NEW YORK (AP) _ Mayor Edward Koch, who complained last year that too many students and teachers did not speak properly, says a new pilot speech program will begin in 10 public schools next fall.

The program, developed by New York University, the Board of Education and the Mayor's Office of Youth Services, will use video cassettes, tape recorders and what officials called ''the techniques of sociodrama.''

''The emphasis will be on the spoken word, pronunciation, diction, presentation of ideas, but these are not mutually exclusive terms,'' Charlotte Frank, executive director of curriculum and instruction at the Board of Education, said Wednesday.

She said students taking the course might act out real-life dramas. For example, in a ''sociodrama'' about teen-age pregnancy they would interview a number of people - a religious leader, a hospital administrator, a doctor - and then act out the roles.

''Now, when each of those members of that subgroup assumes the role of each of those participants, they will recognize that there are certain speaking patterns that reflect the person they had just interviewed,'' she said.

The program will cost $150,000, all of it provided by Leonard Stern, president of the Hartz Mountain Group Inc.

The need for such a course was suggested five months ago by the mayor, who complained that too many students and teachers say ''axed'' instead of ''asked,'' ''nope'' instead of ''no'' and ''yup'' instead of ''yes.''

The course, to be given to 300 students at five intermediate and five high schools in all boroughs, is not expected to eliminate those particulars of speech or accents unique to New York.

''I think,'' Koch said, ''that the New York accent will be preserved.''