Use these topics to increase focus on Mathematics

Mathematics is quite scoring subject for board and IITJEE if students do enough practice with focus. What is important in mathematics is the ability to focus on a problem long enough to solve it. There are questions which can be solved easily while there are ones which require your utmost focus and ability to look at the problem from all angles possible. Especially JEE Advanced problems require you to think from various perspective. For example, many questions in coordinate geometry can be solved using complex number concepts. Many in 3D can be solved by suing the concepts learned in 2D. Vectors can not only help you solve coordinate geometry, both 2D and 3D but also problems in physics. Similarly concepts in theory of equations in Algebra can be used effectively to solve problems in calculus. We all anyway know between huge overlap between permutation and combination with probability.

Distractions cause irreparable damage to your career

The question here is how to overcome students’ propensity to check their devices every now and then. Even when they are switched off, the focus span is too low to really solve long questions. A long question requires focussed work for 20-30 minutes if you are doing it for the first time. Once you get accustomed to such questions, the time reduces to 5-10 minutes. However, the journey from 30 minutes to 10 minutes is crucial. This comes out of nothing but focus and practice, focus and practice, and once more focus and practice. There is no escape.

How do we develop this skill? I am sure many students are really serious about increasing their focus span but fail to do so because of sheer volume of distractions in today’s life. Here is what I think students should try to increase the focus on problem solving. Remember that focus will only come when you solve long questions which require your brain to think and your hands to work. These are the topics which you should solve to increase your focus span. This would enable you tackle challenging problems and also avoid silly mistakes that most of students make while solving a lengthy question.

Here are 5 topics that you can study in details and solve questions to increase your focus span.

Do the elementary operation to find inverse of a matrix

You know what you have to do. You also know the elementary operations that you can do and cannot do. Basically, you know the rules and the objective. All you have to do is apply your common sense and get 1 and 0 in order to get unit matrix out of any given matrix and apply the same in unit matrix to get the inverse. Do it for 3*3 and 4*4 matrices. Get it right the first time.

Solve challenging determinant equality questions

The other way is to solve the questions on determinant where a determinant must be modified to get a given answer. Some of them are really tricky and require you to think from various angles to get it into the right form. In this case too, the rules and clear and objective are given.

Draw graph to solve calculus problems on functions, continuity, and differentiability

Drawing graph requires you to follow few steps and use common sense such as finding the increasing or decreasing nature of function, shape of curve (concave up or down), behaviour of function at infinity, vertical and horizontal asymptotes if any, common points which can help use connect etc. When you think through all these points, you get a complete view of the graph and in turn learn to focus on problems for longer.

Do Bayes’ theorem problems

This too requires you to frame the problem to fit the formula used in Bayes’ theorem. Framing part is important and it requires you to think through the problem and premises given.

Try word problems & transportation problems in linear programming

These types of problems require you to translate the problems from English to mathematics. This requires you to study the problems for objective, premises, decision variables, and constraints. Looking at problem in a wholesome way improves your focus span and concentration.

There are other ways too to help you increase the focus on study of mathematics. I have mentioned few of them which can be used as a stepping stone to start building your ability to focus and work through a problem for longer duration. Solve these topics and see your scores in exam.

~ Pankaj Priyadarshi

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