中考数学复习资料

中考数学复习资料 初中数学复习提纲 实数 ?重点? 实数的有关概念及性质，实数的运算 ?内容提要? 重要概念 1(数的分类及概念 数系表: 正整数 0 整数 (有限或无限循环性数) 负整数 有理数 正分数 分数 负分数 实数 正无理数 无理数(无限不循环小数) 负无理数 :“分类”的原则:1)相称(不重、不漏) 2)有标准 整数 有理数 分数 正数 无理数 实数 0 整数 有理数 分数 负数 无理数 2(非负数:正实数与零的统称。(表为:x?0) 常见的非负数有: 2 a(a为一切实数) ?a? a(a?0) 性质:若干个非负数的和为0，则每个非负担数均为0。 3(倒数: ?定义及表示法 ?性质:A.a?1/a(a??1);B.1/a中，a?0;C.0,a,1时1/a,1;a,1时，1/a,1;D.积为1。 4(相反数: ?定义及表示法 ?性质:A.a?0时，a?-a;B.a与-a在数轴上的位置;C.和为0,商为-1。 5(数轴:?定义(“三要素”) ?作用:A.直观地比较实数的大小;B.明确体现绝对值意义;C.建立点与实数的一一对应关系。 6(奇数、偶数、质数、合数(正整数—自然数) 定义及表示: 奇数:2n-1 偶数:2n(n为自然数) 7(绝对值:?定义(两种): 代数定义: a(a?0) ?a?= -a(a<0) the direct punishment 0.5-10,000 yuan, responsible for the direct responsibility for the accident and the responsibility of leadership, such as concerning administrative sanctions should be dealt with by the personnel Department of the company. (3) personal injury accident occurs, the direct punishment 500-1000, who is directly responsible for the accident responsibility, give notice of criticism and 50-100 economic sanctions against them. (4) to conceal the accident, reported without undue delay or false, to inform the administrative leadership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500-1000 punishment. (5) significant near miss should be attempted as the case of responsible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 GB3323-2005 steel fusion welded butt joints, welding engineering-Ray lighting and quality rating of 2 GB11345-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2000 8 JB4730-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 1 GB150-98 2 GB50128-2005 vertical cylindrical steel pressure vessel steel welded tank code for construction and acceptance of 3 JB/ T4735-1997 steel welded 几何定义:数a的绝对值顶的几何意义是实数a在数轴上所对应的点到原点的距离。 ??a??0,符号“??”是“非负数”的标志;?数a的绝对值只有一个;?处理任何类型的题目，只要其 中有“??”出现，其关键一步是去掉“??”符号。 实数的运算 运算法则(加、减、乘、除、乘方、开方) 运算定律(五个—加法[乘法]交换律、结合律;[乘法对加法的]分配律) 1运算顺序:A.高级运算到低级运算;B.(同级运算)从“左”到“右”(如5??5);C.(有括号时)由“小”5到“中”到“大”。 应用举例(略) 附:典型例题 已知:a、b、x在数轴上的位置如下图，求证:?x-a?+?x-b?=b-a. x a b 2.已知:a-b=-2且ab<0，(a?0，b?0)，判断a、b的符号。 第二章 代数式 ?重点?代数式的有关概念及性质，代数式的运算 ?内容提要? 重要概念 分类: 单项式 整式 多项式 有理式 分式 代数式 无理式 样 1.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。 2.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。 3.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:?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。 ?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， 2x2x =x,=?x?等。 x 4.系数与指数 区别与联系:?从位置上看;?从表示的意义上看 5.同类项及其合并 条件:?字母相同;?相同字母的指数相同 合并依据:乘法分配律 6.根式 -2004 petrochemical JB/ T4708-l specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH352592 technica-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-ay lighting and quality rating of 2 GB11345R-2005 steel fusion welded butt joints, welding engineering-the construction standards and specifications, serial number a 1 GB3323ible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in 1000 punishment. (5) significant near miss should be attempted as the case of respons-the pursuit of leadership, along with 500 ed without undue delay or false, to inform the administrative leadership of the criticism, resulting in serious consequences,100 economic sanctions against them. (4) to conceal the accident, report-1000, who is directly responsible for the accident