名校
解题方法
1 . 已知数列
的前
项和为
,若存在常数
,使得
对任意
都成立,则称数列
具有性质
.
(1)若数列
为等差数列,且
,求证:数列
具有性质
;
(2)设数列
的各项均为正数,且
具有性质
.
①若数列
是公比为
的等比数列,且
,求
的值;
②求
的最小值.
![](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/fc983f1bad03411ae64d84ff7bdf2551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a548095fa134cb2b52721af225cbbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee7ed704a954d0414be6c3148bd566d.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/193a0efaa1aa835eb3e061bb25dad4dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7470297de40027847c5c73fc5d1719c.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee7ed704a954d0414be6c3148bd566d.png)
①若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4338dd5d6ac02dbb9d5069eb98f436d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
7日内更新
|
224次组卷
|
4卷引用:江西省临川第二中学2023-2024学年高二下学期6月月考数学试题
江西省临川第二中学2023-2024学年高二下学期6月月考数学试题河南师范大学附属中学2024届高三下学期最后一卷数学试题江苏省泰州市2024届高三下学期四模数学试题(已下线)高二下期末考前押题卷01--高二期末考点大串讲(人教B版2019选择性必修)
名校
2 . 中国古代建筑中的圆柱,多是根部略粗,顶部略细,这种做法称为“收分”,柱子做出收分,既稳定又轻巧.已知某古代建筑的一根圆柱,每增高
,直径收分
,若该柱子柱根直径为
,柱高
,则柱头直径为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01f8039a874d818f0067ad4dc93bdd33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048b61a5fb5f420c6d7de88db5bc3aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3668a3f3ce5b8a272ad92c2ebd233f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e17ee14bd91bfff409c06fd434f6745.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-05-29更新
|
192次组卷
|
4卷引用:江西省抚州市金溪县第一中学等校2023-2024学年高二下学期期中考试数学试卷
江西省抚州市金溪县第一中学等校2023-2024学年高二下学期期中考试数学试卷 江西省南昌市安义中学2023-2024学年高二下学期4月期中调研测试数学试题(已下线)6.1基本立体图形-【帮课堂】(北师大版2019必修第二册)(已下线)6.1 基本立体图形 同步精品课堂(北师大版2019必修第二册)
名校
解题方法
3 . 近年来中国人工智能产业爆发式的增长,推动了AI电商行业的快速发展,已知2020-2023年中国AI解决方案提供商企业数量分别为1617,2106,2329,2896,从这4个数字中任取2个数字,当所取两个数字差的绝对值小于500时,随机变量
;当所取两个数字差的绝对值不小于500时,随机变量
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f53840590737b3cad20fa4126bf1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ce9db5574a2df6184bdc7cd13b208a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5b9249c10ae3896e2ee96bfa1a153e5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-05-19更新
|
277次组卷
|
2卷引用:江西省抚州市金溪县第一中学等校2023-2024学年高二下学期期中考试数学试卷
4 . 函数
在
上的平均变化率等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/504533db232530466f5fe04837191592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-05-15更新
|
282次组卷
|
2卷引用:江西省抚州市金溪县第一中学等校2023-2024学年高二下学期期中考试数学试卷
名校
5 . 已知
中,点
满足
,点
在
内(含边界),其中
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b487df3bd4826ed3e266f4f8677fee5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5331e29182b4a87e2d68127932ced86.png)
A.若![]() ![]() ![]() | B.若![]() ![]() |
C.若存在![]() ![]() | D.存在![]() ![]() |
您最近一年使用:0次
2024-05-07更新
|
157次组卷
|
4卷引用:江西省抚州市金溪县第一中学等校2023-2024学年高一下学期期中考试数学试卷
名校
6 . 平面几何中有定理:若点
为锐角
的外心,直线
,
,
分别与锐角
外接圆交于另外一点
,
,
,则
.若锐角
的外接圆方程为
,且该圆与
轴的交点分别为
,
,则六边形
的面积的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfdceec9c7010b2ad114e0d72f33d97f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c1a6aada35b8c3676d3bb72b9cec42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/b423e24a65f50b9ca1caa09c3fafdb51.png)
您最近一年使用:0次
2024-05-06更新
|
76次组卷
|
2卷引用:江西省抚州市金溪县第一中学等校2023-2024学年高二下学期期中考试数学试卷
名校
解题方法
7 . 近年来,宠物逐渐成为人们的精神寄托,在供需端及资本的共同推动下中国宠物经济产业迅速增长,数据显示,目前中国养宠户数在全国户数中占比为
.
