2022年新人教版七年级数学上册知识点归纳及练习 .pdf

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2022年新人教版七年级数学上册知识点归纳及练习 .pdf

第一章有理数复习一、正数，负数的定义：大于0 的数叫做正数；小于0 的数叫做负数。注意：0 既不是正数也不是负数。练习：如果收入50 元记作+50 元，那么支出80 元应该记作 _ 例：观察下面9 个数，并给它们进行分类.5、5.6、-6、-3.7、0、3、-2、3/2、-1/2 正整数：零：负整数:正分数：负分数：三、数轴：数轴是规定了原点、正方向、单位长度的一条直线5,2.5,1,+2,+3,11 1 1 1 11 1 1 1 L 1 11-15-2.5-1()+1+2+3+4.5练习：1、若点 A 在数轴上原点的左边，贝卩A 点表示的数是（）A 正数 B 负数 C 整数 _ 的数总比B 右边左边5 个单位长度的点表示的数是A+5 B-5 C 士 5 C、在数轴上表示2 和-2 的点到原点的距离相等D、数轴上一定取向右为正方向5、在数轴上原点及原点左边的点所表示的数是（）A、正数B、负数C、不是负数D、不是正数6 在数轴上 0 与 3 之间（不包括0,3）还有个数。（）A、2 个 B、3 个 C、4 个D、无数个7、一个点从数轴的原点开始，先向左移动3 个单位长度，再向右移动6 个单位长度，这个点最终所对应的数是（）A.+6 B.-3 C.+3 D.-9 四、相反数：一般地a 的相反数是-a（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；注意：0 的相反数还是0;（2）相反数的和为0（3）相反数的商为-1.例：-3 的相反数是：_;9 的相反数是：_;-5+5=_;7 宁（-7）=_ 练习：1.判断：、有理数的分类：正有理数有理数零负有理数整数正整数零有理数负整数分数正分数负分数2、数轴上表示两个数,A、左边右边4、下列说法不正确（A、数轴是一条直）B、数轴上所有的点并不都表示有理数边的数大.正整数正分数负整数负分数例.在数轴上记出下列各数:（1）5 是 5 的相反数（）；（2）5 是一 5 的相反数（）；(3)5 与5 互为相反数()；(4)-5 是相反数()2.-1.6 是的相反数，的相反数是0.3.3.下列几对数中互为相反数的一对为().A.和B.与C.与4.5 的相反数是；a 的相反数是3a-b 的相反数是5.若 a=-13，贝卩-a=；若-a=-则 a=.五、绝对值：一般地，数轴上表示数a 的点与原点的距离叫做数a 的绝对值(1)正数的绝对值等于它本身，(2)0 的绝对值是 0，(3)负数的绝对值等于它的相反数;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)(2)绝对值可表示为：a 0(a 0)a(a 0)|a 是重要的非负数，即|a|0;(4)相反数的绝对值相等例 1?求下列各数绝对值：8.5、-5、4,-0.3,0，-,-8.57 71例 2.2;I 5 _；|5 _；|5 _；(|0.3)_;练习：判断：(1)一个数的绝对值是2，则这数是 2。()(2)|5|=|-5|。()(3)|-0.3|=|0.3|。()(4)|3|0。()(5)|-1.4 0。()(6)有理数的绝对值一定是正数。()若 a=b,则|a|=|b|。()(8)若|a|=|b|,贝 S a=b。()(9)若|a|=-a,则 a 必为负数。()(10)互为相反数的两个数的绝对值相等。填空：(1)-相反数是 _；(2)绝对值最小的数是_.3(3)绝对值等于本身的数是_；(4)绝对值小于 3 的正整数是 _ 六.倒数：乘积为1 的两个数互为倒数；ax-=1，则 a 与-互为倒数。a a注意：0 没有倒数例：-7 的倒数的倒数_。七、有理数比大小：(1)正数永远比 0 大，负数永远比0 小；(2)正数大于一切负数；(3)两个负数比较，绝对值大的反而小；文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 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ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X51 1 例 1.利用数轴，比较3,5,5,2-,4,4,0 的大小。2 2 练习：比较各组数的大小(1)1 和 3；(2)2 和 0；(3)(1)和(2);(4)8和2 3 4；(5)(3)和|21 7 3 八.有理数加法法则：X|k|b|1.c|o|m(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，取绝对值较大加数的符号，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.例：5+3=8;-5+(-3)=-8；5+(-3)=2；3+(-5)=-2；5+(-5)=0；-5+5=0 5+0=5；-5+0=-5 练习：1、有理数的加法：直接写出结果强化练习一、填空题1.