The number of Montgomery County high school students who passed the state's citizenship test improved by 2 percent this year for an overall passing rate of 81 percent, school officials said yesterday.

All minority groups made gains on the exam. Passage will be required for graduation next year; the exam is one of four state-mandated functional tests.

Black students showed the greatest improvement over the past three years. In 1984, 36 percent of black students passed the citizenship test, compared with 67 percent this year, an improvement of 3 percentage points over last year.

Asian students had the greatest one-year improvement, going from 76 percent passing last year to 84 percent.

Hispanic students went from 61 percent passing last year to 64 percent. School officials said the lower passing rate for Hispanics is partly attributable to the fact that many are new to this country and have deficiencies in English and basic skills.

School records show that 41 percent of Hispanics tested had been in the school system for two years or less, and nearly half of that group failed the exam.

This year's seniors must pass the state functional mathematics and reading tests in order to graduate. All but four of this year's more than 8,000 seniors passed the two tests, school officials said. The state's writing test will not count toward graduation until 1989.