The average scores of high school seniors in Fairfax and Arlington counties dropped slightly last spring on the Scholastic Aptitude Test, while scores rose slightly in Alexandria schools, according to test reports released yesterday.

In both Alexandria and Arlington, scores improved on the mathematics section of the two-part college entrance exam, while students in all three school systems lost ground on the verbal section of the test.

The same pattern--generally improving scores in math and declining scores in vocabulary and reading comprehension skills measured by the verbal exam--appeared in the SAT results issued Monday by public schools in Maryland and the District of Columbia.

In the nationwide SAT report, released Sept. 18, the average mathematics score increased one point for the second year in a row, while the verbal average dropped one point.

"In Fairfax County there's been a consistent pattern for over a decade," said Todd Endo, director of research and evaluation for the county school system. "The math has been pretty stable, but cumulatively the verbal score has had a significant decline . . . . There's other evidence that points the same way. It's not just the SAT. We're beginning to put more emphasis on the writing and critical thinking skills that the verbal test requires."

In comparisons of major Washington area school districts, the new results show Montgomery County has moved ahead of Fairfax as the school system with the highest combined average SAT scores. For the past two years Fairfax County had been first, a position that during the 1970s was held by Montgomery or Arlington.

Last spring Arlington was third in the area-wide rankings, while Falls Church, which had only 85 seniors in its one small school, tied with Fairfax for second.

Even though average scores for Fairfax County were down two points in verbal from 1982 to 456 and one point in math to 505, they remained well above the national averages of 425 in verbal and 468 in math.

Montgomery, Arlington, and Falls Church also are far above the national averages, while Alexandria remains considerably above the national average in the verbal section of the SAT with a score of 440 and just matches the average in math.

The average scores in Prince George's County were around the 40th percentile nationwide, meaning the average senior in the county did as well or better than about 40 percent of the 1 million students who took the exam around the country and worse than about 60 percent of those tested. Although scores for D.C. public school seniors have improved substantially over the past two years, the D.C. averages remain around the bottom 20 percent nationwide.

Possible scores on each part of the two-hour multiple choice exam range from 200 to 800 points.

In releasing its SAT results Monday, the Montgomery County school board included average scores for individual high schools, but so far none of the other area school systems has issued school-by-school results.

The Montgomery scores indicated that all of last year's eight-point improvement in that school system was accounted for by female students, while in Fairfax females accounted for all of a three-point decline.

The average verbal score of male students in Fairfax now is 460, eight points higher than that for females, compared with a one-point edge for males in l982. On the math part of the test the male average of 530 is 52 points above that of females, one point greater than a year ago.

For all Fairfax seniors the average SAT math score last spring was one point lower than it had been five years ago and two points lower than 10 years ago. But the declines in the verbal score were much greater. The verbal score was down seven points since 1978 and down 17 points over the past decade.