名校
解题方法
1 . 定义在
上的函数
,其图象与水平直线
的交点从左往右分别记为
.若
,则
的取值范围是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d65bdc820ab87b9a7909d2be591abec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bf11a2546f764640e4c9ee43cec8ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ff39dd1dfc9caf911ad0d11ba21d66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41386b1f8daa54e38ad2c7f11279d2a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8568ff6401d7f8fdcef70270698d76a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
您最近一年使用:0次
名校
解题方法
2 . 已知椭圆
的离心率为
,左右焦点分别为
,
是椭圆上一点,
,
.
(1)求椭圆的方程;
(2)过点
的直线与椭圆交于
两点,
为线段
中点.
(i)求证:
点轨迹方程为
;
(ii)
为坐标原点,射线
与椭圆交于点
,点
为直线
上一动点,且
,求证:点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a74e28144cbed9111d17dd239136f80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6b646abc8ee6b9c8558d898f2af4be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74404619ad5699e6c44c947fb569600f.png)
(1)求椭圆的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0a807a550b61acd46aa4f8677dd6d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(i)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62518b67e16e5c04a2d6be20c476fb0.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84fb85c78522640bcaf889f89ad89de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84fb85c78522640bcaf889f89ad89de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a281a22f6ce9def698919a6d1a04c389.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
您最近一年使用:0次
名校
3 . 设
和
是两个等差数列,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9107b183a776ead2abb6430d12991e81.png)
,其中
表示
,
,
,
这
个数中最大的数.
(1)若
,
,求
,
,
的值;
(2)若
为常数列,证明
是等差数列;
(3)证明:或者对任意正数
,存在正整数
,当
时,
;或者存在正整数
,使得
,
,
,
,
是等差数列.
![](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/9107b183a776ead2abb6430d12991e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4139f450eede11d86247de12a5b431b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f1d0271713debdf8f0542ab79f32e7c.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/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/637f94c79ddadc15f305bed8adc45733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c1ed7b10ac7ca1cd81cdd39a8fcc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ff259bff098430a6512d0e4f6fb2d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76f79be89b8c6227b68eded6b675546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db84454f051d418a4904fa423ab8b304.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(3)证明:或者对任意正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856b137a34d2d5b20671b7a3c7a29606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c738db07e589f0345db84933cfcb189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829442c6473c94fde041595bc18530d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce2bfc84267380660a800786986bb09f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f49a990d5bd3557d6449bb8dd91a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f49a990d5bd3557d6449bb8dd91a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,已知
中
为直角,
是线段
上任意一点(不含端点),沿直线
将
折成
,所成二面角
的平面角为
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172f1b400d9ddec4ea01f6fd040b3802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff0a49b9a3976893039103a7ba3727e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa19f78fd19c8e5601bba0f52e438ca6.png)
A.![]() | B.![]() ![]() ![]() |
C.![]() | D.![]() ![]() ![]() |
您最近一年使用:0次
5 . 近年来,某大学为响应国家号召,大力推行全民健身运动,向全校学生开放了
两个健身中心,要求全校学生每周都必须利用课外时间去健身中心进行适当的体育锻炼.
(1)该校学生甲、乙、丙三人某周均从
两个健身中心中选择其中一个进行健身,若甲、乙、丙该周选择
健身中心健身的概率分别为
,求这三人中这一周恰好有一人选择
健身中心健身的概率;
(2)该校学生丁每周六、日均去健身中心进行体育锻炼,且这两天中每天只选择两个健身中心的其中一个,其中周六选择
健身中心的概率为
.若丁周六选择
健身中心,则周日仍选择
健身中心的概率为
;若周六选择
健身中心,则周日选择
健身中心的概率为
.求丁周日选择
健身中心健身的概率;
(3)现用健身指数
来衡量各学生在一个月的健身运动后的健身效果,并规定
值低于1分的学生为健身效果不佳的学生,经统计发现从全校学生中随机抽取一人,其
值低于1分的概率为0.02.现从全校学生中随机抽取一人,如果抽取到的学生不是健身效果不佳的学生,则继续抽取下一个,直至抽取到一位健身效果不佳的学生为止,但抽取的总次数不超过
.若抽取次数的期望值不超过23,求
的最大值.
