1 . 对于等差数列和等比数列,我国古代很早就有研究成果,北宋大科学家沈括在《梦溪笔谈》中首创的“隙积术”,就是关于高阶等差级数求和的问题.现有一货物堆,从上向下查,第一层有2个货物,第二层比第一层多3个,第三层比第二层多4个,以此类推,记第
层货物的个数为
,则数列
的前10项和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1f1b7e9e20d799ee3c06b89a0611c.png)
_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/241515dbec4be59ea1099bb33e3aa26f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1f1b7e9e20d799ee3c06b89a0611c.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,直线
垂直于梯形
所在的平面,
,
为线段
上一点,
,四边形
为矩形.
是
的中点,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
平面
;
(2)求直线
与平面
所成角的正弦值:
(3)若点
到平面
的距离为
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deeb439906f6d463c9594b41bc4a9172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc5addb203f4b6985880c4cef3ddc14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5bf51c07144386bd23a422d9ceb140.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b489c25405ce48699d4f0a62820bed.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b489c25405ce48699d4f0a62820bed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6486784415f3537c9a13556c05d893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
您最近一年使用:0次
7日内更新
|
786次组卷
|
3卷引用:江西省南昌市第十中学2023-2024学年高二下学期第二次月考数学试题
名校
3 . 下列关于概率统计的说法中正确的是( )
A.某人在10次答题中,答对题数为![]() |
B.设随机变量![]() ![]() ![]() ![]() |
C.已知回归直线方程为![]() ![]() ![]() |
D.两个变量![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
7日内更新
|
1329次组卷
|
3卷引用:江西省南昌市第十中学2023-2024学年高二下学期第二次月考数学试题
解题方法
4 . 如图,在棱长为2的正方体
中,
为线段
的中点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
A.![]() |
B.直线![]() ![]() |
C.平面![]() ![]() ![]() |
D.直线![]() ![]() ![]() |
您最近一年使用:0次
5 . 某机构为了了解某地区中学生的性别和喜爱游泳是否有关,随机抽取了100名中学生进行了问卷调查,得到如下列联表:
已知在这100人中随机抽取1人,抽到不喜欢游泳的学生的概率为
.
(1)请将上述列联表补充完整,并依据独立性检验,判断能否有
认为喜欢游泳与性别有关联;
(2)将样本频率视为总体概率,在该地区的所有中学生中随机抽取3人,计抽取的3人中喜欢游泳的人数为
,求随机变量
的分布列和期望.
附:
.
喜欢游泳 | 不喜欢游泳 | 合计 | |
男生 | 25 | ||
女生 | 35 | ||
合计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4222b8069d08e6ba68c4a31f892f31.png)
(1)请将上述列联表补充完整,并依据独立性检验,判断能否有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c26f1d9579103b8e5577d2fa1cab2c9.png)
(2)将样本频率视为总体概率,在该地区的所有中学生中随机抽取3人,计抽取的3人中喜欢游泳的人数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b6b3f3249878e34e0f33db13aff2996.png)
![]() | 0.100 | 0.050 | 0.010 | 0.001 |
![]() | 2.706 | 3.841 | 6.635 | 10.828 |
您最近一年使用:0次
6 . 已知全集
,集合
,
,那么集合
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa26ede4564b80c035c146272384bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58f19e6bea9f955f655a803c9b417ca3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32247ede98f9ea1e873ac3e6c8bb3208.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4437ed14585a5b64036e9d4289d58b4.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
7 . 已知抛物线
的焦点
与圆
的圆心重合,直线
与
交于
,
两点,且满足:
(其中
为坐标原点且
,
均不与
重合),对于下列命题:
①
,
;②直线
恒过定点
;③
,
中点轨迹方程:
;④
面积的最小值为16.
其中是真命题的有_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80535fc5458973560b8ccfeec4163571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd767240a603ca0c0db5567707eb704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e3dcb7f9fa27f3d07d18a61d4bb36e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c971815096aafba83743ab5e4c89d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc11e7549cfce9220e70250ac943e457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/1dde8112e8eb968fd042418dd632759e.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adfcdcacf75272cb6a20385c8d06134e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b8b0499988ee9f02f3c0ef389deb1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f436117499e8ba9cb034e2704fc0dd.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/b646e7630de8a801824a1c37bb7741ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
其中是真命题的有
您最近一年使用:0次
8 . 已知公差不为0的等差数列
的前
项和为
,且
,
,
成等比数列,
.
(1)求
的通项公式;
(2)若
,求
的前
项和
.
![](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/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7da2f386b78cdf6489efaa2f5820d3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7783bfcf931a0fd34053edf84eed3695.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc095ceed420014bfcdd1681454670b.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)
您最近一年使用:0次
9 . 已知函数
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d2399c2a712a2890dcd0b195d3b9f1c.png)
A.![]() |
B.![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若过点![]() ![]() ![]() |
您最近一年使用:0次
10 . 下列命题为真命题的是( )
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.如果![]() ![]() ![]() |
D.如果![]() ![]() ![]() ![]() |
您最近一年使用:0次