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2021年北师大版初中数学超详细定理、公式汇编.pdf

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1、初中数学定理、公式汇编第一篇数与代数第一节数与式一、实数1.实数的分类：整数(包括:正整数、0、负整数)和分数(包括:有限小数和无限环循小数)都是有理数.如:3,0.231,0.737373,等；无限不环循小数叫做无理数.如:,0.1010010001(两个 1之间依次多 1个 0)等.有理数和无理数统称为实数.2.数轴：规定了原点、正方向和单位长度的直线叫数轴。实数和数轴上的点一一对应。3.绝对值：在数轴上表示数 a的点到原点的距离叫数 a的绝对值，记作 a。正数的绝对值是它本身；负数的绝对值是它的相反数；0的绝对值是 0。如:丨_丨=；丨3.14 丨=3.14.4.相反数：符号不同、绝

2、对值相等的两个数，叫做互为相反数。a的相反数是-a，0的相反数是 0。5.有效数字：一个近似数,从左边笫一个不是 0的数字起,到最末一个数字止,所有的数字,都叫做这个近似数的有效数字.如:0.05972 精确到 0.001 得0.060,结果有两个有效数字 6,0.6.科学记数法：把一个数写成 a10n的形式(其中1an）；幂的乘方法则：幂的乘方，底数不变，指数相乘，即nnnbaab)(（n 为正整数）；零指数：10a（a0）；负整数指数：nnaa1（a0，n 为正整数）；2.整式的乘除法:几个单项式相乘除,系数与系数相乘除,同底数的幂结合起来相乘除.单项式乘以多项式,用单项式乘以多项式的每一

3、个项.多项式乘以多项式,用一个多 _项式的每一项分别乘以另一个多项式的每一项.多项式除以单项式,将多项式的每一项分别除以这个单项式.平方差公式：两个数的和与这两个数的差的积等于这两个数的平方，即22)(bababa；完全平方公式：两数和（或差）的平方，等于它们的平方和，加上（或减去）它们的积的 2 倍，即2222)(bababa3分解因式：把一个多项式化成几个整式的积的形式，这种变形叫做把这个多项式分解因式4分解因式的方法：提公团式法：如果一个多项式的各项含有公因式，那么就可以把这个公因式提出来，从而将多项式化成两个因式乘积的形式，这种分解因式的方法叫名师归纳总结|大肚有容，容

4、学习困难之事，学业有成，更上一层楼第 3 页，共 20 页文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5

5、HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V

6、5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5

7、HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V

8、5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5

9、HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V

10、5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1做提公因式法运用公式法：公式22()()ababab；2222()aabbab5分解因式的步骤：分解因式时，首先考虑是否有公因式，如果有公因式，一定先提取公团式，然后再考虑是否能用公式法分解6分解因式时常见的思维误区：提公因式时，其公团式应找字母指数最低的，而不是以首项为准

11、提取公因式时，若有一项被全部提出，括号内的项“1”易漏掉分解不彻底，如保留中括号形式，还能继续分解等四.分式1分式：整式 A 除以整式 B，可以表示成AB的形式，如果除式B 中含有字母，那么称AB为分式注：（1）若 B0，则AB有意义；（2）若 B=0，则AB无意义；（2）若 A=0 且 B0，则AB=0 2分式的基本性质：分式的分子与分母都乘以（或除以）同一个不等于零的整式，分式的值不变3约分：把一个分式的分子和分母的公团式约去，这种变形称为分式的约分4通分：根据分式的基本性质，异分母的分式可以化为同分母的分式，这一过程称为分式的通分5分式的加减法法则：（1）同分母的分式相加减，分母不变

12、，把分子相加减；（2）异分母的分式相加减，先通分，化为同分母的分式，然后再按同分母分式的加减法则进行计算6分式的乘除法法则：两个分式相乘，把分子相乘的积作为积的分子，把分母相乘的积作为积的分母；两个分式相除，把除式的分子和分母颠倒位置后再与被除式相乘7通分注意事项：（1）通分的关键是确定最简公分母，最简公分母应为各分母系救的最小公倍数与所有相同因式的最高次幂的积；（2）易把通分与去分母混淆，本是通分，却成了去分母，把分式中的分母丢掉8分式的混合运算顺序，先算乘方，再算乘除，最后算加减，有括号先算括号名师归纳总结|大肚有容，容学习困难之事，学业有成，更上一

