The end-of-course exams are designed to set a minimum graduation standard for the state so that students leave high school with basic skills.
They are not intended to ensure that students are ready for college work.
Of the state's 24 school districts, the largest four districts with the highest urban populations have the majority of students who must still pass.
About 76 percent of the students who have not met the requirement attend public schools in Montgomery, Prince George's and Baltimore counties as well as Baltimore City.
Elsewhere the average is about 10 seniors per school. The number is no greater than 25 at 139 of the roughly 200 high schools across the state.
State schools Superintendent Nancy S. Grasmick, who had said consistently that there would be no students who would not graduate because they cannot pass the assessments, moderated her position. She told the board Tuesday that she believed there would be a small number of students who would fail to graduate because they were not willing to put in the work needed to do the projects or to study for the tests.
She also said there would be students, particularly some immigrants who are learning English as a second language, who would probably need a waiver because they were not taught the material to pass the exams until their senior year. The state regulations require that students be given an opportunity to get extra help if they cannot pass a test, and those students would not have time to receive that assistance.
Most students take the exams for the first time as eighth-, ninth- and 10th-graders after they have taken the course for a year. But a few school systems have failed to offer biology or American government until students were juniors or seniors.
State board members had grown increasingly frustrated with receiving estimates but no precise numbers of how many students had failed to meet the requirement. The board requested that the staff call each high school in the state.
Members of the board were given a school-by-school report, but it will not be made public until later this week.
Wilson also said the state will introduce a new test in May that does not require students to do any writing, which takes longer to grade. That will allow students to get the results within two weeks rather than months. The state also plans to introduce an online test.