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1、人教版八年级上册数学知识点及基本方法步骤1名师优秀教案（完整版）资料(可以直接使用，可编辑 优秀版资料，欢迎下载）人教版八年级上册数学知识点及基本方法步骤1八年级上册数学知识点及基本方法步骤 人教版八年级上册数学知识点及基本方法步骤 第十一章 全等三角形 1( 全等三角形的性质:全等三角形对应边相等、对应角相等。 2( 全等三角形的判定:三边相等(SSS)、两边和它们的夹角相等(SAS)、两角和它们的夹边(ASA)、两角和其中一角的对边对应相等(AAS)、斜边和直角边相等的两直角三角形(HL)。 3( 角平分线的性质:角平分线平分这个角，角平分线上的点到角两边的距离相等 4( 角平分线推论:角
2、的内部到角的两边的距离相等的点在叫的平分线上。 5( 证明两三角形全等或利用它证明线段或角的相等的基本方法步骤:?、确定已知条件(包括隐含条件，如公共边、公共角、对顶角、角平分线、中线、高、等腰三角形、等所隐含的边角关系)，?、回顾三角形判定，搞清我们还需要什么，?、正确地书写证明格式(顺序和对应关系从已知推导出要证明的问题). 6( 第十二章 轴对称 1(如果一个图形沿某条直线折叠后，直线两旁的部分能够互相重合，那么这个图形叫做轴对称图形;这条直线叫做对称轴。 2(轴对称图形的对称轴，是任何一对对应点所连线段的垂直平分线。 (角平分线上的点到角两边距离相等。 34(线段垂直平分线上的任意一点
3、到线段两个端点的距离相等。 5(与一条线段两个端点距离相等的点，在这条线段的垂直平分线上。 6(轴对称图形上对应线段相等、对应角相等。 7(画一图形关于某条直线的轴对称图形的步骤:找到关键点，画出关键点的对应点，按照原图顺序依次连接各点。 8(点(x,y)关于x轴对称的点的坐标为(x,-y) 点(x,y)关于y轴对称的点的坐标为(-x,y) 点(x,y)关于原点轴对称的点的坐标为(-x,-y) 9(等腰三角形的性质:等腰三角形的两个底角相等，(等边对等角) 等腰三角形的顶角平分线、底边上的高、底边上的中线互相重合，简称为“三线合一”。 10(等腰三角形的判定:等角对等边。 11(等边三角形的三
4、个内角相等，等于60?， 12(等边三角形的判定: 三个角都相等的三角形是等腰三角形。 有一个角是60?的等腰三角形是等边三角形 有两个角是60?的三角形是等边三角形。 13(直角三角形中，30?角所对的直角边等于斜边的一半。 14(直角三角形斜边上的中线等于斜边的一半 第十三章 实数 2算术平方根:一般地，如果一个正数x的平方等于a，即x=a，那么正数xa叫做a的算术平方根，记作。0的算术平方根为0;从定义可共44页，第1页 八年级上册数学知识点及基本方法步骤 知，只有当a?0时,a才有算术平方根。 2平方根:一般地，如果一个数x的平方根等于a，即x=a，那么数x就叫做a的平方根。 正数有两
5、个平方根(一正一负)它们互为相反数;0只有一个平方根，就是它本身;负数没有平方根。 正数的立方根是正数;0的立方根是0;负数的立方根是负数。 ,自然数(0,1,2,3？), ,整数,？负整数(,1,2,3), ,12,、有理数(整数有限小数无限循环小数),正分数(,？),23,分数(小数),实数,12, ,？负分数(,),23, ,正有理数,无理数(无限不循环小数) ,负有理数, 数a的相反数是-a，一个正实数的绝对值是它本身，一个负数的绝对值是它的相反数，0的绝对值是0 aa ，a，b,aba,0,b,0,(a,0,b,0)bb第十四章 一次函数 1(画函数图象的一般步骤:一、列表(一次函数
6、只用列出两个点即可，其他函数一般需要列出5个以上的点，所列点是自变量与其对应的函数值)，二、描点(在直角坐标系中，以自变量的值为横坐标，相应函数的值为纵坐标，描出表格中的个点，一般画一次函数只用两点)，三、连线(依次用平滑曲线连接各点)。 2(根据题意写出函数解析式:关键找到函数与自变量之间的等量关系，列出等式，既函数解析式。 3(若两个变量x,y间的关系式可以表示成y=kx+b(k?0)的形式,则称y是x的一次函数(x为自变量,y为因变量)。特别地,当b=0时,称y是x的正比例函数。 (1) (1) b.,01，,(2) (2) b.,01，,(3) (3) k,0b,02，,k,0b,02
7、，, ,，b,03,，b,03,共44页，第2页 八年级上册数学知识点及基本方法步骤 4(正比列函数一般式:y=kx(k?0)，其图象是经过原点(0,0)的一条直线。 5(正比列函数y=kx(k?0)的图象是一条经过原点的直线，当k0时，直线y=kx经过第一、三象限,y随x的增大而增大，当k0时,y随x的增大而增大; 当kn). 2. 在应用时需要注意以下几点: ?法则使用的前提条件是“同底数幂相除”而且0不能做除数,所以法则中a?0. 000a,1(a,0)10,1?任何不等于0的数的0次幂等于,1即,如,(-2.5=1),则00无意义. ?任何不等于0的数的-p次幂(p是正整数),等于这个
8、数的p的次幂的倒数,即1p,a,p-1-3-pa( a?0,p是正整数), 而0,0都是无意义的;当a0时,a的值一定是11-2,3(-2),(,2),-p48正的; 当a0时,a的值可能是正也可能是负的,如, ?运算要注意运算顺序. 7(整式的除法 ?1(单项式除法单项式 单项式相除，把系数、同底数幂分别相除，作为商的因式，对于只在被除式里含有的字母，则连同它的指数作为商的一个因式;?2(多项式除以单项式 多项式除以单项式，先把这个多项式的每一项除以单项式，再把所得的商相加，其特点是把多项式除以单项式转化成单项式除以单项式，所得商的项数与原多项式的项数相同，另外还要特别注意符号。 8. 分解
9、因式 1. 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. 2. 因式分解与整式乘法是互逆关系. 因式分解与整式乘法的区别和联系: (1)整式乘法是把几个整式相乘,化为一个多项式; (2)因式分解是把一个多项式化为几个因式相乘. 分解因式的一般方法: 1. 提公共因式法 1. 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做提公因式法. 共44页，第5页 八年级上册数学知识点及基本方法步骤 如: ab，ac,a(b，c)2. 概念内涵: (1)因式分解的最后结果应当是“积”; (2)公因式可能是单项
10、式,也可能是多项式; (3)提公因式法的理论依据是乘法对加法的分配律,即: ma，mb,mc,m(a，b,c)3. 易错点点评: (1)注意项的符号与幂指数是否搞错; (2)公因式是否提“干净”; (3)多项式中某一项恰为公因式,提出后,括号中这一项为+1,不漏掉. 2. 运用公式法 1. 如果把乘法公式反过来,就可以用来把某些多项式分解因式.这种分解因式的方法叫做运用公式法. 2. 主要公式: 22(1)平方差公式: a,b,(a，b)(a,b)222(2)完全平方公式: a，2ab，b,(a，b)222 a,2ab，b,(a,b)?3. 易错点点评: 442222因式分解要分解到底.如就没
