Principles and application of the special value method in Gaokao mathematics multiple-choice questions
高考数学选择题中“特殊值法”的原理与应用

摘要

本文针对高中数学选择题中的“特殊值法”进行系统分析，探讨其背后的数学原理与应用策略。文中指出特殊值法并不是没有理论支撑的应试技巧，而是基于特殊值法应用中所蕴含的三大原理：排他性、特殊与一般的逻辑关系、数学对象的内在属性。文中提出三类特殊值的选取策略，通过高考真题来具体剖析策略的运用，并说明该方法在简化问题、提高解题效率方面的实践价值。同时，文章也强调特殊值法的应用边界，提醒需避免常见陷阱，合理搭配排除法使用，从而在提升解题能力的同时，培养学生的数学思维与创新意识。

Abstract

This paper presents a systematic analysis of the “special value method” as applied to multiple-choice questions in high school mathematics, exploring its underlying mathematical principles and application strategies. It argues that this method is not merely an exam-oriented technique without theoretical foundation, but is grounded in three core principles: exclusivity, the logical relationship between the specific and the general, and the intrinsic properties of mathematical objects. Three categories of selection strategies for special values are proposed, and their practical application is illustrated through representative Gaokao questions, demonstrating the method's effectiveness in simplifying problems and improving solving efficiency. Furthermore, the paper highlights the boundaries of this method, cautioning against common pitfalls and emphasizing its effective combination with the elimination method. Ultimately, it aims to enhance students' problem-solving skills while fostering their mathematical thinking and innovative awareness.