名校
解题方法
1 . 假设在某种细菌培养过程中,正常细菌每小时分裂1次(1个正常细菌分裂成2个正常细菌和1个非正常细菌),非正常细菌每小时分裂1次(1个非正常细菌分裂成2个非正常细菌).若1个正常细菌经过14小时的培养,则可分裂成的细菌的个数为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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今日更新
|
484次组卷
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3卷引用:河北省秦皇岛市青龙满族自治县第一中学2024届高三下学期5月模拟考试数学试题
名校
解题方法
2 . 对于数列
,如果存在等差数列
和等比数列
,使得
,则称数列
是“优分解”的.
(1)证明:如果
是等差数列,则
是“优分解”的.
(2)记
,证明:如果数列
是“优分解”的,则
或数列
是等比数列.
(3)设数列
的前
项和为
,如果
和
都是“优分解”的,并且
,求
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd84622d5883097a686797889192356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)证明:如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33119e0b8e033e27fde4505b90a1c3b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238024e8fa2058c5cbbf2f757ce9a997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e274217ecbdfeea729eaa317359e77.png)
(3)设数列
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b15ebc127b977d405b867a151696b163.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2024-06-11更新
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916次组卷
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5卷引用:河北省保定市保定名校协作体2024届高三五月适应性考试(三模)数学试题
名校
解题方法
3 . 已知函数
的最小正周期为
.
(1)求
的值;
(2)在锐角
中,角A,B,C所对的边分别为a,b,c.c为
在
上的最大值,再从条件①、条件②、条件③这三个条件中选择一个作为已知,求
的取值范围.条件①:
;条件②:
;条件③:
的面积为S,且
.注:如果选择多个条件分别解答,按第一个条件计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8927608114a249f8acb7da7901fc7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(2)在锐角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d51992c05a557cf6058664f1f8961e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f2416d1f75a45a314331146550832e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19dd0c2a4a1107ea28a418a7d281ef5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85b86308eec25f94db0a5e7a58765206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76bf72fe243ab7ba53a1679372f41793.png)
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2024-06-10更新
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625次组卷
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2卷引用:2024届河北省承德市部分示范高中高三三模数学试题
4 . 给定正整数
,设数列
是
的一个排列,对
,
表示以
为首项的递增子列的最大长度,
表示以
为首项的递减子列的最大长度.
(1)若
,
,
,
,
,求
和
;
(2)求证:
,
;
(3)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa79f2092161050c26653fd3b0e91c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20681d18e13968fc0d6c7aa9b0c66392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80fdae3edccbdb22b78b114d3c15524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de122ae929b1acaff321dec137622ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d8e8f821111de8075e5c3dfb22a5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb334e165679c6cb500c994cffa47147.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb0abedd59476f8793d5a8948590a70c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f483a9467cfbb1cd9b636e05247ab9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d46063c5ce508068c8b1f59d39101b.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94536f53897365b8b1d0e89c83738cf6.png)
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2024-06-10更新
|
360次组卷
|
2卷引用:2024届河北省承德市部分示范高中高三三模数学试题
名校
5 . 已知数列
是公差为
的等差数列,若它的前
项的和
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bfe21c96489cb30c544d49ddb4c1c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5596e3d616cd804ad9a29a98b720831d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/079f16bbd0704ecb6e5e44c5725af1d9.png)
A.若![]() ![]() ![]() ![]() |
B.![]() ![]() |
C.![]() |
D.![]() |
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2024-06-08更新
|
336次组卷
|
2卷引用:河北省衡水市2024届高三下学期大数据应用调研联合测评( VIII)数学试题
名校
解题方法
6 . 在初等数论中,对于大于1的自然数,除了1和它自身外,不能被其它自然数整除的数叫做素数,对非零整数a和整数b,若存在整数k使得
,则称a整除b.已知p,q为不同的两个素数,数列
是公差为p的等差整数数列,
为q除
所得的余数,
为数列
的前n项和.
(1)若
,
,
,求
;
(2)若某素数整除两个整数的乘积,则该素数至少能整除其中一个整数,证明:数列
的前q项中任意两项均不相同;
(3)证明:
为完全平方数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8b048de4625c67d7f74a4eda94877a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/451b1923f70f26e57c557ffe606f7016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d9b6c86435e0ceff94d8ad1cd03737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/addee6ce5163a2580888ce2da22714af.png)
(2)若某素数整除两个整数的乘积,则该素数至少能整除其中一个整数,证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ab4a56d5549a49adae4f1f17926dd8b.png)
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7 . 设等差数列
的前n项和为
,e是自然对数的底数,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.当![]() ![]() ![]() ![]() |
B.数列![]() |
C.数列![]() |
D.当p,q均为正整数且![]() ![]() |
您最近一年使用:0次
名校
解题方法
8 . 已知
,动点
满足
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7613f5e7af7b50a65777e046ced4d3c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afe53e549f52d6f0b33aa6ac482ae7e3.png)
A.点![]() ![]() |
B.![]() ![]() |
C.![]() ![]() ![]() |
D.过点![]() ![]() ![]() ![]() ![]() |
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2024-05-28更新
|
524次组卷
|
2卷引用:河北省衡水市2024届高三下学期大数据应用调研联合测评( VIII)数学试题
名校
9 . 若数列
若满足递推关系
其中
为常数,我们称该数列为k阶常系数齐次线性递推数列,并称方程
为递推关系式(*)的特征方程,该方程的根称为数列
的特征根.我们有以下结论:对于k阶常系数齐次线性递推数列,若其不同的特征根为
,
,…,
,且特征根
的重数为
,则数列
的通项公式为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a573c3e3b4c5b02a85d309aee9ffbc2.png)
其中
,
,这里
都是常数,它们由数列初始值可以确定.
(1)若数列
满足
,且
,
,
,求数列
的通项公式;
(2)若数列
满足对于所有非负整数m,n(
),
都成立,且
,求数列
的通项公式;
(3)设边长为1的正六边形ABCDEF,O是六边形的中心,除了六边形的每一条边,我们还从点O到每个顶点连一条线段,共得到12条长度为1的线段,一条路径是指动点沿着上述线段(全部或部分)移动,始点终点均为点O的一条移动路线.求长度为2024的路径共有多少条?(注:根的重数就是方程中同样根的数量)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ab67ba8b0719104e78cfa6ce029290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11e26bb035fe18631ca09dd61ba446d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c87ab1d7f0eaf58fb90e7087ad7e71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/8256967311eda335e21bb88f6e726fb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6ba141730fd5aae78ada1a8eb17d21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d68e94f023b09352f46cf2ff3afb291c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a573c3e3b4c5b02a85d309aee9ffbc2.png)
其中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed9176aeda3df453783774182340e074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f9b96ef08d0169c0c8ff9a06eb0c5d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1c5521a39235f0b9cdf432d5903aa83.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac06043337b08fece3c5762766fdb2a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/329785900390130a04a57d0b55aaa569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddb84ee3769b8977d138638120ed820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd68dad20a530c17474ad6c73be07e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67fc21d26aead8dcbfb36d7df8aa895.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设边长为1的正六边形ABCDEF,O是六边形的中心,除了六边形的每一条边,我们还从点O到每个顶点连一条线段,共得到12条长度为1的线段,一条路径是指动点沿着上述线段(全部或部分)移动,始点终点均为点O的一条移动路线.求长度为2024的路径共有多少条?(注:根的重数就是方程中同样根的数量)
您最近一年使用:0次