First (2003) Primary School Hope Cup National Mathematics Invitational Contest Question Training and Solutions

Author: Zhou Guozhen
Publisher:
Publish Date: 2004-01-01
Features: The "Hope Cup" National Mathematics Invitational has been held annually since 1990 and has now continued for 14 consecutive sessions. The number of participating students has increased year by year, reaching a cumulative total of 11 million. Due to its closely aligned with secondary school mathematics teaching, drawing from textbooks yet exceeding them, all questions are designed to be novel, engaging yet not overly difficult, clever yet not biased, and neither strange nor overly specialized. They are both accessible to a broad audience while maintaining a considerable level of difficulty, effectively combining scientific rigor, knowledge, inspiration, and fun. This has made the invitational widely popular among secondary school students, teachers, and parents.
An increasing number of mathematicians and mathematics educators have enthusiastically praised and supported the invitational, believing it greatly benefits the development of mathematics education in China. The former Ministry of Education fully affirmed the invitational's purpose and direction and provided specific guidance for its operations starting from the third session. In November 1994, the former Ministry of Education officially approved the "Hope Cup" National Mathematics Invitational as the only nationwide competition for primary and secondary school students in grades 1-2 in China.
To make the "Hope Cup" more deeply rooted among the public and 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 conducted repeated research and discussions. They decided that the 14th session of the "Hope Cup" National Mathematics Invitational (2003) would break from tradition by publishing separate volumes for primary and secondary schools. This approach enables readers to choose more targeted materials, making it easier for them to purchase books based on their actual foundation and age group, while also reducing their financial burden.
Against this backdrop, many knowledgeable individuals in the field of domestic and international mathematics education have repeatedly proposed adding a primary school division to the "Hope Cup" Invitational, transforming it into a series of mathematics competitions encompassing primary, secondary, and high school levels. Building on the successful 13th session of the secondary school "Hope Cup" National Mathematics Competition, after more than a year of effort, the th primary school "Hope Cup" Mathematics 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 session, 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" Mathematics 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 information and attempt the questions themselves—thus sparking their hope for success—we have specifically compiled the book "th (2003) Primary School 'Hope Cup' National Mathematics Invitational Test and Training Materials" for use by primary school teachers and students.
As of this year, the "Hope Cup" National Mathematics Invitational has included all stages of basic education, from primary to high school. All questions in the "Hope Cup" are created by experts from the "Hope Cup" Question-setting Committee, who include professors from prestigious universities, researchers from the Chinese Academy of Sciences, mathematics specialty teachers, and senior coaches for the Mathematical Olympiad. They represent the highest level of expertise in China's mathematics competition field. Before each competition, they meticulously develop training materials for systematic preparation and official test papers (first, second, and third tests) for each grade level. After 14 years of accumulation, the "Hope Cup" question bank now possesses nearly 2,000 distinctive and excellent questions, a valuable asset of the organizing committee.
With the growing scale and depth of the "Hope Cup" competition, teachers and students from various regions, as well as those interested in the event, have long called for the organizing committee to compile a authoritative training textbook for nationwide participants. They have eagerly awaited this. After extensive deliberation and careful planning, the organizing committee finally completed the writing of this textbook before the 15th session of the "Hope Cup."
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 encourages students to master textbook knowledge while appropriately broadening their horizons, sparking interest and enthusiasm in mathematics, and cultivating scientific innovation, thinking, and practical abilities.
This series is edited by Zhou Guozhen, Director of the "Hope Cup" National Mathematics Invitational Organizing Committee. The questions selected and compiled 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.