Can I take a test 11 to 13 days past ouvlation.?

Yes, but... I assume you mean a pregnancy test. For a home pregnancy test to become positive, the fertilized egg must implant into the uterus, and the new placenta will release a hormone called hcg. This is what is tested for in the urine. Only tiny amounts are needed to make the pregnancy test positive, but this is most reliable a week or more after the first missed period.
Testing. We need a little more information. What are you testing for and do you have a more specific question so we can help you.
A pregnancy test? A woman can take an over-the-counter urine pregnancy test 1 to 2 weeks after ovulation, and should get a positive result if pregnant. If the result is negative, a repeat test can be done 1 week later. The tests are very accurate.