1 . 已知椭圆
,点
在椭圆上,如图,用
表示椭圆在点
处切线的单位向量.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/198f7b15-d256-45b8-8ad4-3cc9057793bf.png?resizew=120)
(1)设
,求
的最大值;
(2)是否存在定圆
,使得圆
的任一切线与
的交点
满足
,若存在,求出圆
方程,若不存在,请说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4a6e483672a226118dff5a39aa28449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f4fbb5a4568dd3e4baec9f8358552b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e8744362c6e224146461b97faf9821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/198f7b15-d256-45b8-8ad4-3cc9057793bf.png?resizew=120)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75874285daf265905257368573ded035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)是否存在定圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a21698cc2ceabd28d995692ab2bfc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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2 . 已知
,
为整系数多项式,若
,求
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f26cade8fb52ae18a5258ec4e522e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3a84b1415ba4e4ce47676b7a4f4f1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d9a5b3195e5f6fa70f47e5218c2d859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f26cade8fb52ae18a5258ec4e522e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3a84b1415ba4e4ce47676b7a4f4f1d.png)
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3 . 将1~2020的数字按顺时针方向围成一个圆圈,然后从1开始,按顺时针依次隔一个数拿走,即拿走1,3,5,…,这个过程一直进行下去,直到剩下最后一个数字,则最后剩下的数字是___________ .
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4 . 设
,考虑一个含有
项的数列,其中每个数为0、-1或2.现将数列中的数两两相乘,再将这些乘积相加,这样得到的值为“和积值”.例如,取
,数列为0,-1,-1,2,那么乘积为
,
,
,
,
,
,和积值就为
.若一个数列含有2020项,则这个数列的最小和积值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9e5270c151c0c9de54dd93e9687372c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083e29d450e983dc5324fb1125bd7165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083e29d450e983dc5324fb1125bd7165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3b9e0c5796d964c0dcb7e5f6e8156a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff028a1c8b062682400a5c66bf9d9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3e33f3a8303606a6e4db783fee9c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3e33f3a8303606a6e4db783fee9c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16c7e6d83d4088b72a36468947a35ed2.png)
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名校
5 . 如图所示,在单位正方体上有甲、乙两个动点,甲从
点匀速朝
移动;乙从
点匀速出发朝
移动,到达
后速度保持不变并折返.现甲、乙同时出发,当甲到达
时,乙恰好在到达
后折返到
,则在此过程中,甲、乙两点的最近距离为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee6765a83140d745a6de4c85d9b6b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a42da28be159399514cc6179a96e34b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a42da28be159399514cc6179a96e34b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee6765a83140d745a6de4c85d9b6b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a42da28be159399514cc6179a96e34b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/6/ad1e6bc1-8f77-49d8-a008-1cb5fd0350f7.png?resizew=161)
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2021-09-16更新
|
359次组卷
|
3卷引用:2020年浙江省数学夏令营试题
2020年浙江省数学夏令营试题(已下线)第07讲 基本立体图形与直观图(核心考点讲与练)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)江苏省盐城中学2022-2023学年高一创新班下学期3月月考数学试题
解题方法
6 . 已知十进制九位数
,则所有满足
,
的九位数的个数为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b141677a53f3f062307f3d1c58ecdf71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991544df73bffc3e5f97e1ec064f45a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/547d9ed90bed240f398d61a797449817.png)
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7 . 若平面上的点
满足
.
(1)求
的最大值;
(2)设向量
,
,定义运算
.若
,求
的取值范围.(其中О为坐标原点)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/468f2063edc38fdae95c4e7120d00c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66f345f432276db3a164997d9f011ce.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c797a24dfff093f0afb5bd8f09919293.png)
(2)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02a2530966362c93c56617f448f449c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6106eb3b2d8bc8271a13396a37c0b729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfa8f2517f6c2fc5fa0207bd715af63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef157216298d028b940b745ea1ddd694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/410cfca204e3297c6d938d5776fb602d.png)
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