responsibility, give notice of criticism and 50-tment of the company. (3) personal injury accident occurs, the direct punishment 500ing administrative sanctions should be dealt with by the personnel Depar10,000 yuan, responsible for the direct responsibility for the accident and the responsibility of leadership, such as concern-the direct punishment 0.51997 steel welded-elded tank code for construction and acceptance of 3 JB/ T47352005 vertical cylindrical steel pressure vessel steel w-98 2 GB50128-ing 1 GB1502000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineer-procedures of steel pressure vessel NDT 9 JB/T47442005 pressure vessel welding -2000 8 JB4730-2000 of welding procedure qualification for steel pressure vessels 7 JB/47092 中小数理化(加油站) 表示方根的代数式叫做根式。 含有关于字母开方运算的代数式叫做无理式。 注意:?从外形上判断;?区别:、是根式，但不是无理式(是无理数)。 37 7.算术平方根 ?正数a的正的平方根([a?0—与“平方根”的区别]); a ?算术平方根与绝对值 2联系:都是非负数，=?a? a ?区别:?a?中，a为一切实数;a中，a为非负数。 8.同类二次根式、最简二次根式、分母有理化 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:?被开方数的因数是整数，因式是整式;?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。 9.指数 nn(—幂，乘方运算) a? a?a…a=a n个 nnna,0;?a,0时，a,0(n是偶数)，a,0(n是奇数) a,0时， 0a?零指数:=1(a?0) ,ppaa 负整指数:=1/(a?0,p是正整数) 运算定律、性质、法则 1(分式的加、减、乘、除、乘方、开方法则 2(分式的性质 bmb?基本性质:=(m?0) aam b,bb,,,?符号法则: aa,a ?繁分式:?定义;?化简方法(两种) 3(整式运算法则(去括号、添括号法则) naanmnm，nmnm,nmnnnmnnaaaaaa(),aab4(幂的运算性质:??=;??=;?=;?=;? (a)(ab)nbb ba,pp(),()技巧: ab 5(乘法法则:?单?单;?单?多;?多?多。 2226(乘法公式:(正、逆用) (a,b),a,2ab，b 22a,b (a+b)(a-b)= 1997 steel welded-2005 vertical cylindrical steel pressure vessel steel welded tank code for construction and acceptance of 3 JB/ T4735-12898 2 GB50-ing 1 GB1502000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineersanctions against them. (4) to conceal the accident, reported without undue delay or false, to inform the administrative lead-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 8 JB4730-ssels 7 JB/47092000 of welding procedure qualification for steel pressure ve-2004 petrochemical JB/ T4708100 economic -92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-tion and acceptance of field equipment 4 HGJ2222002 industrial pipe welding engineering code for construc-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-Ray lighting and quality rating of 2 GB11345--2005 steel fusion welded butt joints, welding engineering-B3323lty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 Gficant near miss should be attempted as the case of responsible for the accident and construction team injuries accident pena1000 punishment. (5) signi-ership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 5001000, who is directly responsible for the accident responsibility, give notice of criticism and 50-ect punishment 500ative sanctions should be dealt with by the personnel Department of the company. (3) personal injury accident occurs, the diring administr10,000 yuan, responsible for the direct responsibility for the accident and the responsibility of leadership, such as concern-the direct punishment 0.53 第 3 页 共 12 页 3322 (a?b)= a,b(a,ab，b) 7(除法法则:?单?单;?多?单。 8(因式分解:?定义;?方法:A.提公因式法;B.公式法;C.十字相乘法;D.分组分解法;E.求根公式法。 aa229(算术根的性质:,;;(a?0,b?0);(a?0,b,0)(正用、ab,a,baa,(a),a(a,0)bb逆用) bab1,10(根式运算法则:?加法法则(合并同类二次根式);?乘、除法法则;?分母有理化:A.; B.; aaa 1C.. ma,nb n11(科学记数法:(1?a,10,n是整数,) a，10 应用举例(略) 数式综合运算(略) 第三章 统计初步 ?