Analysis of the latest past exam question types for the postgraduate entrance exam mathematics I

Author: Huang Xiankai Cao Xianbing
Publisher:
Publish Date: 2006-06-01
Features: Since the implementation of the unified national entrance examination for postgraduate students in engineering and economics in 1987, it has been 20 years to date, with nearly 100 sets of question papers and over 1,000 questions developed. These questions are the crystallization of the wisdom and labor of the numerous experts and professors who participated in the question-setting process. They not only reflect the requirements of the Mathematics Examination Syllabus for candidates' mathematical knowledge, abilities, and proficiency but also present a comprehensive overview of the mathematics examination since its inception. Moreover, they embody the guiding principles, guidelines, characteristics, and trends of the question-setting experts under the framework of the Mathematics Examination Syllabus, serving as a direct and invaluable reference for candidates and teachers to understand question information, analyze question-setting dynamics, and summarize question-setting patterns.
"Know yourself and know your enemy, and you will never be in danger in a hundred battles." Owning a complete, well-organized, thoroughly analyzed, and standardized collection of past mathematics examination papers is the aspiration of countless candidates preparing for the postgraduate entrance examination. By carefully analyzing and studying past questions, one can identify the characteristics and trends of question-setting, uncover the organic connections between knowledge domains, summarize the key and challenging aspects of each section, and distill problem-solving strategies, methods, and techniques. A thorough understanding and mastery of past questions will not only clarify the direction and focus of revision but also enable candidates to study more effectively and lay a solid foundation for success in the examination.
This book is a completely new compilation based on over a decade of collecting, organizing materials, and providing postgraduate mathematics tutoring. Through meticulous analysis and research of past questions, combined with teaching experiences and students' needs, the authors have crafted this book, confident that it meets everyone's expectations. The book features the following:
1. Comprehensive Coverage: Its all question papers from the past 20 years of the unified examination, enabling candidates to systematically grasp the dynamic changes in past questions. Additionally, typical questions from the other three types of papers are provided as exercises at the end of each chapter (e.g., for each chapter in Mathematics I, selected questions of the same type from Mathematics II, III, and IV are included), allowing candidates to further consolidate their knowledge. With this book, candidates effectively gain access to materials from all four types of papers.
2. Concise Typing: While the number of questions is infinite, the types of questions are finite. The authors have condensed all past questions into approximately 100 typical types, covering all the content required by the Mathematics Examination Syllabus for the four types of papers, thereby saving candidates valuable study time.
3. Rich Typing: According to the requirements of the Mathematics Examination Syllabus, each chapter is categorized by question type, with analysis, summary, and synthesis provided for each type. This allows candidates to study question types systematically, grasp the characteristics and logic of question-setting, and achieve the ability to generalize and apply knowledge.
4. Detailed Explanations: First, the authors analyze the thinking process and methods of solving the problem, then provide detailed and standardized solutions, followed by annotations summarizing the problem-solving strategies, techniques, key knowledge points, question-setting intentions, and potential extensions. By offering such in-depth and meticulous explanations of question-setting logic, problem-solving key points, and difficulties, the book is expected to help candidates grasp problem-solving patterns, expand analytical thinking, and refine response techniques, thereby significantly improving their exam performance.
5. Direct Comparison: At the beginning of each section, the book lists the content and requirements stipulated by the Mathematics Examination Syllabus, followed by question categorization and analysis, all in the same order as the syllabus and general textbooks, facilitating candidates' comparative study.
6. Complete Summaries: In addition to summarizing each question type, each chapter also provides a summary of the distribution and scores of past examination questions by question type, helping candidates understand the frequency and proportion of each type of question, thereby identifying key and frequently tested question types for more targeted revision.
The book is organized by chapter according to the content of the examination but also provides complete sets of question papers. For early-stage review, candidates are advised to study in synchronization with the textbook and revision guides. In later stages, the book can be used as simulated training material. Although each question is thoroughly explained, readers are encouraged not to immediately consult the analysis, solutions, and annotations but to attempt solving the problems independently first. After completing each question, candidates should review and study their own analysis, thinking process, and solutions, comparing them with those in the book. If discrepancies exist, candidates should strive to identify the causes—whether they lack fundamental theories, concepts, or methods, or whether they need to improve in problem-solving techniques and the comprehensive and flexible application of knowledge.
Note that this process of summarization and reflection is essential and even more important than solving problems themselves. By reviewing the entire book in this manner, readers are expected to achieve a significant improvement in their grasp of fundamental theories, concepts, and methods, as well as in their ability to comprehensively and flexibly apply knowledge and train their thinking skills.
On one hand, this book retains the strengths of our previous analyses of past examination questions. On the other hand, during this revision process, we referred to numerous relevant textbooks and revision guides, though we cannot list them all here. We sincerely thank all the authors of these related works for their contributions.