How to Solve Difficult Numerical Problems
Generally, students feel problem in solving numerical problems due to a number of reasons. Most of the time problem arises due to the wrong approach towards the problem. In this article, you will find a simple and most efficient approach with which you can solve any problem correctly.
Solving numericals definitely requires knowledge and skills which can only be acquired by diligent practice. But, the correct approach to solve a numerical problem plays a more important role besides knowledge. Numerical problems are often asked in board exams as well as engineering entrance exams.
Most of the 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 numeric problem.
Students should not get disappointed if they face difficulty in solving a new problem initially as this is usual rather than exceptional. In this context, the following few suggestions are given which students can follow according to their convenience.
Step # 1: Understand the statement of the problem before working out for solution
Image Source: spin.atomicobject.com
The major difficulty in solving a numerical is the wrong understanding or incorrect interpretation of the data. Overlooking a keyword in the problem or being unsure of what is asked in the problem can be a dead-end or lead to incorrect solutions. Always mark or underline keywords and keep an eye on the system of units in case the numerical is from science section.
Step # 2: Make a complete list of all data and quantities asked in the question
Image Source: info.mckissock.com
Students should make a complete list of all the data and quantities using conventional symbols. What is given and what is being asked must be chalked out while going through the problem. Be careful with the units of physical quantities, they must be expressed in units in which each quantity is expressed.
Step # 3: Draw a suitable diagram
Image Source: graphicsfuel.com
Try to draw a reasonably good diagram depending on the nature of the problem e.g. force diagram if it is a problem in mechanics, ray diagram if it is a question in optics, indicator diagram if it is a problem of thermodynamics, etc. In board examinations, students also get marks for a neat and clean labelled diagram. However, in competitive examinations rough diagrams are helpful to visualize the problem.
Step # 4: Identify the principles and concepts involved in the problem
Image Source: logistics.ilm.edu
A numerical in CBSE board exam may be formula based or may be based on simple concepts. However, in JEE Main and Advanced, a problem may involve two or more concepts/principles followed by complicated mathematical equations. So, it is very important to understand the principles or formulae involved in the problem.
Step # 5: Translate the data into algebraic equations
Image Source: 1.bp.blogspot.com
This is the next important step for solving 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. are involved. In the case of competitive examinations like JEE Main and Advanced, more complicated concepts of mathematics such as equations involving nth power, nth root, higher order derivatives etc., are common. Hence, the data extracted must be carefully translated into algebraic equations.
Step # 6: Substituting values in the algebraic equation
Image Source: sub.allaboutcircuits.com
After translating the problems into algebraic equations and making the necessary conversion of units (wherever required), solve the equations carefully. Before solving, students must remember that the number of solutions of algebraic equations must be equal to the number of unknowns in all algebraic equations.
Step # 7: Rechecking the final answer
Image Source: thehowtoworld.com
Last but not the least quick rechecking of the each and every step of the solution is very necessary after you chalk out the solution in order to make sure that if the final answer is the correct answer.
Initially, it will be difficult and time taking to follow all the steps but as you practice more and more problems, the amount of time will reduce and you will get the correct solution in a single attempt, and solving difficult numericals will become a cup of tea for you.
Now, given below are some important articles that may be very useful for students preparing for CBSE exams