The students, members of the first class that must pass the science exam in order to receive a diploma, will have at least two more chances to take the test before school officials face the difficult prospect of barring them from the graduation stage.

Those who do not pass by graduation day would probably have to delay any college plans and return to high school for more science instruction, then take the test again the following February. Or they could instead try to earn a General Educational Development credential, which involves passing multiple tests.

The seniors’ plight surfaced yesterday as state education officials announced the results of the spring’s MCAS exams, which showed progress at most grade levels in most subjects, but a lingering disparity between students from different socioeconomic and racial backgrounds.

Although state education officials expressed concern about the failure rate in science, they emphasized that the prob lem is not nearly as widespread as earlier this decade when passing the English and math MCAS exams first became a graduation requirement, starting with the class of 2003. When those students entered their senior year, 19 percent of them still had not passed one or both of the tests.

This year, 10 percent of seniors have not yet passed all three test subjects, with failure on the science exam representing by far the largest chunk.

“I’m always concerned if students are not being successful,’’ Mitchell Chester, the state’s commissioner of elementary and secondary education, said in an interview. “But I do think holding onto this requirement [passing the science exam] is the right thing to do. It’s important to prepare students for opportunities after high school.’’

Since last fall, as members of the class of 2010 have retaken the exams and passed, they have cut their failure rate in half, from 20 percent.

Chester said the state is working with individual high schools to help students pass the exam this year, but officials also are preparing for an onslaught of requests from high schools to exempt students from the testing requirement.

Last year, the state Board of Elementary and Secondary Education eased rules for bypassing the science test requirement, in recognition that students often show an understanding of the subject through experiments. As long as students have strong grades in a comparable science course, schools can appeal after the student fails the exam just once, instead of after three failures as is required for English and math appeals.

The department received 319 appeals last year for the class of 2010, representing just a small fraction of those who failed, and approved all but two requests. The small number of appeals suggests students who struggle with the exam might also be experiencing difficulty in science courses. Students have the option of taking the science test in either biology, chemistry, physics, or engineering/technology.

Seven years ago, the prospect of more than 10,000 high school seniors not graduating because of MCAS failure led to several revolts, including an unsuccessful lawsuit on behalf of some students and threats from a handful of school committees that they would award diplomas against the state’s wishes.

By year’s end, however, the number who didn’t pass the exam had dwindled to 4,200, and those students had an opportunity to retake the exam in the summer - an opportunity that no longer exists.

So far, that level of anxiety appears to be largely absent this year, several educators and statewide education groups said, but that could change once individual students and their parents learn they are among the 6,000 who failed the science test.

“Obviously, the kids and parents will be upset and disappointed, and it’s understandable,’’ said Thomas Scott, executive director of the Massachusetts Association of School Superintendents, but at this point, he said, “Students have another shot at the test.’’

The state has scheduled retakes of the exam for February and June. Because the latter date will be too late for hopeful graduates, the state is planning to hold a make-up session in April or May, promising to quickly grade the exams so high schools can make calls on graduation.

In an effort to avoid denying students a diploma, high schools across the state have been overhauling science courses to include all the material that is covered on MCAS as well as creating remedial programs for students who fail the test.

Several school districts, including Boston, declined to comment on how many seniors were affected because of a state embargo on discussing school-by-school results until they are released later this month.

Marilyn Segal of Citizens for Public Schools, a grass-roots nonprofit that opposes the MCAS, said the science exam risks turning students off to the subject, short-circuiting the state’s goal of trying to grow a larger workforce in the areas of health care, high-tech, and bio-sciences.

“It’s the worst way to teach science,’’ she said. “Memorizing facts is not learning about science. It’s doing labs. The test was set up to fail a bunch of kids.’’

This year’s junior class had better luck on their first encounter with the science exam, with 91 percent passing so far - compared with just 83 percent for the class of 2010. Overall, 83 percent of the class has passed all three subjects, a 3 percentage point increase from the previous year.

Pushing up this year’s junior class results were improved performances among all subgroups, including African-American, Latino, and low-income students, as well as those with disabilities or limited fluency in English.

On most sections of the exam, 65 percent or more of white and Asian students scored in the two highest categories, compared with 45 percent or less of African-American or Latino students.