For about 5 years, there was a copy of the SAT published that was written using common slang and situations that African-American students used in everyday life. It came to be known as the "Black SAT". The rationale was as you suggest, that the SAT was slanted to the white middle class background. Students participating in the experiment were administered both versions of the test.
At the end of the experiment, it was discovered that the difference between the scores of both versions of the test were, at best, negligible.