最新苏教版初一数学上册知识点优秀名师资料.doc
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1、苏教版初一数学上册知识点初一数学(上)应知应会的知识点 代数初步知识 1. 代数式:用运算符号“, , ? ”连接数及表示数的字母的式子称为代数式(字母所取得数应保证它所在的式子有意义,其次字母所取得数还应使实际生活或生产有意义;单独一个数或一个字母也是代数式) 2.列代数式的几个注意事项: (1)数与字母相乘,或字母与字母相乘通常使用“? ” 乘,或省略不写; (2)数与数相乘,仍应使用“”乘,不用“? ”乘,也不能省略乘号; (3)数与字母相乘时,一般在结果中把数写在字母前面,如a5应写成5a; 13(4)带分数与字母相乘时,要把带分数改成假分数形式,如a应写成a; 1223(5)在代数式
2、中出现除法运算时,一般用分数线将被除式和除式联系,如3?a写成的形式; a(6)a与b的差写作a-b,要注意字母顺序;若只说两数的差,当分别设两数为a、b时,则应分类,写做a-b和b-a . 3.几个重要的代数式:(m、n表示整数) 222 (1)a与b的平方差是: a-b ; a与b差的平方是:(a-b) ; (2)若a、b、c是正整数,则两位整数是: 10a+b ,则三位整数是:100a+10b+c; (3)若m、n是整数,则被5除商m余n的数是: 5m+n ;偶数是:2n ,奇数是:2n+1;三个连续整数是: n-1、n、n+1 ; 222 2 (4)若b,0,则正数是:a+b ,负数是
3、: -a-b ,非负数是: a,非正数是:-a. 有理数 1.有理数: q(p,q为整数且p,0)(1)凡能写成形式的数,都是有理数.正整数、0、负整数统称整数;正分数、负分数p统称分数;整数和分数统称有理数.注意:0即不是正数,也不是负数;-a不一定是负数,+a也不一定是正数;,不是有理数; total heavy model number (m) weight (t) 1 gate dam flat work door door leaves 6.2x2.0 2 2.50 sliding block 7.00 13.00 fixed type winch opening and closi
4、ng machine 2x100 5 .00 2 electrical equipment 2-containing plate working gate slot of sluice and dam 6.2x2.0 of 2 2.50 2.00 4.00 3 flat access door leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate s
5、lot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.0
6、0 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 . Table 1-1 the main characteristics of the penstock number item parameter type controller size head a long pipe diameter pipe length 11 hydropo
7、wer station penstock open-air exposed pipe, single pipe joint water supply 1.3M 931m 0.8M 8.3*2m 22 hydropower station penstock open-air exposed pipe, single pipe joint water supply 1.4m 1063.506 m 0.8M 10*2m table 1-2 hydropower station Hydraulic metal structure main characteristics table number pr
8、oject name gate, and stopped dirt gate, and door (Gate) slot opening and closing machine track notes hole mouth size (wide x high) (MXM) number (sets) design head (m) supports type type single heavy (t) total heavy (t) type type opening and closing capacity (KN) head (trip) (m) number (sets) single
9、heavy total heavy model number (m) weight (t) 1 gate dam flat work door door leaves 6.2x2.0 2 2.50 sliding block 7.00 13.00 fixed type winch opening and closing machine 2x100 5 .00 2 electrical equipment 2-containing plate working gate slot of sluice and dam 6.2x2.0 of 2 2.50 2.00 4.00 3 flat access
10、 door ,正整数,正整数,正有理数,整数零正分数,负整数(2)有理数的分类: ? ? 有理数零有理数,负整数,正分数,负有理数分数,负分数负分数,(3)注意:有理数中,1、0、-1是三个特殊的数,它们有自己的特性;这三个数把数轴上的数分成四个区域,这四个区域的数也有自己的特性; (4)自然数, 0和正整数;a,0 , a是正数;a,0 , a是负数; a?0 , a是正数或0 , a是非负数;a? 0 , a是负数或0 , a是非正数. 2(数轴:数轴是规定了原点、正方向、单位长度的一条直线. 3(相反数: (1)只有符号不同的两个数,我们说其中一个是另一个的相反数;0的相反数还是0; (
11、2)注意: a-b+c的相反数是-a+b-c;a-b的相反数是b-a;a+b的相反数是-a-b; (3)相反数的和为0 , a+b=0 , a、b互为相反数. 4.绝对值: (1)正数的绝对值是其本身,0的绝对值是0,负数的绝对值是它的相反数;注意:绝对值的意义是数轴上表示某数的点离开原点的距离; a(a,0),a(a,0),a,a,0(a,0)(2) 绝对值可表示为:或 ;绝对值的问题经常分类讨论; ,a(a,0),a(a,0),aa,1,a,0,1,a,0(3) ; ; aaaa,(4) |a|是重要的非负数,即|a|?0;注意:|a|?|b|=|a?b|, . bb5.有理数比大小:(1
12、)正数的绝对值越大,这个数越大;(2)正数永远比0大,负数永远比0小;(3)正数大于一切负数;(4)两个负数比大小,绝对值大的反而小;(5)数轴上的两个数,右边的数总比左边的数大;(6)大数-小数 , 0,小数-大数 , 0. 1a6.互为倒数:乘积为1的两个数互为倒数;注意:0没有倒数;若 a?0,那么的倒数是;倒数是本身的atotal heavy model number (m) weight (t) 1 gate dam flat work door door leaves 6.2x2.0 2 2.50 sliding block 7.00 13.00 fixed type winch
13、opening and closing machine 2x100 5 .00 2 electrical equipment 2-containing plate working gate slot of sluice and dam 6.2x2.0 of 2 2.50 2.00 4.00 3 flat access door leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat
14、 emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.
