I am pretty familiar with your school system. I went to Brooklyn Technical High School. People as you know get lazier as technology increases. I am not too optimistic about your attempts to reverse the entire river by yourself. Seems like you are the boy and the dyke. I do wish you the best though and will assist you with specific questions.
In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.
I don't know how the grades equate. That year 10 class was a 'bottom set' ie weakest in the year at math.
Lower down the page you'll find SATs and GCSE papers with a higher level of question.
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei