23-24高二下·全国·课前预习
1 . 排列数公式
(1)乘积形式:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f718a6609df82e457930536bdf7c50.png)
______ .(这里
且
)
(2)阶乘形式:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f718a6609df82e457930536bdf7c50.png)
______ .(
,且
)
(1)乘积形式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f718a6609df82e457930536bdf7c50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86150a39a819bfb4f6262291bb7c234b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7870c36161f465fc992534b5fc3777f3.png)
(2)阶乘形式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f718a6609df82e457930536bdf7c50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86150a39a819bfb4f6262291bb7c234b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7870c36161f465fc992534b5fc3777f3.png)
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23-24高二下·全国·课前预习
2 . 知识点四 复合函数的导数
(1)复合函数的概念
一般地,对于两个函数
和
,如果通过中间变量
,
可以表示成
的函数,那么称这个函数为函数
和
的复合函数,记作![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070d1ea22a92808dad7489438c239629.png)
______ .
(2)复合函数的求导法则
一般地,对于由函数
和
复合而成的函数
,它的导数与函数
,
的导数间的关系为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b3e44f4bf079c2b5981a3699c855920.png)
______ ,即
对
的导数等于______ .
(1)复合函数的概念
一般地,对于两个函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6177dca23dc77a226368411aeaea26fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24b2aa5eac36282fb2192c4a19fde10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad481cbfb67ac9cdbc0537f3de23b022.png)
![](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/6177dca23dc77a226368411aeaea26fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24b2aa5eac36282fb2192c4a19fde10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070d1ea22a92808dad7489438c239629.png)
(2)复合函数的求导法则
一般地,对于由函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6177dca23dc77a226368411aeaea26fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24b2aa5eac36282fb2192c4a19fde10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a876d70607e661282d61705b36ae40df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6177dca23dc77a226368411aeaea26fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24b2aa5eac36282fb2192c4a19fde10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b3e44f4bf079c2b5981a3699c855920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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23-24高二下·全国·课前预习
解题方法
3 . 等差数列前
项和的性质
(1)若数列
是公差为
的等差数列,则数列
也是等差数列,且公差为______ .
(2)若
分别为等差数列
的前
项,前
项,前
项的和,则
,
也成等差数列,公差为______ .
(3)设两个等差数列
的前
项和分别为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6322378e9dc138599481f035cfe3b38.png)
______ .
(4)在等差数列中,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2e0d4d2e550f00b36d6f00111418ba.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dea1dd4ffcb4cf0697ca43079f6a1f2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35ddff98f658432f3723f43951abd46e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad491e5b5e14c49ef8b7004ebcfcef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade9841a8e6840efddcfd8620a6fc1fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b477afc102fe376cc777fffe0548cb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aacaf4a1b543085ebf2617cd600c011a.png)
(3)设两个等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/478421b81927e435cbcf5acafa89efd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6322378e9dc138599481f035cfe3b38.png)
(4)在等差数列中,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bcbc6ca5f2b222970ce2473603d54b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2e0d4d2e550f00b36d6f00111418ba.png)
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23-24高一下·全国·课前预习
4 . 古典概型的概率公式
对任何事件
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992a45dcac87eeb949b409602a95917a.png)
_____ ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
_______ .
对任何事件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992a45dcac87eeb949b409602a95917a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
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23-24高一下·全国·课前预习
解题方法
5 . 平面向量数乘运算的坐标表示及中点坐标公式
(1)实数与向量的积的坐标等于用这个实数乘原来向量的___________ ;
(2)设向量
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f521439862094eb8fd9ee9f347612f14.png)
__________ .
(3)中点坐标公式:若
的坐标分别为(x1,y1),(x2,y2),线段
的中点P的坐标为(x,y),则____________ .
(1)实数与向量的积的坐标等于用这个实数乘原来向量的
(2)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21622782a1b33b3be43d7824ac5f1c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f521439862094eb8fd9ee9f347612f14.png)
(3)中点坐标公式:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5425108c557f0f21474c045334f97d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a949c00526fddf435423272cf10f25.png)
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