Basically Avalon, Prenton and Redcourt exist for the 11+ and will devote much time and effort to it. That's not to say it's impossible to fail!
It is worth saying that the entrance exam for St Anselms is not 11+ in style (tho Upton Hall is), so Redcourt may not be so good for Calday/Wirral as Avalon/Prenton.
This is true however Birkenhead School will teach them the maths which is required certainly on the Upton Hall papers which simply is not taught until after the 11+ in state schools.
My daughter had completed the Upton exam after 30 mins whilst her old classmates from state were scratching their heads as the poor souls hadn't been taught what was on the paper despite being tutored.
Have you looked around St Anselms ? It's very how can I put this ... Catholic, you really wouldn't go there unless you were devote.