How to prepare for JEE Advanced from class 11th

So you got 96% in your 11th test conducted by your school. You are entering in class 12th. The usual clamor for the preparation for JEE has started in the family and in your friend circle. You don’t care much because you have done wonderful with your 11th. So you start solving problems of JEE related to the syllabus of class 11th. The first question you encounter is finding the possible number of real roots of a polynomial with degree 4. You are stumped. This is not what you studied in class 11th. All you did was few equations of degree 2. Then what is this?

The reason for this is difference between the “depth” of some of the topics in 11th versus the syllabus of JEE Advanced comprising the 11th topic. Since 12th syllabus is pretty vast, you do not have time to go through 11th chapters once again. This creates problems because not doing 11th topics well will reduce your chances further.

Had it not been better if you knew the topics which are hardly touched by your NCERT books? Let me list some of the topics which you need to go through in depth before you can call them “complete”. The chapters in NCERT hardly touch the surface of these topics.

Theory of Equation

In your 11th book, there is a chapter on quadratic equation. This is such a small chapter that you can finish it in 2-3 hours irrespective of your intelligence. Yes, try that if you haven’t.

However, JEE is notorious for going deep into this. Theory of equations is a very important topic both from calculus and algebra point of view. It literally has no bound. The rules governing nature of roots, sum and product of roots, sign of roots, sum of series of various forms of roots, relation between the roots of an equation and its derivative, and nature of equation between two values of x, convergence or divergence of equation with x tending to infinity, division of an expression, finding highest common factors (HCF), and many more phenomenon are huge in number. The syllabus does great injustice to this one of the most important topics for JEE main and advanced.

Complex number

The NCERT book for 11th combines quadratic equation and complex number in one chapter which can be studies in one sitting. The real scope of complex number in JEE is humongous. This is one of the toughest topics for students. JEE question setters just love this chapter. Playing with arguments of a complex number with different sign of real and imaginary part, using geometry with complex numbers, and twisting all-pervading and unpronounceable De-Moivre’s theorem are some of the ways JEE questions complicate the already complex topic.

Conic Section

The content in conic section in NCERT book is pretty small. They cover just the basic of conic sections. It doesn’t cover tangents, normal, pole & polar, combination of various conics, other forms of conics etc. Once again, JEE loves conic sections, especially JEE Advanced. They have almost abandoned the poor straight line and circle to favour conic section.

What should you do?

While nobody expects CBSE to go deeper into such topics as they are not meant for coaching you for JEE but treatment of theory of equation, complex number, and conic sections given in the 11th textbook is too shallow. There are few more chapters but they cover about 50% or more (at least concept wise).

Hence to prepare well for JEE and do not get overburdened with your 11th topics in your 2nd year, focus on theory of equation and complex number in great details. You must make it sure to cover the gap between CBSE syllabus and JEE standard. You can go through any of the JEE books (Cengage, Arihant, Eduwiser etc.) and study complex numbers and theory of equation in details, solve each and every question, and note down the lessons learnt, important formula, important concepts etc. so that this comes handy for last minute preparation.

Conic section is time consuming. It will require discipline and hours of practice to get expertise. Thankfully since the syllabus of 11th is small compared to 12th, you get more time to study. Use this time to achieve a certain level of expertise before you go to class 12th. Class 12th syllabus is huge. Coupled with the pressure of board, it is highly unlikely that you will have to time to study the 11th syllabus in details in your second year.

Work through these topics and do better in JEE.

~ Pankaj Priyadarshi

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What is the relation between the roots of f(x) and its derivative

Very often students come across questions where they have to deduce the number of roots of a function based on the number of roots of its derivative and vice versa.  Even though there are exact rules regarding the relation between the roots of a function and its derivatives, students get confused. Here is some of the concepts defining the relation. Let’s take some of the typical scenarios.

In all the cases, assume that the function f(x) is differentiable for all x on the set of real numbers, i.e. R. Naturally; f(x) will be continuous for all x on R too.

  1. If a function f(x) is a polynomial of degree n has p real roots and n-p imaginary roots, what can be said about the number of real roots of its derivative, i.e. f’(x).
  2. If f(x) is a polynomial of degree n has n real roots and no imaginary roots, what can be said about the number of real roots of its derivative, i.e. f’(x).
  3. If f’(x) is a polynomial of degree n has q real roots, what can be said about the nature of roots of f(x).
  4. If f(x) and f’(x) has common roots, how to know about this.

