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I am an adult learner, revising my high school mathematics from pre-calculus to calculus. I never took calculus in high school - trying to self-learn it. I was never good at mathematics.

I revised Algebra 2 and Pre-Calculus few months back, mostly via KhanAcademy, watching some videos and completing some exercises. Now while learning Calculus, I've been unable to recall/grasp some of the concepts in Algebra 2/Pre-Calculus. I had to revisit those lectures and exercises multiple times.

Is this perfectly normal to forget High School mathematics after sometime? How can I really master the concepts and remember "formulae" by heart? How do I improve on my understanding on maths and speed up the progress?

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    $\begingroup$ It is $200\%$ normal (except in statistics, where its probably something like $86\%$). Indeed, this is why we have Google. You should, however, be able to do everything much more easily the second time around. $\endgroup$ Commented Feb 28, 2017 at 15:38
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    $\begingroup$ In order to improve my advice is simple: learn by doing. And math.stackexchange is a great place to do exactly that. Pick any problem you see here and try to solve it. That's at least how I've gotten back in the game. $\endgroup$
    – freakish
    Commented Feb 28, 2017 at 15:42
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    $\begingroup$ Nobody would expect to stay good at, say, golf without regular practice. Mental skills are not so different. $\endgroup$
    – Joffan
    Commented Feb 28, 2017 at 15:42
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    $\begingroup$ Well, they use it all the time, for years... and in my experience, they still don't remember everything... $\endgroup$ Commented Feb 28, 2017 at 16:22
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    $\begingroup$ @SimplyBeautifulArt haha, so true. Even worse is knowledge of college level math... I have yet to meet a high school math teacher who has been out of college for a while and can still remember complex analysis, abstract algebra, etc. I'm sure there are some (evidently even users on here such as Jack D'Aurizio) but they are more rare than common I'm afraid $\endgroup$ Commented Feb 28, 2017 at 21:05

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It is perfectly normal for humans to forget things after a period of time. However, here are some tips to help you "relearn" the material you have forgotten.

From your question, I understand that most of your learning came from KhanAcademy. While KhanAcademy is a great learning tool, it was never intended to replace a full year-long (or semester-long) course. Instead, it is mostly used as a supplement to reinforce concepts learned in the classroom.

Khan Academy is a great tool; however, it should not comprise the majority of your work on a subject. If you still have your high school textbooks, dust off the cover and reread them. Do the exercises at the end of each chapter - I know most textbooks have answers to odd-numbered questions. If you can't do a question, ask for help (like here!)

If you don't have them anymore and you don't want to buy a $200 textbook, you can get free exercises online. Just search up, say, "trigonometric identities practice" or "polar equations review problems". The more math you do, the better you will become.

In the beginning, it will be tough. You might be frustrated, and it might seem like you aren't making any progress. However, it will get much easier as you progress, and you might even find yourself enjoying the problems that you are doing.

But no matter what, don't procrastinate! The sooner you start, the more you will learn. And the more you do, the better you will get. You shouldn't have to memorize formulas by heart, strive for understanding, not for memory. For example, consider all those complicated trigonometric identities like $\sin(x+y)=\sin x\cdot\cos y+\sin y\cdot\cos x$ Do not memorize these formulas; instead, understand why they are true. Only this way will you be able to remember them.

Good luck, and have fun with the problems! :)

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  • $\begingroup$ I feel that I am rote learning or just memorising the steps, which resulted in the learn and forget process. How can I really understand Maths? $\endgroup$ Commented Mar 1, 2017 at 12:15
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    $\begingroup$ Every time you learn a new theorem, property, or identity, try to rederive it yourself. Understand the "why" behind every step. Then, a few days later, come back to that theorem and try to derive it again. If you get stuck, reread the proof, etc. and repeat the process. If you find that you keep forgetting, it's possible that you don't fully understand the proof. That's when you should ask for help online (like here). This way, you can avoid memorizing and instead understand the math. $\endgroup$ Commented Mar 1, 2017 at 18:27

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