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教育头条 > 初中数学 > 初一数学知识点重要概念统计、圆、整式和分式

初一数学知识点重要概念统计、圆、整式和分式

初中数学 08-16 浏览量: 分享:

  1.总体:考察对象的全体。


  2.个体:总体中每一个考察对象。


  3.样本:从总体中抽出的一部分个体。


  4.样本容量:样本中个体的数目。


  5.众数:一组数据中,出现次数最多的数据。


  6.中位数:将一组数据按大小依次排列,处在最中间位置的一个数(或最中间位置的两个数据的平均数)


  计算方法


  1.样本平均数:⑴ ;⑵若 , ,…, ,则 (a—常数, , ,…, 接近较整的常数a);⑶加权平均数: ;⑷平均数是刻划数据的集中趋势(集中位置)的特征数。通常用样本平均数去估计总体平均数,样本容量越大,估计越准确。


  2.样本方差:⑴ ;⑵若 , ,…, ,则 (a—接近 、 、…、 的平均数的较“整”的常数);若 、 、…、 较“小”较“整”,则 ;⑶样本方差是刻划数据的离散程度(波动大小)的特征数,当样本容量较大时,样本方差非常接近总体方差,通常用样本方差去估计总体方差。


  同类二次根式


  化为最简二次根式以后,被开方数相同的二次根式叫做同类二次根式。


  满足条件:①被开方数的因数是整数,因式是整式;②被开方数中不含有开得尽方的因数或因式。


  把分母中的根号划去叫做分母有理化。


  单项式与多项式


  没有加减运算的整式叫做单项式。(数字与字母的积—包括单独的一个数或字母)


  几个单项式的和,叫做多项式。


  说明:①根据除式中有否字母,将整式和分式区别开;根据整式中有否加减运算,把单项式、多项式区分开。②进行代数式分类时,是以所给的代数式为对象,而非以变形后的代数式为对象。划分代数式类别时,是从外形来看。如,=x,=│x│等。


  圆


  定义:圆周的简称


  静止定义:平面上所有到定点的距离等于定长的点的集合。


  运动定义:平面上,一动点以一定点为圆心,一定长为距离运动一周的轨迹。


  基本公式:S=лr2=лd2/4=C2/4л


  C=2лr=лd=√(4лS)


  相关公式:两圆外公切线长=√[d2-(R-r)2]


  两圆内公切线长=√[d2-(R+r)2]


  n度的圆心角所对的弧长=nлr/180


  n度的圆心角所对的扇形面积=nлr2/360


  l的扇形弧长所对的扇形面积=0.5rl


  初一数学整式和分式


  含有加、减、乘、除、乘方运算的代数式叫做有理式。


  没有除法运算或虽有除法运算但除式中不含有字母的有理式叫做整式。


  有除法运算并且除式中含有字母的有理式叫做分式。


  代数式与有理式


  用运算符号把数或表示数的字母连结而成的式子,叫做代数式。单独的一个数或字母也是代数式。


  整式和分式统称为有理式。


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