重点? 内容提要? 要概念 重 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: 1x,(x，x，？，x)?; 12nn ''''?若，，„，,则x,x，a(a—常数，，，„，x接近较整的xxx,x,ax,x,ax,x,an1nn21122 常数a); xf，xf，？，xf1122kkx,(f，f，？，f,n)?加权平均数:; 12kn ?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: 12222s,[(x,x)，(x,x)，？，(x,x)]?; n12n 22221'''''2''s,[(x，x，？，x),nx]xx,x,a?若,,„,,则(a—接近、x,x,ax,x,an121nn1122n 2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-ay lighting and quality rating of 2 GB11345R-2005 steel fusion welded butt joints, welding engineering-the construction standards and specifications, serial number a 1 GB3323ible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in 1000 punishment. (5) significant near miss should be attempted as the case of respons-the pursuit of leadership, along with 500 ed without undue delay or false, to inform the administrative leadership of the criticism, resulting in serious consequences,100 economic sanctions against them. (4) to conceal the accident, report-1000, who is directly responsible for the accident responsibility, give notice of criticism and 50-tment of the company. (3) personal injury accident occurs, the direct punishment 500ing administrative sanctions should be dealt with by the personnel Depar10,000 yuan, responsible for the direct responsibility for the accident and the responsibility of leadership, such as concern-the direct punishment 0.51997 steel welded-elded tank code for construction and acceptance of 3 JB/ T47352005 vertical cylindrical steel pressure vessel steel w-98 2 GB50128-ing 1 GB1502000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineer-procedures of steel pressure vessel NDT 9 JB/T47442005 pressure vessel welding -2000 8 JB4730-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2004 petrochemical JB/ T4708-l specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH352592 technica-4 中小数理化(加油站) 、„、的平均数的较“整”的常数);若、、„、较“小”较“整”， xxxxxnn122 212222则; s,[(x，x，？，x),nx]n12n ?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。 23(样本标准差: s,s 应用举例(略) 第四章 直线形 ?重点?相交线与平行线、三角形、四边形的有关概念、判定、性质。 内容提要? 直线、相交线、平行线 1(线段、射线、直线三者的区别与联系 从“图形”、“表示法”、“界限”、“端点个数”、“基本性质”等方面加以分析。 2(线段的中点及表示 3(直线、线段的基本性质(用“线段的基本性质”论证“三角形两边之和大于第三边”) 4(两点间的距离(三个距离:点-点;点-线;线-线) 5(角(平角、周角、直角、锐角、钝角) 6(互为余角、互为补角及表示方法 (角的平分线及其表示 7 8(垂线及基本性质(利用它证明“直角三角形中斜边大于直角边”) 9(对顶角及性质 10(平行线及判定与性质(互逆)(二者的区别与联系) 11(常用定理:?同平行于一条直线的两条直线平行(传递性);?同垂直于一条直线的两条直线平行。 12(定义、命题、命题的组成 13(公理、定理 14(逆命题 三角形 分类:?按边分;?按角分 1(定义(包括内、外角) 2(三角形的边角关系:?角与角:?内角和及推论;?外角和;?n边形内角和;?n边形外角和。?边与边:三角形两边之和大于第三边，两边之差小于第三边。?角与边:在同一三角形中， 大边 小边 大角 小角 等边 等角 3(三角形的主要线段 讨论:?定义 ???线的交点—三角形的?心 ?性质 ?高线?中线?角平分线?中垂线?中位线 ?一般三角形?特殊三角形:直角三角形、等腰三角形、等边三角形 4(特殊三角形(直角三角形、等腰三角形、等边三角形、等腰直角三角形)的判定与性质 5(全等三角形 ?一般三角形全等的判定(SAS、ASA、AAS、SSS) ?特殊三角形全等的判定:?一般方法?专用方法 6(三角形的面积 ?一般计算公式?性质:等底等高的三角形面积相等。 7(重要辅助线 ?中点配中点构成中位线;?加倍中线;?