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2000年全国高考数学文、理两科的最后一道试题全面考查了解析几何中双曲线的概念和性质、定比分点坐标公式等基础知识,坐标法、参数法、消去法等基本方法,等式与不等式的变换等基本技能,全面考查了逻辑思维能力,运算能力,对图形的识别和处理的能力,将创新性、应用性、综合性适度结合,充分体现了解析几何的学科特点,具有一定的难度和较好的区分度,对今后中学数学教学及高考数学总复习有较好的导向作用.1.应用坐标法。建立坐标系,设定相关点坐标本题给出了两个已知的几何条件:在梯形 ABCD中|AB|=2|CD|;分有向线段(?)为定比λ的分点 E 与
In 2000, the final test questions of the two major subjects of mathematics and science in the National College Entrance Examination examined the concepts and properties of the hyperbola in analytic geometry, and the basic knowledge of the fixed point coordinate formula, coordinate methods, parameter methods, elimination methods, and other basic methods. Basic skills such as transformation of inequalities, comprehensive examination of logical thinking ability, computational ability, ability of recognition and processing of graphics, appropriate combination of innovation, applicability, and comprehensiveness fully embody the characteristics of analytical geometry and have certain characteristics. The degree of difficulty and the better distinction between the secondary school mathematics teaching and college entrance examination mathematics review has a better guiding role. 1. Apply coordinate method. Set up the coordinate system and set the coordinates of the relevant point. This question gives two known geometric conditions: in the trapezoidal ABCD |AB|=2|CD|; the directed line segment (?) is the division point of the constant ratio λ E