WHEN VIRGINIA high school students took the state's new competence test the first time, last fall, a good many failed. When they took it again last spring, the scores improved. It means that both students and school systems are beginning to take the test seriously. That's a healthy sign. These tests promise their greatest benefits to precisely those children who have failed them on these first rounds.

Beginning with the high school classes of 1981, students who cannot pass the test will not graduate. That may seem cruel, but ask yourself whether a high school diploma shouldn't represent something more than mere attendance. The tests are now identifying those children who risk, as seniors in the spring of 1981, remaining below the basic level of ability that the state has now set. Failing scores exert a pressure on both students and their schools to do something about it while there is time.

The tests are models of common sense. The reading section requires an ability to understand the directions on a bottle of medicine and the warranty limitations on a new stereo set. The student has to be able to fill out a job application. Surely those are necessary abilities for survival in America. The mathematical section requires a student to be able to write a check, and deduct it from the previous balance.

A lot of youngsters had trouble with the checkbook question. It turned out that they had never seen checkbooks. Some of the school systems have hastily put the checkbook into their math curriculum, a simple improvement that serves several useful purposes at once.

Failure rates are higher among black students than among whites. Some of the civil-rights organizations question whether the test is not culturally biased. The answer is, yes, it is biased -- but it is in favor of the culture in which all Americans earn their livings and spend their money. The test doesn't measure children's personal worth, or intelligence. It is a device to see only whether the student, with the help of the school, has learned the basic abilities required to deal with a complicated and not always friendly world.

In Prince Edward County, with its predominantly black enrollment, barely half of the students passed both parts of the test the first time. In response, the schools there sharply revised their program and, in the spring, 90 percent passed. If a small, rural county can make such remarkable improvements, there is little reason for the school systems of Northern Virginia to remain content with the rather unimpressive scores that their students have achieved so far.