Welcome to the forum Whitehart
My initial thought having read your post was; could the Head Teacher at her primary school confirm the Maths Master Class? Our former primary school had to put forward children to this type of scheme at the GS so the HT would have been able to include that in any supporting statement. If the HT is willing to support your appeal it is worth having a brief chat to discuss what you need from the letter. In our case the HT was brilliant and even re wrote it after I (respectfully) pointed out I really needed her to say x, y and z!
I referred to the English written task in our appeal and am sure other parents do.
What you do need to be is very concise and to the point about why you want the school. If there was a cut off score which DD didn't reach you need to point out why this was. No waffling!
If you want to post the CAT scores the mods will comment on how good or average they are.
You will have read that it is best to source as many indicators of suitable ability as you can, and that you need to communicate to the panel why this school is most suitable for DD. This could be all manner of things and ideally will be very individual to your case rather than sweeping, general statements.
I would recommend the feedback post by dejavu. A few of us stole her format and it certainly worked for me, but am sure it wouldn't be for everybody. (depends if you have a touch of OCD....)