I'm in High School, and in studying for the ACT Math exam, I discovered that the secret to doing well on it is not simply to know the Math, but to understand the Math. For example, if you know how to solve an equation, but you don't readily think of what the next step could be to simply an already nearly simplified equation or in a question that doesn't make it obvious that an equation could be simplified, you use time trying to think; after 30 seconds wasted, you may see the next step - or you may not.
Another example: A pentagon has 5 vertices and 5 diagonals. An octagon has 8 vertices. How many diagonals does an octagon have? I immediately thought (8)(5), since 1 vertices has 5 diagonals. However, (8)(5) counts every vertex twice, as it counts the number of diagonals coming out of each vertex, not just the vertices they start in.
I want to also be able to see a situation and relate it very quickly to a relation, function, etc. I've started to look at some resources
How to build a solid foundation in mathematics????
and I was curious of what tips might be offered at this forum. I want a deep understanding of how the principles of mathematics work. Thank you in advance for the help.
Resources like these are amazing:
What is a trig function?
I had never seen a visual representation of what trigonometry is before this. It makes it much more clear.