The D.C. School Board voted last night to increase the number of courses required for graduation from high school here and to require all students to pass standardized competency tests before they are given their high school diplomas.

By this action, District of Columbia students will be required to take more courses, to qualify for high school graduation than students in any of the area's other school systems. Washington also will become the first school system in the area to require all students to take one year of a foreign language.

In a separate action designed to meet severe budget constraints for the school year beginning next September, the board voted to eliminate about 700 teaching positions -- about half by attrition -- cuts in the number of staff personnel at the school board and in central administration, and to reduce spending for driver education courses and the prekindergarten program.

Board members said the reduction in the number of teaching positions would mean an increase in the elementary school pupil-to-teacher ratio to 28 to 1 from the current 26 to 1.

Under the new graduation standards, students will be required to take two years each of mathematics and science, one-half year of D.C. history and one year of a foreign language in addition to existing requirements. Currently they take only one year of math and one year of a lab science. There is no D.C. history and no foreign language requirement.

Other present requirements for graduation include four years of English, one year of U.S. history, a half year of half of health and physical education.

Under the new plan, students will be able to take seven credits in electives instead of the current eight and a half. A one-year course is equal to one credit. A semester course is equal to a half credit.

Under the requirements approved last night, students must spend a year in an "every day skills seminar." Although the details of this seminar have not yet been worked out, it is in this course that students will be tested in the 11th grade to verify that they have sufficient level of competency in English, mathematics, science, social science and health.

The seminar will be slightly different for students who plan to go directly from high school into the working world in that the tests will be designed to verify their ability in the career field they plan to follow, said Dr. James Guines, instruction supervisor for the public schools.

The requirements will become effective in September with students entering the ninth grade.

A student who took business courses rather than college preparatory courses would be tested in such areas as business math, business English and shorthand, Guines said.

A college-bound student will be tested "in the kinds of things a typical person, headed for college should know," he added. For example, "in the area of English literature, we would want the student to know about . . . the great tragedies of Shakespeare, their plots and characters."

The District of Columbia now will credits for graduation to have 20 1/2 credits for graduation instead of the current 17 1/2. Currently Alexandria, Montgomery and Prince George's counties require 20 credits, and Fairfax and Arlington counties require 18.

School Superintendent Vincent E. Reed said when the increased requirements were proposed that such measures were needed because "too many students are graduating without the skills and competencies the [high school] diploma certifies."

Seniors in D.C. schools have for many years placed lower on the standarized college entrance exams than 12th graders in other area jurisdictions. Their scores on such exams have also been lower than the national average.

With the budget cuts made last night, the school board must still find ways to cut an additional $12 million from the 1981 fiscal year budget. The school system have initially asked for $279 million from the city for the next school year, but Mayor Marion Barry has asked the board to limit spending to $244 million. School officials also expect Congress, which must give final approval to the budget, to cut an additional $4 million, bringing the total difference to $39 million.

Cuts in the numbers of teaching positions voted last night are expected to save about $15.4 million, board members said. A further saving of $2.4 million is expected to result from reductions in staff positions in central administration and at the school board. About $2.4 million will be cut from the prekindergarten instruction program, and about $206,000 from funds spent for drivers' education courses.

The board's action means that prekindergarten clases will be shortened from full-day to half-day. Funds for drivers' education courses will be only about one-third of what is available now. The board did not specify whether or not the drivers' education program will be drastically reduced in all schools that offer it now or whether fewer schools will offer the classes.

The board also voted to keep at 16 the number of community schools -- which offer adult education classes. Reed had proposed eliminating five of these schools to cut costs.