Published: March 15, 2005 | By DAVID M. HERSZENHORN | New York Times

In the fall, when New York State Education Department officials distributed sample questions and answers for the annual standardized mathematics exam, they fully intended to help students study and prepare for the test. What they did not intend was to give about 400,000 seventh and eighth graders an advance peek at actual test questions.

But in a gaffe that officials acknowledged was embarrassing to the state and even more humiliating to the test publisher, CTB/McGraw-Hill, three questions on the seventh-grade sample test and one question on the eighth-grade sample test reappeared on the real exams, which are being administered this week to about 200,000 students in each grade. This year, for the first time, the tests will be used to measure school performance in the city under the federal No Child Left Behind law.

Officials in Albany and at CTB/McGraw-Hill in Monterey, Calif., issued terse statements last night promising to adjust for the mistake in the scoring of the exams. The reused questions were all from the multiple-choice portion of the tests, which means they are graded by machine. Education officials and testing experts said there was little choice but to ignore those questions in the tabulation of final scores.

But neither state nor company officials offered an explanation of how the mistake occurred, nor would they speculate on what impact, if any, the repeated questions might have on the overall validity of the tests.

Kelley Carpenter, a spokeswoman for CTB/McGraw-Hill, acknowledged that it had prepared both the sample tests and the actual exams. But the company declined to take immediate responsibility for the error, and would not say if it planned to apologize to students or to New York State.

"We're working closely with the State Department of Education to investigate what transpired, and we'll also work closely with them on an effective solution," Ms. Carpenter said.

The state's annual reading and math exams in grades three through eight are used to measure school performance in meeting requirements of the No Child Left Behind law. Under the law, schools that fail to show adequate yearly progress face potential penalties. In some cases, students are then entitled to transfer to another school or receive free tutoring.

In grades three, five and seven, New York City also uses the exams to make decisions about promotion. Because the state's seventh-grade math curriculum was recently changed, city officials previously said that it would be unfair to base promotion on the math test, and that this year they would use only reading scores in determining whether students will advance.

There were 30 multiple-choice questions on the seventh-grade test, each worth one point out of a total of 50 points on the test, and there were 28 multiple-choice questions on the eighth-grade test, each worth one point out of a total of 69 points on the exam.

Some schools are still administering the exams over the rest of this week, and state officials said they should proceed without any adjustments.

"At the close of the testing period on March 24, the State Education Department will release more information on the affected multiple-choice questions," officials said in a statement. "We will also provide specific guidance on how this will be accounted for in the final scoring in a way that is fair to students, schools and districts."

The major publishing companies typically rely on large banks of potential exam questions in developing the annual tests.

CTB/McGraw-Hill has a five-year, $22.5 million contact to publish the New York State exams through 2009.

New York City education officials, who have had their own standardized testing problems in recent years, did not place blame last night and instead issued a statement leaving the matter firmly in Albany's hands.

"We're aware of the problem and have been assured by the state that it will be resolved fairly for all students," said David Cantor, a spokesman for Schools Chancellor Joel I. Klein.

In 2002, New York City declined to renew a contract with CTB/McGraw-Hill, which had published the city's standardized reading exam, after a series of highly publicized disputes over possible scoring errors.