School administrators across New York State are charging that the Regents exam in mathematics offered this week was far too difficult, and that a huge number of high school seniors may be barred from graduating next week because they failed it.

Though many districts have not finished tabulating their scores, superintendents, principals and math department heads are reporting preliminary results that some described yesterday as "abysmal," "disastrous" and "outrageous."

"Kids have walked out of the exam in tears knowing they are just not graduating," said one veteran assistant principal in Brooklyn, adding that officials from other schools had been deluging him with horror stories about the test. "One of the comments I got from a colleague is that summer school is going to be very crowded this year."

School officials are also crying foul about the Regents physics exam, though that situation is not so dire because the test is not a graduation requirement. E-mail bulletin boards for the state's math and physics teachers have been bombarded with complaints about the exams in recent days.

This is the second straight year that educators have criticized the physics exam — in fact, a group of superintendents from Westchester County and Long Island unsuccessfully sued the State Education Department last year on the ground that the exam was an inaccurate measure of skills. But while all agree that the math exam introduced two years ago, known as Math A, is challenging, they say the version administered on Tuesday crossed the line from difficult to impossible.

Bill Hirschen, an Education Department spokesman, said department officials had heard that "some of the success rates have been lower," but that the state would not tally the scores of either test until mid-July, the deadline for schools to report their results. Mr. Hirschen later called back to say that because of complaints about the math exam, the state would ask schools to report their results immediately.

Meanwhile, Assemblyman Ryan S. Karben, a Rockland County Democrat, asked Education Commissioner Richard P. Mills yesterday to immediately investigate what he called "the aberrantly low pass rates" on the math exam. In a news release, Mr. Karben said preliminary reports in Rockland County showed passing rates of 8 percent to 50 percent, "far below the traditional rates."

The math exam, which became a graduation requirement in 2001, covers algebra and geometry, along with some theoretical probability and statistics. It has four parts, including 20 multiple-choice questions and a number of word problems in which students explain how they arrive at an answer.

Most students take and pass the exam as sophomores, after a year-and-a-half-long Math A class, though those who struggle with math often put it off until senior year.

While many math teachers hailed the new exam as appropriately rigorous when it was introduced in 1999, some of those same teachers say the version given this week was far too difficult, even for the brightest students.

Some said it was short on algebra, which is the primary focus of the Math A course, and heavy on difficult geometry questions. Some questions were unnecessarily wordy, they said, while others had more than one correct answer and used terms the students had not been taught. Perhaps their biggest criticism was that the test packed too many tasks into single questions.

"The failure rate is way out of proportion to what we would have anticipated on the basis of how our kids did on previous exams," said William H. Johnson, superintendent of schools in Rockville Centre, who led the lawsuit against the physics exam last year. "We don't know what they are measuring anymore. It's an absolute guessing game."

Dr. Johnson said that only 19 percent of the roughly 95 students who took the math exam this week passed, compared with 78 percent of the 336 who took it in January. While most of the students who took the exam this week were "repeaters" who had failed it at least once before, Dr. Johnson said he expected that at least half would pass because they knew what to expect.

Complaints about this week's math and physics exams are the latest in a series that have plagued the Education Department since it stiffened graduation requirements in 1996. Students must now pass Regents exams in English, math, American history, world history and science to graduate. Educators have complained that the English and history exams are too easy or scored too leniently.

In 2001-02, 68 percent of students statewide who took the Math A exam passed it. In New York City, 50.8 percent passed. Students currently need a score of 55 to pass the math test, and while the passing score is supposed to rise to 65 in 2005, the Regents are considering keeping it at 55.

One state education official said the complaints, especially from suburban educators, were part of a growing reaction against standardized testing. "They refuse to teach to the test," the state official said. "They haven't done well for that reason."

Middle-class and wealthy school districts have actively protested the rise in make-or-break tests, even urging their students to boycott them. But urban educators were just as vehement in their criticism yesterday. Those in New York City would not speak for attribution, saying that Chancellor Joel I. Klein's office had instructed them not to.

Merryl H. Tisch, a member of the State Board of Regents from Manhattan, said that school officials were jumping to conclusions.

"We need to get some data in from a variety of schools before people start to make ad hominem comments about the process and the tests," Ms. Tisch said. "It is much too early to determine the reliability and validity of them."