90' TZR 125 jumpy after gear changes

HI all, if anyone can help it would be very much appreciated.

I bought a TZR 125 yesterday, it sounds nice, smells nice, corners nice however, is doesn't accelerate nicely. If I pull off in first gear and give it some, it reaches 6k and I believe that's where the powerband kicks in, when I shift into second, to try and keep the power going, the bike starts to judder and jump as if there isn't enough rev's on (this is the same irrespective of what gear), is it something I'm doing wrong with my shifting or could the engine be lean/rich, I haven't had a chance to check the sparks yet and I'm going to get the chain properly tensioned again later this evening as it is quite tight at present.

If anyone could help I'll owe them an e-beer.

Thanks and Regards,

Nic P.