11、有分解到底. x,y,(x，y)(x,y)4. 运用公式法: (1)平方差公式: ?应是二项式或视作二项式的多项式; ?二项式的每项(不含符号)都是一个单项式(或多项式)的平方; ?二项是异号. (2)完全平方公式: ?应是三项式; ?其中两项同号,且各为一整式的平方; ?还有一项可正负,且它是前两项幂的底数乘积的2倍. 3. 因式分解的思路与解题步骤: (1)先看各项有没有公因式,若有,则先提取公因式; (2)再看能否使用公式法; (3)用分组分解法,即通过分组后提取各组公因式或运用公式法来达到分解的目的; (4)因式分解的最后结果必须是几个整式的乘积,否则不是因式分解; (5)因式分解的结
12、果必须进行到每个因式在有理数范围内不能再分解为止. 共44页，第6页 八年级上册数学知识点及基本方法步骤 4( 分组分解法: 1. 分组分解法:利用分组来分解因式的方法叫做分组分解法. 如: am，an，bm，bn,a(m，n)，b(m，n),(a，b)(m，n)2. 概念内涵: 分组分解法的关键是如何分组,要尝试通过分组后是否有公因式可提,并且可继续分解,分组后是否可利用公式法继续分解因式. 3. 注意: 分组时要注意符号的变化. 5. 十字相乘法: 21.对于二次三项式,将a和c分别分解成两个因数的乘积, , ax，bx，ca,a,a12ac11ca22, 且满足,往往写成 的形式,将二次
13、三项式进c,c,cb,ac，ac121221行分解. 2如: ax，bx，c,(ax，c)(ax，c)11222的分解: 2. 二次三项式x，px，q2a1 p,a，bq,ab x，px，q,(x，a)(x，b)1b3. 规律内涵: 2(1)理解:把分解因式时,如果常数项q是正数,那么把它分解成两x，px，q个同号因数,它们的符号与一次项系数p的符号相同. (2)如果常数项q是负数,那么把它分解成两个异号因数,其中绝对值较大的因数与一次项系数p的符号相同,对于分解的两个因数,还要看它们的和是不是等于一次项系数p. 4. 易错点点评: (1)十字相乘法在对系数分解时易出错; (2)分解的结果与原
14、式不等,这时通常采用多项式乘法还原后检验分解的是否正确. 共44页，第7页 八年级上册数学知识点及基本方法步骤 (英文版 ) Two regulations promulgated for implementation is in the party in power for a long time and the rule of law conditions, the implementation of comprehensive strictly strategic plan, implementation in accordance with the rules and discipli
15、ne to manage the party, strengthen inner-party supervision of major initiatives. The two regulations supporting each other, the adhere to a positive advocate, focusing on morality is of Party members and Party leading cadres can see, enough to get a high standard; around the party discipline, discip
16、linary ruler requirements, listed as negative list, focusing on vertical gauge, draw the party organizations and Party members do not touch the bottom line . Here, the main from four square face two party rules of interpretation: the first part introduces two party Revised regulations the necessity
17、and the revision process; the second part is the interpretation of the two fundamental principles of the revision of laws and regulations in the party; the third part introduces two party regulations modified the main changes and needs to grasp several key problems; the fourth part on how to grasp t
18、he implementation of the two regulations of the party. and revised the necessity and revised history of the CPC Central Committee the amendment to the Chinese Communist Party members and leading cadres honest politics several guidelines and column 1 by 2021 to strengthen 共44页，第8页 八年级上册数学知识点及基本方法步骤 p
19、arty laws and regulations focus. Two party regulations revision work lasted a Years, pooling the wisdom of the whole party, ideological consensus, draw historical experience, respect for the wisdom of our predecessors, which reflects the unity of inheritance and innovation; follow the correct direct
20、ion, grasp the limited goals, adhere to the partys leadership, to solve the masses of the people reflect a focus on the problem. The new revision of the and , reflects the partys 18 and the eighth session of the third, the spirit of the fourth plenary session, reflecting the experience of studying a
