1 . 瞬时速度与瞬时加速度
(1)一般地,当
无限趋近于0时,运动物体位移
的平均变化率______ 无限趋近于一个常数,那么这个常数称为物体在
时的______ .
(2)一般地,当
无限趋近于0时,运动物体速度
的平均变化率_____ 无限趋近于一个常数,那么这个常数称为物体在
时的______ .
(1)一般地,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a4958df52dd9f9cba15f4d1675fc6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f5451a66fb4f48811e042d8ca250f51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82120861c1c4f7cc1a7a3f169f082a81.png)
(2)一般地,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a4958df52dd9f9cba15f4d1675fc6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e127daca60c7927cd7a98cfbdb8d3120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82120861c1c4f7cc1a7a3f169f082a81.png)
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23-24高二上·江苏·课后作业
2 . 抛物线的定义
平面内到一个定点
的距离和一条直线
(定点
不在直线
上)的距离相等的点的轨迹叫做抛物线,定点
叫作抛物线的____ ,定直线
叫作抛物线的_____ .
平面内到一个定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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3 . 抛物线的焦半径公式
已知抛物线的方程为
,
为抛物线的焦点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9db2d2c038cfaabe76ce95c91e17ed78.png)
_______
已知抛物线的方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24006ff4717aed4b2af03a5886be43f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9db2d2c038cfaabe76ce95c91e17ed78.png)
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4 . 等比数列的前
项和
已知
为等比数列且公比为
,
为其前
项和.
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
____________ 或者![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
___________ .
(2)我们用方法_______________ 推导
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
(2)我们用方法
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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5 . 在坐标平面中,对于直线
上的两点
,如果
,则称 ____ 为直线的
的斜率.如果
,那么直线
的斜率____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1325c6fe42a9e5c04520d8a9bb6821b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f333263260646c494225db8a7476c00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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6 . 在平面直角坐标系中,对于一条与
轴相交的直线,把
轴绕交点按逆时针旋转到与直线重合,所转过的____ 称为这条直线的倾斜角.
(1)规定:与
轴平行或重合的直线的倾斜角为____ ;
(2)直线倾斜角的范围为____ .
(3)直线的斜率
与倾斜角
的关系:
①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
____ ,
;
②当
时,斜率____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)规定:与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)直线倾斜角的范围为
(3)直线的斜率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e0386e8b10754df5af4f9c6edc15a95.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1460b21d391529bca6f56bbe4d347148.png)
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7 . 等差数列的通项公式
若
为等差数列,公差为
.
(1)
的通项公式为_______ ,
(2)
为递增数列的充要条件为_____ ;
为递减数列的充要条件为_____ ;
为常数列的充要条件为______ .
若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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8 . 等差数列的性质
若
为等差数列,公差为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f41be28dde65afb2fecd475276bc477.png)
_____ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5432047d5cbe902bd82fd3ba790b66.png)
_____ .
(2)若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ff695a8f3460f611843351203f4de63.png)
_____ .
(3)若_______ ,则
为等差数列.
若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f41be28dde65afb2fecd475276bc477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5432047d5cbe902bd82fd3ba790b66.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb679318d0c9819b82e51a1750b502a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ff695a8f3460f611843351203f4de63.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e40ebba1ff31c193ff699fd53a5cd3d0.png)
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9 . 等差数列的定义
(1)一般地,如果一个数列从第二项起,每一项与减去它的前一项所得的差都等于___________ ,那么这个数列就叫做等差数列,这个常数叫做等差数列的公差,通常用
表示.
(2)如果数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f982b5f3b4da44ba3fbcfdf507e6d41c.png)
______________________ ,则
为等差数列.
(1)一般地,如果一个数列从第二项起,每一项与减去它的前一项所得的差都等于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(2)如果数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f982b5f3b4da44ba3fbcfdf507e6d41c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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10 . 等差中项
(1)如果三个数
成等差数列,则
叫作
的____ .
(2)如果
为
的等差中项,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
_____ .
(1)如果三个数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96d444cb9c5db8ff0829ef8a30c3d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
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