添加辅助平行线 8(证明方法 1997 steel welded-2005 vertical cylindrical steel pressure vessel steel welded tank code for construction and acceptance of 3 JB/ T4735-12898 2 GB50-ing 1 GB1502000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineerect punishment 500-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 8 JB4730-ssels 7 JB/47092000 of welding procedure qualification for steel pressure ve-2004 petrochemical JB/ T4708ative sanctions should be dealt with by the personnel Department of the company. (3) personal injury accident occurs, the dir-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-tion and acceptance of field equipment 4 HGJ2222002 industrial pipe welding engineering code for construc-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-Ray lighting and quality rating of 2 GB11345-ing administr2005 steel fusion welded butt joints, welding engineering-B3323lty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 Gficant near miss should be attempted as the case of responsible for the accident and construction team injuries accident pena1000 punishment. (5) signi-ership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500sanctions against them. (4) to conceal the accident, reported without undue delay or false, to inform the administrative lead100 economic -10,000 yuan, responsible for the direct responsibility for the accident and the responsibility of leadership, such as concern1000, who is directly responsible for the accident responsibility, give notice of criticism and 50--the direct punishment 0.55 第 5 页 共 12 页 ?直接证法:综合法、分析法 ?间接证法—反证法:?反设?归谬?结论 ?证线段相等、角相等常通过证三角形全等 ?证线段倍分关系:加倍法、折半法 ?证线段和差关系:延结法、截余法 ?证面积关系:将面积表示出来 四边形 分类表: 1(一般性质(角) ?内角和:360? ?顺次连结各边中点得平行四边形。 推论1:顺次连结对角线相等的四边形各边中点得菱形。 推论2:顺次连结对角线互相垂直的四边形各边中点得矩形。 ?外角和:360? 2(特殊四边形 定义?性质?判定 ?研究它们的一般方法: 对对角 面边 称积 角 性 线 轴中 对心 称对 称 ?平行四边形、矩形、菱形、正方形;梯形、等腰梯形的定义、性质和判定 ?判定步骤:四边形?平行四边形?矩形?正方形 ??菱形??? ?对角线的纽带作用: 相等且互相平分 矩形 垂直 相等 互相平分 相等且互相垂直 四边形 平行四边形 正方形 相等 垂直 菱形 互相垂直平分 互相垂直平分且相等 3(对称图形 ?轴对称(定义及性质);?中心对称(定义及性质) 4(有关定理: ?平行线等分线段定理及其推论1、2 ?三角形、梯形的中位线定理 ?平行线间的距离处处相等。(如，找下图中面积相等的三角形) 5(重要辅助线:?常连结四边形的对角线;?梯形中常“平移一腰”、“平移对角线”、“作高”、“连结顶点 和对腰中点并延长与底边相交”转化为三角形。 6(作图:任意等分线段。 应用举例(略) 2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-ay lighting and quality rating of 2 GB11345R-2005 steel fusion welded butt joints, welding engineering-the construction standards and specifications, serial number a 1 GB3323ible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in 1000 punishment. (5) significant near miss should be attempted as the case of respons-the pursuit of leadership, along with 500 ed without undue delay or false, to inform the administrative leadership of the criticism, resulting in serious consequences,100 economic sanctions against them. (4) to conceal the accident, report-1000, who is directly responsible for the accident responsibility, give notice of criticism and 50-tment of the company. (3) personal injury accident occurs, the direct punishment 500ing administrative sanctions should be dealt with by the personnel Depar10,000 yuan, responsible for the direct responsibility for the accident and the responsibility of leadership, such as concern-the direct punishment 0.51997 steel welded-elded tank code for construction and acceptance of 3 JB/ T47352005 vertical cylindrical steel pressure vessel steel w-98 2 GB50128-ing 1 GB1502000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineer-procedures of steel pressure vessel NDT 9 JB/T47442005 pressure vessel welding -2000 8 JB4730-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2004 petrochemical JB/ T4708-l specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH352592 technica-6 中小数理化(加油站) 第五章 方程(组) ?重点?一元一次、一元二次方程，二元一次方程组的解法;方程的有关应用题(特别是行程、工程问题) 内容提要? 