Challenging the Mathematical Finale of Senior High School Entrance Examination is a book published by East China Normal University Press in 2009 by Ma Xuebin, Shu Yaoli and Peng Yucheng. The book is divided into four parts, and the final collected questions are selected from the mathematical simulation questions of the senior high school entrance examination in Shanghai in 2009 and the senior high school entrance examination questions of some provinces and cities in China in 2008 and 2009.
This book is divided into four parts. The first part is the existence of points in function images. The main feature of this part of the finale problem is to find the analytical formula of the function first, and then explore the qualified points in the function image.
The second part is the functional relationship in graphic movement. The main feature of this part is to explore the functional relationship between two variables in the process of graphic movement change, and to explore the definition domain of the function according to the actual situation, and then to explore the particularity of meeting the conditions in general. Exploring the particularity of eligibility is usually closely related to the idea of classified discussion.
The third part is the calculation and reasoning in graphic motion. The main feature of this part of the finale is to give a figure to study first, then study whether the conclusion changes after the position of the figure changes, and then prove it. The key to solve this part of the finale problem is to master the data characteristics and invariant relations in the process of graphic movement and reasoning through calculation.
The fourth part is the translation, folding and rotation of graphics. The main feature of this sub-project is to find constants, grasp laws and explore relationships in the translation, folding and rotation of graphics.
Other topics:
Another main feature is to combine the symmetry of graphics with the idea of classified discussion, that is, as the saying goes, there are many solutions to one problem. Such questions are generally arranged in the last two questions of the fill-in-the-blank questions or multiple-choice questions in the senior high school entrance examination papers, as the basic part of multiple-choice questions.