(完整word版)初中数学各种公式(完整版).pdf

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1、第 1 页 共 9 页1 数学各种公式及性质1 乘法与因式分解(ab)(ab)a2b2；(a b)2a2 2abb2；(ab)(a2abb2)a3b3；(ab)(a2abb2)a3b3；a2b2(ab)22ab；(ab)2(ab)24ab。2 幂的运算性质am anam+n；am anam-n；(am)namn；(ab)nanbn；(ab)nnnab；a-n1na，特别：()-n()n；a01(a0)。3 二次根式()2a(a0)；丨a丨；(a0，b0)。4 三角不等式|a|-|b|a b|a|+|b|（定理）；加强条件：|a|-|b|a b|a|+|b|也成立，这个不等式也可称为向量的三角不

2、等式（其中a，b 分别为向量 a和向量 b）|a+b|a|+|b|；|a-b|a|+|b|；|a|b-bab；|a-b|a|-|b|；-|a|a|a|；5 某些数列前 n 项之和1+2+3+4+5+6+7+8+9+n=n(n+1)/2；1+3+5+7+9+11+13+15+(2n-1)=n2；2+4+6+8+10+12+14+(2n)=n(n+1)；12+22+32+42+52+62+72+82+n2=n(n+1)(2n+1)/6；13+23+33+43+53+63+n3=n2(n+1)2/4；1*2+2*3+3*4+4*5+5*6+6*7+n(n+1)=n(n+1)(n+2)/3；6 一元二

3、次方程对于方程：ax2bxc0：求根公式 是x242bbaca，其中 b24ac叫做根的判别式。当0时，方程有两个不相等的实数根；当0时，方程有两个相等的实数根；当0时，方程没有实数根注意：当0 时，方程有实数根。第 2 页 共 9 页2 若方程有两个实数根x1和x2，则二次三项式ax2bxc可分解为 a(xx1)(xx2)。以a和b为根的一元二次方程是 x2(ab)xab0。7 一次函数一次函数ykxb(k 0)的图象是一条直线(b是直线与y轴的交点的纵坐标，称为截距)。当k0时，y随x的增大而增大(直线从左向右上升)；当k0时，y随x的增大而减小(直线从左向右下降)；特别地：当b0时，yk

4、x(k0)又叫做正比例函数(y与x成正比例)，图象必过原点。8 反比例函数反比例函数 y(k 0)的图象叫做双曲线。当k0时，双曲线在一、三象限(在每一象限内，从左向右降)；当k0时，双曲线在二、四象限(在每一象限内，从左向右上升)。9二次函数（1）.定义：一般地，如果cbacbxaxy,(2是常数，)0a，那么 y 叫做x的二次函数。（2）.抛物线的三要素：开口方向、对称轴、顶点。a的符号决定抛物线的开口方向：当0a时，开口向上；当0a时，开口向下；a 相等，抛物线的开口大小、形状相同。平行于 y 轴（或重合）的直线记作hx.特别地，y 轴记作直线0 x。（3）.几种特殊的二次函数的图像特征

5、如下：函数解析式开口方向对称轴顶点坐标2axy当0a时开口向上当0a时开口向下0 x（y 轴）（0,0）kaxy20 x（y 轴）(0,k)2hxayhx(h,0)khxay2hx(h,k)cbxaxy2abx2(abacab4422，)（4）.求抛物线的顶点、对称轴的方法文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O

6、5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文

7、档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL

8、1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M

9、8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ

10、8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D

11、8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 Z

12、R10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5第 3 页 共 9 页3 公式法：abacabxacbxaxy442222，顶点是），（abacab4422，对称轴是直线abx2。配方法：运用配方的方法，将抛物线的解析式化为khxay2的形式，得到顶点为(h,k)，对称轴是直线hx。运用抛物线的对称性：由于抛物线是以对称轴为轴的轴对称图形，对称轴与抛物线的交点是顶点。若已知抛物线上两点12(,)(,)、xyxy（及 y 值相同），则对称轴方程可以表示为：122xxx（5）.抛物线cbxaxy2中，cba,的作用a决定开口方向及开口大小，

