1 . 给出下列4个命题:
①若事件
和事件
互斥,则
;
②数据
的第
百分位数为10;
③已知
关于
的回归方程为
,则样本点
的离差为
;
④随机变量
的分布为
,则其数学期望
.
其中正确命题的序号为( )
①若事件
![](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/516cc3b619715f0309749aaed4fd2e66.png)
②数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e22d37bfc7b992a08acfa415bcd46677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aa86faa9bfef703aead8c2606684dc5.png)
③已知
![](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/78b0e64e3c752d3ef6501692e4fd6bcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8833ba3833480237f47774984958c01d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9862b46c3ae76bb684a7e534f97eefad.png)
④随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2dbae74a31ee10b99b31ec01bd35b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433c7aab3056671b683c392db76117c7.png)
其中正确命题的序号为( )
A.①② | B.①③ | C.②③ | D.②④ |
您最近一年使用:0次
2 . 若数列
满足
(n为正整数,p为常数),则称数列
为等方差数列,p为公方差.
(1)已知数列
的通项公式分别为
判断上述两个数列是否为等方差数列,并说明理由;
(2)若数列
是首项为1,公方差为2的等方差数列,数列
满足
,且
,求正整数m的值;
(3)在(1)、(2)的条件下,若在
与
之间依次插入数列
中的
项构成新数列
,
,求数列
中前50项的和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595955aa3a2670abcd60c78a5086f2fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c56c975b8b3195cea6ef4b9949e5d0b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd9764763cde4a065aa276c7dbe91773.png)
(2)若数列
![](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/73d4d1ac46eb6cf5f711cdfa8662dd6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a647029ac8d38aba9dda5b94588dcbd4.png)
(3)在(1)、(2)的条件下,若在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4741eb4c177d75ca74fe2d36e52ecbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cf52946ef832dd2fa7a82dcd6d1bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362832fa3d3c13c1eafd565349d66dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41806cbde05bd95cc402c702485bd84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50ee5f150f0dbd416e0f8fe9c80ce9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cc1e7a87da7751da31f851ae6d46aff.png)
您最近一年使用:0次
2023-06-07更新
|
731次组卷
|
3卷引用:上海市华东师范大学第一附属中学2023届高三三模数学试题
3 . 本市某区对全区高中生的身高(单位:厘米)进行统计,得到如下的频率分布直方图.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/fd9921cf-0a6a-404e-9c56-714b6949761b.png?resizew=311)
(1)若数据分布均匀,记随机变量X为各区间中点所代表的身高,写出X的分布列及期望;
(2)已知本市身高在区间
的市民人数约占全市总人数的10%,且全市高中生约占全市总人数的1.2%.现在要以该区本次统计数据估算全市高中生身高情况,从本市市民中任取1人,若此人的身高位于区间
,试估计此人是高中生的概率;
(3)现从身高在区间
的高中生中分层抽样抽取一个80人的样本.若身高在区间
中样本的均值为176厘米,方差为10;身高在区间
中样本的均值为184厘米,方差为16,试求这80人的方差.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/fd9921cf-0a6a-404e-9c56-714b6949761b.png?resizew=311)
(1)若数据分布均匀,记随机变量X为各区间中点所代表的身高,写出X的分布列及期望;
(2)已知本市身高在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7cb4d95fe8a9c9619c1b66454ae104a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7cb4d95fe8a9c9619c1b66454ae104a.png)
(3)现从身高在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eb58836514f463d4c99af9cf1bd87ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e8f61b61ebd9102ebe932a55ea2047d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cb73dfaadf7b49b83c70306934b78f.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,某公园拟划出形如平行四边形
的区域进行绿化,在此绿化区域中,分别以
和
为圆心角的两个扇形区域种植花卉,且这两个扇形的圆弧均与
相切.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/24/81b7720d-9243-42e8-88b5-20e7d7732db9.png?resizew=240)
(1)若
,
,
(长度单位:米),求种植花卉区域的面积;
(2)若扇形的半径为10米,圆心角为
,则
多大时,平行四边形绿地
占地面积最小?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3702b5620dbee356a8e560c78d223ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4189a0821a0ffab9dc171ecd279ba442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/24/81b7720d-9243-42e8-88b5-20e7d7732db9.png?resizew=240)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64756816485784ee017b03ec7574f75b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6848ef9be4dd05447bdecbc3f5eebd7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b50b8c699f9dac858f5f5df565313db4.png)
(2)若扇形的半径为10米,圆心角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cde7aace5b888a1a1c26fb911e2f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60b47abcacc10f90489c0d52a9e269ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2022-06-23更新
|
1444次组卷
|
8卷引用:上海市虹口区2022届高三二模数学试题
上海市虹口区2022届高三二模数学试题(已下线)专题13 解三角形-备战2023年高考数学母题题源解密(全国通用)湖南省长沙市长郡中学2022-2023学年高二上学期第一次月考数学试题(已下线)第06讲 任意角三角函数、诱导公式及恒等式-2江西省赣州市赣县第三中学2022-2023学年高二上学期开学考试数学试题(已下线)专题04三角函数必考题型分类训练-2上海市位育中学2023届高三下学期开学考试数学试题(已下线)模块四 专题3 三角函数与解三角形
解题方法
5 . 某地政府决定向当地纳税额在4万元至8万元(包括4万元和8万元)的小微企业发放补助款,发放方案规定:补助款随企业纳税额的增加而增加,且补助款不低于纳税额的50%.设企业纳税额为
(单位:万元),补助款为
(单位:万元),其中
为常数.
