Simone J. (Sim) Pace, a Republican, was elected chairman of the Arlington School Board yesterday and pledged to consider lengthening the school day and examine whether students are being given enough homework.

Claude M. Hilton, also a Republican and former board chairman, was elected vice chairman along with Pace by a unanimous vote.

Pace is expected to be the last Republican until at least 1987 to head the board, whose five members are appointed by the Arlington County Board. Until yesterday, when Democratic appointee Gail Nuckols joined the school board, all five school board seats were held by Republicans.

Next summer, when the terms of Republican appointees Evelyn Reid Syphax and Hilton expire, the Democrats, who now control the County Board, will have the opportunity to appoint two new school board members to four-year terms, shifting control of the school system to the Democrats.

Pace, who campaigned unsuccessfully in 1980 for a seat on the County Board, said that his goals for Arlington parallel those of the National Commission on Educational Excellence which recently called for more rigorous academic standards in public schools across across the country.

In his inaugural speech, Pace outlined his objectives for the coming year, including consideration of adding a seventh period to the school day in the high schools and reconsideration of the system's current practice of releasing elementary school students at midday on Wednesdays. He said the early releases once a week add up to 90 days out of the classroom by the time an Arlington student has finished sixth grade.

Pace also said the board should decide whether it needs a compensation plan for teachers based on performance, a proposal that has been pushed by the national commission and President Reagan and suggested by an Arlington task force on county and school employes.

During the past year, the Arlington School Board dealt with controversial issues including school closings and the busing of black children only from South Arlington to achieve integration. Pace voted with the majority to change the busing plan and supported the recent decision to close three elementary schools.