Elmer Cooper, the controversial former president of the San Francisco Bay Area Rapid Transit System, left his position as a consultant to the Commodity Futures Trading Commission yesterday, the first anniversary of his appointment at the agency.

The CFTC also announced the appointment yesterday of Donald Tendick as executive director, a post which has been filled by successive acting directors for nearly all of the agency's three years of operation.

Congressional critics frequently have cited administrative problems at the CFTC. Both a General Accounting Office study and a House Appropriations Committee investigative report released last week noted that significant improvements have been made in this area in the past six months. Tendick has been acting executive director since August.

Cooper did not respond to a reporter's telephone calls through yesterday. The CFTC's formal statement on his departure was confined to a terse two-sentence announcement delivered by a spokesman:

"Elmer Cooper completed one year as a consultant to the commission on March 1. He is no longer employed by the commission as a consultant."

Commission sources said Cooper has joined an international consulting firm involved in projects in developing countries.

Cooper has come under the scrutiny of two San Francisco grand juries in 1975 and 1976 over the handling of his expense accounts while an official of BART. No charges were brought against him following a 13-month investigation, but he resigned as president in January 1977 and repaid BART $2,338.72 for some of the undocumented expenses. He had filed $19,-713.75 in expenses for the first nine months of 1975 while he was vice president of BART, the grand jury report disclosed.