The high schools in Shanghai eligible to take the exam are typically those recognized for their academic excellence and rigorous curriculum. These institutions are often affiliated with the Shanghai Municipal Education Commission and are known for their strong performance in national and international assessments. Notable schools include Fudan University High School, Shanghai Jiao Tong University High School, and Wuxi No. 1 High School, which are consistently ranked among the top in China.

The eligibility of these schools is based on several factors. Firstly, they must meet the academic standards set by the Shanghai Municipal Education Commission. This includes having a strong track record of student achievement, particularly in standardized tests such as the Gaokao (China's national college entrance examination). According to the Shanghai Education Bureau's data, schools with a graduation rate of over 90% and a Gaokao average score of above 600 points are generally considered eligible.

Secondly, the schools must demonstrate a commitment to fostering a well-rounded education. This is reflected in their extracurricular activities, international exchange programs, and emphasis on character development. For instance, Fudan University High School has been recognized for its comprehensive curriculum and its focus on nurturing students' creativity and critical thinking skills. The school's academic achievements are further supported by its partnership with prestigious universities, which provides students with access to advanced courses and research opportunities.

Additionally, the eligibility of these schools is influenced by their reputation and historical significance. Shanghai Jiao Tong University High School, for example, has a long-standing tradition of excellence in education, having been established in 1865. Its rich history and academic achievements have made it a leading institution in Shanghai and China as a whole.

Data from the Shanghai Education Bureau indicates that the top-performing high schools in Shanghai have a higher chance of being eligible for the exam. In 2020, for instance, the average Gaokao score of students from the top 10 high schools in Shanghai was 643 points, significantly higher than the national average of 531 points. This highlights the rigorous academic environment and high standards of education in these institutions.

In conclusion, the high schools in Shanghai eligible to take the exam are those that meet stringent academic criteria, demonstrate a commitment to comprehensive education, and have a strong reputation. Fudan University High School, Shanghai Jiao Tong University High School, and Wuxi No. 1 High School are prime examples of such institutions, consistently ranked among the best in China.