Detailed Solutions to the Problems of the 1st to 15th "Hope Cup" National Mathematics Invitational Contest (Grade 8)

Author: Zhou Guozhen
Publisher:
Publish Date: 2005-07-01
Features: Each question in the book is like a step on a staircase. With confidence, diligence, and perseverance, one can climb step by step to forge their own path to success. The circular shape represents the vast sky. The English word "HOPE" resembles a bird with spread wings.
Meaning: The "Hope Cup" National Mathematics Invitation Contest has opened up a broad space for the healthy development of scientific thinking skills among young people, allowing them to soar freely. The "since 1990" inscription indicates that the "Hope Cup" National Mathematics Invitation Contest was established in 1990. Since its inception in 1990, the "Hope Cup" National Mathematics Invitation Contest has held 15 editions. The first edition had 110,000 middle school students participate, and from the 9th edition onwards, the number of participants each year exceeded one million. Over the past 15 editions, the cumulative number of participating middle school students has exceeded 12 million. Among domestic middle school subject competition activities, no other event has such a large scale or such a large number of participants, except for the "Hope Cup." This fully demonstrates the popularity of the "Hope Cup" among middle school students.
Why do middle school students enjoy participating in the "Hope Cup"? A very important reason is that the questions are well-designed and beautifully crafted, offering ample space for thinking. The "Hope Cup" question-setting committee consists of top domestic experts in mathematical competitions, who meticulously compile the questions for each edition. Additionally, over a thousand outstanding mathematics teachers, research personnel, and students across the country have contributed many self-composed questions. Through solving these problems, students learn from them and study them, thereby solidifying and broadening their knowledge, enhancing their wisdom and abilities, boosting their confidence in learning, and achieving outstanding results.
The "Hope Cup" is like a golden key—it not only opens the door to wisdom for each participating middle school student but also opens the door to confidence. This is the charm of the "Hope Cup." Mathematics teachers who teach in middle schools, just like their students, also love the "Hope Cup"—because the endless stream of problems emerging from this "cup" provides rare materials and valuable insights for improving their teaching and nurturing high-level students.