15、5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 . Table 1-1 the main characteristics of the penstock number item parameter type controller size head a long pipe diameter pipe
16、length 11 hydropower station penstock open-air exposed pipe, single pipe joint water supply 1.3M 931m 0.8M 8.3*2m 22 hydropower station penstock open-air exposed pipe, single pipe joint water supply 1.4m 1063.506 m 0.8M 10*2m table 1-2 hydropower station Hydraulic metal structure main characteristic
17、s table number project name gate, and stopped dirt gate, and door (Gate) slot opening and closing machine track notes hole mouth size (wide x high) (MXM) number (sets) design head (m) supports type type single heavy (t) total heavy (t) type type opening and closing capacity (KN) head (trip) (m) numb
18、er (sets) single heavy total heavy model number (m) weight (t) 1 gate dam flat work door door leaves 6.2x2.0 2 2.50 sliding block 7.00 13.00 fixed type winch opening and closing machine 2x100 5 .00 2 electrical equipment 2-containing plate working gate slot of sluice and dam 6.2x2.0 of 2 2.50 2.00 4
19、.00 3 flat access door 数是?1;若ab=1, a、b互为倒数;若ab=-1, a、b互为负倒数. 7. 有理数加法法则: (1)同号两数相加,取相同的符号,并把绝对值相加; (2)异号两数相加,取绝对值较大的符号,并用较大的绝对值减去较小的绝对值; (3)一个数与0相加,仍得这个数. 8(有理数加法的运算律: (1)加法的交换律:a+b=b+a ;(2)加法的结合律:(a+b)+c=a+(b+c). 9(有理数减法法则:减去一个数,等于加上这个数的相反数;即a-b=a+(-b). 10 有理数乘法法则: (1)两数相乘,同号为正,异号为负,并把绝对值相乘; (2)任何数
20、同零相乘都得零; (3)几个数相乘,有一个因式为零,积为零;各个因式都不为零,积的符号由负因式的个数决定. 11 有理数乘法的运算律: (1)乘法的交换律:ab=ba;(2)乘法的结合律:(ab)c=a(bc); (3)乘法的分配律:a(b+c)=ab+ac . a即无意义12(有理数除法法则:除以一个数等于乘以这个数的倒数;注意:零不能做除数,. 013(有理数乘方的法则: (1)正数的任何次幂都是正数; nnnn(2)负数的奇次幂是负数;负数的偶次幂是正数;注意:当n为正奇数时: (-a)=-a或(a -b)=-(b-a) , 当nn nnn为正偶数时: (-a) =a或 (a-b)=(b
21、-a) . 14(乘方的定义: (1)求相同因式积的运算,叫做乘方; (2)乘方中,相同的因式叫做底数,相同因式的个数叫做指数,乘方的结果叫做幂; 222(3)a是重要的非负数,即a?0;若a+|b|=0 , a=0,b=0; total heavy model number (m) weight (t) 1 gate dam flat work door door leaves 6.2x2.0 2 2.50 sliding block 7.00 13.00 fixed type winch opening and closing machine 2x100 5 .00 2 electrica
22、l equipment 2-containing plate working gate slot of sluice and dam 6.2x2.0 of 2 2.50 2.00 4.00 3 flat access door leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2
23、 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5
24、slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 . Table 1-1 the main characteristics of the penstock number item parameter type controller size head a long pipe diameter pipe length 11 hydropower station penstock open-air expo
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