There are more As and Bs and fewer Fs in the second round of letter grades handed out to public schools, but the improvements are not silencing questions about how much meaning the grades hold.

The rising tide was buoyed by big improvements on state reading and math tests last year.

Test scores account for 85% of each school’s report card grade, with schools getting credit for both their students’ overall scores and for how much their scores rose from one year to the next. The rest of the grade is based on attendance rates and a survey of parent, student, and teacher satisfaction.

Mayor Bloomberg and Chancellor Joel Klein implemented the grades last year as a way to give parents information — and a way to encourage schools to improve.

Staff at schools that receive high grades are eligible for cash bonuses, and schools that receive D and F grades could face closure.

Although there were some high-profile cases of schools dropping in the grades handed out yesterday — such as P.S. 8 in Brooklyn Heights, which got an F, as the New York Times first reported over the weekend, and P.S. 116 in Manhattan, which dropped to a C from an A — schools making dramatic gains were more common.

An elementary school in Inwood, the Muscota New School, jumped to a B from an F; P.S. 58 in Carroll Gardens got an A, up from a D, and a middle school in Battery Park City that last year was given a D, I.S. 289, received an A.

Overall, 71% of schools that received Cs and Ds last year got As and Bs this year, school officials said.

Mr. Bloomberg said the report cards themselves deserve credit for the rising test scores and better report card grades.

“Accountability leads to better results,” he said.

He and Mr. Klein pointed to the school where they held the press conference, P.S. 5 in Bedford-Stuyvesant, which rose to an A this year from an F, as an example.

The principal of the school, Lena Gates, said she made a concerted effort to improve test scores, involving not just teachers but also parents and students in her push for a better grade.

Other principals said they were not affected by the report cards, and both the president of the principals union, Ernest Logan, and the teachers union president, Randi Weingarten, put out statements yesterday raising concerns about the quality of the report card judgments.

The principal at I.S. 289, Ellen Foote, said her staff had made no changes in response to their D, which the school received two weeks after winning a Blue Ribbon award from the federal government.

Ms. Foote said that rather than think about the report card grade, she focused on a battery of internal assessments that look not just at test scores but also science reports, writing samples, and math projects.

Ms. Foote said that when she finally opened the report card and found an A, she laughed; what meaning could the letter grade have if it had given the same school such different grades? she asked.

“I was just rolling on the floor,” Ms. Foote said.

The grades released so far are only for elementary and middle schools; grades for high schools are still to come.