(1)把频率作为概率,从中国家庭中随机取4户,求这4户中至少有3户养宠物的概率;
(2)随机抽取200名成年人,得到如下列联表:
是否有
的把握认为是否养宠物与性别有关?
(3)记2018-2023年的年份代码
依次为1,2,3,4,5,6,中国宠物经济产业年规模为
(单位:亿元),由这6年中国宠物经济产业年规模数据求得
关于
的回归方程为
,且
.求相关系数
,并判断该回归方程是否有价值.
参考公式:
,其中
,
时有99%的把握认为变量有关联.
回归方程
,其中
,
,相关系数
,若
,则认为
与
有较强的相关性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ffd5c35bba71ea54c28622b6cf505d.png)
(1)把频率作为概率,从中国家庭中随机取4户,求这4户中至少有3户养宠物的概率;
(2)随机抽取200名成年人,得到如下列联表:
成年男性 | 成年女性 | 合计 | |
养宠物 | 38 | 60 | 98 |
不养宠物 | 62 | 40 | 102 |
合计 | 100 | 100 | 200 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a363cc53497fdfac77b43f656424f973.png)
(3)记2018-2023年的年份代码
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/0ef1a1123f3cbf1c4d9896ba82051f89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2962cd7823d2ef0e6e0263b667a5d29f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2187714e660234f0b72f2b47d3ea685a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb8236aa47286c8cbc95fcb564a4a3a4.png)
回归方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a10cb9fd6d5c388cd9d28556d9e9dd8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dbdbf02e0dd324daba7488c3e3bf31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31815979a4ab71755f89089d4e988a3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ae9421919944d997c304d7711b4b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2991502b0be7df4183b9e42b6c53c6e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2024-05-06更新
|
189次组卷
|
2卷引用:江西省抚州市金溪县第一中学等校2023-2024学年高二下学期期中考试数学试卷
名校
8 . 若数列
满足
,从数列
中任取2项相加,把所有和的不同值按照从小到大排成一列,称为数列
的和数列,记作数列
.
(1)已知等差数列
的前n项和为
,且
.
①若
,
,求
的通项公式,并写出
的前5项;
②若
,
,求数列
的前50项的和;
(2)若
,证明:对任意
或
,
,并求数列
的所有项的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a5945ce5c2114af8c18718ca8dc899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c320a0619c63a5b650a1a94c0a5679.png)
(1)已知等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a5945ce5c2114af8c18718ca8dc899.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58365ff21052f2f978c11844b002b933.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb3fdeeb4afe6485ffb00bf83023e704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c320a0619c63a5b650a1a94c0a5679.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751859e4f0b1cb2c94fd5cca373de9af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a50c3a2b8abc17a7e110f9811296a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c320a0619c63a5b650a1a94c0a5679.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559497cb5b10c9c489ee0cdc11fa2a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12329f3ac81209a815f8c4fa12c4b6cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d149f4ed2b72f3e3ee850e163ba35473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e23ba0aeb43a20799d1f414650203ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c320a0619c63a5b650a1a94c0a5679.png)
您最近一年使用:0次
2024-04-30更新
|
109次组卷
|
2卷引用:江西省抚州市金溪县第一中学等校2023-2024学年高二下学期期中考试数学试卷
名校
解题方法
9 . 如图所示,某广场的六边形停车场由4个全等的等边三角形拼接而成,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1de42e94c20ad6289a162bd0cf9a71c4.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-04-30更新
|
188次组卷
|
5卷引用:江西省抚州市金溪县第一中学等校2023-2024学年高一下学期期中考试数学试卷
名校
10 . 已知A,B,C三座小岛的位置如图所示,其中B岛在A岛的南偏西
方向,C岛在B岛的正东方向,A,C两岛相隔4千海里,一货轮由A岛出发沿着
的方向直线航行了
的路程后,到达M岛进行补给后再前往C岛,若M岛到B岛的距离与M岛到A岛的距离相同,则B,C两岛的距离为______ 千海里.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ad1b0a76a887783392268ae203ad22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
您最近一年使用:0次
2024-04-30更新
|
146次组卷
|
4卷引用:江西省抚州市金溪县第一中学等校2023-2024学年高一下学期期中考试数学试卷