Analytic Method

Analytic method

1. The word analytic is derived from the word ‘analysis’ which means breaking up or resolving a thing in to its constituent elements. This method is based on analysis and therefore in this method we break up the problem in hands in to its constituent parts so that it ultimately gets connected with something obvious or already known. In this process we start with what is to be find out (unknown) and then think of further step and possibilities which may connect with the known and find out the desired result. ANALYTIC METHOD

2. EXAMPLE 1 if a 2 +b 2 =7ab prove that 2log ( a+b ) = 2log3+loga+logb Proof: To prove this using analytic method, begin from the unknown. The unknown is 2log ( a+b ) = 2log3+loga+logb Now, 2log (a+b) = 2log 3+ log a+ log b is true If log (a+b) 2  = log 3 2  + log a + log b is true If log (a+b) 2  = log 9 + log ab is true If log (a+b) 2  = log 9ab is true If (a+b) 2  = 9ab is true if a 2 +b 2 =7ab which is known and true Thus if a 2 +b 2 = 7ab prove that 2log (a+b) = 2log3+loga+logb

3. EXAMPLE2 If a/b = c/d, then P.T (ac +4b 2 ) / bc =( + 4bd)/dc. Solution: To prove this using analytic method, begin from the conclusion. The unknown is (ac + 4b 2 )/ bc = (c 2 +4bd)/dc. =>( ac+ 4b 2 )/b = (c 2 +4bd)/d. is true => d(ac+ 4b 2 ) = b(c 2 +4bd) is true => dac + 4db 2 = bc 2 +4b 2 d. => dac = bc 2 . da = bc . => a/b = c/d. This type of the solution of the problem can be easily obtained by analysis. .  

4. MERITS Develops the power of thinking and reasoning It leaves no doubt in the minds of the students as every step is justified. Helps in a clear understanding of the subject because the students have to go through the whole process themselves. It is a psychological method Develops originality and creativity among the students.

5. Students participation is maximum It helps in developing the spirit of enquiry and discovery among the students. No cramming is necessary in this method each step has its reason and justification Students take active role in the learning process resulting in longer retention and easier longer of what they learn. It develops self- confidence in the students as they tackle the problems confidently and intelligently.

6. DEMERITS Time consuming and lengthy method ,so it is uneconomical With this method it is difficult to acquire efficiency and speed This method may not be suitable for all topics of mathematics. Facts are not presented in a neat and systematic manner. Does not find favour with all the students because below average students fail to follow this method. Every teacher cannot use this method effectively