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本文通过对两道高中数学常见习题的解题分析,强调了一题多解的学习价值——联系各种数学学科知识、提高数学思维水平.习题1是“给式asinx+bcosx=m求角x”问题,运用了五个通解,所用知识包括三角函数的辅助角公式、同角三角函数的“平方关系”与“商数关系”、直线与圆的方程等;习题2是以物理中反射现象为载体求解直线方程斜率的问题,运用了三个解法,所用知识包括相似三角形及相似比、直线的倾斜角与斜率的关系、点关于直线对称等.本文知识简单易懂,希望可以给各位学生提供一个回顾知识与反思学习的机会.
This article analyzes the common problems of two high school mathematics, emphasizes the learning value of one problem and multiple solutions - to contact various mathematics disciplines and improve the level of mathematical thinking.Experiment 1 is to give “asinx + bcosx = m Angle x ”problem, the five general solutions are used. The knowledge used includes the auxiliary angle formula of trigonometric function, the relationship between “ square ”and " quotient of the same angle trigonometric function, the equation of line and circle, etc .; 2 is the problem of solving the slope of a straight line equation by using the reflection phenomenon in physics as a carrier, and three solutions are used, and the knowledge used includes similar triangles and similar ratios, the relationship between the slope angle and the slope of a straight line, point symmetry and the like. Understand, hope to give students a chance to review knowledge and reflect on learning.