Junior High School Mathematics Competition Champion School Exam Paper: Pre-competition Practical Simulation

Author: Compiled by the Mathematics Teaching and Research Group of Zhuji Hujiang Middle School
Publisher:
Publishing Date: 2005-03-01
Features: As is well known, the junior high school stage is very important in a person's life. If it goes well, getting into a key high school and going to university will not be a problem; otherwise, it will be a different life. Therefore, it receives great attention and concern from students, parents, and schools. During this stage, junior high school mathematics competitions play a very special role. The high-scoring questions and challenging problems in the college entrance examination cannot be separated from it. There is a saying that "winning the competition means winning the exam." Zhejiang is a major province in mathematics education, and Zhuji Hujiang Middle School is one of the top performers in junior high school mathematics in Zhejiang. In the process of exploring and discovering their effective methods, people found that their success was due to creating a unique training method called "rolling training." This method is closely related to their classroom teaching; it is closely related to their comprehensive training starting from the first grade; and it is closely related to the overall improvement of their entire teaching and research group. Introducing and promoting their training methods will benefit more teachers and students. The specific arrangement of "rolling training" is as follows: There are 12 thematic teaching contents each year, with one training paper for each theme, totaling 12 thematic training papers. Then, the rolling training begins sequentially: every three thematic contents roll over, divided into "Rolling Training A Paper" and "Rolling Training B Paper." The content of "Rolling Training A Paper" is deeper and more flexible than the thematic papers, while "Rolling Training B Paper" is even deeper and more flexible. After this in-depth and interconnected "rolling" of knowledge points, knowledge is consolidated, memory is strengthened, knowledge expansion is deepened, and techniques are integrated in the process, making progress both effortless and solid. Generally, we tend to think that mathematics competitions are about solving difficult problems. If you isolate and do the "Rolling Training B Paper" in isolation, you will feel overwhelmed by the difficulty, as it is full of challenging problems. This reminds me of the couplet on the "Lingquan Pavilion" between Hangzhou's Lingyin Temple and Feilai Peak: "Where does the wind come from, when does the water start to cool?" Interpreting the Buddhist mystery is not easy. If we ask ourselves in a similar way, "Where do the questions start to be difficult?" and "Where do the methods become flexible?" then the current rolling training series can provide you with the answers you seek. The principle is simple: the addition of a few simple questions can result in a very profound question, and the combination of a few single ideas can lead to a more ingenious idea. After understanding the meaning of "rolling," it is not difficult to understand the use of this book. When working on a specific theme, follow it with the corresponding "Rolling Training A Paper" and "Rolling Training B Paper." In this way, the 12 thematic training papers, along with the two sets of rolling training, total 36 papers. After a year of "rolling," 9 "pre-competition practical training papers" are arranged at the end to test your year's progress. The fourth volume of this series is a comprehensive training after completing the entire junior high school, which is the "pre-competition practical simulation training" for junior high school mathematics competitions. We hope that this "rolling training" series can help you achieve excellent results in mathematics competitions. Using an idiom from the field of physics: overcoming "sliding" is tiring, while overcoming "rolling" is the most effortless. The preliminary draft of this book was reviewed and modified by Professor Wang Zuyu, the former Director of Popularization Work of the Zhejiang Mathematical Society and the Hangzhou University of Electronic Science and Technology, and myself. Open University Press has given strong support to the publication of this book, carefully editing it, especially in terms of the psychological perspective of students independently completing the papers. The questions are arranged in front and back, and if you cut along the perforation, you get an independent paper. At the end of the book are all the answers, and you can check them directly without looking at the solution process. We strongly recommend that you review the reference solutions after independently completing the questions, as the ideas there may inspire you. Especially for the questions marked with ★, the solutions are considered typical, innovative, and satisfying by the authors. Of course, a satisfying work is not necessarily a perfect one. Some questions may have more ingenious solutions. We welcome everyone to point out any errors and suggest improvements during use to make the series more perfect.