基本概念 1(方程、方程的解(根)、方程组的解、解方程(组) 分类: 一次方程 二次方程 整式方程 高次方程 有理方程 方程 分式方程 无理方程 解方程的依据—等式性质 1(a=b??a+c=b+c 2(a=b??ac=bc (c?0) 解法 1(一元一次方程的解法:去分母?去括号?移项?合并同类项? 系数化成1?解。 元一次方程组的解法:?基本思想:“消元”?方法:?代入法 ?加减法 一元二次方程 21(定义及一般形式: ax，bx，c,0(a,0)2(解法:?直接开平方法(注意特征) ?配方法(注意步骤—推倒求根公式) 2,b,b,4ac2x,(b,4ac,0)?公式法: 1,22a ?因式分解法(特征:左边=0) 2,,b,4ac3(根的判别式: bcx，x,,x,x,,4(根与系数顶的关系: 1212aa 2x,mx，n,0逆定理:若x，x,m,x,x,n，则以x,x为根的一元二次方程是:。 121212 2225(常用等式: x，x,(x，x),2xx121212 22 (x,x),(x，x),4xx121212可化为一元二次方程的方程 1(分式方程 ?定义 去分母 ?基本思想: 分式方程 整式方程 1997 steel welded-2005 vertical cylindrical steel pressure vessel steel welded tank code for construction and acceptance of 3 JB/ T4735-12898 2 GB50-ing 1 GB1502000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineer--2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 8 JB4730-ssels 7 JB/47092000 of welding procedure qualification for steel pressure ve-2004 petrochemical JB/ T47081000, who is directly responsible for the accident responsibility, give notice of criticism and 50-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-tion and acceptance of field equipment 4 HGJ2222002 industrial pipe welding engineering code for construc-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-Ray lighting and quality rating of 2 GB11345--2005 steel fusion welded butt joints, welding engineering-B3323lty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 Gficant near miss should be attempted as the case of responsible for the accident and construction team injuries accident pena1000 punishment. (5) signi-ership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500sanctions against them. (4) to conceal the accident, reported without undue delay or false, to inform the administrative lead100 economic ect punishment 500ative sanctions should be dealt with by the personnel Department of the company. (3) personal injury accident occurs, the diring administr10,000 yuan, responsible for the direct responsibility for the accident and the responsibility of leadership, such as concern-the direct punishment 0.57 第 7 页 共 12 页 3x,62x，2?基本解法:?去分母法?换元法(如，) ，,7x，1x,2 ?验根及方法 列方程(组)解应用题 ?概述 列方程(组)解应用题是中学数学联系实际的一个重要方面。其具体步骤是: ?审题。理解题意。弄清问题中已知量是什么，未知量是什么，问题给出和涉及的相等关系是什么。 ?设元(未知数)。?直接未知数?间接未知数(往往二者兼用)。一般来说，未知数越多，方程越易列，但越难解。 ?用含未知数的代数式表示相关的量。 ?寻找相等关系(有的由题目给出，有的由该问题所涉及的等量关系给出)，列方程。一般地，未知数个数与方程个数是相同的。 ?解方程及检验。 ?。 综上所述，列方程(组)解应用题实质是先把实际问题转化为数学问题(设元、列方程)，在由数学问题的解决而导致实际问题的解决(列方程、写出答案)。在这个过程中，列方程起着承前启后的作用。因此，列方程是解应用题的关键。 ?常用的相等关系 行程问题(匀速运动) 基本关系:s=vt C A B ?相遇问题(同时出发): 相遇处 ?乙 甲? +=; sst,ts乙乙甲AB甲 ?追及问题(同时出发): C A B 乙? 甲? (相遇处) (甲)? A B s,s，s;t,t AC乙乙(CB)甲甲(AB)乙? (相遇处) 若甲出发t小时后，乙才出发，而后在B处追上甲，则 s,s;t,t，t 乙乙甲甲 ?水中航行:v,船速，水速v,船速,水速; 顺逆 配料问题:溶质=溶液?浓度 溶液=溶质+溶剂 n,13(增长率问题: a,a(1,r)n1 4(工程问题:基本关系:工作量=工作效率?工作时间(常把工作量看着单位“1”)。 5(几何问题:常用勾股定理，几何体的面积、体积公式，相似形及有关比例性质等。 ?注意语言与解析式的互化 如，“多”、“少”、“增加了”、“增加为(到)”、“同时”、“扩大为(到)”、“扩大了”、„„ 又如，一个三位数，百位数字为a，十位数字为b，个位数字为c，则这个三位数为:100a+10b+c，而不是abc。 ?注意从语言叙述中写出相等关系。 如，x比y大3，则x-y=3或x=y+3或x-3=y。又如，x与y的差为3，则x-y=3。?注意单位换算 如，“小时”“分钟”的换算;s、v、t单位的一致等。 