The Prince George's County Board of Education will support most of the tougher graduation standards under consideration for all Maryland students, but will not support a mandatory fine-arts course or a requirement that all school systems offer students credit for community service.

County school board members are backing addition of a "certificate of distinction" for students who perform well, a requirement that students spread their high school courses over four years and the addition of a mandatory third year of mathematics. Prince George's schools already require three years of math in high school.

The board agreed last night to present its recommendations at a public hearing scheduled Oct. 30 before the state Board of Education. The state board has given tentative approval to the stricter standards and is expected to vote on the proposals by the end of the year. The new requirements would then be applied in the fall of 1985.

State Superintendent David W. Hornbeck originally proposed a requirement that students complete 100 hours of community service, but that proposal was revised to require only that school systems offer credit courses for students who wish to perform such service.

Testimony prepared for the hearing and accepted by Prince George's school board members last night says: "Although we believe community service is very important and certainly may be a part of existing elective courses, we do not feel it is appropriate to offer a specific course in community service."

The testimony also cautions: "We are enthusiastic supporters of the fine arts . . . However, to add a specific required course in fine arts to all students' schedules may make it very difficult for some students to pursue special areas of academic or career interests."

The board also recommends that a B average be the minimum required to earn a certificate of distinction.