Eleven states applied for waivers exempting them from key provisions of the No Child Left Behind law by the federal government’s first deadline, promising in return to adopt higher standards and carry out other elements of the Obama administration’s school improvement agenda, the Department of Education said on Tuesday.

Colorado, Florida, Georgia, Indiana, Kentucky, Massachusetts, Minnesota, New Jersey, New Mexico, Oklahoma and Tennessee asked the department for relief from some No Child provisions, including the requirement that all students be proficient in English and math by 2014. In their applications, the states outlined plans to develop their own locally designed school accountability systems, create new educator-evaluation systems and overhaul their lowest-performing schools, the department said.

President Obama said in announcing the waiver program in September that it was necessary because many states had already adopted new common academic standards and were taking other steps that were in conflict with the requirements of the 2002 No Child law. Since Congress had made little progress in rewriting the law, Mr. Obama said, his administration felt obligated to offer states relief.

Secretary of Education Arne Duncan has invited states to apply for the waivers in several rounds. The first deadline was Monday, and a second is scheduled for mid-February.