The Prince George's County Board of Education decided last night to require additional math and social studies courses for a high school diploma and paved the way for increasing the number of courses necessary for graduation.

The new requirements, drafted by a task force of administrators, principals and teachers, mean that students in grades 9 through 12 will be required to take 14 units in academic subjects (English, math, science and social studies)--more than any other major school system in the area.

The requirements will first be imposed on ninth graders next year. Students now in high school will not be affected.

The requirements are aimed in part at keeping Prince George's high school seniors in class their last year of school. But they are also geared toward bringing traditional high school curriculum in line with the needs of the increasingly technological 1980s.

The authors of the requirements wanted to add the county's first mandatory computer literacy requirement, but the idea was sidetracked because the school system lacks money to buy enough computers for the students.

The tougher curriculum "is consistent with the changing requirements for the job market and requirements for entrance to colleges," said Louise F. Waynant, who is in charge of instruction for the county schools. Waynant noted that the University of Maryland, which accepts a large part of the county's college-bound residents, will soon require three years of math for entry into the undergraduate program.

Waynant cochaired the task force charged in September 1981 with refining the high school program.

The task force issued its 43-page report last summer, and the school board has been working on it since the fall. Board members adopted the following major recommendations for grades 9 through 12:

* Increasing the required years of social studies from three to four.

* Increasing the number of required years of math from two to three.

* Asking the State Board of Education to increase the total number of year-courses required for graduation from the present 20 to 22 or 24. Superintendent Edward J. Feeney is chairman of a state board subcommittee looking into that question.

"I like the idea of requiring more," Board Member Catherine Burch of Adelphi said yesterday. "I don't think that kids always make the best choices and although the parents are supposed to be involved they are not always."

Under the present Maryland requirement of 20 units for graduation, high school students often start their senior year needing only one or two courses for a diploma. Sometimes they spend the remaining hours working part-time jobs but some students, administrators say, get involved in other activities, including crime.

In Montgomery County, 11 core subjects are presently required for graduation; in Fairfax County, 12; in the District, 12.

The Prince George's board rejected a proposal to issue certificates recognizing achievement in a specific course of study like business, general or college preparatory to accompany the standard diploma. Some board members objected variously that it would be "elitist," "pompous" and "discriminatory."