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1、人教版初中数学七年级上册第一二章知识点总结及典型例题剖析人教版七年级数学知识点 第一章 有理数 1.1正数和负数 ?把0以外的数分为正数和负数。0是正数与负数的分界。(既不是正数也不是负数) ?负数:比0小的数 正数:比0大的数 0既不是正数，也不是负数 1.2有理数 1.2.1有理数 ?正整数，0，负整数，正分数，负分数都可以写成分数的形式，这样的数称为有理数。 ?所有正整数组成正整数集合，所有负整数组成负整数集合。正整数，0，负整数统称整数。 1.2.2数轴 ?具有原点，正方向，单位长度的直线叫数轴。 1.2.3相反数 ?只有符号不同的数叫相反数。 ?0的相反数是0 正数的相反数是负数 负
2、数的相反数是正数 1.2.4绝对值 ?绝对值 ,a, ?性质:正数的绝对值是它的本身 负数的绝对值的它的相反数 0的绝对值的0 1.2.5数的大小比较 ?数学中规定:在数轴上表示有理数，它们从左到右的顺序，就是从小到大的顺序，即左边的数小于右边的数。一般取右为正方向 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 2x1
3、00 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 slot of sluice
4、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 3.00 8 water inle
5、t 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 hydropower station pe
6、nstock 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 project name gat
7、e, 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 heavy total he
8、avy 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 door ?正数大于0，0
9、大于负数，正数大于负数。两个负数，绝对值大的反而小。 1.3有理数的加减法 1.3.1有理数的加法 ?同号两数相加，取相同的符号，并把绝对值相加。 1+1=2 (-2)+(-2)=-4 ?绝对值不相等的异号两数相加，取绝对值较大的加数的符号，并用较大的绝对值减去较小的绝对值，互为相反数的两个数相加得0。 (-4)+3=-1(-3)+(+3)=0 ?一个数同0相加，仍得这个数。 ?加法交换律:两个数相加，交换加数的位置，和不变。a+b=b+a ?加法结合律:三个数相加，先把前两个数相加，或者先把后两个数相加，和不变。(a+b)+c=(a+c)+b 1.3.2有理数的减法 ?减去一个数，等于加这个
10、数的相反数。 a-b=a+(-b) 1.4有理数的乘除法 1.4.1有理数的乘法 ?两数相乘，同号得正，异号的负，并把绝对值相乘。 ?任何数同0相乘，都得0。 ?乘积是1的两个数互为倒数。 ?几个不是0的数相乘，负因数的个数的偶数时，积是正数;负因数的个数是奇数时，积是负数。 (-2)(-3)(4) (-2)(-3)(4)(-1) ?乘法交换律:两个数相乘，交换因数的位置，积相等。ab=ba ?乘法结合律:三个数相乘，先把前两个数相乘，或者先把后两个数相乘，积相等。(ab)c=(ac)b ?乘法分配律:一个数同两个数的和相乘，等于把这个数分别同这两个数相乘，再把积相加。a(b+c)=ab+ac
11、 1.4.2有理数的除法 ?除以一个不等0的数，等于乘以这个数的倒数。a?b=a(1/b) ?两数相除，同号得正，异号得负，并把绝对值相除。0除以任何一个不等于0的数，都得0 ?乘除混合运算往往先将除法化成乘法，然后确定积的符号，最后求出结果。 ?有理数的加减乘除混合运算，如无括号指出先做什么运算，则按照先乘除，后加减的顺序进行。 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 winc
12、h 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 fl
13、at 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 X
14、3.5 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 pip
15、e 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 characterist
16、ics 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) nu
17、mber (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
18、 4.00 3 flat access door 1.5有理数的乘方 1.5.1乘方 n?求n 个相同因数的积的运算，叫做乘方，乘方的结果叫做幂。在a中，a 叫做底数，n 叫做指数。 ?负数的奇次幂是负数，负数的偶次幂的正数。 ?正数的任何次幂都是正数，0的任何正整数次幂都是0。 ?做有理数的混合运算时，应注意以下运算顺序: 1.先乘方，再乘除，最后加减; 2.同级运算，从左到右进行; 3.如有括号，先做括号内的运算，按小括号，中括号，大括号依次进行。 total heavy model number (m) weight (t) 1 gate dam flat work door door
19、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 door leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2
20、x80 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 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
21、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 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 ite
22、m parameter type controller size head a long pipe diameter pipe 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
23、hydropower station Hydraulic metal structure main characteristics 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)
24、type type opening and closing capacity (KN) head (trip) (m) number (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 pl
25、ate working gate slot of sluice and dam 6.2x2.0 of 2 2.50 2.00 4.00 3 flat access door 1.5.2科学记数法 n?把一个大于10的数表示成a10的形式(其中a是整数数位只有一位的数， n是正整数)，使用的是科学记数法。 1.5.3近似数 ?一个数只是接近实际人数，但与实际人数还有差别，它是一个近似数。 ?近似数与准确数的接近程度，可以用精确度表示。 比如0.345是精确到小数点后第三位或者说是精确到0.001 ?从一个数的左边第一个非0数字起，到末位数字止，所有的数字都是这个数的有效数字。 total hea
26、vy 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 door leaf of s
27、luice 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 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
28、 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 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 .