(1)分别判断
,
时,
是否符合发放方案规定,并说明理由;
(2)若函数
符合发放方案规定,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f16edb741ffbc0498992d4a681b68e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(1)分别判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
2021-12-15更新
|
370次组卷
|
3卷引用:上海市虹口区2022届高三一模数学试题
名校
解题方法
6 . 在平面直角坐标系
中,
在以原点
为圆心半径等1的圆上,将射线
绕原点
逆时针方向旋转
后交该圆于点
,设点
的横坐标为
,纵坐标
.
(1)如果
,
,求
的值(用
表示);
(2)如果
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef1b76bed51a5efaea983bdbd5a31581.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96ffe2a488a1a7f561319c8531fb28f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7912edefe1cf9bdcb3051f99d705ec0b.png)
(1)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e90285b4943db2befa410d4bcec380c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe9e329f2730b2be926b121f1ae04c0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c35b3fef2353dc0d1755d43f2e9bf922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/008474329708d06981e0ab7e86999fb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17bf75c6cb46557c4d8dec0a4999e82a.png)
您最近一年使用:0次
2021-12-15更新
|
1015次组卷
|
6卷引用:上海市虹口区2022届高三一模数学试题
上海市虹口区2022届高三一模数学试题海南省2022届高三高考数学仿真卷数学试题上海市复旦大学附属中学2023届高三毕业考试数学试题上海市奉贤中学2021-2022学年高一下学期3月月考数学试题(已下线)专练36 任意角与弧度制、任意角的三角函数、诱导公式-2021-2022学年高一数学上册同步课后专练(人版A版2019必修第一册)x上海市向明中学2021-2022学年高一下学期期末数学试题
解题方法
7 . 已知
,复数
(其中i为虚数单位)满足
,给出下列结论:①
的取值范围是
;②
;③
的取值范围是
;④
的最小值为2;其中正确结论的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4360ce512aea78e001e81beaf19e1b9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c40fedd7f82d2f33570f1cdf6d7befc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa36f0567c7fde232aa0be47609f028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c925be255ca736a53b24d13ddede1a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dccf1f9faac56117d6d3dd1dddd286d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078e0296f75cef422c24c0391ccb4760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0c048c36f2b32c5750b82e18a44fef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f6f693a154b09330bad58feb9d7fd54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0687b9f2612100122ef9e2f4a85bce.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
8 . 在平面上,已知定点
,动点
.当
在区间
上变化时,动线段
所形成图形的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0338630beeca9e7fa803f63f6b1ce089.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66fe292b96f43ce1421caab14b91ec57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4814cc69393408433ac56a06c8e86855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
9 . 已知椭圆
的方程为
.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712321353637888/2718228101832704/STEM/d0b1f36d-b345-4b0d-a430-34a4d6718812.png?resizew=237)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712321353637888/2718228101832704/STEM/5746b78d-f94b-488f-abce-a1cad298b5e8.png?resizew=236)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712321353637888/2718228101832704/STEM/d4ba530b-f4a7-4281-ac34-ada03587e915.png?resizew=264)
(1)设
是椭圆
上的点,证明:直线
与椭圆
有且只有一个公共点;
(2)过点
作两条与椭圆只有一个公共点的直线,公共点分别记为
、
,点
在直线
上的射影为点
,求点
的坐标;
(3)互相垂直的两条直线
与
相交于点
,且
、
都与椭圆
只有一个公共点,求点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712321353637888/2718228101832704/STEM/d0b1f36d-b345-4b0d-a430-34a4d6718812.png?resizew=237)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712321353637888/2718228101832704/STEM/5746b78d-f94b-488f-abce-a1cad298b5e8.png?resizew=236)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712321353637888/2718228101832704/STEM/d4ba530b-f4a7-4281-ac34-ada03587e915.png?resizew=264)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7bc97d4acc37ccb7480571754737cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da744f1fe4ccafc57429536ff249ecd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6fcc80c8f221bfd1c575b7c95fbe66b.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(3)互相垂直的两条直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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解题方法
10 . 如图某公园有一块直角三角形
的空地,其中
,
,
长
千米,现要在空地上围出一块正三角形区域
建文化景观区,其中
、
、
分别在
、
、
上.设
.
(1)若
,求
的边长;
(2)当
多大时,
的边长最小?并求出最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ba5383e768dc86e1bfd79c10f96f4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed0c25b0cde4d101058efe70766d25cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6818a6807251bee6fb3cc68b4ec473cb.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc1f08c7640e62e8717abf4d44a6c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
您最近一年使用:0次
2021-05-10更新
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1580次组卷
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