参考数据:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)该校学生甲、乙、丙三人某周均从
![](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/ce472cf8af4a2aa4a7d8e638fa3721ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)该校学生丁每周六、日均去健身中心进行体育锻炼,且这两天中每天只选择两个健身中心的其中一个,其中周六选择
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(3)现用健身指数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9229d897efe7523e91ab537a53e668f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78290d979af58467e3aff12979a83acb.png)
您最近一年使用:0次
2024-04-04更新
|
1715次组卷
|
8卷引用:上海市宜川中学2024届高三下学期2月开学考试数学试题
上海市宜川中学2024届高三下学期2月开学考试数学试题2024届辽宁省名校联盟高考模拟卷(调研卷)数学试题(一)(已下线)第2套 全真模拟篇 【模块三】(已下线)第8章 概率 章末题型归纳总结-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第二册)(已下线)7.3离散型随机变量的数字特征 第三练 能力提升拔高江苏省南京航空航天大学苏州附属中学2023-2024学年高三下学期二模阳光测试数学试题江苏省海安高级中学2023-2024学年高二下学期期中考试数学试卷福建省福州延安中学2024届高三下学期第一次模拟数学试题
名校
6 . 对三次函数,如果其存在三个实根
,则有
.称为三次方程根与系数关系.
(1)试讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65abf75c103f74720b2be7190eab3443.png)
(2)对三次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19951f3364fb04433feed743bc37975d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c765461ae1a6c70f5cbdcb6c932a22b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f07ad90ca228230b03f12eb48ee0c1d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427ce68306450bb73af5e71b32531ff6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/944ede342597c070831052dc06bca45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6517ec3e0be52d6c6fe87d945d86a2c0.png)
(3)称
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26a454d302bbc647eb47fc7c95efc9c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4225be6a8f18e980e0d55e2f469861.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b507ca2539b60489ddbd6137323b1812.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8530bca5123179cfede86d03738495e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20948d4feaf61728d84bb7695a598a15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4a90cfdbfa05577b6ec0b22739e7c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d97b51756740950b8a9304755b4224.png)
(i)证明:在
上存在两个极值点的充要条件是
;
(ii)求点组成的点集,满足
是
上的广义正弦函数.
您最近一年使用:0次
名校
7 . 整数列,
,
,对
有
,
为固定正整数,求使
成立时,
的值为
您最近一年使用:0次
名校
8 . 已知点
、
,椭圆
:
与双曲线
:
有相同的焦点.
(1)求双曲线
的方程与离心率.
(2)点
为双曲线
的一部分
(
且
)上的动点,证明:存在过点P的双曲线
的切线等分
的面积(O为原点).
(3)设双曲线
的切线l与椭圆
交于C、D两点,求动弦
中点M的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f54dd475ff1321041c80738b201c3b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cad955f235c6dc064b5cc814b8c0656.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f96848b9ec6c8d71adca5d8afa07582d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56ba9b5b35d150c969383b464b9eb952.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56ba9b5b35d150c969383b464b9eb952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b06ba630c1ea702753cb6bbc8099aafd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
(3)设双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
名校
解题方法
9 . 如图,点
分别是正四面体
棱
上的点,设
,直线
与直线
所成的角为
,则对于以下两个命题,各选项判断正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/070db60b-0d0f-4b26-adb5-c332ddfd10c4.png?resizew=147)
①当
时,
随着
的增大而减小;
②当
时,
随着
的增大而增大
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f2a9b923a355694ea487f6c5669a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/070db60b-0d0f-4b26-adb5-c332ddfd10c4.png?resizew=147)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfcdbf35c6ca1c7e580583630f1ee097.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4a24b387673d21c3d381bf2f3eae63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
A.①②都是真命题 | B.①是假命题,②是真命题 |
C.①是真命题,②是假命题 | D.①②都是假命题 |
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2024-03-19更新
|
323次组卷
|
2卷引用:上海市宜川中学2024届高三下学期2月开学考试数学试题
名校
解题方法
10 . 已知函数
的值域是
,当
时,实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eadd634a5bf414e0d1d3af3db523698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa66623cf54b42d6d12be4c8edaa7071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714e169b4a3968718c3c00b1b72d494d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次