High school seniors in Fairfax County achieved higher combined average Scholastic Aptitude Test scores last year than students in any other school system in the Washington area, new College Board figures show.

It was the first time that Fairfax has surpassed Montgomery and Arlington counties, which traditionally had higher scores in the widely used tests of verbal and mathematical abilities.

Overall, average SAT scores increased slightly last year in most major school systems in the Washington area while nationwide scores were unchanged after falling for 17 years.

Also for the first time the average statewide SAT total was higher in Virginia than in Maryland.

In District of Columbia public schools, the average score rose four points from a year earlier on the math part of the test, but it fell two points on the verbal portion. Despite this overall improvement, the District's combined average scores were still in the bottom 20 percent of all students taking the test nationwide, more than 200 points below the combined national averages in both verbal skills and math.

The exams are widely regarded as a measure of the key academic abilities that are developed in school and required for college work. In math, the exam concentrates on problem-solving, using arithmetic reasoning, and basic algebra and geometry. The verbal part of the test measures reading comprehension and vocabulary.

The new reports -- both local and national -- are based on the most recent SAT exams taken by members of the high school class of 1981, which graduated last June. The exams, sponsored by the College Board, most often are taken in the fall of the senior year. Nationally, the data includes test scores of approximately 1 million students.

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

In Fairfax, average scores rose one point on the verbal part of the exam to 457 and four points in math to 507 -- compared to the national averages of 424 in verbal and 466 in math.

By contrast, Arlington County, which had the highest scores locally last year, fell 10 points in verbal and five points in math.

Charles Nunley, Arlington's school superintendent since last July, said he was uncertain why the scores fell so sharply last year, but he suggested that the county's large number of Asian students with language problems may have pulled down scores on the verbal exam.

"They are highly motivated toward education," Nunley said, "but many of them have (English) language deficiences that must be overcome."

In Fairfax County, Superintendent Linton Deck said he was gratified by the results.

"I think that sometimes people fail to realize that these scores represent the average scores of all our students who took the test," Deck said in a statement. "It is particularly noteworthy that such an average was achieved considering the extremely high percentage of (Fairfax) students who took the test (75 percent of last year's seniors), compared to the nationwide sample (about 33 percent)."

Besides Arlington, total scores fell substantially in Alexandria and Falls Church, each of which has only one high school.

In Prince George's County, there was a three-point gain in the verbal part of the exam and no change in math. The total score in Prince George's remained the only one in the Washington suburbs that was below the national average though it was far above that in the District of Columbia.

Over the last five years, as the nationwide total score fell 13 points, Prince George's total score dropped 19 points. In Arlington the five-year drop was 35 points, in Alexandria 21 points. In Fairfax and Washington, the drop since 1976 was just two points; in Montgomery, six points.

For Virginia as a whole, scores went up two points this year and matched the national norm in verbal skills for the first time. Maryland fell one point last year and 18 points over the last five years. The five-year drop in Virginia was just five points.

State officials in Maryland and Virginia had no firm explanations for the shift in the relative standing of the two states.

Gerald W. Bracey, director of research and testing for the Virginia Education Department, said the good record of Fairfax, which accounts for almost 20 percent of students taking the College Board exams in the state, may account for much of the result.

Sheldon Knorr, the Maryland state commissioner of higher education, said he was particularly concerned that the number of students with very high SAT scores appears to have fallen.

"Nobody seems to have a good explanation for it," Knorr said. "We have slipped, but we don't know why."

James Myerberg, director of testing in Montgomery County, noted that students in his school system have made slight gains for two years after major losses earlier. "We've started back up again," Myerberg said, "but I'd like to see a more substantial recovery."