计算1 15 3(1)3+4 6+7=5 2(2)3-6+36=2.2+34=+=+()=+=3.已知：a=11,b=12,c=5计算：(1)a+b+c二2 a b+c=_ 3 a(b+c)=_ 4 b(a c)=_ 4._ 将(一 3)+(2)(+7)(6)去括号后可变形为_(1)加法的父换律：a+b=b+a；(2)加法的结合律：(a+b)+c=a+(b+c).(1)(-17)+(-15)(2)(+12)+(+14)九.有理数加法的运算律：(3)(+3)+(-5)(4)-0.3+4.7(5)(-2)+2十.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)练习、有理数的减法：计算(1)(-14)-(+16)(3)(-7)-(-10)(5)15-(-15)混合运算(1)(-7)-(+5)+(-4)-(-10)(2)(+6)-(-13)(4)(+5)-(+9)(6)0-13(7)(2)(-0.8)+1.2+(-0.7)-(+2.1)-(-0.8)+(+3.5)有理数的减法法则：减去一个数，等于加上这个数的相反数16-38 文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 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ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X541 2 5.2与3的相反数的绝对值之和是_.6?已知 a、b 互为相反数，c 是绝对值最小的数，d 是负整数中最大的数，则a+b+c d=_ 7.若|2x 3|+|3y+2|=0,贝卩 x y=_.8._ 某次考试初一年级数学平均分为73 分，其中最高分高出平均分 25 分，最低分比平均分低 24 分，请问最高分比最低分高分.9.某地上午气温为5 C,中午气温上升7C,晚上又下降了16C，则晚上的气温为_ 1 210.(1)当 a 0 时，a,5 6a,3a,2a,3a,由小到大的排列顺序为_(2)_ 当 bv 0 时，a+2b,a+b,a b,a-2b,a,由小到大的顺序为 _.二、选择题11.如果|c|=C,则 c2一定是 A.正数B.负数C.0 D.可能为正数也可能为负数12 与 a+b c 的值相等的是 C.a+(b)c D.a+(c b)13.如果一个整数加4 为正，力口2 为负，那么这个数与2 的和为 A.4 B.5 C.5 D.4 14.下面等式错误的是 1111 1 1 A.235=2(3+5)B.5+2+4=4 (5+2)C.(+3)(2)+(1)=3+2 1 D.2 3 4=(2)(+3)+(4)三、解答题15 计算(1)(18)(8.9)(7.5)(4.2)(35)|11 121 5 3(4)(14)(3)(14)(3)(5)(3)A.a (b)(c)B.a (b)(+c)2)29 I文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 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ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5有理数_ 2、在数轴上表示下列各数:1 1 3 3 2 2 3 3 4 2，2,2，2,3，3,4，4,33、相反数:代数意义：不同的两个数叫做互为相反数。几何意义：数轴上相等的两个点表示的数叫做互为相反数。4、绝对值:几何意义：数轴上表示数 a 的点叫做 a 的绝对值，记作 a。(a 0)代数意义：a(a 0)或 a _(a 0)或 a _(a 0)(a 0)_(a 0)(a 0)1 1 1 15、按要求分类。5,-,0.62,4,0,1,1-,6.4,7,1,20%。3 6 3 2正整数：非负数：分数：非负整数：6、若现在北京时间是下午2 点，洛杉矶与北京时差是-16,首尔与北京的时差是+1,那么现在洛杉矶时间是首尔时间是 _。7、21 日买进公司股票 7000 股，每股 27 元，以后涨跌情况如下，22 日：+4,23 日：5，24 日：+2,那么在 24 日卖掉所有股票，共盈利 _，若交易(买进和卖出)手续费均为3%。，则利润是_。8 足球循环赛中，红队胜黄队 4:2,黄队胜蓝队 2:0,蓝队胜红队 2:1,三场比赛中，红队、黄队、蓝队的净胜球数分别为 _、_、_。9、规定一种新运算e:ae b-b，则2e(3)e 3=_。ab10、_ 将数 1 所表示的点沿数1 有理数分类:典型习题(一)有理数文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8X1 ZR3B6X5E5X5文档编码:CZ8U1F6T4B7 HT1T1Q8E8

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