七、应用举例(略) 第六章 一元一次不等式(组) -2005 steel fusion welded butt joints, welding engineering-the construction standards and specifications, serial number a 1 GB3323ible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in 1000 punishment. (5) significant near miss should be attempted as the case of respons-the pursuit of leadership, along with 500 ed without undue delay or false, to inform the administrative leadership of the criticism, resulting in serious consequences,100 economic sanctions against them. (4) to conceal the accident, report-1000, who is directly responsible for the accident responsibility, give notice of criticism and 50-tment of the company. (3) personal injury accident occurs, the direct punishment 500ing administrative sanctions should be dealt with by the personnel Depar10,000 yuan, responsible for the direct responsibility for the accident and the responsibility of leadership, such as concern-the direct punishment 0.51997 steel welded-elded tank code for construction and acceptance of 3 JB/ T47352005 vertical cylindrical steel pressure vessel steel w-98 2 GB50128-ing 1 GB1502000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineer-procedures of steel pressure vessel NDT 9 JB/T47442005 pressure vessel welding -2000 8 JB4730-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2004 petrochemical JB/ T4708-l specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH352592 technica-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-ay lighting and quality rating of 2 GB11345R8 中小数理化(加油站) ?重点?一元一次不等式的性质、解法 内容提要? 定义:a,b、a,b、a?b、a?b、a?b。 一元一次不等式:ax,b、ax,b、ax?b、ax?b、ax?b(a?0)。 一元一次不等式组: 不等式的性质:?a>b??a+c>b+c ?a>b??ac>bc(c>0) a>b??acb,b>c?a>c ?a>b,c>d?a+c>b+d. 5(一元一次不等式的解、解一元一次不等式 6(一元一次不等式组的解、解一元一次不等式组(在数轴上表示解集) 7(应用举例(略) 第七章 相似形 ?重点?相似三角形的判定和性质 ?内容提要? 一、相似三角形性质 1(对应线段„;2(对应周长„;3(对应面积„。 二、相关作图 ?作第四比例项;?作比例中项。 三、证(解)题规律、辅助线 1(“等积”变“比例”，“比例”找“相似”。 amcmm,,,(为中间比)2(找相似找不到，找中间比。方法:将等式左右两边的比表示出来。? bndnn amcm',,,,n,n? 'bndn ''amcmmm'',,m,mn,n或,,(,)? ''bndnnn 3(添加辅助平行线是获得成比例线段和相似三角形的重要途径。 4(对比例问题，常用处理方法是将“一份”看着k;对于等比问题，常用处理

办法

鲁班奖评选办法下载鲁班奖评选办法下载鲁班奖评选办法下载企业年金办法下载企业年金办法下载

是设“公比”为k。 5(对于复杂的几何图形，采用将部分需要的图形(或基本图形)“抽”出来的办法处理。 应用举例(略) 第八章 函数及其图象 ?重点?正、反比例函数，一次、二次函数的图象和性质。 内容提要? 一、平面直角坐标系 1(各象限内点的坐标的特点 2(坐标轴上点的坐标的特点 3(关于坐标轴、原点对称的点的坐标的特点 4(坐标平面内点与有序实数对的对应关系 二、函数 1(表示方法:?解析法;?列表法;?图象法。 2(确定自变量取值范围的原则:?使代数式有意义;?使实际问题有 意义。 3(画函数图象:?列表;?描点;?连线。 三、几种特殊函数 (定义?图象?性质) 1997 steel welded-2005 vertical cylindrical steel pressure vessel steel welded tank code for construction and acceptance of 3 JB/ T4735-12898 2 GB50-ing 1 GB1502000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineer--2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 8 JB4730-ssels 7 JB/47092000 of welding procedure qualification for steel pressure ve-2004 petrochemical JB/ T47081000, who is directly responsible for the accident responsibility, give notice of criticism and 50-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-tion and acceptance of field equipment 4 HGJ2222002 industrial pipe welding engineering code for construc-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-Ray lighting and quality rating of 2 GB11345--2005 steel fusion welded butt joints, welding engineering-B3323lty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 Gficant near miss should be attempted as the case of responsible for the accident and construction team injuries accident pena1000 punishment. (5) signi-ership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500sanctions against them. (4) to conceal the accident, reported without undue delay or false, to inform the administrative lead100 economic ect punishment 500ative sanctions should be dealt with by the personnel Department of the company. (3) personal injury accident occurs, the diring administr10,000 yuan, responsible for the direct responsibility for the accident and the responsibility of leadership, such as concern-the direct punishment 0.59 第 9 页 共 12 页 正比例函数 ?