Mathematics is very much the most challenging subjects and most students face difficulty in solving challenging problems of mathematics. However, with a bit of smart work (and hard work), you can surely be an expert in mathematics and ace the competitive exams easily.
First of all, understand that mathematics requires great analytical ability – the ability to read, comprehend, make conclusions and use the known techniques to solve a problem. So, to be good at mathematics, you will have to develop the analytical ability – the ability to think critically.
Now, there is of-course no shortcut or trick that will help develop your skills overnight. It’s a process of dedicated hard work & patience. But you can achieve that following a few crucial points:
Think Back on what you learned:
When facing a new problem, try correlating it to a problem you have done before. This will help you to analyse the problem better. Of-course, for gaining that kind of command, you would have to solve a large number of problems of varying concepts and difficulty level.
If you fall down, get back up:
Never let your shortcomings affect your goals. It is very easy to set a big goal without tentative planning during you preparations and lose hope when things does’t go according to the plans. Always set smaller and short-term goals leading you to your ultimate target. Always make your study plans best suited to you. You can always take support and guidance from your mentors, guardians and teachers, but in the end there is no true or better judge of one than oneself.
Spend time on a problem before giving up:
Of course, your time is precious and you have more to do than just sit stuck on a single problem. However, the time you spend in analyzing the problems from various angles is when your analytical ability will be built. You will not learn anything new by solving a problem you already know. All you will do is end up improving your speed and possibly accuracy which can alternately be done by giving weekly tests and assessments. The actual learning happens when you spend time on a new problem and try to come up with a solution yourself after assembling what you have learnt.
Always make clear readable notes. People always make this mistake when it comes to mathematics. Always write down important points in theory and new concepts and techniques you learnt on various occasions during your preparations. These are the points which will help you in making a quick review of topics before you appear in competitive examinations.
Focus on core concepts:
Focus on the core concept rather than simple non trivial aspects of a problem. Whenever you approach a new problem with critical reasoning, you will always spend maximum time to crack that first step, where you get the direction to solve a problem, and that is the crucial step where you get explore your capabilities and extent of your practice. Though, for the sake of avoiding silly calculation mistakes, you should always solve a to the end to match the answer.
Mathematics is a hard learnt subject and can only be learned from lots of practice. There is no other formula to be good at mathematics. Always try to attempt the problems on your own, revisit the concepts your learned and then try again. Only after this, if you find yourself a loss, approach your friends or teachers for hints.
Will you all a very good luck. I hope this post helps you in your preparation.