e5637a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90c998886b1483221a5b4941f6e874c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec3a3c25d32c153f1170e5bcdb10f849.png)
(1)求出满足条件的最小正整数,并写出第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)在不超过4200的正整数中,求所有满足条件的数的和.(提示:可以用首尾进行相加).
您最近一年使用:0次
2024-02-23更新
|
732次组卷
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4卷引用:湖北省襄阳市第五中学2024届高三下学期开学考试数学试题
湖北省襄阳市第五中学2024届高三下学期开学考试数学试题云南省昆明市第一中学2023-2024学年高一上学期入学考试数学试题(已下线)压轴题高等数学背景下新定义题(九省联考第19题模式)练贵州省毕节市金沙县部分学校2024届高三下学期高考模拟(六)数学试题
名校
2 . 已知
,函数
,其中
…为自然对数的底数.
(1)证明:函数
在
上有唯一零点;
(2)记
为函数
在
上的零点,证明:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3adb9acead48e36b705874dc96979f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/597de8046b5baecf54be4b0516de67ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9405dfcca25b76af059fb4c308983eae.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c89e13ea43300cc01379c96614d8e9cc.png)
您最近一年使用:0次
2021-10-12更新
|
558次组卷
|
3卷引用:湖北省武汉市部分重点中学2021-2022学年高二下学期期末联考数学试题
名校
3 . 已知关于
的方程
在复数范围内的两根为
、
.
(1)若p=8,求
、
;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e9bca6b2ef4b5953b72592f09b7c5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(1)若p=8,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89a49fc90138dcbe233f6192acf10416.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
您最近一年使用:0次
2021-04-07更新
|
1591次组卷
|
13卷引用:湖北省恩施州咸丰春晖学校2020-2021学年高一下学期第三次月考数学试题
湖北省恩施州咸丰春晖学校2020-2021学年高一下学期第三次月考数学试题湖南省长沙市雅礼中学2020-2021学年高一下学期3月月考数学试题湖南省湘中部分学校2020-2021学年高一下学期期末数学试题河北省定州市2020-2021学年高一下学期期中数学试题(已下线)上海期末全真模拟试卷(5)-2020-2021学年高一数学下册期中期末考试高分直通车(沪教版2020必修第二册)(已下线)9.1 复数及其四则运算(作业)-【上好课】2020-2021学年高一数学下册同步备课系列(沪教版2020必修第二册)(已下线)第18讲复数全章复习(讲义)-【教育机构专用】2021年春季高一数学辅导讲义(沪教版2020必修第二册)河北省武安市第一中学2020-2021学年高一下学期第二次月考数学试题上海市吴淞中学2021-2022学年高一下学期期末数学试题(已下线)高二数学上学期开学摸底考试卷(沪教版2020)-2022-2023学年高二数学考试满分全攻略(沪教版2020必修第三册)第12章 复数(单元测试)-2022-2023学年高一数学同步精品课堂(苏教版2019必修第二册)广东省云浮市罗定中学城东学校2022-2023学年高一下学期期中数学试题(已下线)上海市高一下学期期末真题必刷03-期末考点大串讲(沪教版2020必修二)
名校
4 . 有一大批产品,其验收方案如下,先做第一次检验:从中任取8件,经检验都为优质品时接受这批产品,若优质品数小于6件则拒收;否则做第二次检验,其做法是从产品中再另任取3件,逐一检验,若检测过程中检测出非优质品就要终止检验且拒收这批产品,否则继续产品检测,且仅当这3件产品都为优质品时接受这批产品.若产品的优质品率为0.9.且各件产品是否为优质品相互独立.
(1)记
为第一次检验的8件产品中优质品的件数,求
的期望与方差;
(2)求这批产品被接受的概率;
(3)若第一次检测费用固定为1000元,第二次检测费用为每件产品100元,记
为整个产品检验过程中的总费用,求
的分布列.
(附:
,
,
,
,
)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)求这批产品被接受的概率;
(3)若第一次检测费用固定为1000元,第二次检测费用为每件产品100元,记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
(附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62f65d65c83f18eac8539ee787e6c46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/640513792121f58176c100b81237615f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503054b701bcbde512e1c341c9d88f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289198673260a570941a2a74d2c0f7c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cd2dca19ed5263086782bf8490dad9.png)
您最近一年使用:0次
2020-01-30更新
|
273次组卷
|
2卷引用:湖北省黄冈市2019-2020学年高二上学期期末数学试题
名校
5 . 如图,直线
,点
是
之间的一个定点,过点
的直线
垂直于直线
,
(
为常数),点
分别为
上的动点,已知
.设
(
).
