This document presents the Secretary of Education's personal concept of a sound secondary school core curriculum. It is called "James Madison High School" in honor of President James Madison and his strong views that the people, in order to govern properly, must arm themselves with knowledge. The theoretical curriculum consists of four years of English, and three years each of social studies, mathematics, and science, two years each of foreign language and physical education, and a half-year each of art and music. A brief discussion is offered on the desirability of a curriculum that makes available a shared body of knowledge and skills, a common language of ideas, and a common moral and intellectual discipline. A chart describing the four-year plan of the program shows the number of years required for each core subject and the names of the courses that fulfill them. To demonstrate the flexibility of the program, sample schedules for three students pursuing different goals are outlined. Profiles of seven exemplary high school programs provide an insight into what is currently being accomplished with rigorous core curriculums. The profiled schools, each serving students of diverse backgrounds, are: (1) A. Philip Randolph Campus High School (New York); (2) CAL High School (Iowa); (3) James A. Garfield High School (California); (4) Shawnee Mission South High School (Kansas); (5) Portland High School (Maine); (6) Xavier Prep School (Louisiana); and (7) Wayland High School (Massachusetts). (JD)