TITLE: How should I learn maths?
QUESTION [6 upvotes]: I am 17 now and I have several questions to you. To let you better answer my questions I think I should tell more about me. I am pretty good at maths at school(but I often make silly mistakes thats why I am not scoring only 5 <- that's the best mark in my country) I am quite good at school level but I really suck at competitions. My teacher makes me feel like I am not worth her attention and she is spending more time with students that are better than me thus making me feel like I am useless.
  Here are my questions:

Is math just really hard work and that's only thing I need to do?
I want to start solving exercises from school. Should I start from beggining of my book or from the point I am currently on in school? Or maybe I should solve problems from competitions( even if they are way to hard for me)
Should I consider making silly mistakes a big problem? How can I fight with it because I am really annoyed that I am getting a lot of 4s instead of 5s.

REPLY [2 votes]: This became too long for a comment:
Have fun with it: Try to think up (relatively simple) problems that seems right on the border of what you think you are able to solve... You'll most likely need to learn some new techniques in order to solve the problem, and that's a great way of learning math! A famous mathematician, John Conway, very much has this approach to doing research (much of his most important work comes from him considering games). 
The silly mistakes don't matter so much outside of competition math (and competition math doesn't really matter) - real math is about thinking abstractly and creatively; the algebra skills will come with practice, and your mistakes should become rarer. 
And as has been said in the comments, don't worry about the scores. It seems like some of your motivation for doing math comes form a desire to be validated (which is perfectly natural, mind you!), but try to instead steer your mindset toward just enjoying math for the crazily beautiful and mysterious subject it is; enjoy the thrill of discovery, enjoy wondering about the deep structures of numbers, algebras, geometric objects, etc., and enjoy bettering yourself. Becoming good at something in life often gives a sense of confidence, which (partly, at least) makes the desire to receive validation and admiration from others less important. 
Good luck!