Here is the thorny math problem facing New York State education officials: If the percentage of students passing the Algebra I exam falls to 63 percent from 72 percent, and the passing grade is scheduled to increase by 9 points in coming years, should the test be made easier?

In 2013, concerned that high school graduates were not prepared for college, the State Board of Regents revamped the exams students must pass to graduate, starting with the English and Algebra I tests. The board decided that, where previously students needed a score of only 65 on a 100-point scale to pass, in coming years they would have to score at a “college- and career-ready” level, which this year was deemed to be a 79 in English, and a 74 in Algebra.

The result: On the 2015 Algebra I exam, which was supposed to align with the new Common Core curriculum, the percentage of students passing fell to 63 percent, down nine points from the old exam last year. And less than a quarter of students scored at the college-ready level. In New York City, which has a concentration of poor and minority students, only 52 percent of students passed the 2015 exam, down from 65 percent the previous year on the old exam. Just 16 percent reached the “college-ready” level.

Confronted with the consequences of higher standards, the Regents, like education officials across the country, are now rethinking them.