Michael R. Bloomberg has staked much of his reputation as the mayor of New York City on improving students’ test scores, and has trumpeted gains in math and reading as validation of his 12-year effort to remake the city’s schools.

But the mayor’s telling of history is poised to receive one of its most vigorous challenges yet on Wednesday, when New York State is expected to report drastic drops in student performance across the state because of a new set of tougher exams.

In New York City, the proportion of students deemed proficient in math and reading could decrease by as many as 30 percentage points, city officials said, threatening to hand Mr. Bloomberg a public relations problem five months before he is set to leave office.

Already, many of Mr. Bloomberg’s rivals — the teachers’ union, parent groups, and several of the Democratic candidates vying to succeed him — have begun to use the prospect of a steep drop in scores to call into question the mayor’s record on education.