Six districts say they will implement the requirement this year. Another 36 failed to notify the Texas Education Agency of their plans.
Spokeswoman Debbie Ratcliffe said the agency assumes districts that didn't formally request the delay will implement the requirement. All are very small, however.
In February, the agency authorized delaying until 2012 to 2013 a requirement that State of Texas Assessments of Academic Readiness results count 15 percent of ninth graders' final grades.
But to qualify, districts needed to seek a waiver by Tuesday.
Students began taking STAAR in March. The reprieve is to help districts fully implement the new test before it affects grades.