Let’s take these questions one by one.

  1. If the function f(x) of degree n has p real roots, then its derivative has at least p-1 real roots. The keyword here is at least. There are cases when the derivatives can have more real roots than the function. For example, take a simple quadratic equation f(x) = x2 + x + 1 has 0 real roots while its derivative f’(x) = 2x + 1 has one real root. There are other cases such as f(x) = x3 – 3x + 5 and f’(x) = 3x2 – 3. The function f(x) has just one real root while f’(x) has 2 real roots.
  2. If the function f(x) of degree n has n real roots, then f’(x) will have n-1 real roots and f’’(x) will have n-2 real roots etc. The degrees of f’x) and f’’(x) are n-1 and n-2 respectively. This means all the roots are real. This means if all the roots of a function f(x) are real, then all the roots of f’(x), f’’(x), f’’’(x) etc. will be real.
  3. If any of the derivative of f(x), i.e. f’(x), f’’(x), f’’’(x) and more do not have all real roots, then f(x) doesn’t have all real roots. So it is useful test if you have to find if a polynomial has all real roots. Keep differentiating and checking if the derivative has got any complex roots. If yes, then the polynomial doesn’t have all real roots.
  4. If f(x) and f’(x) have common roots, you can take HCF (highest common factor) between f(x) and f’(x). If the HCF is an expression in x, then the roots of that expression are also the common roots of f(x) and f’(x). If the HCF is 1, then there is no common expression between f(x) and f’(x). This means there is no common root.

By the way, do you know how to find HCF of two expressions?

~ Pankaj Priyadarshi

How to take competitive tests and use your time effectively

In pen and paper test format, you have the ability to take a look at all the questions in one go. This provides you with certain advantages that online test takers do not have. Online test takers can see only one question at a time. The comprehensive view of the entire question paper helps you plan your strategy better.

Despite the flexibility offered by pen & paper test, students tend to do the same mistakes. This is not surprising though as each year the test takers change and for them the same mistake is new mistake. Here are some of the most common mistakes in tests that students make. These mistakes play havoc with their chances of clearing the test and scoring good marks.

  1. Spending excessive time in solving a difficult question thus leaving less amount of time for easier ones.
  2. Leaving few easy questions because of lack of time
  3. Making silly mistakes in easy questions because of lack of time
  4. Leaving out revision because of lack of time

All these mistakes are common. You may not make all of them but some of them. If someone is not making these mistakes, he or she is well on the path of success. Good luck.

However, if you are one of those who can identify with these mistakes, here we are giving some thoughts on how you can avoid them and use your time more effectively. These are simple, yet powerful strategies known to improve the score as well as provide framework for disciplined way of taking tests.

Here is what can be done to improve the efficiency and thus score in the tests.

Spend few minutes in going through the question paper

As soon as you get the question paper, give some time to it rather than start solving from the start. Go through the questions. This will give you a fair idea about the “toughness” of the paper.

Categorize the problems

Categorize the questions in 3 types; namely easy, medium, and difficult. Mark these problems on the question paper in any symbol that you can use. For example, you can use tick mark for easy, circle for medium, and star for difficult ones. Now the question is how you categorize the questions under these categories. The easy ones are those which are easier to solve for you. You know the process and you also know the result that the process generates.

The medium ones are those which you know how to approach initially but depending on the interim results, you will use further concepts to solve. For example, a question on functional equations may come under medium for you because you may know that partial differentiation is way to go, but whether this produces the equation in right form for further work is not clear.

Difficult ones are those which you either cannot solve or have a vague idea about how to approach.

Go in the order of easy, medium, and difficult

Start with solving the easy ones. Solving them first not only gives you a solid start but also initial confidence. The initial confidence is crucial in any competitive test. Many careers are wasted because students lose confidence in the first few minutes of the tests. So start with the ones you can solve.

Once you complete easy ones, attack the medium ones. Some of these questions will open up more as you start working on them and you will find your answer. Some of them will give you hard time and you fail to get the answer. In such cases, try the process of elimination. Usually, you will be able to eliminate 2 guesses. For the remaining two, you will have to work little more. Use values, work backward etc. to eliminate the last wrong answer and select the right. Of course, the process is elimination is more useful in case of single choice. For multiple choice and other types, you have no option but to solve. This can be extremely useful in JEE Main as the questions are all single choice.