21、nd implementing the General Secretary Xi Jinping series of important speech, reflects the partys eighteen years comprehensive strictly practice. (a) revised two regulations of the party need of in based on revised, the promulgation and implementation of January 2021, to strengthen the construction o
22、f the contingent of leading cadres play an important role. But with the party to manage the party strictly administering the deepening, has not been able to fully meet the actual needs. Content is too complicated, eight prohibition, 52 are not allowed to hard to remember, and also difficult to put i
23、nto practice; the second is concisely positive advocated by the lack of prohibited provisions excessive, no autonomy requirements; the third is banned terms and discipline law, both with the party discipline, disciplinary regulations 共44页，第9页 八年级上册数学知识点及基本方法步骤 repeat and Criminal law and other laws
24、and regulations repeat; the fourth is to clean the theme is not prominent, not for the existing problems, and is narrow, only needle of county-level leading cadres above. is in 1997 based on revision, in December 2003 the promulgation and implementation, to strengthen the construction of the party p
25、lay very important role. Along with the development of the situation, which many provisions have been unable to fully meet the comprehensive strictly administering the practice needs. One is Ji law, more than half of the provisions and criminal law and other countries laws and regulations Repetition
26、; two is the political discipline regulations is not prominent, not specific, for violation of the party constitution, damage the authority of Party Constitution of misconduct lack necessary and serious responsibility to pursue; third is the main discipline for the leading cadres, does not cover all
27、 Party members. Based on the above situation, need to and the two is likely to be more relevant regulations first amendment. By revising, really put the authority of Party discipline, the seriousness in the party tree and call up the majority of Party members and cadres of the party constitution of
28、party compasses party consciousness. (II) two party regulations revision process the Central Committee of the Communist Party of China attaches great importance to two regulations revision . Xi Jinping, general books recorded in the Fifth 共44页，第10页 八年级上册数学知识点及基本方法步骤 Plenary Session of the eighth ses
29、sion of the Central Commission for Discipline Inspection, on the revised regulations made clear instructions. According to the central deployment, the Central Commission for Discipline Inspection from 2021 under six months begin study two regulations revision. The Standing Committee of the Central C
30、ommission for Discipline Inspection 4 review revised. Comrade Wang Qishan 14 times held a special meeting to study two regulations revision, amendment clarifies the direction, major issues of principle, path and target, respectively held a forum will listen to part of the province (area) secretary o
