When the state announced plans to push back the date of the annual tests, some teachers and administrators bristled. But now the change is complicating a rite of passage: figuring out which students are promoted to the next grade and which are going to summer school.

This year’s delayed testing schedule puts New York City in the awkward position of choosing which students to send to summer school without knowing whether they passed the state’s annual math and English exams. Currently, schools have their students’ raw test scores, but they don’t know whether the scale score passes the official state cut-off for passing, because the state hasn’t set cut-off scores yet.

In response, the city is working with the state to set their own cutoff scores months before the official results come out in August.

In order to qualify for summer school, students have to score very low on the tests — getting a one or a two out of a possible four.

“We will determine based on prior years’ data what we believe a two, three, or four would equate to this year,” said a spokesman for the city’s Department of Education, Daniel Kanner, adding that the cutoffs will be set higher this year than in the past.

In a memo the city Department of Education sent to principals, officials referred to the cutoffs as “promotional cut scores,” meaning they will only be used to decide who is required to go to summer school.

The city’s decision will result in two sets of cut off scores that may not match up. If the official cutoff is set higher than the first one, students could be promoted to the next grade only to find that they officially failed the test. The reverse could also happen: a student could be required to attend summer school and then learn that her test scores put her in the passing range set by the official cutoff.

Kanner said that if the first scenario happens, the city will not force the student to repeat a grade. “We will not take promotion away from any student we grant it to,” he said.

The change will not affect high school students, who are promoted or held back based on their Regents exam scores and whether they pass their classes.

City officials have said they will offer summer school in as many schools as they did last year — 369 schools — but without test results it remains unclear how many students will be required to attend or how much money schools will be given to spend on the program.

A preliminary budget sent to principals this week shows a citywide decrease in summer school spending. But Ann Forte, a spokeswoman for the DOE, said schools’ funding would change once the city figured out how many students it would require to go to summer school. “It’s too early to tell what the difference is and we’ll have a better idea once we get the scores and budgets adjusted,” she said.

Last year when fewer students scored low enough to qualify for summer school, the city’s summer school budget went down 22 percent and classes were offered in 369 schools, down from 562 in 2008.