Mastering Mathematics for hacking basics

For mastering hacking to the core, your mathematics skills should be perfect. In this article, I present you some facts required for mastering mathematics using a simple example of how to crack the IIT-JEE mathematics paper. You may wonder whats the connection between IIT-JEE and hacking? In a recent study conducted by appin, best hackers in India hail from IIT’s. This is an embed to educate people how the IIT’ians think about mathematics. Goal is to get the basics right.

“I have practiced more questions than others, still I score less. Can you tell me why?” This is a common question students ask after any Mathematics paper. The answer to this question lies in the fact that practice does make perfect, but the assumption is that you practice the right set of questions, and do them correctly while practicing as if you were giving the actual paper.

There are some interesting facts about pattern of Mathematics examinations in IIT-JEE. For example, in the year 1996, the exam had really simple questions but it was lengthy. In this examination scenario, rarely would a person complete such an exam and thus the success would lie in an individual’s ability to select the set of questions that would need minimum time and fetch maximum marks. However in the year 2000, the exam had only 10 questions, with each question having 2 parts where, although not mentioned explicitly, the result of 1st part was used in 2nd in all questions. Students who didn’t identify this fact had a touch time in attempting the 2nd part and wasted a lot of time. Taking another instance, in the year 2001, the examination level was moderate. Examination had a good mix of simple and tricky questions. A person with cool mind with an ability to identify the simple questions would generally perform well in it. In case someone attempted the tricky ones, they might get discouraged and may not be able to attempt the easier ones as well. I strongly recommend you to solve previous year papers and identify their patterns while solving. This will help you in identifying the patterns of examinations that come, revising concepts and creating an exam like atmosphere during practice.

There are also certain tips I will pitch in for certain topics There are several problems that can boggle a student in Quadratic Equations. My recommendation for students is to draw a graph of all possible cases of a quadratic equation to get a mental picture of the problem. Let’s try to draw the graph of

2 x^2 + ax+ 2 =0

• The coefficient of x^2 is 2 >0 thus the graph opens upwards
• Discriminant D = a ^ 2 -16. Assuming real roots, D>= 0 for a>= 4 or a<= -4 which implies that the lowermost point of graph intersects the axis under these conditions.
• For complex roots, the lowermost point is above X-Axis.
• Intersection with Y –Axis can be found out by putting x=0, comes out to be y=2.

Thus within half a minute or a minute you will be able to visualize the whole problem.

Certain other topics like Progressions, Logarithms, and inequalities keep on coming either as a part of a bigger question or as short questions. You need to revise these topics as they are generally simple and form part of bigger questions, and without understanding them thoroughly, you may lose out on a simple big question. It may seem basic to many students, but many often get confused between log (to the base 10) and ln (to the base e) during the IIT-JEE examination. This kind of sensory acuity during the exam again requires one to maintain a cool head during exam and loads of practice to embed these in one’s nervous system as opposed to just doing it once or twice.

You can also revise formula of logarithms right now. The formula mentioned below are good enough to solve most of the problems in logarithms. You can also try out some problems in logarithms using these formula

Integral calculus is a very important chapter and you need to try right methods while solving a question. It may seem very basic to you but I have seen people solving the problems in following ways:

∫ tanx dx = ∫ (Sinx / Cosx) dx = (∫sinx dx) / (∫ cosx dx)

This is absolutely wrong, as although you could have taken a similar approach in Differentiation, you can’t do the same in Integration. So beware of these disastrous mistakes as they might cost you selection, don’t ignore them as silly mistakes. All the formula of integral calculus need to learn t and applied in a very structured manner. This is necessary when you practice questions towards the end, as the way you apply them during practice will be the way you will apply them in your exam.

The science of Neural Linguistic Programming has come out with bright techniques to remember formula. One important technique to remember the formula is to place right eye in the upper right position. This accelerates visualization of the formula. In fact I used to learn all formula using this technique. For example – In coordinate Geometry I used to first visualize the figure say a circle and then I used to mug up all formula by visualization. This not only prevented confusion among different formula but also helped in fast retrieval.

At the same time you can use a small trick. Problems in which you want to prove questions you can work the solution other way round. For example, in case you know that you need to prove a result, you can assume the result and backtrack to see if the premise or the assumptions hold true. For example – If you are given the following problem: a>4, prove that the graph of equation: 2 x^2 + ax+ 2 =0 intersects X-Axis twice, you can solve this problem by assuming that the equation has real unequal roots (implying intersection) and find assumption when the statement is true (a>4).

Generally the topic Complex numbers is considered tough. There are many problems in Complex Numbers which become the easiest in Coordinate Geometry and Vectors. Remember, you can always imagine a complex number as a 2-D Vector.

In the end I will like to mention few check points:

• On solving a problem, learn its technique as well as similar problems that can be solved using same technique.
• Learn all formula in a structured way keeping in mind the kind of questions that use them.
• Practice previous year papers and understand their psychology.
• During the examination identify the pattern of examination and perform accordingly.
• Enjoy Life and Relax