2023高二·全国·专题练习
1 . 贝叶斯公式
设
是一组两两互斥的事件,
,且
,则对任意事件
,
,有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c7d48d4f708f33f50d9f9be0205549.png)
_________ =_________ ,
.
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252bab154aa5bdc9b4bce4c0d43aaf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08767405a1044072bcd4c770c18b39d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3b5c916beac03a695b859c45b89773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749c94f5d5fb7f67f75536f823ef440a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63c8bdf56ec2f33d199122653509b62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c7d48d4f708f33f50d9f9be0205549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b0e3b00fe47801afb53ec56706c21a.png)
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2 . 椭圆的离心率
若椭圆的方程为
,半焦距为
,则焦距与长轴长的比
叫作椭圆的离心率,记为
.
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/323b5d7dab7e42aba74920c293e063b1.png)
____________ ;
(2)
趋向于1时,椭圆越___ ;
趋向于0时,椭圆越____ ;
若椭圆的方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b246aa3b56becc905d3fb64c6d5ec4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/323b5d7dab7e42aba74920c293e063b1.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b246aa3b56becc905d3fb64c6d5ec4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b246aa3b56becc905d3fb64c6d5ec4a.png)
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名校
3 . 请默写基础初等函数的导数公式:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd340fc840812c706940b55aa7f3d660.png)
_____________ ,
为常数;
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5adebfc541d066458d35f1728c1f7bd.png)
____________ ,
为常数;
(3)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5852e6c61667c0ca8cf138f4c809fa3.png)
____________ ,
为常数,
且
;
(4)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a5ee0ab5ac24861816bd2588eb8591a.png)
______________ ,
为常数,
且
;
(5)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0c2d02122b8080460cc1f2557980f6.png)
______________ ;
(6)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba555ef24d75f59b18f031167b910aa.png)
_____________ .
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd340fc840812c706940b55aa7f3d660.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5adebfc541d066458d35f1728c1f7bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5852e6c61667c0ca8cf138f4c809fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a5ee0ab5ac24861816bd2588eb8591a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(5)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0c2d02122b8080460cc1f2557980f6.png)
(6)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba555ef24d75f59b18f031167b910aa.png)
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23-24高二上·全国·课前预习
名校
4 . 直线的倾斜角
的取值范围为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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23-24高二上·上海·课后作业
5 . 直线与平面平行的判定定理:
文字语言:如果______ 一条直线和此______ 的一条直线______ ,那么______ 和______ 平行.该定理常表述为“若线线平行,则线面平行”.
图形语言:如图所示.
符号语言:若
,且______ ,则
.
文字语言:如果
图形语言:如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/19/22b61f8a-44d7-44e3-a635-8d4392d424d8.png?resizew=164)
符号语言:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fbc714c63815dad9a27418f6492f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4d6a7aec04e1d5768ef830b534460a7.png)
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23-24高二上·上海·课后作业
6 . 直线与平面平行的性质定理:
文字语言:一条直线和一个平面平行,如果过______ 的平面和______ 相交,那么这条直线与______ 平行.
图形语言:如图所示.
符号语言:若
,且______ ,则
.
文字语言:一条直线和一个平面平行,如果过
图形语言:如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/19/5ced1f2e-8ea4-4dd8-8d99-92e33f807176.png?resizew=166)
符号语言:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea730233033e2fca0bce6a369a32582f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc8444d63d1ca92651c62fe9b220859.png)
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7 . 教材 10.3.4 两个平面平行的判定定理∶"如果一个平面上的________ 与另一个平面平行,那么这两个平面平行.
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8 . 椭圆的顶点
若椭圆的方程为
,
(1)椭圆有四个顶点,它们分别为_____________ ;
(2)
称为椭圆的长轴,
称为椭圆的短轴,它们的长度分别为____ ,
分别叫作椭圆的____________ .
若椭圆的方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
(1)椭圆有四个顶点,它们分别为
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473913c0887bb64d386f4c02f1853452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc9076974ebd6331d67055302be8167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
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9 . 椭圆的范围
若椭圆的方程为
,则椭圆上横坐标纵坐标的范围分别为: _________ ;
若椭圆的方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
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21-22高二·全国·课后作业
10 . 判断正误
(1)若两圆没有公共点,则两圆一定外离.( )
(2)若两圆外切,则两圆有且只有一个公共点,反之也成立.( )
(3)若两圆有公共点,则
.( )
(1)若两圆没有公共点,则两圆一定外离.
(2)若两圆外切,则两圆有且只有一个公共点,反之也成立.
(3)若两圆有公共点,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42049aea99bf2d435088392a455a560.png)
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