中学代数公式大全

目录一、初中代数·······································································································2二、高中代数·······································································································52.1、函数········································································································52.1.1不等式·································································································92.1.1数列···································································································112.1.1三角函数·····························································································122.1.1复数···································································································152.2排列、组合································································································162.3平面几何···································································································182.3.1直线与角·····························································································182.3.2三角形································································································192.4立体几何···································································································202.4.1直线与平面··························································································202.4.2多面体、棱柱、棱锥···············································································232.5解析几何···································································································242.5.1方程与曲线··························································································242.5.2直线···································································································252.5.3圆······································································································272.5.4椭圆···································································································282.5.5双曲线································································································282.5抛物线···································································································302.6向量部分···································································································312.6.1空间向量·····························································································312.6.2平面向量·····························································································32三、常用公式······································································································333.1常用公式···································································································333.2几何图形及计算公式·····················································································35四、坐标几何和二维、三维图形··············································································384.1坐标几何···································································································384.2二维图形···································································································404.3三维图形···································································································41一、初中代数【实数的分类】【自然数】表示物体个数的1、2、3、4···等都称为自然数【质数与合数】一个大于1的整数，如果除了它本身和1以外不能被其它正整数所整除，那么这个数称为质数。一个大于1的数，如果除了它本身和1以外还能被其它正整数所整除，那么这个数知名人士为合数，1既不是质数又不是合数。【相反数】只有符号不同的两个实数，其中一个叫做另一个的相反数。零的相反数是零。【绝对值】一个正数的绝对值是它本身，一个负数绝对值是它的相反数，零的绝对值为零。从数轴上看，一个实数的绝对值是表示这个数的点离开原点距离。【倒数】1除以一个非零实数的商叫这个实数的倒数。零没有倒数。【完全平方数】如果一个有理数a的平方等于有理数b，那么这个有理数b叫做完全平方数。【方根】如果一个数的n次方（n是大于1的整数）等于a，这个数叫做a的n次方根。【开方】求一数的方根的运算叫做开方。【算术根】正数a的正的n次方根叫做a的n次算术根，零的算术根是零，负数没有算术根。【代数式】用有限次运算符号（加、减、乘、除、乘方、开方）把数或表示数的字母连结所得的式子，叫做代数式。【代数式的值】用数值代替代数式里的字母，计算后所得的结果，叫做当这个字母取这个数值时的代数式的值。【代数式的分类】【有理式】只含有加、减、乘、除和乘方运算的代数式叫有理式【无理式】根号下含有字母的代数式叫做无理式【整式】没有除法运算或者虽有除法运算而除式中不含字母的有理式叫整式【分式】除式中含字母的有理式叫分式【有理数的运算律】【等式的性质】【乘法公式】【因式分解】【方程】方程含有未知数的等式叫做方程。方程的解在未知数允许值范围内，能使方程两边相等的未知数的值叫做方程的解。解方程在指定范围内求出方程所有解，或者确定方程无解的过程，叫做解方程。【一元一次方程】一元一次方程：只含有一个未知数且未知数的次数是一次的整式方程叫做一元一次方程【一元二次方程】二、高中代数2.1、函数【集合】指定的某一对象的全体叫集合。集合的元素具有确定性、无序性和不重复性。【集合的分类】【集合的表示方法】名称定义图示性质子集真子集交集并集补集函数的性质定义判定方法函数的奇偶性函如果对一函数f(x)定义域内任意一个x，都有f(-x)=-f(x),那么函数f(x)叫做奇函数；函如果对一函数f(x)定义域内任意一个x，都有f(-x)=f(x),那么函数f(x)叫做偶函数函数的单调性对于给定的区间上的函数f(x)：函数的周期性对于函数f(x)，如果存在一个不为零的常数T，使得当x取定义域内的每一个值时，f(x+T)=f(x)都成立，那么就把函数y=f(x)叫做周期函数。不为零的常数T叫做这个函数的周期。（1）利用定义（2）利用已知函数的周期的有关定理。函数名称解析式定义域值域奇偶性单调性正比例函数RR奇函数反比例函数奇函数一次函数RR二次函数R函数名称解析式定义域值域奇偶性单调性正比例函数RR奇函数反比例函数奇函数一次函数RR二次函数R2.1.1不等式不等式用不等号把两个解析式连结起来的式子叫做不等式不等式的性质含绝对值不等式的性质几个重要的不等式一元一次不等式的解形式解集R法一元二次不等式的解法R绝对值不等式的解法无理不等式的解法2.1.1数列名称定义通项公式前n项的和公式其它数列按照一定次序排成一列的数叫做数列，记为{an}如果一个数列{an}的第n项an与n之间的关系可以用一个公式来表示，这个公式就叫这个数列的通项公式等差数列等比数列数列前n项和与通项的关系：无穷等比数列所有项的和：数学归纳法适用范围证明步骤注意事项只适用于证明与自然数n有关的数学命题设P(n)是关于自然n的一个命题，如果(1)当n取第一个值n0(例如：n=1或n=2)时，命题成立(2)假设n=k时，命题成立，由此推出n=k+1时成立。那么P(n)对于一切自然数n都成立。（1）第一步是递推的基础，第二步的推理根据，两步缺一不可（2）第二步的证明过程中必须使用归纳假设。2.1.1三角函数角一条射线绕着它的端点旋转所产生的图形叫做角。旋转开始时的射线叫角的始边，旋转终止时的射线叫角的终边，射线的端