For difficult ones, try with the ones which come from your relatively stronger subject. For example, if your Algebra is relatively stronger than your calculus, start with difficult questions from Algebra. You will have higher chances of getting it right than if you start with calculus.

Leave 15-25 minutes in the end for marking, revising etc.

This is the most crucial step. Many students circle the options in the OMR sheet at the end of the test. If you are one of them, leave ample time for marking and revision. If you did it before the time, you can go back to solving the remaining questions.

At all cost, avoid rush in filling up the options in OMR sheet. Any mistake in sequence of questions and wrong filling the answers will do irreparable damage.

Take these steps and see your results getting better.

~ Pankaj Priyadarshi

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

Studying geometry in complex number – I

Complex number is worth its name, complex.

While complex number itself gives hard time to students, its use in geometry adds further difficulty. How do you represent geometric shapes in complex number? What is the meaning of the equations when represented in terms of complex numbers?

While this is a difficult topic, little bit if care and observations can go a long way in making this topic simpler for students. Let’s look at some of the typical examples and how to interpret them.

For JEE (Main and Advanced), you need to know these basic application of complex numbers in geometry and how to apply them in solving questions.

You really don’t need to solve Loney’c coordinate geometry using complex numbers. Loney’s coordinate geometry can be solved using the coordinate geometry concepts which are far easier than complex number.

More on this in my next post.

~ Pankaj Priyadarshi

JEE Main score – Is there any correlation with your performance in upcoming JEE Advanced

There is absolutely no weightage of JEE Main score for admission into IITs and hence there is no impact on your chances if you have scored low as long as you have come in top 2 lakhs people who can take JEE Advanced. So focus on your study, prepare hard, and do well on 21st May, the D-Day for you.

My purpose is to find if there is any correlation between the JEE Main score and JEE Advanced. Does the JEE Main score say anything about your possible JEE Advanced score. This is purely based on my experience in dealing with JEE aspirants.

JEE Main and JEE Advanced – The difference

JEE Main and Advanced have different standard of questions and they test your ability in many different areas. JEE Main is relatively easier as far as standard of questions is concerned. In case of JEE Main, the questions can be relatively easier but time is vital. Judicious use of time can make you chances bright while wasting away your time in silly mistakes, deriving formulae, spending too much on one subject and neglecting others can kill your chances.

Moreover JEE Main tests your skill of problem solving. There is very little scope of creativity. Most of the concepts are duly explained in your textbook (Arihant, Cengage, K C Sinha etc.). However, the syllabus is exhaustive. If you have gone through the syllabus and concepts thoroughly, JEE Main can be less stressful.

However, don’t get deceived by the questions of JEE Main that look easier. Most of the students end up making silly mistakes and losing 1 mark. Actually you are losing 5 marks, 1 for wrong answer, 4 as opportunity loss.

Hence JEE Main tests your problem solving, accuracy, and diligence.

On the other hand, JEE Advanced is relatively more difficult. In all the subjects, physics, chemistry, and mathematics, JEE Advanced is tougher. At the same time, the degree of toughness in mathematics is altogether at a different level. I am sure all of you have experienced this. JEE question makers love to combine different concepts in mathematics and roll all of them into one nice difficult question.

Solving JEE Advanced problems not only require your problem solving skills but also presence of mind and use of creativity. Using diagrams, taking cases, putting values, and little bit of insight helps you work through the problems. When I use the word creativity, this doesn’t mean the “smart” way of solving which requires no effort. Creativity comes out of focused practice of problem solving. Hence you cannot avoid problem solving. Lot of “boing” hours of study and practice are spent behind the “smart” exterior.

Your score in JEE Main and its correlation with JEE Advanced

First, if your score is very high and you fall under 250+ bracket, you are already set to get good score in JEE Advanced unless there is big mess up. You have burned midnight oil, worked hard, and deserved your success in JEE Main. All that you have to do now is to revise the concepts, revise the difficult concepts twice, work out some problems which give you hard times, go through all the past JEE Advanced questions, do 10-20 mock test papers available in the market. Arihant and Cengage keep publishing such books.

When the score in JEE Main is below 200, the correlation between the score of JEE Main and JEE Advanced becomes even less. I have seen students scoring 180+ in JEE Main but failed to get selected in JEE Advanced. At the same time, I know few students who barely passed JEE Main but ended up ranks below 5000 in JEE Advanced scoring 150+.

