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.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.
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