13、层楼第 4 页，共 20 页文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码

14、:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9

15、T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码

16、:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9

17、T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码

18、:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9

19、T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1里面的9对于化简求值的题型要注意解题格式，要先化简，第二节方程与不等式一、一元一次方程1方程：含有未知数的等式叫方程2一元一次方程：只含有一个未知数，并且未知数的指数是1（次）系数不为0，这样的方程叫一元一次方程一般形式：axb=0（a0）3解一元一次方程的一般步骤：去分母，去括号，移项，合并同类项，未知数系数化为一。二、二

20、元一次方程（组）1二元一次方程：含有两个未知数，并且所含未知数的项的次数都是1 的方程叫做二元一次方程2二元一次方程组：含有两个未知数的两个一次方程所组成的一组方程，叫做二元一次方程组3二元一次方程组的解：二元一次方程组中各个方程的公共解，叫做这个二元一次方程组的解4二元一次方程组的解法（1）代人消元法：解方程组的基本思路是“消元”一把“二元”变为“一元”，主要步骤是，将其中一个方程中的某个未知数用含有另一个未知数的代数式表示出来，并代人另一个方程中，从而消去一个未知数，化二元一次方程组为一元一次方程，这种解方程组的方法称为代人消元法，简称代人法（2）加减消元法：通过方程两边分别相加（减）消去

21、其中一个未知数，这种解二元一次方程组的方法叫做加减消元法，简称加减法三、分式方程1分式方程：分母中含有未知数的方程叫做分式方程2.解分式方程的步骤:去分母,化为整式方程;解整式方程;验根;下结论.3分式方程的增根问题：增根的产生：分式方程本身隐含着分母不为0 的名师归纳总结|大肚有容，容学习困难之事，学业有成，更上一层楼第 5 页，共 20 页文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T

22、1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:

23、CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T

24、1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:

25、CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T

26、1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:

27、CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T

28、1X9 ZC5Y9H4V5Y1条件，当把分式方程转化为整式方程后，方程中未知数允许取值的范围扩大了，如果转化后的整式方程的根恰好使原方程中分母的值为0，那么就会出现不适合原方程的根 l 增根；验根：因为解分式方程可能出现增根，所以解分式方程必须验根四、一元二次方程1一元二次方程：只含有一个未知数，未知数的最高次数是2，且系数不为0，这样的方程叫一元二次方程一般形式：ax2bx+c=0(a0）2一元二次方程的解法：配方法：配方法是一种以配方为手段，以开平方为基础的一种解一元二次方程的方法用配方法解一元二次方程：ax2bx+c=0(k0）的一般步骤是：化二次项系数为1，即方程两边同除以二次项系数；

29、移项，即使方程的左边为二次项和一次项，右边为常数项；配方，即方程两边都加上一次项系数的绝对值一半的平方；化原方程为(x+m）2=n 的形式；如果 n0 就可以用两边开平方来求出方程的解；如果n=0，则原方程无解公式法：公式法是用求根公式求出一元二次方程的解的方法它是通过配方推导出来的一元二次方程的求根公式是aacbbx242(b24ac0)因式分解法：用因式分解的方法求一元二次方程的根的方法叫做因式分解法它的理论根据是两个因式中至少要有一个等于0，因式分解法的步骤是：将方程右边化为0；将方程左边分解为两个一次因式的乘积；令每个因式等于 0，得到两个一元一次方程，解这两个一元一次方程，它们的