定义:y=kx(k?0) 或y/x=k。 ?图象:直线(过原点) ?性质:?k>0，„?k<0，„ 一次函数 ?定义:y=kx+b(k?0) ?图象:直线过点(0,b)—与y轴的交点和(-b/k,0)—与x轴的交点。 y y y y o o o o x x x x (k>0,b>0) (k<0,b>0) (k>0,b<0) (k<0,b<0) ?性质:?k>0,„?k<0,„ ?图象的四种情况: 二次函数 2?定义: y,ax，bx，c(a,0)(一般式) 2 y,a(x,h)，k(a,0)(顶点式) 22都是二次函数。 特殊地，y,ax(a,0),y,ax，k(a,0) 2?图象:抛物线(用描点法画出:先确定顶点、对称轴、开口方向，再对称地描点)。y,ax，bx，c(a,0) 2用配方法变为，则顶点为(h,k);对称轴为直线x=h;a>0时，开口向上;a<0时，y,a(x,h)，k(a,0) 开口向下。 ?性质:a>0时，在对称轴左侧„，右侧„;a<0时，在对称轴左侧„，右侧„。 4.反比例函数 k,1y,,kx?定义:或xy=k(k?0)。 x ?图象:双曲线(两支)—用描点法画出。 ?性质:?k>0时，图象位于„，y随x„;?k<0时，图象位于„，y随x„;?两支曲线无限接近于坐标轴 但永远不能到达坐标轴。 四、重要解题方法 用待定系数法求解析式(列方程[组]求解)。对求二次函数的解析式，要合理选用一般式或顶点式，并应充 分运用抛物线关于对称轴对称的特点，寻找新的点的坐标。如下图: y 2(利用图象一次(正比例)函数、反比例函数、二次函数中的k、b;a、X=2 b、c的符号。 (-1,5) 六、应用举例(略) o x 第九章 解直角三角形 求解析式? ?重点?解直角三角形 内容提要? 一、三角函数 1(定义:在Rt?ABC中，?C=Rt?，则sinA= ;cosA= ;tanA= . 特殊角的三角函数值: ay lighting and quality rating of 2 GB11345R-2005 steel fusion welded butt joints, welding engineering-the construction standards and specifications, serial number a 1 GB3323ible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in 1000 punishment. (5) significant near miss should be attempted as the case of respons-the pursuit of leadership, along with 500 ed without undue delay or false, to inform the administrative leadership of the criticism, resulting in serious consequences,100 economic sanctions against them. (4) to conceal the accident, report-1000, who is directly responsible for the accident responsibility, give notice of criticism and 50-tment of the company. (3) personal injury accident occurs, the direct punishment 500ing administrative sanctions should be dealt with by the personnel Depar10,000 yuan, responsible for the direct responsibility for the accident and the responsibility of leadership, such as concern-the direct punishment 0.51997 steel welded-elded tank code for construction and acceptance of 3 JB/ T47352005 vertical cylindrical steel pressure vessel steel w-98 2 GB50128-ing 1 GB1502000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineer-procedures of steel pressure vessel NDT 9 JB/T47442005 pressure vessel welding -2000 8 JB4730-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2004 petrochemical JB/ T4708-l specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH352592 technica-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-10 中小数理化(加油站) 0? 30? 45? 60? 90? sinα cosα tgα / 互余两角的三角函数关系:sin(90?-α)=cosα;„ 三角函数值随角度变化的关系 5(查三角函数表 二、解直角三角形 定义:已知边和角(两个，其中必有一边)?所有未知的边和角。 222依据:?边的关系: a，b,c ?角的关系:A+B=90? ?边角关系:三角函数的定义。 注意:尽量避免使用中间数据和除法。 三、对实际问题的处理 俯、仰角: 2(方位角、象限角: 3(坡度: 北 i h 西 α 仰角 东 l 俯角 i=h/l=tgα 南 4(在两个直角三角形中，都缺解直角三角形的条件时，可用列方程的办法解决。 四、应用举例(略) 第十章 圆 ?重点??圆的重要性质;?直线与圆、圆与圆的位置关系;?与圆有关的角的定理;?与圆有关的比例线段 定理。 内容提要? 一、圆的基本性质 1(圆的定义(两种) 2(有关概念:弦、直径;弧、等弧、优弧、劣弧、半圆;弦心距;等圆、同圆、同心圆。 3(“三点定圆”定理 4(垂径定理及其推论 5(“等对等”定理及其推论 与圆有关的角: ?圆心角定义(等对等定理) ?圆周角定义(圆周角定理，与圆心角的关系) ?弦切角定义(弦切角定理) 二、直线和圆的位置关系 1.三种位置及判定与性质: d>R 直线与圆相离 d=R 直线与圆相切 dR+r 外离 d=R+r 外切 R-r