![](https://img.xkw.com/dksih/QBM/2020/1/30/2388072192073728/2388181329387520/STEM/259f8d3625d64876909c2ad47f08f89a.png?resizew=186)
(1)求
面积
关于角
的函数解析式
;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1095c036b49c3327baaa2c3c7f746134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f419750fe2e81297e21646268adb07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57fdd2a3642716fcf5100011eb3ec88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da24c3c749a2daba3d3a5136c16fdb24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50515b0461f55861fd28f2774a2f01dc.png)
![](https://img.xkw.com/dksih/QBM/2020/1/30/2388072192073728/2388181329387520/STEM/259f8d3625d64876909c2ad47f08f89a.png?resizew=186)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8135ce2fc33a303efd2087106709d44e.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8135ce2fc33a303efd2087106709d44e.png)
您最近一年使用:0次
2020-01-30更新
|
1100次组卷
|
7卷引用:湖北省武汉市华中师范大学第一附属中学2021-2022学年高一上学期期末数学试题
解题方法
6 . 如图,在
中,已知
,若长为
的线段
以点
为中点,问
与
的夹角
取何值时
的值最大?并求出这个最大值.
![](https://img.xkw.com/dksih/QBM/2020/3/1/2410340921073664/2410894216069120/STEM/3b7a0c4b95ba4d63842a8ad0a9f74382.png?resizew=78)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8f88798ec42a58dccd212586382b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e781a2489271bfd1597cba1bb6f5887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/878e89b6eca35e34c863e832a2c661db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e00e4e17dc8a2ef88e23e348439edf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d792a2aa25763e14cc2863be3887000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de6d9ecb0f5430a6eb59354d615eaa1d.png)
![](https://img.xkw.com/dksih/QBM/2020/3/1/2410340921073664/2410894216069120/STEM/3b7a0c4b95ba4d63842a8ad0a9f74382.png?resizew=78)
您最近一年使用:0次
7 . 设
为数列
的前
项和,
.数列
前
项和为
且
.数列
满足
.
(1)求数列
和
的通项公式;
(2)记
表示
的个位数字,如
,求数列
的前30项的和.
![](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/4300dca231e2f4b37f70900b33439d5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e926475c154644af560cd152a0f203f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2257d49ff5a72b0f468c6ecaba3049ce.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a7d0e556bfc4abc6a2e6747b7ca4db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5882203e68d6a09fd544202c0ed9a344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/979485f7116e7bbb751f76fd55695bd8.png)
您最近一年使用:0次
2020-05-03更新
|
400次组卷
|
4卷引用:湖北省孝感市五校协作体2018-2019学年高三上学期期中文科数学试题
湖北省孝感市五校协作体2018-2019学年高三上学期期中文科数学试题湖北省孝感市五校协作体2018-2019学年高三上学期期中理科数学试题广东省广州市西关外国语学校2020-2021学年高二上学期期中数学试题(已下线)模块二 专题6《数列》单元检测篇 A基础卷 (人教A)
名校
8 . 已知函数
的最小值为M.
(1)求M;
(2)若正实数
,
,
满足
,求:
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41fc69c21ff43797710c4dc1776f48df.png)
(1)求M;
(2)若正实数
![](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/aaba7863fad4c79a7c3c6aa2d85c28f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1771b8f48a829c9be482a0400b561d.png)
您最近一年使用:0次
2019-09-25更新
|
1157次组卷
|
5卷引用:2020届湖北省襄阳市优质高中高三联考数学(理)试题
9 . 如图,圆
与
轴相切于点
,与
轴的正半轴相交于
两点(
在
的上方),且
.
![](https://img.xkw.com/dksih/QBM/2018/12/17/2098769825038336/2100165567504384/STEM/b6045216-4c49-4dc1-8c89-9dde85a233f5.png?resizew=254)
(1)求圆
的方程;
(2)设过点
的直线
与椭圆
相交于
两点,求证:射线
平分
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a63f7b42555f7f81bcb18b9247bf9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/368fc197b61e01fe6a4a168bb7b375cd.png)
![](https://img.xkw.com/dksih/QBM/2018/12/17/2098769825038336/2100165567504384/STEM/b6045216-4c49-4dc1-8c89-9dde85a233f5.png?resizew=254)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c763113a1fc48e8acc83787b8cd24eec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd8cb171425253834dfd7fa1a9da9ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7023ec0f513c7d0ef86859a5ede54.png)
您最近一年使用:0次
2018-12-19更新
|
296次组卷
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4卷引用:湖北省九校教研协作体2022-2023学年高二上学期9月联考数学试题
10 . 在
中,
分别表示它的三个内角,且满足
,试判断该三角形的形状.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23beb7fa35ed321584f95c7507b8b78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86bcf3d809a21860c9a2f0c374da4560.png)
您最近一年使用:0次
2018-12-16更新
|
181次组卷
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2卷引用:湖北省九校教研协作体2022-2023学年高二上学期9月联考数学试题