31、f the Party committee, Secretary of the Discipline Inspection Commission, part of the central ministries and state organs Department The first party committee is mainly responsible for people, views of experts and scholars and grassroots party organizations and Party members. Approved by the Central
32、 Committee of the Communist Party of China, on 7 September 2021, the general office of the Central Committee of the Party issued a notice to solicit the provinces (autonomous regions, municipalities) Party, the central ministries and commissions, state ministries and commissions of the Party (party)
33、, the General Political Department of the military, every 3 people organization of Party of two regulations revision opinion. Central Commission for Discipline Inspection of extensive solicitation of opinions, careful study, attracting, formed a revised sent reviewers. In October 8 and October 12, C
34、entral Committee Political 共44页，第11页 八年级上册数学知识点及基本方法步骤 Bureau Standing Committee and the Political Bureau of the Central Committee After consideration of the two regulations revised draft. On October 18, the Central Committee of the Communist Party of China formally issued two regulations. Can say,
35、two laws amendment concentrated the wisdom of the whole party, embodies the party. Second, and revision of the basic principles of two party regulations revision work and implement the partys eighteen, ten eight plenary, the spirit of the Fourth Plenary Session of the Eleventh Central Committee and
36、General Secretary Xi Jinping important instructions on the revised and , highlighting the ruling party characteristics, serious discipline, the discipline quite in front of the law, based on the current, a long-term, advance as a whole, with Bu Xiuding independent and . Main principle is: first, adh
37、ere to the party constitution to follow. The constitution about discipline and self-discipline required specific, awaken the party constitution of party compasses party consciousness, maintaining the authority of the constitution. General Secretary Xi Jinping pointed out that no rules, no side round
38、. Party constitution is the fundamental law, the party must follow the general rules. In early 2021 held the eighth session of the Central Commission for Discipline Inspection Fifth Plenary Session of the 16th Central Committee, Xi Jinping again pointed out that constitution is the party must follow
39、 the general rules, but also the general rules. the revision 共44页，第12页 八年级上册数学知识点及基本方法步骤 of the and is Method in adhere to the regulations established for the purpose of combining rule of virtue is to adhere to the party constitution as a fundamental to follow, the constitution authority set up, wake up the party constitution and party rules the sense of discipline, the party constitution about discipline and self-discipline specific requirements. 4 second is to adhere to in accordance with the regulations