Ok, so hi!
I AM the daughter so I'll give some tips, seeing as I've been through it all ( AND got in to St Pauls!
), now first of all, I'd like to say that the surprise paper was science comprehension. Although that was this year, maybe next year will be something different!?
Here's the really important bit though, if you have tutored your child a lot and if you are a pushy parent ( no offense ), it will be quite hard for your daughter to get in. Except if she is naturally bright ( which she probably is ), then there is a huge chance.
You see, she may have been tutored for ages on end, but you really have to think on the St Pauls test. You think of ways how to answer and solve the question!
I come from a minute state school and I still got in because I used my brain!
I hoped that helped! If it did but you still want maybe some more information, then please tell me, maybe by private messaging me. But if it didn't, then I'll just thank you for wasting my time!
Good luck to your daughter,