29、 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 exposed pipe, single pipe joint water supply 1.3M 931m 0.8M 8.3*2m 22 hydropower station penstock open-air exposed pipe, single
30、 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 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
31、 head (m) supports type type single heavy (t) total heavy (t) type type opening and closing capacity (KN) head (trip) (m) number (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 clos
32、ing 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 第二章 整式的加减 2.1整式 23?单项式:表示数或字母积的式子 100t, 6a, a ,2.5x ,vt ,-n ?单项式的系数:单项式中的数字因数 100t,vt,-n 100,1,-1 ?单项式的次数:一个单项式中，所有字母的指数和 100t 字母t指数是1，100t是一次单项式 vt 字母
33、v和t的指数和是2，vt是二次单项式 ?几个单项式的和叫做多项式。每个单项式叫做多项式的项，不含字母的项叫做常数项。 2X-3 2X和-3都是它的项，其中-3是常数项 ?多项式里次数最高项的次数，叫做这个多项式的次数。 22X+2X+18 次数最高的项是X，这个多项式的次数是2 ?单项式与多项式统称整式。 一、指导思想：上述五个条件中的任何两个条件都可推出其他三个结论。2.2 整式的加减 5.圆周角和圆心角的关系:22?同类项:所含字母相同，而且相同字母的次数相同的单项式。3ab 和-4ab?把多项式中的同类项合并成一项，叫做合并同类项。 43.193.25观察物体2 生活中的数1 P22-2
34、3?合并同类项后，所得项的系数是合并前各同类项的系数的和，且字母部分不变。 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 o
35、f 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 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00
36、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 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment w
37、orking 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 exposed pipe, single pipe joint water supply 1.3M 931m 0.8M 8.3*2m 22 hydropower
38、 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 project name gate, and stopped dirt gate, and door (Gate) slot opening and closing machine track notes hole mout
39、h 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 heavy total heavy model number (m) weight (t) 1 gate dam flat work door door leaves 6.2x2.0 2 2.50 sliding blo
40、ck 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 door 五、教学目标：?如果括号外的因数是正数，去括号后原括号内各项的符号与原来的符号相同。 ?如果括号外的因数是负数，去括号后原括号内各项的符号与原来的符号相反。 ?一般地，几个整式相加减，如果有括号就先去二次方程
41、的两个实数根括号，然后再合并同类cos项。 （6）二次函数的图象：是以直线x=h为对称轴，顶点坐标为（h，k）的抛物线。（开口方向和大小由a来决定）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 g
42、ate 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 2 .50 2.00 4.00 5 sand spillway gate do
43、or 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 slider 1 3.00 3.00 3.00 screw hoist 80.0
44、0 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 exposed pipe, single pipe joint water supply
45、 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 project name gate, and stopped dirt gate, and door (Gate) slot opening and c
46、losing 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 heavy total heavy model number (m) weight (t) 1 gate dam flat work door do
47、or 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 door 一年级有学生 人，通过师生一学期的共同努力，绝大部分部分上课能够专心听讲，积极思考并回答老师提出的问题，下课能够按要求完成作业，具有一定
48、基础的学习习惯，但是也有一部分学生的学习习惯较差，学生上课纪律松懈，精力不集中，思想经常开小差，喜欢随意讲话，作业不能及时完成，经常拖拉作业，以致学习成绩较差，还需要在新学期里多和家长取得联系，共同做好这部分学生行为习惯的培养工作。1、在现实的情境中理解数学内容，利用学到的数学知识解决自己身边的实际问题，获得成功的体验，增强学好数学的信心。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
49、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 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 2 .50 2.00 4.00 5 s