The 14th (2003) Hope Cup National Mathematical Invitational Competition High School Question Training and Solutions

Author: Zhou Guozhen
Publisher:
Publish Date: 2004-01-01
Features: The "Hope Cup" National Mathematical Invitational has been held annually since 1990 and has now continued for 14 consecutive editions. The number of participating students has increased year by year, with a cumulative total of 11 million participants. Due to the competition's questions being closely tied to secondary school mathematics teaching, drawing from textbooks yet exceeding them, all problems are designed to be novel, engaging yet not overly difficult, clever yet not biased, and neither strange nor overly complex. They are both accessible to a broad audience while maintaining a certain level of difficulty, effectively combining scientific rigor, knowledge, inspiration, and fun. As a result, the competition has been widely welcomed by secondary school students, teachers, and parents.
An increasing number of mathematicians and mathematics educators have expressed enthusiastic praise and attention toward the invitational, believing it greatly benefits the development of mathematics education in China. The former Ministry of Education fully affirmed the purpose and direction of the invitational and provided specific guidance for its operations starting from the third edition. In November 1994, the former Ministry of Education officially approved the "Hope Cup" National Mathematical Invitational as the only national-level competition for primary and secondary school students in grades 1 and 2 in China.
To make the "Hope Cup" competition more deeply rooted among the public and to allow readers to achieve the greatest return with the smallest investment, the editorial team of the Great Encyclopedia and the experts of the organizing committee repeatedly studied and discussed, ultimately deciding that the 14th edition of the "Hope Cup" National Mathematical Invitational, along with its training materials and solutions, would be published in two separate volumes for primary and secondary schools this year (2003). This approach allows readers to choose more targetedly, making it easier for them to purchase books based on their actual foundation and age group, while also reducing their financial burden, enabling them to buy the most suitable books for their needs at a minimal cost.
Against this backdrop, many knowledgeable figures in the field of domestic and international mathematics education have repeatedly proposed adding a primary school division to the "Hope Cup" Mathematical Invitational, transforming it into a series of mathematical competitions encompassing primary, secondary, and high school levels. Building on the successful 13th edition of the secondary school "Hope Cup" National Competition, after more than a year of effort, the th primary school "Hope Cup" Mathematical Invitational was finally held in Beijing in the spring of 2003. A total of 230,000 students from 58 cities, including Beijing, Shanghai, Chongqing, Guangzhou, Shenzhen, Harbin, Taiyuan, Xi'an, Lanzhou, Guiyang, Guilin, and Urumqi, participated in this edition, with over 12,000 students winning awards, including 101 gold medals and 616 silver medals.
To summarize the activities of this year's first primary school "Hope Cup" Mathematical Invitational and leave a true record, to spread the news of the invitational across the country, and to allow countless students who had no opportunity or time to participate to access the competition's information and attempt the questions themselves, thereby sparking their hope for success, we have specifically compiled and published the book "th (2003) Primary School 'Hope Cup' National Mathematical Invitational Test Training and Solutions" for the use of primary school teachers and students.
To date, the "Hope Cup" National Mathematical Invitational has included all stages of basic education, from primary to secondary school. All questions in the "Hope Cup" are created by experts from the "Hope Cup" Question-setting Committee, who include mathematics professors from prestigious universities, researchers from the Chinese Academy of Sciences, mathematics distinguished teachers, and senior coaches for the Mathematical Olympiad, representing the highest level in China's mathematics competition field. Before each competition, they meticulously draft training materials for systematic training of participants and official test papers for the first and second rounds. After 14 years of accumulation, the "Hope Cup" question bank now holds nearly 2,000 unique and outstanding questions, a valuable asset of the "Hope Cup" competition organizing committee.
As the "Hope Cup" competition expands and deepens, teachers and students from all over the country, as well as those interested in the competition, have increasingly demanded that the "Hope Cup" organizing committee compile a authoritative training textbook for national participants. They have eagerly awaited this for a long time. After extensive deliberation and meticulous planning, the organizing committee finally completed the writing of this textbook before the 15th "Hope Cup" competition.
Guided by the newly issued secondary school education curriculum, this textbook strives to fully reflect the characteristics of the "Hope Cup," providing teachers and students with systematic, comprehensive, and practical mathematical content, ideas, and methods. It aims to encourage students to study their textbooks diligently, appropriately broaden their knowledge, inspire interest and enthusiasm for mathematics, and cultivate scientific innovation, thinking, and practical abilities. This series of books is edited by Zhou Guozhen, Director of the "Hope Cup" National Mathematical Invitational Organizing Committee. The questions selected and compiled by him are novel in type and cleverly designed, taking into account the comprehensive knowledge students have acquired while requiring flexible application of various concepts. Each question is a gem among questions of the same difficulty level.
Additionally, the editorial team meticulously reviewed every word during editing, carefully designed the layout, and performed extreme diligence in proofreading. The cover design of the entire series is fresh, elegant, and unconventional, with excellent printing quality. All these features make this series a true masterpiece.