30、解就是原一元二次方程的解3一元二次方程的注意事项：在一元二次方程的一般形式中要注意，强调 a0因当 a=0 时，不含有二次项，即不是一元二次方程如关于x 的方程（k21）x2+2kx+1=0 中，当k=1 时就是一元一次方程了应用求根公式解一元二次方程时应注意：化方程为一元二次方程的一般形式；确定 a、b、c 的值；求出 b24ac的值；若 b24ac0，则代人求根公式，求出 x1,x2若 b24a0，则方程无解名师归纳总结|大肚有容，容学习困难之事，学业有成，更上一层楼第 6 页，共 20 页文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X

31、9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV

32、8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X

33、9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV

34、8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X

35、9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV

36、8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X

37、9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1 方程两边绝不能随便约去含有未知数的代数式如2(x4)2=3（x4）中，不能随便约去（x4）注意解一元二次方程时一般不使用配方法（除特别要求外）但又必须熟练掌握，解一元二次方程的一般顺序是：开平方法因式分解法公式法五、一元一次不等式(组)1不等式：用不等号（“”“”“”“”）表示不等关系的式子2不等式的基本性质：（）不等式的两边都加上（或减去）同一个整式，不等号的方向不变（2）不等式的两边都乘以（或除以）同一个

38、正数，不等号的方向不变（3）不等式的两边都乘以（或除以）同一个负数，不等号的方向改变3不等式的解：能使不等式成立的未知数的值，叫做不等式的解4不等式的解集：一个含有未知数的不等式的所有解，组成这个不等式的解集5解不等式：求不等式解集的过程叫做解不等式6一元一次不等式：只含有一个未知数，并且未知数的最高次数是1，系数不为零的不等式叫做一元一次不等式7解一元一次不等式易错点：（1）不等式两边部乘以（或除以）同一个负数时，不等号的方向要改变，这是同学们经常忽略的地方，一定要注意；（2）在不等式两边不能同时乘以08解一元一次不等式的步骤：去分母，去话号，移项，合并同类项，系数化为 1 9求不等式的正

39、整数解，可负整数解等特解，可先求出这个不等式的所有解，再从中找出所需特解10一元一次不等式组：关于同一个未知数的几个一元一次不等式合在一起，就组成一个一元一次不等式组11一元一次不等式组的解集：一元一次不等式组中各个不等式的解集的公共部分，叫做这个一元一次不等式组的解集12解不等式组：求不等式组解集的过程，叫做解不等式组13不等式组的分类及解集(ab）名师归纳总结|大肚有容，容学习困难之事，学业有成，更上一层楼第 7 页，共 20 页文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ

40、6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y

41、1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ

42、6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y

43、1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ

44、6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y

45、1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ

46、6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y114解一元一次不等式组的步骤：（1）分别求出不等式组中各个不等式的解集（2）利用数轴或口诀求出这些解集的公共部分，即这个不等式的解。第三节函数一.平面直角坐标系1平面直角坐标系：（1）在平面内，两条互相垂直且有公共原点的数轴组成平面直角坐标系通常，两条数轴分别置于水平位置与铅直位置，取向右与向上的方向分别为两条数轴的正方向水平的数轴叫做x 轴或横轴，铅直的数轴叫做y 轴或纵轴，x轴和 y 轴统称坐标轴，它们的公共原点O 称为直角坐标系的原点这个平面叫做坐标平面(2)象限:二

47、.一次函数1一次函数：若两个变量 x、y 间的关系式可以表示成y=kxb(k、b 为常数，k 0）的形式，则称y 是 x 的一次函数(x 是自变量,y 是因变量特别地，当b=0 时，称 y 是 x 的正比例函数2一次函数的图象：一次函数 y=kx+b 的图象是经过点(0，b),(bk，0）的一条直线，正比例函数y=kx 的图象原点(0，0）的一条直线，如下表所示3.一次函数的图象和性质:y=kx+b(k、b为常数 k0)的图象是一条直线(b 是直线名师归纳总结|大肚有容，容学习困难之事，学业有成，更上一层楼第 8 页，共 20 页文档编码:CV8Z4

48、C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 Z

49、C5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4C5Q8M5 HZ6K4G9T1X9 ZC5Y9H4V5Y1文档编码:CV8Z4

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关键词：: 2021 北师大初中数学详细定理公式汇编

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