Back pain during sit ups

I have to take a fitness test which I have been trying to prepare for. I need to br able to do many sit ups, push ups and run a certain distance within a certain time. I have started doing sit ups, both with my feet pinned down and without. But I get this horrible pain on the top bit of my back after a while. I'm a teenager, so surely it can't be something wrong with my back. At first I thought it might be my technique, so I tried doing it with my arms crossed in front of my chest and behind my head and I focus on using my abs, and as mentioned before i've tried it with my feet pinned down and not. However the back pain keeps coming and it's really really painful so I can't actually do many sit ups at once! I don't think it's so much about my abs, because I can do many push ups easily, much more than is required for the fitness test, but I would really like to know why my back hurts so much when doing sit ups!