How math question is solved?

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How math question is solved?

It cannot be further emphasized that math is the art of learning how to tackle a practical problem. So what do you do  to solve a practical problem at hand? Well, all that applied to solving a mathematics question.

Understand the Requirements& Expectations

It is not an exaggeration that only a good reader can be a good writer. So before embarking on the hunt for solution  of a math question read it first then reread and if there is iota of doubt please do not hesitate to read two more times.  But that’s not end. Keeping reading question until you have clear sketch in your mind for, at least, what you  are told about and what you are expected to do. Once you have clearly understood the given set of data and desired  outcome, you can start filling the gap by considering the steps and setting up milestones that would be  required to reach the desired outcome.

Keep an Eye on Desired Result

Whether it is an expression or a value, you just need to keep that as your goal to achieve while solving a  mathematics question. The solution starts with identification of one or more pathways to reach the desired goal,  whether expression or value. All the midway steps between starting point and the objective must be leading towards  the desired goal. 

Approach

Be sure, there is no panacea, therefore, no single strategy that works equally well for all math questions. However, a  student equipped with both forward and backwards approach tactics is sure to handle any kind of math question. 

Forwards Approach

Starting point of forwards approach while solving a math question is given data. You can always find something  which can be calculated or inferred from the given data and which also can be obviously helpful to achieve the desired solutions. Then by careful analysis and with the tactful manipulation of both given and inferred or calculated information we can move one more step closer to the objective. And the process keeps on going until you  reach the solution. However, theoretical background like procedures and formulae help these inferences and  manipulations to achieve the each next milestone towards the solution of the question.

 Backwards Approach

Desired solution is the starting point in case of backwards approach. One needs to understand what all is required to find the desired solution and how it can be found, inferred or calculated by manipulations of given data. Again inferences and manipulations are at work which require theoretical background like procedures and formulae help  these inferences and manipulations to achieve the each next milestone towards the solution of the question.

Making A Sketch of Procedure

Based on most suitable and convenient approach to you, make a sketch of solution procedure in your mind. The  sketch may consist of several steps in between the problem statement and the desired solution. If such is the case,  further details in terms of manipulations and formulae must be kept in mind which may be required to move from one  milestone of procedure to the next before finally achieving the desired solution.

Linking Several Parts

It is almost certain and that there lies some connecting link between successive parts of a single mathematical question, barring a few highly unlikely cases.

So if you have applied forwards and/or backwards approach to solve one part of the question, before embarking upon solution of next part read the successive part carefully and in addition to given data in this part also  consider the outcome of previous part as given data for next part.

It will not only fill the gaps in provided information but also shapes and guides one’s over all approach towards the  solution of the question. It is often seen that this consideration is missing on student’s approach to solve the  question which at times bogs students down to tedious approaches and manipulations or totally distracts some from  the solutions of the question at hand. Both lead to undesirable consequences for the student.

Look Back

Once you have achieved the goal and you perceive it as required by the question, do not let your cautions drop.  Read the question again afresh. Understand the requirement, also afresh. Have a look on your approach and  recheck the formulae and manipulations for any mistake and, if possible, check the answer by substitution or  comparison whatever the case may be.

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