Test scores achieved this year by Alexandria high school seniors on a nationally administered Scholastic Aptitude Test (SAT) rose 15 points in the verbal category and 23 points in the mathematical category. Superintendent John L. Bristol announced last week.

In both cases Alexandria scores were above the national average, though slightly below the average for scores of Fairfax County students.

The combined score for both Alexandria males and females in the verbal category was 443, compared to last year's score of 428 and the national average of 429, Bristol said.

Alexandria students' combined score in the math category was 487, compared to last year's score of 464 and the national average of 468, Bristol told a press conference.

Administered to college-bound high school seniors and juniors each year, SATs are used as a gauge of ability and knowledge, educators said. The top score is 800 in each category, with 500 considered average, Bristol said.

In the verbal category, the combined Alexandria averages represented the sixth time in the last eight years that local scores have exceeded the national average. In one instance, the Alexandria scores were only one point below the national averages, according to a series of charts released at the press conference.

The only time in his decade that verbal scores achieved by Alexandria students were below the national average was during the 1970-1971 school year, the last year that racial segregation existed within the school system. School officials went out of their way to highlight the difference in scores before and after integration. Although the officials would not elaborate on the differences in scores, their report seemed aimed at the fears expressed by some members of the community that integration would lower the quality of education in the schools.

In the math category, the combined local scores represented the fifth time in this decade that local scores have equaled or surpassed the national average. Local scores were below the national average during the 1970-1971 term, the 1971-1972 term last year, according to the figures.

Fairfax County seniors averaged 449 in the verbal category compared to 443 for Alexandria students and the national score of 429. In math, Fairfax students averaged 494, Alexandria students averaged 487 and the national average was 468.

Nationally, students have scored increasingly poorly on the SAT tests during the past decade, a trend that has worried educators and parents. While Alexandria scores in both categories have generally stayed above the national average, they too have fallen from earlier scores.

In the 1971-1972 school year, for example, Alexandria students scored 471 in the verbal category, 28 points higher than the scores achieved this year.

Bristol said he was unsure of the specific reasons for the slight rise this year in SAT scores. However, he said he "suspected" that the school system's new insistence on classroom attendance and discipline "may" have something to do with it. "If children aren't here, I can't teach them," Bristol said.

"Last year we initiated our minimum competency standards, one of which was attendance," he added.

There are about 12,000 students in the Alexandria public school system. The school system has 710 seniors, all of whom attend T. C. Williams High School, and of these 376 took the SAT tests. Participation in the test is voluntary.