While many students who work with enormous due diligence can get great score by avoiding such mistakes, they cannot use the same diligence in JEE Advanced, may be because of exhaustion or distraction in JEE Advanced. At the same time, many bright students taking questions too lightly end up making mistakes which lowers their score. They take it as lesson learnt and avoid the same mistake in JEE Advanced.

Finally the point here is to convey to students that if your score is good in JEE Main, maintain the same due diligence and hard work for another 3 weeks. Additionally, students who did average or just passed JEE Main, avoid the same mistake in JEE Advanced.

This is not yet the end. Picture abhi baaki hai.

~ Pankaj Priyadarshi

Approach to problem solving in mathematics

While mathematics falls under science, problem solving is an art. Just like in art, you get better and better as you do more; you get better at problem solving as you solve more and more problems. However, you need a structured way to solve problems to make it more effective and internalize the lessons learnt. Here I will list few steps and how students can apply these steps in problem solving for their board, and JEE main & advanced. This is again a very mathematics oriented approach. If this helps in Physics and chemistry, it is well and good.

Draw a diagram whenever possible

Chinese saw it long back when they said, “A picture is worth a thousand words”. Is it the reason why mathematics Olympiad is dominated by Chinese students?

This becomes extremely important in coordinate geometry. I have seen reluctance from students from drawing the picture. They find it difficult to draw diagrams. This shouldn’t be so. Take for example, drawing 3 normal lines on a parabola. Students dread this because the normal lines do not look like normal at all. But have you seen the real drawing in your book. Just check. The point from where 3 normal lines are drawn on the parabola is little farther from the vertex. Moreover, out of 3 normal lines, only one is in the same side of the point while 2 are on the other side. If you look carefully and keep these things in mind, drawing is not at all a problem. In fact it will make things quite easy for you. Similar pattern you can find in all the difficult drawings especially in conic section of coordinate geometry.

The same thing can be done in 3D even though drawing 3D is difficult. Draw only the relevant things that are asked. For example, if you have to draw a line on a plane, simply draw two perpendiculars line and assume that you are looking at it from the side view so that the plane looks like a line. This will help you draw.

Identify the purpose of the problem

The purpose of question is to find or prove something. It may be find the value of an expression, value of variable, prove or disprove a hypothesis. While this sounds quite obvious, it doesn’t look so when you see interpretation of problem by many students. It is not that the language is difficult but the span of concentration is low in today’s times where instant gratification is the most desired thing in the world. Read the question carefully and clearly note down what the question is asking.

Note down any information given about the quantities, both known and unknown

Information about any variable helps you set the boundary of your problem solving. If it says that the variable whose value is to be found is positive. You can remove all negative real numbers including 0 out of your options.

Note down the information and inferences that you can draw

Sometimes you have to draw the information by looking at the equations and problems. For example, if an equation of odd degree is given, you can be very sure that all its roots are not imaginary. If there is an equation of even degree with leading positive coefficient and negative last term, you can be sure that there are at least 2 real roots, one positive and one negative.

Give a name to all variables and constants in the problem

Once you have written down the unknown and known quantities, give those names (x, y etc.) which can be readily used in framing the equations and working through formulae.

Then use all related knowledge till you find sufficient equations for unknowns

Finally solve. Use all your knowledge to solve the question. Your goal is to solve the problem and get the right answer. While solving, keep your mind open for any new insight that you can get into the problem. Remember that solving mathematical problems is also a skill that you build by using formulae, processes, methods, and finally insight or intuition. Most of the students confuse this insight with tips and tricks. This insight or intuition comes from solving lot of problems of different types. Keep solving and discovering.

~ Pankaj Priyadarshi

How to approach functional equations problems

A function is the relation between 2 variables. These are important because in most of the situation in life, you find variables. Some are dependent, some are independent. And the relation between them is known as function. For example, y = 5x + 7 is a function. This is an example of explicit function where y is on one side and an expression involving x is on the other side. This is of the form y = f(x).

On the other hand, you have implicit function where the relation between x and y are shown in an indirect way. Some of the implicit functions can be changed to explicit by rearranging the variables while some cannot be changed. For example, x + xy + 2y = 0 is an example of implicit function. If we write the same function in the form of y = -x / (2+x), this becomes explicit. However, functions such as xy = sin y + x2 – y2 cannot be changed into explicit form.

