GREENVILLE, S.C. — A sign in a classroom here at Berea High School, northwest of downtown in the largest urban district in the state, sends this powerful message: “Failure Is Not an Option. You Will Pass. You Will Learn. You Will Succeed.”

By one measure, Berea, with more than 1,000 pupils, is helping more students succeed than ever: The graduation rate, below 65 percent just four years ago, has jumped to more than 80 percent.

But that does not necessarily mean that all of Berea’s graduates, many of whom come from poor families, are ready for college — or even for the working world. According to college entrance exams administered to every 11th grader in the state last spring, only one in 10 Berea students were ready for college-level work in reading, and about one in 14 were ready for entry-level college math. And on a separate test of skills needed to succeed in most jobs, little more than half of the students demonstrated that they could handle the math they would need.

It is a pattern repeated in other school districts across the state and country — urban, suburban and rural — where the number of students earning high school diplomas has risen to historic peaks, yet measures of academic readiness for college or jobs are much lower. This has led educators to question the real value of a high school diploma and whether graduation requirements are too easy.