How to Solve the Difficult Numerical Problems


This article titled ‘How to Solve the Difficult Numerical Problems’ gives you the clinch knowledge in solving the difficult numerical problems. These tips are more suitable for students from Class 9 to Class 12 students.

Solving numerical requires knowledge, ideas and skills which can only be acquired by diligent practice. But, knowing the proper approach in solving a problem plays a crucial and important role. Many a times students know everything about a topic but they fail to get the correct answer. This is due to their incorrect approach towards the solution of a problem.

Initially, do not get discouraged when you encounter difficulty in solving a new problem as this is usual rather than exceptional. In this context, the following are few suggestions given which you can follow according to your convenience.

1. Begin with Interpretation 

Usually, the students fail to understand the statement of the problem before jumping to find the solution of that problem. The major difficulty for students is wrong understanding of the data. Overlooking a keyword in the problem or not being sure of what is asked for in the problem is the dead end lead to incorrect solutions. Always mark the keywords and keep an eye on the system of units in case if the numerical is from science section.

2. Make a list of complete data and quantities 

Students should make a complete list of all the data and quantities using conventional symbols which are mentioned in the question. What is given and what is being asked must be jotted down while going through the problem. Be attentive with the units of physical quantities, they must be expressed in units in which each quantity is expressed and the unit expected for the answer.

3. Draw a relevant diagram

Try to make a good diagram according to the nature of problem. For instance, for a problem in mechanics make a force diagram, if it is a question in optics make a ray diagram, make a indicator diagram if it is a problem of thermodynamics, etc. In board examinations, students do get marks for a neat and clean labelled diagram. But however, in competitive examinations rough diagrams are helpful to envision the problem.

4. Identify the principles and concepts 

A numerical in school board exams may be formula based or may be on simple concepts. In JEE Main and Advanced, a problem may contain two or more concepts/principles followed by complicated mathematical equations. So, it is very necessary to understand the principles or formulas involved in the problem.

5. Convert the data into algebraic equations

This is the next necessary step to solve a difficult numerical or problem, in the case of CBSE board exams simple concepts of mathematics such as quadratic equations, properties of log, basic calculus etc. would be involved. In the case of competitive examinations like JEE Main and Advanced, even more complicated concepts of mathematics such as equations involving nth power, nth root, higher order derivatives etc., are general. Hence, the data derives must be carefully converted to algebraic equations.

6. Substituting values in the algebraic equation

After translating the problems into algebraic equations and making the necessary conversion of units (wherever required), solve the equations carefully. Before solving, students must recall that the number algebraic equations should be equivalent to the number of unknown.

7. Review your final answer

Finally, last but not the least quick recheck each and every step of your answer. This is very much necessary after you finish writing the solution in order to make sure that if the final answer is the correct answer.

Initially, it will be hard and time consuming to follow all the steps but as you get along and practice more and more problems, the amount of time that you used to consume eventually reduce and you will be able to get the correct solution in a single attempt, and solving difficult numerical problem will become a cup of tea for you.


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