13、这与2axy中的a完全一样。b和a共同决定抛物线对称轴的位置.由于抛物线cbxaxy2的对称轴是直线。abx2，故：0b时，对称轴为 y轴；0ab（即a、b 同号）时，对称轴在y 轴左侧；0ab（即a、b 异号）时，对称轴在y 轴右侧。c的大小决定抛物线cbxaxy2与 y 轴交点的位置。当0 x时，cy，抛物线cbxaxy2与 y 轴有且只有一个交点（0，c）：0c，抛物线经过原点;0c,与 y 轴交于正半轴；0c,与 y 轴交于负半轴.以上三点中，当结论和条件互换时，仍成立.如抛物线的对称轴在y 轴右侧，则0ab。（6）.用待定系数法求二次函数的解析式一般式：cbxaxy2.已知图像上三点

14、或三对x、y 的值，通常选择一般式.顶点式：khxay2.已知图像的顶点或对称轴，通常选择顶点式。交点式：已知图像与x轴的交点坐标1x、2x，通常选用交点式：21xxxxay。（7）.直线与抛物线的交点 y 轴与抛物线cbxaxy2得交点为(0,c)。抛物线与x轴的交点。二次函数cbxaxy2的图像与x轴的两个交点的横坐标1x、2x，是对应一元二次方程02cbxax的两个实数根.抛物线与x轴的交点情况可以由对应的一元二次方程的根的判别式判定：a有两个交点(0)抛物线与x轴相交；b 有一个交点（顶点在x轴上）(0)抛物线与x轴相切；c 没有交点(0)抛物线与x轴相离。平行于x轴的直线与抛物线的交

15、点文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:

16、CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R

17、1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7

18、HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I

19、9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10

20、 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N

21、7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5第 4 页 共 9 页4 同一样可能有 0 个交点、1 个交点、2 个交点.当有 2 个交点时，两交点的纵坐标相等，设纵坐标为 k，则横坐标是kcbxax2的两个实数

22、根。一次函数0knkxy的图像 l 与二次函数02acbxaxy的图像 G 的交点，由方程组cbxaxynkxy2的解的数目来确定：a 方程组有两组不同的解时l 与G 有两个交点；b 方程组只有一组解时l 与 G 只有一个交点；c 方程组无解时l 与 G 没有交点。抛 物 线 与x轴 两 交 点 之 间 的 距 离：若 抛 物 线cbxaxy2与x轴 两 交 点 为0021，xBxA，则12ABxx10统计初步（1）概念：所要考察的对象的全体叫做总体，其中每一个考察对象叫做个体从总体中抽取的一部份个体叫做总体的一个样本，样本中个体的数目叫做样本容量在一组数据中，出现次数最多的数(有时不止一个)

23、，叫做这组数据的 众数将一组数据按大小顺序排列，把处在最中间的一个数(或两个数的平均数)叫做这组数据的 中位数（2）公式：设有 n 个数 x1，x2，xn，那么：平均数为：12.nxxxxn+=；极差：用一组数据的最大值减去最小值所得的差来反映这组数据的变化范围，用这种方法得到的差称为极差，即：极差=最大值-最小值；方差：数据1x、2x,nx的方差为2s，则2s=()()()222121.nxxxxxxn轾-+-+-犏臌标准差：方差的算术平方根。数据1x、2x,nx的标准差s，则s=()()()222121.nxxxxxxn轾-+-+-犏臌文档编码:CL1S1R1M8W7 HQ8T7I9D8L

24、10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR1

25、0N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X

26、7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编

27、码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S

28、1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W

29、7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T

30、7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5第 5 页 共 9 页5 一组数据的方差越大，这组数据的波动越大，越不稳定。11频率与概率（1）频率频率=总数频数，各小组的频数之和等于总数，各小组的频率之和等于1，频率分布直方图中各个小长方形的面积为各组频率。（2）概率

31、如果用 P 表示一个事件 A 发生的概率，则 0P（A）1；P（必然事件）=1；P（不可能事件）=0；在具体情境中了解概率的意义，运用列举法（包括列表、画树状图）计算简单事件发生的概率。大量的重复实验时频率可视为事件发生概率的估计值；12 锐角三角形设A是ABC的任一锐角，则 A的正弦：sinA，A的余弦：cosA，A的正切：tanA并且 sin2Acos2A1。0sinA1，0cos A1，tanA0A越大，A的正弦和正切值越大，余弦值反而越小。余角公式：sin(90o A)cosA，cos(90o A)sinA。特殊角的三角函数值：sin30o cos60o ，sin45o cos45o，

