2021年七年级下册数学公式.pdf

初一下册数学公式1 过两点有且只有一条直线2 两点之间线段最短3 同角或等角的补角相等4 同角或等角的余角相等5 过一点有且只有一条直线和已知直线垂直6 直线外一点与直线上各点连接的所有线段中，垂线段最短7 平行公理经过直线外一点，有且只有一条直线与这条直线平行8 如果两条直线都和第三条直线平行，这两条直线也互相平行9 同位角相等，两直线平行10 内错角相等，两直线平行11 同旁内角互补，两直线平行12 两直线平行，同位角相等13 两直线平行，内错角相等14 两直线平行，同旁内角互补15 定理三角形两边的和大于第三边16 推论三角形两边的差小于第三边17 三角形内角和定理三角形三个内角的和等于180 18 推论 1 直角三角形的两个锐角互余19 推论 2 三角形的一个外角等于和它不相邻的两个内角的和20 推论 3 三角形的一个外角大于任何一个和它不相邻的内角21 全等三角形的对应边、对应角相等精品w o r d 可编辑资料-第 1 页，共 9 页-22 边角边公理(SAS)有两边和它们的夹角对应相等的两个三角形全等23 角边角公理(ASA)有两角和它们的夹边对应相等的两个三角形全等24 推论(AAS)有两角和其中一角的对边对应相等的两个三角形全等25 边边边公理(SSS)有三边对应相等的两个三角形全等26 斜边、直角边公理(HL)有斜边和一条直角边对应相等的两个直角三角形全等27 定理 1 在角的平分线上的点到这个角的两边的距离相等28 定理 2 到一个角的两边的距离相同的点，在这个角的平分线上29 角的平分线是到角的两边距离相等的所有点的集合30 等腰三角形的性质定理等腰三角形的两个底角相等(即等边对等角）31 推论 1 等腰三角形顶角的平分线平分底边并且垂直于底边32 等腰三角形的顶角平分线、底边上的中线和底边上的高互相重合33 推论 3 等边三角形的各角都相等，并且每一个角都等于60 34 等腰三角形的判定定理如果一个三角形有两个角相等，那么这两个角所对的边也相等（等角对等边）35 推论 1 三个角都相等的三角形是等边三角形36 推论2 有一个角等于60的等腰三角形是等边三角形37 在直角三角形中，如果一个锐角等于30那么它所对的直角边等于斜边的一半38 直角三角形斜边上的中线等于斜边上的一半39 定理线段垂直平分线上的点和这条线段两个端点的距离相等40 逆定理和一条线段两个端点距离相等的点，在这条线段的垂直平分线上41 线段的垂直平分线可看作和线段两端点距离相等的所有点的集合42 定理 1 关于某条直线对称的两个图形是全等形精品w o r d 可编辑资料-第 2 页，共 9 页-文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N843 定理2 如果两个图形关于某直线对称，那么对称轴是对应点连线的垂直平分线44 定理 3 两个图形关于某直线对称，如果它们的对应线段或延长线相交，那么交点在对称轴上45 逆定理如果两个图形的对应点连线被同一条直线垂直平分，那么这两个图形关于这条直线对称平均数问题公式（一个数+另一个数）2 反向行程问题公式路程(大速+小速同向行程问题公式路程(大速小速）行船问题公式同上列车过桥问题公式（车长+桥长）车速工程问题公式1速度和 盈亏问题公式（盈+亏）两次的相差数利率问题公式总利润成本 100 中小学数学应用题常用公式1 每份数份数总数总数每份数份数总数份数每份数2 1 倍数倍数几倍数几倍数 1 倍数倍数几倍数倍数 1 倍数3 速度时间路程路程速度时间路程时间速度4 单价数量总价精品w o r d 可编辑资料-第 3 页，共 9 页-文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8总价单价数量总价数量单价5 工作效率工作时间工作总量工作总量工作效率工作时间工作总量工作时间工作效率6 加数加数和和一个加数另一个加数7 被减数减数差被减数差减数差减数被减数8 因数因数积积一个因数另一个因数9 被除数除数商被除数商除数商除数被除数小学数学图形计算公式1 正方形C 周长 S 面积a 边长周长边长 4 C=4a 面积=边长边长S=a a 精品w o r d 可编辑资料-第 4 页，共 9 页-文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N82 正方体V:体积a:棱长表面积=棱长棱长6 S 表=a a6 体积=棱长棱长棱长V=a aa 3 长方形C 周长 S 面积a 边长周长=(长+宽)2 C=2(a+b)面积=长宽S=ab 4 长方体V:体积s:面积a:长 b:宽 h:高(1)表面积(长宽+长高+宽高)2 S=2(ab+ah+bh)(2)体积=长宽高V=abh 5 三角形s 面积a 底 h 高面积=底高2 s=ah 2 三角形高=面积 2底精品w o r d 可编辑资料-第 5 页，共 9 页-文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8三角形底=面积 2高6 平行四边形s 面积a 底 h 高面积=底高s=ah 7 梯形s 面积a 上底b 下底h 高面积=(上底+下底)高 2 s=(a+b)h2 8 圆形S 面积 C 周长 d=直径r=半径(1)周长=直径=2 半径C=d=2 r(2)面积=半径半径9 圆柱体v:体积h:高 s;底面积r:底面半径c:底面周长(1)侧面积=底面周长高(2)表面积=侧面积+底面积 2(3)体积=底面积高（4）体积侧面积 2半径10 圆锥体v:体积h:高 s;底面积r:底面半径精品w o r d 可编辑资料-第 6 页，共 9 页-文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8体积=底面积高 3 总数总份数平均数和差问题的公式(和差)2大数(和差)2小数和倍问题和(倍数 1)小数小数倍数大数(或者和小数大数)差倍问题差(倍数 1)小数小数倍数大数(或 小数差大数)植树问题1 非封闭线路上的植树问题主要可分为以下三种情形:如果在非封闭线路的两端都要植树,那么:株数段数 1全长株距 1 全长株距(株数 1)株距全长(株数 1)如果在非封闭线路的一端要植树,另一端不要植树,那么:株数段数全长株距全长株距株数株距全长株数如果在非封闭线路的两端都不要植树,那么:株数段数 1全长株距 1 全长株距(株数 1)株距全长(株数 1)精品w o r d 可编辑资料-第 7 页，共 9 页-文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N82 封闭线路上的植树问题的数量关系如下株数段数全长株距全长株距株数株距全长株数盈亏问题(盈亏)两次分配量之差参加分配的份数(大盈小盈)两次分配量之差参加分配的份数(大亏小亏)两次分配量之差参加分配的份数相遇问题相遇路程速度和相遇时间相遇时间相遇路程速度和速度和相遇路程相遇时间追及问题追及距离速度差追及时间追及时间追及距离速度差速度差追及距离追及时间流水问题顺流速度静水速度水流速度逆流速度静水速度水流速度静水速度(顺流速度逆流速度)2 水流速度(顺流速度逆流速度)2 浓度问题溶质的重量溶剂的重量溶液的重量溶质的重量溶液的重量100%浓度溶液的重量浓度溶质的重量精品w o r d 可编辑资料-第 8 页，共 9 页-文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J2N7A9C4 ZC10V7D8B1N8文档编码:CM10F8F9I3R6 HQ2J