2007 postgraduate entrance exam mathematics I Easy Pass series

Author: Huang Qinghuai
Publisher:
Publish Date: 2006-03-01
Features: Today, with the massification of higher education, the trend of postgraduate entrance exams has gradually formed. It is well-known that the difficulty of postgraduate entrance exams lies in mathematics, which serves as a threshold. The mathematics questions in the postgraduate entrance exam are appropriately scaled, with a distribution of 7:3 between subjective and objective questions. Subjective questions include computational problems, proof problems, comprehensive problems, and applied problems, while objective questions are fill-in-the-blank questions and multiple-choice questions. Over the years, the questions have primarily focused on testing basic concepts, methods, and principles of mathematics, while also emphasizing students' ability to abstract and generalize, logical thinking, spatial imagination, and comprehensive application of knowledge to analyze and solve problems. Fill-in-the-blank questions are mainly used to test the "three basics" and important properties of mathematics, with medium-difficulty questions as the majority. Multiple-choice questions mainly assess candidates' understanding of mathematical concepts and properties, as well as their ability to make simple deductions, judgments, and comparisons. Comprehensive questions test the organic integration of knowledge points, while applied questions are generally combined with relevant background knowledge common to candidates' majors. This approach not only benefits the selection of high-level talents by the state but also promotes the improvement of teaching quality in various mathematics courses in higher education institutions.
This series of books consists of four volumes, and this volume is Postgraduate Entrance Exam Mathematics:·Mathematics I. Based on the latest examination syllabus announced by the Ministry of Education, the series is closely aligned with the syllabus, emphasizing problem-solving methods and techniques. It is meticulously compiled by experienced professors from renowned universities and high-scoring candidates, drawing on years of research on postgraduate entrance exam questions.
Postgraduate Entrance Exam Mathematics:·Mathematics I includes 12 sets of national postgraduate entrance exam questions from 1995 to 2006. These questions embody the collective wisdom of the experts and professors who participated in the question-setting process over the past 12 years, making them a valuable resource. They not only reflect the testing requirements of the Mathematics Examination Syllabus for candidates' mathematical knowledge and abilities but also fully demonstrate the basic guiding principles and philosophies of the question-setters. Moreover, they comprehensively showcase the structure and characteristics of the exam papers, enabling candidates to gain an early understanding of the "trends" of postgraduate entrance exam mathematics questions and formulate their study plans accordingly.
In terms of structure and question arrangement, this book incorporates the opinions of experts and professors from various universities and has been refined based on feedback from high-scoring candidates. The arrangement is as follows:
1. In the Part, we have compiled all the mathematics I questions from 1995 to 2006. The questions are arranged in reverse chronological order (2006–1995) to allow candidates to quickly grasp the structure, question types, difficulty levels, and point distribution of recent years' postgraduate entrance exam mathematics questions. This arrangement is designed to help candidates understand the latest trends of postgraduate entrance exam mathematics in the shortest time.
2. In the Part, we have scientifically organized all the mathematics I questions from 1995 to 2006 based on the testing requirements of the Mathematics Examination Syllabus (Mathematics I), categorizing them by subject and knowledge points. This ensures that the content is closely aligned with the syllabus while highlighting problem-solving techniques. It also clarifies the hierarchy of knowledge points and enables candidates to integrate and apply them flexibly. In the analysis, detailed solutions, and annotations, we group similar or related knowledge points together for explanation. This approach facilitates comparative analysis for candidates and provides an important insight: candidates will notice that similar or related knowledge points are often revisited in questions set years apart, as well as the changes in tested knowledge points and question types, thereby deepening their understanding of the fundamental patterns of question-setting.
For each question in this part, we provide answers, analysis, detailed solutions, and annotations. The answers section helps verify the correctness of candidates' responses; the analysis section offers hints, primarily focusing on problem-solving strategies, to guide candidates in quickly recalling relevant knowledge and finding solutions, thereby strengthening their mathematical thinking skills and problem-solving abilities. The detailed solutions section provides a step-by-step explanation of the problem-solving process, enabling candidates not only to solve the question correctly but also to refine their writing process and achieve practical results in daily practice. The annotations section expands on the knowledge points based on the question, guiding candidates to apply their knowledge to different scenarios and achieve a deeper understanding.
To complement the use of this book, we recommend the following:
(1) Focus on foundational knowledge. The difficulty of postgraduate entrance exam mathematics questions has remained relatively stable (though the computational load is high), with about 70% of questions being basic and the remaining 30% slightly more challenging. This requires candidates to master the basics thoroughly, but simply reviewing undergraduate textbooks is insufficient, as postgraduate questions have their own style and question-setting approaches, necessitating targeted guidance from instructors.
(2) Focus on problem-solving methods and techniques. Since the overall approach of postgraduate exam questions is to assess the mastery and application of mathematical knowledge, the computational load is substantial. For the same question, different methods can lead to varying time commitments.
(3) Focus on answer presentation. During practice, candidates should solve problems according to the postgraduate grading standards, ensuring that even if a question cannot be fully solved, key scoring points are clearly outlined.
(4) Focus on time management. In past exams, many students failed to complete all questions. In fact, some of the unanswered questions were quite simple, and some candidates didn't even get a chance to see them. This underscores the need for candidates to avoid getting stuck on difficult questions during practice and to manage their time effectively, prioritizing overall progress rather than spending excessive time on a single problem. After three hours, they can revisit the unfinished questions.