Seishun Scrap!

From MangaHelpers: A new program has been set in place for a certain area, where children are separated by gender into eastern and western territories. They're raised with no contact with the opposite sex, and made to only focus on their studies. Of course, there are a few bad apples, and the worst of these are sent to a co-ed school with the troublemakers from both sides. Unfortunately, this school soon became known as a place where the teenagers would battle to determine who was the strongest, and many boys and girls tried to be sent there. At this school, the girls have an advantage, since the boys mysteriously get nosebleeds whenever they look at them. However, the strongest girl, Jun, is shocked to find that the strongest boy, Kyo, doesn't get a nosebleed when he looks at her! It turns out that both of them have had some experience with the opposite sex in the past, and they both have embarrassing secrets in the present.