Average college board scores in most Washington-area school systems rose slightly last year as scores nationwide continues a downward slide uninterrupted since the early 1960s.

The local increase was greatest in Alexandria, where the average score on the verbal part of the Scholastic Aptitude Test (SAT) rose eight points to 447 and the average in math climbed three points to 485.

Arlington, with average scores of 463 on the verbal examination and 503 on the math, had the area's highest SAT scores last year, as has been the case almost every year since the mid-1970s.

A perfect score on each half of the two-hour multiple choice exam is 800. The lowest is 200.

There was a total gain of three points in both Arlington and Montgomery counties, and a one-point increase in the District of Columbia. The District's scores were still by far the lowest in the area -- more than 100 points below the national average on both the verbal and math parts of the test.

In Fairfax County, the total score fell three points -- all on the verbal test. But Fairfax remained far above the national norm and was tied with Montgomery as the second highest-scored school system in the area.

Nationally, the average verbal score dropped three points to 424, while the math average fell a point to 466.

Except for several years when they didn't change, national SAT scores have fallen substantially since 1963 -- a decline that has been widely noted as signalling lower academic achievement in American high schools. During the 17-year slump, the average score on the verbal section of the exam has dropped 54 points, while math scores have fallen 36 points.

The new national report includes the scores of approximately 1 million college-bound high school seniors, about a third of all students who graduated last June. According to the College Board, the verbal part of the test measures reading comprehension and vocabulary, while the math part concentrates on "problem-solving abilities closely related to college work." The SAT scores, along with high school grades, are an important factor in college admissions and counseling.

"It looked for awhile like the scores around the country were going to bottom out," said James Myerberg, coordinator of testing for Montgomery County Schools. "But it didn't turn out that way -- they're still going down . . .

"There were a lot of people who blamed (the decline) on the problems of the late '60s -- that the kids lost their motivation (to learn). We're past all that now. The kids taking the test now were in the first- and second-grade way back then."

In Montgomery County the three-point increase last year followed a 14-point decline in 1979. For the three years before that, the county's SAT scores had been stable after falling steeply in the early 1970s.

The larger increase in Alexandria followed a smaller drop the year before. However, both of Alexandria's scores now are higher than they have been any year since 1975. Compared to 1972, Alexandria's math SAT score is up six points, while the nationwide score has dropped 18 points. But the city's verbal score dropped 24 points compared to a nationwide drop of 29.

"I don't think anyone's completely sure why all this is happening," said Dorothy Murden, Alexandria's director of guidance. "But I'm just tickled with this year's report. I should like to hope we are doing our job and that the children are becoming more serious."

The only local school system which declined Prince George's County. Its deputy superintendent. Allan I. Chotiner, said his staff planned to analyze and discuss the figures before making them public. hWhen called Friday, Falls Church superintendent Warren J. Pace said he hadn't yet received the SAT report.

Besides recording yet another drop in scores, the national SAT report indicates a substantial shift in the areas that college-bound seniors plan to study, particularly among women. For the sixth year in a row more women than men took the SAT. For the first time slightly more women said they planned to major in business. Since 1973, the report said, the percentage of women interested in studying business has almost tripled, while women also are showing much more interest in communications and in studying for graduate degrees.

Also, greater numbers of girls are taking four years or more of math in high school than in the past, though boys still take more math than girls and their math SAT scores are conspicuously higher -- last year by 48 points, a gap which has stayed about the same for about a decade. Males scored eight points higher than females on the verbal part of the test.

"These trends forecast that women will be seen in ever-increasing numbers in the work force, especially in the professions, business and commerce, communications, computer science-related and engineering fields," said Robert G. Cameron, executive director of access services for the College Board.

Because of inflation and rising taxes, the College Board said the families of college-bound seniors can afford to spend less on their education now than several years ago even though college costs have risen steeply. The gap is being met primarily, officials said, by increases in federal loans and grants -- a policy that has had the effect of shifting much of the cost of college from family savings onto the future earnings of college students themselves.

According to the score reports, statewide SAT scores fell in both Maryland and Virginia about as much as they did nationwide. Over the past decade, however, the drop has been much greater in Maryland, and last year for the first time Virginia students were one point ahead on the verbal of the test though Maryland still scored three points higher in math.