32、sin60o cos30o，tan30o，tan45o 1，tan60o。斜坡的坡度：i铅垂高度水平宽度 设坡角为 ，则itan 。13 正（余）弦定理（1）正弦定理a/sinA=b/sinB=c/sinC=2R；注：其中R 表示三角形的外接圆半径。正弦定理的变形公式：(1)a=2RsinA,b=2RsinB,c=2RsinC；(2)sinA:sinB:sinC=a:b:c（2）余弦定理b2=a2+c2-2accosB；a2=b2+c2-2bccosA；c2=a2+b2-2abcosC；注：C所对的边为 c，B所对的边为 b，A所对的边为 a 14 三角函数公式（1）两角和公式sin(A+B)

33、=sinAcosB+cosAsinB sin(A-B)=sinAcosB-sinBcosA h l 文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7

34、H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码

35、:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1

36、R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7

37、 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7

38、I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L1

39、0 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5第 6 页 共 9 页6 cos(A+B)=cosAcosB-sin

40、AsinB cos(A-B)=cosAcosB+sinAsinB tan(A+B)=(tanA+tanB)/(1-tanAtanB)tan(A-B)=(tanA-tanB)/(1+tanAtanB)ctg(A+B)=(ctgActgB-1)/(ctgB+ctgA)ctg(A-B)=(ctgActgB+1)/(ctgB-ctgA)（2）倍角公式tan2A=2tanA/(1-tan2A)ctg2A=(ctg2A-1)/2ctga cos2a=cos2a-sin2a=2cos2a-1=1-2sin2a（3）半角公式sin(A/2)=(1-cosA)/2)sin(A/2)=-(1-cosA)/2)co

41、s(A/2)=(1+cosA)/2)cos(A/2)=-(1+cosA)/2)tan(A/2)=(1-cosA)/(1+cosA)tan(A/2)=-(1-cosA)/(1+cosA)ctg(A/2)=(1+cosA)/(1-cosA)ctg(A/2)=-(1+cosA)/(1-cosA)（4）和差化积sinA+sinB=2sin(A+B)/2)cos(A-B)/2 cosA+cosB=2cos(A+B)/2)sin(A-B)/2)tanA+tanB=sin(A+B)/cosAcosB tanA-tanB=sin(A-B)/cosAcosB ctgA+ctgBsin(A+B)/sinAsinB

42、-ctgA+ctgBsin(A+B)/sinAsinB（5）积化和差2sinAcosB=sin(A+B)+sin(A-B)2cosAsinB=sin(A+B)-sin(A-B)2cosAcosB=cos(A+B)-sin(A-B)-2sinAsinB=cos(A+B)-cos(A-B)15 平面直角坐标系中的有关知识（1）对称性：若直角坐标系内一点P（a，b），则 P 关于 x 轴对称的点为 P1（a，b），P关于y 轴对称的点为 P2（a，b），关于原点对称的点为P3（a，b）。（2）坐标平移：若直角坐标系内一点P（a，b）向左平移 h 个单位，坐标变为P（ah，b），向右平移 h 个单位，

43、坐标变为P（ah，b）；向上平移 h 个单位，坐标变为P（a，bh），向下平移 h 个单位，坐标变为P（a，bh）.如：点 A（2，1）向上平移 2 个单位，再向右平移 5 个单位，则坐标变为A（7，1）。16 多边形内角和公式多边形内角和公式：n边形的内角和等于(n2)180o（n3，n是正整数），外角和等于360o17 平行线段成比例定理（1）平行线分线段成比例定理：三条平行线截两条直线，所得的对应线段成比例。文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL

44、1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M

45、8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ

46、8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D

47、8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 Z

48、R10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O

49、5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文

50、档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5文档编码:CL1S1R1M8W7 HQ8T7I9D8L10 ZR10N7O5X7H5第 7 页 共 9 页7 如图：abc，直线 l1与 l2分别与直线 a、b、c 相交与点 A、B、C 和 D、E、F，则有,ABDEABDEBCEFBCEFACDFACDF。（2）推论：平行于三角形一边的直线截其他两边（或两边的延长线），所得的对应线段成比例。如 图：ABC中，DEBC，DE与AB、AC相 交 与 点D、E，则 有：,ADAEAD