For the first time in 19 years the nationwide average rose last spring on both the verbal and mathematics parts of the Scholastic Aptitude Test (SAT), taken by almost 1 million college-bound high school seniors annually.

Although the rise was slight, officials of the College Board, which reported the scores yesterday, said it probably reflects a turn to tougher courses and stiffer grading after years of declining standards.

Others noted the proportion of private high school students taking the test had increased markedly.

The College Board said the SAT scores had risen from 1981 to 1982 by two points to 426 on the verbal portion of the test and by one point to 467 in math.

"I think this may be a watershed," said Robert G. Cameron, executive director of research and development for the board, which is an association of about 2,500 schools and colleges. "In 1981 the scores were stable. This year they're up. The trend line is important here. I could be wrong, but I'm optimistic from what I know is going on in American education that they'll go up next year too."

Cameron noted the gains on the SAT were matched by higher scores on the Test of Standard Written English for the first time since it was introduced by the board in 1975. Average scores also went up on subject matter achievement tests, he said, and seniors reported taking more foreign languages, math and science, reversing a trend toward easier courses.

Also, widespread grade inflation, which accompanied the long slide in test scores, may have come to an end, Cameron said. The average grades reported by students taking the SATs have been unchanged for three years a row. They have dropped slightly from the heights reached in the mid-1970s.

From 1963, when SAT scores reached their peak, to 1980, when they hit bottom, the verbal score fell 54 points from 478 and the math average dropped 36 points from 502.

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

"After such a large drop, it's hard to know if this is really a turnaround," said Alexander Astin, a professor of higher education at the University of California at Los Angeles, who directs a nationwide survey of college freshman. "Any slide has to bottom out sometime. There's not infinite room for the scores to keep going down. The real question is if they ever will rise again to the point where they used to be."

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

As the scores went down, they were widely interpreted as a barometer of lower academic achievement, though in a major study in 1977 the College Board said most of the decline before 1970 came from a vast increase in lower-ability students taking the exam. These were mostly women and blacks, who traditionally had low rates of college attendance. Since the early 1970s about a third of all high school graduates and half those going to college have taken the SAT every year.

In its announcement of the new SAT scores, College Board officials attributed the increase to stiffer standards, and to harder work by students.

Astin, however, noted that the long decline in test scores was blamed partly on a change in the types of students taking the test. He suggested this year's rise may also reflect such a change -- a slight drop in the proportion of women and blacks taking the exam. Women went down from 51.9 to 51.8 percent of all test-takers, blacks from 9.0 to 8.9 percent.

The number of Asians continued to rise, from 2 percent to 3.8 percent of all test-takers in the past seven years. So did the proportion of students going to private schools, which climbed from 17.5 to 19 percent since 1978.

Although the new report does not contain detailed information on all these groups, previous test data indicate that private school youngsters score higher than those in public schools. Among racial groups Asians score slightly higher on average than whites and blacks lower.

This year female students were 10 points lower than males on the verbal part of the SAT and 50 points lower in math. Overall, females went up three points in verbal scores compared with a one point increase by males. But on the math exam the score for males rose one point while the female scores were unchanged.

Since the mid-1970s scores on standardized reading and math exams have gone up throughout the country in elementary and junior high grades. But so far scores for senior highs have sagged or stayed the same.

Recently, many senior highs have paid more attention to preparing students directly for the SATs and commercial coaching courses have expanded, though figures on this trend are unavailable.

"I think there has been a lot more concern in the secondary schools with standards and quality," Astin said. "Most states have instituted some kind of minimum competency tests, which I think have had an effect on tightening things up. But it's still hard to know if the great laxity in curriculum and grading is really over."

Scores for local school systems in the Washington area were not available yesterday. In statewide figures, the College Board said combined scores for the two parts of the SAT went up five points in Maryland and three points in Virginia. Virginia again matched the national average in the verbal test, but both states were slightly below the average in math.