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How should I develop intuition for maths and physics?

Hello guys,

Im a sixth former studying maths, I will give some background information with my maths in general to help you get a better understanding of me.

GCSE maths was fairly easy for me, getting 8 without revision and got a 9 with minimal revision but looking back, GCSE maths meant nothing. Fast forward to year 12 (currently), I am finding the concepts rather easy too and usually get full/high marks on exercises we do in class. I want 100 percent on my maths exams but I don't really achieve that due to lack of revision because A-Level maths doesnt require much intuition.

Recently, I have purchased "Advanced problems in mathematics" and began working my way through them. Sometimes, I get along the right lines but usually end up at wrong answer because I either missed a step or took an extra unnecessary step. Some of the other questions which are classed as easy, I can't even start on. What really annoys me is when I read the solution and I still don'y understand it. I can't help but think that I have been memorising techniques rather than understanding because I struggle so much when it comes to applying concepts in these STEP questions. I find UKMT MUCH easier than STEP, perhaps it's meant to be that way.

My questions are:

What are the steps to take to be able to fully understand maths at this level?

How to develop my intuition(problem solving skills)?

What would help my train of thought when solving these problems?

How to tell when I am meant to apply which concept?

Personal stories which have helped you go from my position to a better position.

Many thanks

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