Best strategy for QR, do all quick and or easy questions first, then go back and do the others. You should be able to gauge how difficult each question is at a glance. If you don't know it right away, guess, mark, move on. Then you should have plenty of time and know you at least got all the easy ones!
That's what I do (did) and I got 24 & 22 on Topscore QR 1 & 2 respectively.