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数学思想方法是数学知识的精髓,又是知识转化为能力的桥梁。重视对数学思想方法的考查,既是高考数学命题的一个宗旨,又是数学学科自身的需要。在大跨度试题面前灵活运用数学思想方法,就能统摄信息量、理清来龙去脉、找到突破口,机智转向、落笔有神。本文结合部分高考解析几何试题,简述几种数学思想方法的运用,供参考。一、数形结合思想数形结合思想是解析几何的基本思想,它是在深刻分析方程或已知条件中的几何性质之下,以形助数的方法,往往使问题简捷、清晰地得以解决。例1(96年全国高考题)已知圆 x~2+y~2-6~x-7=O 与抛物线 y~2=2px(P>0)的准线相切,则 p=______.简析与解:圆 x~2+y~2-6~x-7=0,即(x-3)~2+y~2=16,其圆心为 O_1(3,0),半径 R=4,画出如图1所示的图形.由题意得到抛物线的准线方程为 x=-1,显然p=2.简评:运用了数形结合思想,以形助数,解法简捷、
Mathematical thinking and methods are the essence of mathematics knowledge and the bridge from which knowledge is transformed into competence. Paying attention to the examination of mathematical thinking methods is not only a purpose of the college mathematics proposition, but also the needs of the mathematics discipline itself. By using mathematical thinking methods in front of the long-span test questions, we can capture the amount of information, sort out the context, find breakthroughs, and turn wit to make ends meet. This article combines some of the college entrance examination analytical geometry questions, briefly describes the use of several mathematical ideas and methods for reference. First, the combination of number and shape ideas The idea of number and shape is the basic idea of analytic geometry. It is based on the analysis of the geometric properties of equations or known conditions, and the method of forming numbers is often used to make the problem simple and clear. . Example 1 (96 national college entrance examination question) Known circle x~2+y~2-6~x-7=O is tangent to the parabola of parabola y~2=2px(P>0), then p=______. Brief analysis and solution: circle x~2+y~2-6~x-7=0, that is (x-3)~2+y~2=16, its center is O_1(3,0), radius R= 4. Draw a graph as shown in Figure 1. The equation for the parabola from the question meaning is x = -1, apparently p = 2. Brief comment: Using the idea of combination of numbers and shapes to help the number, the solution is simple,