First of all, found out
for yourself if the head of department will not allow retakes. I don't know about your school but if you were within ten marks of the next grade, they'll remark it, and if you're one or two grades under your projected grade, they let you retake it. Check if the same policy applies at your school. Also, you may not be allowed to only retake ONE of your core science exam, you might have to retake it all.
My advice is that you go and ask your hod if you can retake, explaining why you might have not gotten the desired grade ("i felt a little sick that day/I was incredibly nervous and worried/for some reason I didn't process and answer the questions the right way"
but be prepared to get rejected, or given the choice where you repeat everything, or nothing.
If you aren't allowed to retake that particular test,
and you're really desperate, I'd suggest you get a teacher (preferably one that likes you and was slightly disappointed with your grade - not that it was a bad grade) and ask them to foght for you on their behalf. Adults or more likely to follow another adults request than a high school students one.
Don't forget to be prepared for rejection, and don't beat yourself up over it. Use the above excuses mentioned and hopefully it will work. Good luck.