The Arlington School Board approved last night a $74.3 million budget request for the next school year that calls for expenditure of $56.7 million in county funds. The budget contains several improvements in programs ranging from the sciences to the humanities.

The board's vote was 3-to-1-to-1, with member Simone J. Pace dissenting to protest what he said were some unnecessary expenses, and Margaret Bocek abstaining. They are the five-member board's only Republican appointees.

The budget, which represents a total 6.3 percent increase over last year, calls for 5.1 percent more in county funds, Budget Director Joseph G. Guter said. That sum is about $2.8 million over what the County Board, which funds the bulk of the school budget, recommended as a spending "guideline" to the School Board this year.

The difference between the county's $56.7 million share of the budget and the $74.3 million is made up from federal and state aid.

In addition to the operating budget, which includes a $200,000 contingency fund, the board approved requests for almost $1.2 million for capital improvements, $3.5 million for community activity expenses that are shared with the county, such as the high school swimming pools, and $1.9 million for food services.

School Board Chairman Gail H. Nuckols and members Dorothy Stambaugh and Frank Wilson, all Democratic appointees, said they believe the improvements are justified. "This budget is neither a basic subsistence-level budget nor is it an extravagant one," Nuckols said, adding that it addresses priorities set by the board and also meets some community-requested improvements.

Unlike previous years, the board did not set a salary increase for the county's 900-plus teachers. That figure is to be established when the County Board adopts its budget in April. Guter said that if the county and schools give their employes 4 percent raises as County Manager Larry J. Brown has recommended, the schools will get an extra $2.4 million.

The new school budget provides for 63 new jobs, all but 23 of them in the teaching field, to staff program improvements and accommodate a projected enrollment of 14,895 next fall, 423 more than previously expected.

Among the funds earmarked for program improvements are $300,000 to begin an optional seven-period day for high school students wanting to fit in more electives next year, and for extended Saturday classes.

Many of the budget improvements are aimed at meeting the demand for expanded science and math courses since the board opted not to send Arlington students to the new state "magnet" school for science and technology opening next year in Fairfax County.