How to score good marks in Mathematics
How to Score Good Marks in Mathematics
Mathematics, as we know, is the most dreaded subject for some and the most interesting for others. Some students always score very poorly in mathematics whereas there are others who regret for not having scored full marks even if they get in nineties There is reason behind it.
I have been teaching mathematics for a long time and the range of my students starts from lower standards and goes up to 10+2 level and sometimes even higher. I often try to find out the reasons why some students are so adept in mathematical skills and some perform poorly in the subject even though their marks in other subjects are good. Having interacted with students of varying abilities, trying to introduce manifold methods to make the subject comprehensive and interesting and after consulting many mathematical Gurus I have zeroed in on some crucial points which will help the students to get rid of any phobia of mathematics and enable them to score good marks in the examination.
1.Develop Analytical Habits: Make them a way of life. I said to one of my students one day, “Inflation is scaling different heights everyday. In our family we require about 30 kg of rice every month. At present it has become a substantial percentage of my expenditures.” I was talking plainly in the context of rising inflation. To this my student replied, “ Sir, you are slightly wrong. Since the cost of all the things has risen more or less, so your total expenditure has also gone up. Hence expenditure in rice has almost remained the same percentage of total expenditures. But yes, percentage of rice expenditure has become a more significant percentage of your income or salary.” I was a bit irritated at this poking but my student was right. And it is a fact that he has always scored in nineties in mathematics.So the moral is that develop these habits as soon as possible to score well in mathematics and the next time you see a jar full of biscuits, start calculating mentally its volume and the free space left inside it!
2.Think Clearly, Think logically: Always try to think logically and clearly. For this, basic concepts of the chapter in question must be very clear. Confusion arises only because one tries to solve the problems without first thoroughly understanding the basics. Understanding the formulae of the concerned chapter and going through some solved problems helps a lot. If you are confused at some point , think how many things are you confused about or how many ways ahead are there. Now consider each option and eliminate the less likely ways or options. Automatically you will be guided to the right path.
3.Try to get what is required: While solving a tricky problem, too many confusing thoughts cloud the mind. Hence it is important to get after what is exactly required right from the very beginning. And in the process we have to go on finding out whatever is required for the main answer.
4.Always solve yourself and practise well: A numerical problem may look very easy but its solution may not be that easy when you yourself go for solving it. So even if you feel that a particular question is easy, test your skills by solving it yourself. It also sharpens your abilities by minimising the time taken. Practising solving of problems repeats the entire thought process involved in the solution and thus one develops expertise.
5.Never say die: Try try again. Never say, “I will not be able to solve this problem.” Challenge yourself into solving any problem easy or tough, which comes your way. With this, you will be able to develop alternative courses of action if one of your actions fail.
6.Practise beforehand and glance through different sorts of questions before the examination: Practising time is during the period when examination is still at a distance. One should only observe and solve different patterns of questions before the examination. At this time only selective and tough questions should be given time. Also solving previous years' question papers helps.
7.Think fast: Hone your skill of thinking fast. This helps you to avoid any distractions whatsoever. Since you want to reach the answer without losing any time, your reaction time is reduced. This habit is specially useful in muliple choice type objective questions.
8.Expand the solution in steps: Very often a student fails to reach the correct answer because he or she tries to apply a shortcut. For example, a calculation is done mentally and the final answer is written without opening the brackets and without displaying the results of the individual expressions inside the brackets properly.
9. Attempt solving a problem by different methods: Always there are various methods to solve the same problem. If you try to solve a problem in more than one ways, it will give you a chance of comparing different methods in terms of time taken and ease of solving,so you can apply the most apt method in the examination. Moreover, it will result in increasing your operational abilities.
10.Display your answer clearly: Many a time it so happens that a mark or two is deducted for not displaying the answer perfectly even though the entire process of problem solving is right. So always after you have finished solving the problem, leave a small space and write the answer clearly and in somewhat bigger letters/ numbers.
11.Answer the questions in the order you find convenient: It is not necessary that you answer the questions in serial order. Answer as per your convenience. Once you solve a good number of problems correctly, you feel confident and chances are that you will be able to solve a good percentage, if not all, of difficult questions too.
Let us illustrate the above tips with the help of solution to a problem involving use of an equation.The guiding principles have also been displayed by the side of steps of the solution.
Question: A cyclist traverses a distance of 12 km in some time riding with uniform speed. He takes 1 hour less if he increases his speed by 1km/hour. Find his original speed.
Solution:
Let cyclist's original speed=x km/hr. [Try to get what is required ]
Let the time to cover 12 km=t hrs.
.
As per condition (1), x t=12 ….............(1) [Think Clearly, Think logically]
As per condition (2), (x+1)(t-1)=12.......(2)
From (2), x t-x+t-1=12
=>x.(12/x)-x+(12/x)-1=12 ( Substituting for 't' in terms of 'x' from 1)
=>12-x+(12/x)-1=12
=>(12/x)-x=12-12+1
=>(12-x²)/x=1 [Expand the solution in steps]
=>12- x²=x
=> x²+x-12=0
=> x²+4x-3x-12=0
=>(x+4)(x-3)=0
=>x= -4 or 3
A negative quantity is ruled out as the value of speed. [ Think logically]
So, x=3
Answer: The original speed of the cyclist= 3 km/hr. [Display your answer clearly]
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