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1、中考数学总复习专题基础知识回顾一实数一、单元知识网络：二、考试目标要求：了解有理数、无理数、实数的概念；会比较实数的大小，知道实数与数轴上的点一一对应，会用科学记数法表示有理数；理解相反数和绝对值的概念及意义.进一步，对上述知识理解程度的评价既可以用纯粹数学语言、符号的方式呈现试题，也可以建立在应用知识解决问题的基础之上，即将考查的知识、方法融于不同的情境之中，通过解决问题而考查学生对相应知识、方法的理解情况.了解乘方与开方的概念，并理解这两种运算之间的关系.了解平方根、算术平方根、立方根的概念，了解整数指数幂的意义和基本性质.具体目标：1.有理数(1)理解有理数的意义，能用数轴上的点表示有理
2、数，会比较有理数的大小.(2)借助数轴理解相反数和绝对值的意义，会求有理数的相反数与绝对值(绝对值符号内不含字母).(3)理解乘方的意义，掌握有理数的加、减、乘、除、乘方及简单的混合运算(以三步为主).(4)理解有理数的运算律，并能运用运算律简化运算.(5)能运用有理数的运算解决简单的问题.(6)能对含有较大数字的信息作出合理的解释和推断.2.实数(1)了解平方根、算术平方根、立方根的概念，会用根号表示数的平方根、立方根.(2)了解开方与乘方互为逆运算，会用平方运算求某些非负数的平方根，会用立方运算求某些数的立方根，会用计算器求平方根和立方根.(3)了解无理数和实数的概念，知道实数与数轴上的点
3、一对应.(4)能用有理数估计一个无理数的大致范围.(5)了解近似数与有效数字的概念.在解决实际问题中，能用计算器进行近似计算，并按问题的要求对结果取近似值.三、知识考点梳理知识点一、实数的分类1.按定义分类：2.按性质符号分类：注：0 既不是正数也不是负数.3.有理数：整数和分数统称为有理数或者“形如(m，n 是整数 n0)”的数叫有理数4.无理数：无限不循环小数叫无理数5.实数：有理数和无理数统称为实数知识点二、实数的相关概念1.相反数(1)代数意义：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 的相反数是 0.(2)几何意义：在数轴上原点的两侧，与原点距离相等的两个点表示的两个数
4、互为相反数，或数轴上，互为相反数的两个数所对应的点关于原点对称.(3)互为相反数的两个数之和等于0.a、b 互为相反数a+b=0.2.绝对值文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 Z
5、K1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5
6、N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 Z
7、K1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5
8、N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 Z
9、K1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5
10、N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1文档编码:CU2L5N7F7E2 HD2M4T9A2S4 ZK1K8W6N5U1(1)代数意义：正数的绝对值是它本身；负数的绝对值是它的相反数；0 的绝对值是0 可用式子表示为：(2)几何意义：一个数a 的绝对值就是数轴上表示数a 的点与原点的距离距离是一个非负数，所以绝对值的几何意义本身就揭示了绝
11、对值的本质，即绝对值是一个非负数用式子表示：若 a 是实数，则|a|03.倒数(1)实数的倒数是；0 没有倒数；(2)乘积是 1 的两个数互为倒数a、b 互为倒数.4.平方根(1)如果一个数的平方等于a，这个数就叫做a 的平方根一个正数有两个平方根，它们互为相反数；0 有一个平方根，它是0 本身；负数没有平方根a(a 0)的平方根记作(2)一个正数a 的正的平方根，叫做a 的算术平方根a(a 0)的算术平方根记作5.立方根如果 x3=a，那么 x 叫做 a 的立方根一个正数有一个正的立方根；一个负数有一个负的立方根；零的立方根仍是零知识点三、实数与数轴数轴定义：规定了原点，正方向和单位长度的直
12、线叫做数轴，数轴的三要素缺一不可每一个实数都可以用数轴上的一个点来表示，反过来，数轴上的每一个点都表示一个实数知识点四、实数大小的比较1.对于数轴上的任意两个点，靠右边的点所表示的数较大.2.正数都大于0，负数都小于0，两个正数，绝对值较大的那个正数大；两个负数；绝对值大的反而小.3.对于实数a、b，若 a-b0ab；a-b=0a=b；a-b 0ab.文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编
13、码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P
14、8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编
15、码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P
16、8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编
17、码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P
18、8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U94.对
19、于实数a，b，c，若 ab，bc，则 ac.5.无理数的比较大小：利用平方转化为有理数：如果 a b0，a2b2ab；或利用倒数转化：如比较与.知识点五、实数的运算1.加法同号两数相加，取相同的符号，并把绝对值相加；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；一个数同0 相加，仍得这个数2.减法减去一个数等于加上这个数的相反数3.乘法几个非零实数相乘，积的符号由负因数的个数决定，当负因数有偶数个时，积为正；当负因数有奇数个时，积为负几个数相乘，有一个因数为0，积就为 04.除法除以一个数，等于乘上这个数的倒数两个数相除，同
20、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05.乘方与开方(1)an 所表示的意义是n 个 a 相乘，正数的任何次幂是正数，负数的偶次幂是正数，负数的奇次幂是负数(2)正数和 0 可以开平方，负数不能开平方；正数、负数和0 都可以开立方(3)零指数与负指数6.实数的六种运算关系加法与减法互为逆运算；乘法与除法互为逆运算；乘方与开方互为逆运算.7.实数运算顺序加和减是一级运算，乘和除是二级运算，乘方和开方是三级运算这三级运算的顺序是三、二、一如果有括号，先算括号内的；如果没有括号，同一级运算中要从左至右依次运算8.实数的运算律加法交换律：a+b=b+a 加法结合律：(a
