A Study On The Inequality Of Mathematics In High School Mathematics Competition And College Entrance Examination

Sequence and inequality are the core content in high school mathematics textbooks, whose intersection has enjoyed a priority and high frequency in College Entrance Examination, In fact, sequence is a manifestation of the function, which is of great importance in mathematics and throughout high school mathematics teaching. As a special function, sequence possesses both the nature of function and the sequence, thus is frequently adopted in contests and the College Entrance Examination. Early in 1990, it was suggested that:"considering the widely application of inequality in real life, as well as its significant importance in both high school and advanced mathematics, inequality will be attached greater attention in the College Entrance Examination". Therefore, learning inequality is of vital necessity,In addition, the design of sequence inequality questions are mostly with creative ideas, diversified forms, strong comprehensiveness, and various challenges, requiring high demands for students’thinking capacity like skills in terms of exploring, observing, analyzing and inducting. Such tests can be categorized to the middle-difficult questions, becoming the highlights and hot spots in math contests and the college entrance exam. Hence, along with the gradual development of new curriculum standards, each teacher should think over the new curriculum ideas and its requirements, as well as stick to the demands of College Entrance Examination or higher standards.Based on the introduction to mathematical competitions and College Entrance Examination, this paper discussed the basic knowledge on sequence and inequality. Later, combining the author’s own study and practical experience, an interview outline on the nature and proving methods of sequence inequality were designed. The author summarized interview transcription and explored the common ways of proving sequence inequality in mathematical competitions and College Entrance Examination such as important inequality method, the nature of law, scaling law, mathematical induction, and the fundamental theorem of normalization method, classification discussion and analysis, equivalence relations and monotonicity of function. Finally, according to the research, the author put forward some suggestions on the sequence inequality teaching and learning for reference.