@LesterKnopf
Thanks for the responses and tips about the mock exams at other schools - I didn't know they were an option.
To those questioning why I am confident she will pass the exam - well if I didn't think she stood a chance on her own merit why would I even consider the school. I don't believe in getting an external tutor because it's not sustainable throughout her time at the school. If she can't pass on her own merit /effort she won't be happy /able to cope at the school long term. We will help her at home, do practice questions etc because that is more reflective of the support she will have after she starts at the school. We will also be looking for non selective schools she could be happy at so there is not too much pressure on her at exam time.
LesterKnopf- your second message clarifies a lot and I think what you're planning is a sensible approach. We had no outside tutor either, but DH and I helped our dd's with the work at home, so did home tutoring as do many of the other parents that I know of whose dc's get places at grammar schools.
I think there is a difference between saying that you are confident that she will pass without tutoring with only extra work at school (as you said in your original post) and saying that you want her to pass and will provide help at home. From your original post I got the impression that you didn't think tutoring is a good idea, but home tutoring is tutoring too, so I thought you were just relying on the school helping her prep for the 11+, which doesn't happen unless your dd goes to a private school.
I hear this all the time that tutored children will struggle if they get in. This will be true for some, but tutoring can really help unlock a dc's potential that may not have been realised at their primary school. My oldest dd is very shy and quiet and fell completely under her teachers radar at primary, once we started working with her towards the 11+ at home it made such a difference to her confidence.
You'd be surprised how well they adjust without the need for extra support once they are in. My dds are thriving and I don't remember last time I've had to help with any school work. There will of course always be exceptions, but having 2 dc's at grammar schools I have seen first hand how the peer group has a big impact, it's cool to be clever and studious at these schools and it's contagious.
Definitely a good idea to look for a non-selective that you are in the catchment of so that you have a good plan B. We really bigged up our local comp in case dc's didn't get into the grammars. It took a lot of the pressure off.