21、+b)+c=a+(b+c)乘法交换律：ab=ba 文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K
22、4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y
23、8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K
24、4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y
25、8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K
26、4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y
27、8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9乘法结合律：(ab)c=a(bc)乘法分配律：(a+b)c=ac+bc 知识点六、有效数字和科学记数法1.近似数：一个近似数，四舍五入到那一位，就说这个近似数精确到哪一位2.有效数字：一个近似数，从左边第一个不是0 的数字起，到精确到的数位为止，所有的数字，都叫做这个近似数的有效数字3.科学记数法：把一个数用
28、(1 10，n 为整数)的形式记数的方法叫科学记数法四、规律方法指导1.数形结合思想实数与数轴上的点一一对应，绝对值的几何意义等，数轴在很多时候可以帮助我们更直观地分析题目，从而找到解决问题的突破口.2.分类讨论思想（算术）平方根，绝对值的化简都需要有分类讨论的思想，考虑问题要全面，做到既不重复又不遗漏.3.从实际问题中抽象出数学模型以现实生活为背景的题目，我们要抓住问题的实质，明确该用哪一个知识点来解决问题，然后有的放矢.4.注意观察、分析、总结对于寻找规律的题目，仔细观察变化的量之间的关系，尝试用数学式子表示规律.对于阅读两量大的题目，经常是把规律用语言加以叙述，仔细阅读，找到关键的字、词
29、、句，从而找到思路.经典例题精析考点一、实数概念及分类1.（2010 上海）下列实数中，是无理数的为（）A.3.14 B.C.D.思路点拨：考查无理数的概念.【答案】C 2.下列实数、sin60、3.14159、中无理数有()个文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7
30、J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:C
31、A1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7
32、J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:C
33、A1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7
34、J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:C
35、A1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9A1 B 2 C3 D4 答案：C.无理数有sin60、.总结升华：对实数进行分类不能只看表面形式，应先化简，再根据结果去判断举一反
36、三：【变式 1】把下列各数填入相应的集合里：(1)自然数集合：(2)整数集合：(3)分数集合：(4)无理数集合：答案：(1)自然数集合：(2)整数集合：(3)分数集合：(4)无理数集合：3（2010 北京）右图为手的示意图，在各个手指间标记字母A，B，C，D请你按图中箭头所指方向(即 ABCDCBABC的方式)从 A开始数连续的正整数1，2，3，4，当数到12 时，对应的字母是；当字母 C第 201 次出现时，恰好数到的数是；当字母 C第 2n+1 次出现时(n 为正整数)，恰好数到的数是（用含 n 的代数式表示）思路点拨：字母C第“奇数”次出现时，恰好数到的数是这个“奇数”的3 倍。【答案】
37、B,603，6n 3 考点二、数轴、倒数、相反数、绝对值文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7
38、C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9
39、A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7
40、C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9
41、A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7
42、C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9
43、A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U94（2010 湖南益阳）数轴上的点A到原点的距离是6，则点 A表示的数为（）A.或B.6 C.D.或思路点拨:数轴上的点A到原点的距离是6 的点有两个，原点的左边、右边各有一个。【答案】A 5(1)a的相反数是，则 a 的倒数是 _(2)实数 a、b 在数轴上对应点的位置如图所示:则化简=_思路点拨:(
44、1)注意相反数和倒数概念的区别，互为相反数的两个数只有性质符号不同，互为倒数的两个数要改变分子分母的位置；或者利用互为相反数的两个数之和等于0，互为倒数的两个数乘积等于 1 来计算.由a 的相反数是，所以 a=，的倒数为5.(2)此题考查绝对值的几何意义，绝对值和二次根式的化简.注意要去掉绝对值符号，要判别绝对值内的数的性质符号.由图知：答案：(1)5；(2)-a-b.举一反三：【变式 1】化简-(-2)的结果是()A-2 B C D 2 答案：选 D.【变式 2】若 m+1与 m 3 互为相反数，则m=_.思路点拨：互为相反数的两个数之和等于0.m+1+m 3=0，解得 m=1.答案：1.【
45、变式 3】-2 的倒数是 _.思路点拨：注意倒数与相反数的区别，乘积为1 的两个数互为倒数.答案：.文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2
46、A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 Z
47、B7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2
48、A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 Z
49、B7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2
50、A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 ZB7C6K4D2U9文档编码:CA1I2A9A2Y8 HB5T6P8P7J4 Z