1 . 已知椭圆
,
,
为
的两个焦点,P为
上一动点,射线
,
上取点M,N,满足
.
另交
于点Q,已知PQ长度的取值范围为
.
(1)证明:直线MN过定点,并求出该定点坐标;
(2)若直线MN另交
于A,B,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee90e546232d08bb57108f2d5f87439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5076829e649b3f3866d4a7e07a5713e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697c20fca284394bf5d5b9e5f6d952e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17f996886a5e199c0f4db742244e890.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dccf1f9faac56117d6d3dd1dddd286d.png)
(1)证明:直线MN过定点,并求出该定点坐标;
(2)若直线MN另交
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35031ade086c0cb5adcd82aaef62462.png)
您最近一年使用:0次
名校
2 . 函数
.
(1)若
与
有相同的极小值点,求a的值;
(2)已知数列
满足:
,
;
①证明:存在等比数列
和唯一的公比q,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5cdb2f40e495cc14661765cb7b9d883.png)
②设
的前n项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f8b04ebbe16316cf3b2a5e80c8dd464.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/226debf072f859e0141eaa8777e7122a.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a3362c3c0badce56b2d8889a24c061.png)
①证明:存在等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5cdb2f40e495cc14661765cb7b9d883.png)
②设
![](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/1087be7e13a660eca9ef4ff818a37ec0.png)
您最近一年使用:0次
名校
解题方法
3 . 正锥体具有良好的对称性.
(1)在正三棱锥
中,证明:
;
(2)已知正棱锥
.请在下列两个条件中,选择一个命题填到___________上,并证明:
①当
,
时,存在
,使得
;
②当
,
时,不存在
,使得
.
注:如果选择多个条件分别解答,按第一个解答计分.
(1)在正三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a15a004f7d47ed595f063e60075223a.png)
(2)已知正棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a751517ae8956a455e181aeb7558e4d0.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef30a12b66b3faaa4804c8a7e573543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deffbcb0165f1a90a435d50118a14b68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5e1fb8d700e02034369a0c96800688.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34c4641a29675158925670f8096479a.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cf26f196ea6e8190cb6f94feb4e6c35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deffbcb0165f1a90a435d50118a14b68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5e1fb8d700e02034369a0c96800688.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34c4641a29675158925670f8096479a.png)
注:如果选择多个条件分别解答,按第一个解答计分.
您最近一年使用:0次
名校
4 . 某学校常年开设某课程,今年该校在某年级开设的该课程共有若干个班,由若干位不同的老师授课,其中某位老师班上的评分标准如下:每位同学该课程的分数(满分
分)由两部分组成,一部分为“平时分”,学期内共有
次考勤,每次出勤计
分,另一部分为“期末分”,是由期末考试的卷面成绩(满分
分)按照卷面成绩比期末分
的比例折算而来.如,一名同学出勤
次,期末考试的卷面成绩为
分,则该同学该课程的最终评分为:
(分).
(1)一同学期末考试的卷面成绩为
分,假设该同学每次考勤时出勤的概率均为
且互相独立,求该同学的最终评分及格(即大于等于
分)的概率
(结果保留三位小数);
(2)经过统计,教务处公布今年该课程的该年级平均分约为
,标准差约为
,且学生成绩
近似满足正态分布
.据此,该老师估计该年级几乎没有需要重修(即分数未达到
分)的学生,请用所学知识解释老师的这一观点;
(3)泊松分布可以用来描述某些小概率事件的发生.若随机变量
服从参数为
的泊松分布(记作
),则
,其中
为自然对数的底数.根据往年的数据,我们认为该课程每年每个班级需要重修的学生数量
近似服从泊松分布,假设
,证明每年每个班级出现多于一名需要重修该课程的学生的概率低于百分之一.
