On Wednesday, juniors at 92 New York City high schools will pick up their pencils, open their test booklets and take the SAT, with no fee and during regular school hours. It is the first step in a plan to give the test next year in all 438 city high schools, which the de Blasio administration hopes will help make college more accessible for thousands of students.

Participation in college admissions testing has lagged in New York: Only 56 percent of the class of 2015 took the SAT exam at least once. Many have praised the effort to make the exam a baseline expectation for high schoolers. But the initiative also raises difficult questions about whether, without significant preparation, low-income students will do well enough on the SAT to get into colleges where they are likely to succeed.

“The predictors are, if you come from a high-income family or a family that graduated from college, the data is there — their kids are going to do much better on the SATs,” said David O’Hara, the principal of Leaders High School in Gravesend, Brooklyn. He said 90 percent of his students, if admitted, would be the first in their family to attend college. Last year, all his students took the SAT, and their average score was 1212 out of 2400, less than the city average. (This year the test is moving back to a 1600-point scale.)

Mr. O’Hara said he was glad that the Department of Education was setting an expectation that students should apply to college. But he hoped that the city would give schools more money to help prepare students. His school offers yearlong Saturday SAT preparation sessions to 20 juniors, through a partnership with the volunteer organization New York Cares. But there are not enough resources for all 70 students in his junior class, he said.