完整版)北师大版初一数学知识点梳理

完整版)北师大版初一数学知识点梳理

北师大版初一数学定理知识点汇总——七年级上册

第一章丰富的图形世界

1.几何图形的分类

几何图形由点、线、面构成，几何体与外界的接触面或我们能看到的外表就是几何体的表面。几何的表面有平面和曲面；面与面相交得到线；线与线相交得到点。

2.常见几何体的特征和分类

常见的几何体有：柱体、棱体、锥体、球体。其中，柱体的底面是圆面，侧面是曲面；棱体的底面是多边形，侧面是正方形或长方形；锥体的底面是圆面，侧面是曲面，侧面都是三角形；球体由球面围成。

3.棱柱和棱锥的特征和分类

在棱柱中，任何相邻两个面的交线都叫做棱；相邻两个侧面的交线叫做侧棱，所有侧棱长都相等。棱柱的上、下底面的

形状相同，侧面的形状都是长方形。根据底面图形的边数，人们将棱柱分为三棱柱、四棱柱、五棱柱、六棱柱……它们底面图形的形状分别为三边形、四边形、五边形、六边形……长方体和正方体都是四棱柱。

4.圆柱和圆锥的特征

圆柱的表面展开图是由两个相同的圆形和一个长方形连成；圆锥的表面展开图是由一个圆形和一个扇形连成。

5.多边形的特征和计算公式

设一个多边形的边数为n（n≥3，且n为整数），从一个

顶点出发的对角线有(n-3)条；可以把n边形成(n-2)个三角形；这个n边形共有n(n-3)/2条对角线。

6.圆的特征

圆上两点之间的部分叫做弧，弧是一条曲线。扇形，由一条弧和经过这条弧的端点的两条半径所组成的图形。

7.多边形的分类

凸多边形和凹多边形都属于多边形。有弧或不封闭图形都不是多边形。

第二章有理数及其运算

1.有理数的分类

有理数包括正整数、负整数、零、正分数、负分数。

2.数轴的基本要素

数轴的三要素是原点、正方向、单位长度，三者缺一不可。

3.有理数的表示

任何一个有理数，都可以用数轴上的一个点来表示。反过来，不能说数轴上所有的点都表示有理数。

4.相反数的概念

如果两个数只有符号不同，那么我们称其中一个数为另一个数的相反数，也称这两个数互为相反数。

On a number line。two points that are opposite to each other are located on either side of the origin and are equidistant from the

origin。Positive numbers are to the right of the origin。while negative numbers are to the left of the origin。The absolute value of a number is defined as the distance een the point on the number line that represents the number and the origin。The absolute value of a is denoted by |a|.

The absolute value of a positive number is the number itself。while the absolute value of a negative number is the opposite of the number。The absolute value of zero is zero.

For a。0.|a| = a。for a < 0.|a| = -a。for a = 0.|a| = 0.

As we move to the right on the number line。the numbers XXX。As we move to the left。the numbers XXX.

The properties of absolute value are: except for zero。each number has two absolute values that are opposite to each other。the absolute value of two numbers that are opposite to each other (except for zero) is the same。the absolute value of any number is always non-negative。i.e。|a| ≥ 0.

When comparing two negative numbers。the one with the larger absolute value is actually smaller。To compare two negative numbers。follow these steps: 1) find the absolute value of each number。2) compare the absolute values。3) make the

correct judgment based on the fact that "two negative numbers

with larger absolute values are actually smaller."

The properties of absolute value are: 1) for any nal number a。|a| ≥ 0.2) if |a| = 0.then a = 0.and vice versa。3) if |a| = b。then a = ±b。4) for any nal number a。|a| = |-a|.

XXX: 1) when adding two numbers with the same sign。add their absolute values and keep the same sign。2) when adding two numbers with different signs。if their absolute values are the same。the sum is zero。if their absolute values are different。keep the sign of the larger number and subtract the absolute value of the smaller number from the absolute value of the larger number。3) adding a number to itself results in the same number.

XXX.

By flexibly applying the laws of ns and using n。the following rules are usually followed: 1) add the opposite numbers first。2) add numbers with the same sign first。3) add numbers with the same denominator first。4) if several numbers can be added to get an integer。add them first.

XXX a number is the same as adding XXX.