In solving any mathematical problem, and moreover the IIT-JEE problems, it helps to have a working procedure. You need to have strategies to solve different types of problems.
the four fundamental steps of these strategies are as follows-
# TO UNDERSTAND- Before you solve any problem you must first thouroughly understand the problem. Read and re-read it to find all the clues and determine what teh question is asking you to find. You can ascertain yourself on the following counts atleast :
@ What is unknown?
@ What are the data?
@ What is the condition?
# TO PLAN- Once you understand the question and the clues, it's time to use your previous experience and expertise with similar problems to look for strategies and tools to answer the question. Consider the following questions:
@ Do you know a related problem?
@ Look at the unknown ! and try to thinkof a familiar problem having similar unknown?
# TO TRY THE IDEA- after deciding on a plan, you should try it and see what answer you come up with. Answer yourself the following questions-
@ Can you see clearly that the step is correct?
@ But can you also prove that the step is correct?
# LOOKING BACK- Once you've tried it found an answer, go back to the problem and see whether you have really answered the question. Some times it's easy to overlook something. If you missed something, check your plan and try the problem again.
Finally check these questions:
@ Can you check the result?
@ Can you check the arguments of the question?
@ Can you derive the result diffrently?
Applying the above idea of problem-solving in mathematics would be difficult initially,but if you keep on approaching anyproblem by dividing in these four parts, slowly you will develop an expertise in tackling mathematics problems at the level of IIT-JEE.
SOURCE: ARIHANT MAGAZINES
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