The D.C. Board of Education approved a new standardized achievement test in reading and mathematics last night, despite misgivings that the exam might be outdated before it can first be given in May 1987.

The multiple-choice exam, which is the 1981 edition of the Comprehensive Test of Basic Skills (CTBS), was recommended last month by Superintendent Floretta D. McKenzie. It will replace the 1973 version of the same tests, which has been used by D.C. schools for 12 years.

"We're about to buy a test that will be five years old when we first give it," said board member Bob Boyd. "Soon after buying this test, it will be obsolete."

Member R. Calvin Lockridge criticized school administrators for saying that the schools needed one more year to "match" the curriculum to the new test instead of switching to it this spring.

"Are we teaching the test?" he asked. But despite their criticisms, Lockridge and Boyd later joined seven other board members in approving the exam in a unanimous voice vote.

The board chose the oldest of three achievement tests under final consideration by school administrators. It was the one on which D.C. students scored highest in a sample testing last spring, although the grade equivalent averages fell one month to 1.4 years below the city's scores on the older CTBS.

Last month, McKenzie said she had recommended the exam because it most closely follows the school's present curriculum and would produce the least change in scores.

In other business last night, the school board:

*Received a report from an advisory committee on AIDS that generally endorsed the district's interim policy. That policy, which calls for a "case by case" review, allows students and employes with the disease to remain in regular classes as long as they do not put others at risk. A hearing will be held before the policy is adopted.

*Gave preliminary approval to a requirement that students maintain at least a C average to participate in interscholastic sports or other extracurricular activities. But the requirement would be waived for those serving on student governments.

After last night's vote on the new standardized exam, member Eugene Kinlow said the board had approved the test because "we wanted to support the superintendent."

In February, school officials said they had delayed recommending a new exam for one year because of concern that it would yield lower scores. On the old test, based on sample nationwide testing in 1972-73, D.C. students have shown substantial improvement for seven years.

Yesterday Boyd said scores would be lower on the new test, based on a sample testing in 1980-81, because "this is a harder test" and "we have raised the hurdle." But Boyd emphasized that the actual achievement of students would not be lower. He said matching the curriculum to the test is "common practice around the country. We are not teaching children the exact questions on the test."