188宝金博页面版

1《初中数学竞赛中的解题方法与策略》讲义目 录第一部分 代数篇........................................................................................................................................... 31.1 巧用平方差公式...............................................................................................................................31.2 恰当换元...........................................................................................................................................61.3 利用判别式解题.............................................................................................................................101.4 试试韦达定理.................................................................................................................................141.5 主元素方法.....................................................................................................................................171.6 利用对称性处理.............................................................................................................................201.7 恰当放缩.........................................................................................................................................23第二部分 几何篇......................................................................................................................................... 272.1 面积公式及其应用.........................................................................................................................272.2 平移、旋转与翻折.........................................................................................................................332.3 构造相似.........................................................................................................................................392.4 利用圆的性质.................................................................................................................................462.5 利用代数方法处理几何问题.........................................................................................................53第三部分 数论篇......................................................................................................................................... 613.1 奇偶分析.........................................................................................................................................613.2 素因数分析.....................................................................................................................................643.3 选择合适的模.................................................................................................................................673.4 作出适当的估计.............................................................................................................................69第四部分 组合篇......................................................................................................................................... 744.1 抽屉原理.........................................................................................................................................744.2 染色或赋值.....................................................................................................................................774.3 分类与枚举.....................................................................................................................................814.4 递推和归纳.....................................................................................................................................844.5 极端原理.........................................................................................................................................884.6 从局部到整体.................................................................................................................................914.7 将命题一般化或特殊化.................................................................................................................944.8 先猜后证.........................................................................................................................................97习题解答........................................................................................................................................................101