参考数据:
,
,
,
若
,则
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b184c94e38f1e5dbe750b2168c2a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38064aedee831ea4fdfca26976b93676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/180ea775f2af05650404d764384e7faa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a17161b28b6ad8f57abc5b11e1b6c671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f455431a80dcca93996dcabdea684be9.png)
(1)一同学期末考试的卷面成绩为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f70f0c1b960fa850d67c4091e04400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52dbd64028ab37a28942a961993ad21d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b3779b4ea5477aebfe85113b0de1d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)经过统计,教务处公布今年该课程的该年级平均分约为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d0810522a5ee9fbc0097f9520a1e50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b4ad4f30355002ab3715f11f2c3d5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45683f6ce2a361c2e2ca398c97b0b0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b3779b4ea5477aebfe85113b0de1d60.png)
(3)泊松分布可以用来描述某些小概率事件的发生.若随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b045ce84b90175882dc7d566deb1ee2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07af517aa3eba50e7c8e2d5bb8b5cc05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8d43f3c2c6a3c478d35c74314c3b49.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fb86581ec1bb61dd8c41da4365a620c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4da174915809038b73a2934c5822ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb3473bfae3d5e1b1c6c7a2575a2efa8.png)
若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1290917c2c835b61384480b335cc1d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94939ad21cfa269ff6ca60cb4abdbd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58aec81374123b483c24c877e1be2413.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ca90ea0b9c050c6525ca9a15eb149f.png)
您最近一年使用:0次
名校
5 . 用由3个小方格组成的
形(可旋转)和
的小方格不重叠地覆盖的
正方形棋盘,覆盖方法的种数为___________ .(旋转、对称后重合的视为不同方法)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d338f176b562d715d5741cf454b9c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/777d8fccf0cf8b55a68488fe48b78744.png)
您最近一年使用:0次
名校
解题方法
6 . 双曲线
上的点M,位于第一象限,
,
,
的角平分线过点
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b984dfccad3b21955104b552e2e19f34.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd656bff9ae48800b86252291ad44c04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb497263ce963c572ae1b8afbd0899e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29079b1752ce83177b6a730b0c3cf921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de09f6ca7228b51ce3b623bd57147b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1803dc3c76fd2b51696647aa18602412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b984dfccad3b21955104b552e2e19f34.png)
您最近一年使用:0次
7 . 定义一个可导函数
在定义域内一点处
的弹性为
,请写出一个定义在正实数集上且任意一点处的弹性均为
的可导函数___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e7a7523a8174e8d686e1885b1516dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
您最近一年使用:0次
名校
8 . 习近平总书记2021年10月22日在深入推动黄河流域生态保护和高质量发展座谈会上的讲话中讲到:“要统筹发展和安全两件大事,提高风险防范和应对能力.高度重视水安全风险,大力推动全社会节约用水,”节约用水对民生各个方面都有着积极影响,某校为开展“节约用水一起行”活动,对20位同学进行了调查,调查了他们每户近9个月每个月的月用水量的平均值y.其中某两个月的月用水量数据分别如下:
15.90 17.47 14.15 13.08 16.98 14.46 14.85 15.03 12.72 16.02
16.30 17.17 17.61 19.39 15.66 17.46 12.07 16.29 13.67 16.31
17.85 16.93 18.49 13.34 15.74 13.04 16.64 13.00 15.89 14.47
17.69 16.20 14.60 13.38 16.07 14.48 14.32 12.76 14.96 15.56
M月 N月(第九个月)
且根据近9个月每个月的月用水量,得到了月平均用水量的回归方程
,其中x为月份序数.则( )
15.90 17.47 14.15 13.08 16.98 14.46 14.85 15.03 12.72 16.02
16.30 17.17 17.61 19.39 15.66 17.46 12.07 16.29 13.67 16.31
17.85 16.93 18.49 13.34 15.74 13.04 16.64 13.00 15.89 14.47
17.69 16.20 14.60 13.38 16.07 14.48 14.32 12.76 14.96 15.56
M月 N月(第九个月)
且根据近9个月每个月的月用水量,得到了月平均用水量的回归方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d22dc3c7f5c400a5a2b013423ff7f2f.png)
A.月份M为第五个月. | B.月份N的残差的平均值为0.54. |
C.月份M的80百分位数为17.65. | D.预报第12个月月平均用水量为14.52. |
您最近一年使用:0次
名校
解题方法
9 . 数列
的各项均不为0,前1357项均为正数,且有:
,则
的可能取值个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0390c2afe997fe66cc791ef5bee75a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f134238f2381a1d81e95c4fc5cb5e5d5.png)
A.665 | B.666 | C.1330 | D.1332 |
您最近一年使用:0次
名校
10 . Logistie分布在数据分析中常常用于分类变量回归,若连续随机变量
满足:
,则称
服从位置参数为
,形状参数为
的Logistic分布,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684cdda577f7fabe134ca959fd44bc8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd84e6778f774fb13c4dfff0af95fbf5.png)
A.满足二项分布的随机变量也是连续随机变量 |
B.若连续随机变量![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
您最近一年使用:0次