It would be very unusual for the HIV test to be negative at 10 weeks post contact and then become positive at 12 weeks but some people do take longer to make antibodies to HIV than others. This is why testing at 12 weeks is considered to be most accurate time to do a HIV antibody test and that result is conclusive.
This answer was posted on March 4, 2018.
This answer was updated on February 7, 2022.