Review of Graduate Entrance Exam Mathematics for Science and Engineering

Author: Cai Zihua
Publisher:
Publishing Date: 2005-03-01
Features: Students often ask in postgraduate entrance exam review classes, "Why are the mathematics test papers for the national unified postgraduate entrance exam so difficult?" From the results, it indeed appears so.
From 1997 to 2003, over seven years, the average scores of four categories of 28 exam papers (with a total score of 100) showed that 7 papers had an average score of 45 or below, 11 papers had an average score between 45 and 50 (inclusive), and only 9 papers had an average score above 50. This means that 69% of the papers had low scores, especially one paper with an average score of 37.2 (the 1998 and 2001 papers for Category 1). On the surface, the papers are indeed too difficult. However, an in-depth analysis reveals that, aside from a few sections that are genuinely challenging, the low score rates are also due to the following reasons:
1. Candidates' weak grasp of concepts, with a superficial understanding of basic concepts and theories (some candidates even unaware of the content specified in the exam syllabus). In light of this, as a teacher with years of experience in postgraduate mathematics tutoring and grading, I feel it necessary to incorporate my insights and experiences into my writings to guide candidates in adopting correct study methods, focusing on the "three basics," and ultimately achieving success in the exam. The features of this book are as follows:
1. Completely aligned with the requirements of the National Postgraduate Entrance Exam Mathematics Syllabus, without any content beyond the syllabus.
2. The content summary briefly explains the concepts of the exam and the key points to note when understanding them, eliminating knowledge blind spots and solidifying the mastery of various knowledge points, ensuring candidates can fully comprehend their intrinsic connections and integrate them seamlessly.
3. Emphasizes key areas, highlighting recent years' exam focuses, guiding candidates into the "Solved Examples Analysis" with these knowledge points. In the solved examples analysis, various basic problem-solving methods are summarized and organized systematically. For more challenging problems, there is an analysis before and a summary after, enabling candidates to deeply understand concepts and overcome difficulties through the guidance of examples. For important problem types, the book systematically categorizes them and provides unique solutions, facilitating candidates' ability to generalize and fully master them.
4. Addressing the current issue where candidates struggle to apply mathematical knowledge in practice, the book includes numerous applied problems to guide candidates in mastering the basic methods of establishing mathematical models and improving their ability to solve real-world problems.
5. The selected examples in this book are highly representative, with difficulty levels comparable to past exam papers, striving to avoid biased or obscure questions.
6. Each chapter includes a large number of practice questions, with answers provided at the end of the book (with detailed solutions or hints for more challenging questions), allowing candidates to verify the correctness of their answers.
7. To bridge the connections between knowledge in different disciplines, the fourth part of the book provides comprehensive problem-solving examples, guiding candidates in applying mathematical knowledge to solve integrated problems.
Since the mathematics exam subjects were adjusted in 2003, the impact of the mathematics subject score on the total score has once again been demonstrated and emphasized. This is partly due to the nature of the mathematics subject itself, and partly because mathematical education is fundamentally a form of quality-oriented education, which aligns with the selection nature of the postgraduate entrance exam. Candidates should first understand this point and prepare early, studying diligently, progressing step by step, maintaining a calm mindset, and avoiding.