In all these functions, variables are the building blocks.

There are other functions which use functions instead of variables. These are called functional equations. You have come across such functional equations in your 11th/12th while preparing for JEE. These equations are expressed in terms of functions. Some of the most common ones are Cauchy’s functional equations, Jensen’s, and a lot of variants derived out of these. These are the most usual ones you will encounter:

f(x + y) = f(x) + f(y); f(x + y) = f(x).f(y); f(xy) = f(x) + f(y); f(xy) = f(x).f(y). There are more complicated ones a=such as f(x).f(1/x) = f(x) + f(1/x), f((x+y)/2) = (f(x) + f(y))/2 and many more.

You are usually asked to find the function f(x) or the value of the function for a given value of x such as f(2). Here are some of the ways you can approach the problems.

Observation of functional equation

Your syllabus is limited even though it looks like never ending. What is never ending is creativity of JEE question makers which is what makes JEE challenging either by time or by level of difficulty. The function will come from the usual category; these are polynomial with mostly highest degree term with a constant, logarithmic function, exponential, rational, or trigonometric. Looking at the function will give you some insight into the type of function f(x) might be. Some of the questions are dead giveaways and you don’t have to make lot of effort. Some may require more work. For example, sum in the left hand side and product on the right hand side may be a sign of exponential function. You may have to find the multiplication factor and the constant though to get the right answer. These can be found by the additional information given in the question.

Use differentiation by first principle

This “low priority” concept is very useful in functional equation. Using differentiation by first principle gives you the required equation with the term f(x + h). f(x + h) can be used to involve the functional equation given in the question. Using differentiation by first principle shows the relation between the function and its derivative. Once this relation is discovered, you can use integration to find the function.

Use of partial differentiation

The final way is to use partial differentiation. In partial differentiation, either x or y is taken as constant and the whole functional equation is differentiated with respect to the other variable. This means if x is taken as constant, differentiate with respect to y or vice versa. Once this is done, replace one of the variables with a constant. The value of constant depends on the question. If the question doesn’t specifically mentions it, some experiment with 0, 1, -1 etc. should give you enough hint. Once this is done, you get an equation involving function and its derivative. Now use integration to get the right function.

Functional equations can be as difficult and as easy. The scope of variation is humongous and so are the ways of finding the solutions. Many functional equations may still require more work but for your level, these should be enough. You may have to combine these concepts with “theory of equations” concepts in difficult cases though.

~ Pankaj Priyadarshi

Can one crack JEE (Advanced) by starting serious study in 12th

So you just saw your 11th class test and got depressed and went to Facebook & WhatsApp to release your tension and hey they are all discussing the class tests there too and 90%+ marks in almost all the subjects. You even saw your close friend getting 99% mathematics. Now this kills. 99%… did the examiner make some mistake? The social media looks like full of anti-social elements securing high marks and bringing social disharmony. Remember the movie “3 Idiots”. If your friend fails, you feel sad. If he tops the class, you feel sadder. Human nature…

But let’s get serious. Despite all your temporary defeatist thoughts, you cherish a desire to get back to study and be serious this time. There is just one year left and you have to take Board, JEE Main, Advanced, NEET, BITSAT, and may be SAT if you want to study abroad.

So here is the question most of the students, who spent more time in youthful venture than on the table studying for their career, ask. Did they already miss the bus or can they still jump in the race to crack some of the toughest entrance tests in India. Let me answer this with my experience.

The answer will largely depend on two factors:

  1. Your comfort with the 11th syllabus
  2. Your willingness to focus in class 12th

First, a little about the syllabus In JEE Advanced, almost 60% of the questions come from class 12th. Hence the proportion of 12th is higher. However, questions from chapters of 11th such as permutations and combinations, complex numbers, theory of equations or quadratic equation, probability, and coordinate geometry almost always appear in the test. These are favorite topics of question paper makers from 11th syllabus. Hence ignoring 11th is not an option at all if you want to succeed in JEE Advanced.

Now let’s answer your question:

Your comfort level with 11th syllabus

As mentioned above, look at the complete syllabus of 11th. Select the topics which you haven’t done well. Topics mentioned above are pretty vast in scope. If you have left all difficult topics then you have to work extremely hard and long hours to understand them. Moreover, there is no one to help you as your school will teach you class 12th. You may ask your coaches to revise these topics. But remember that you have to put lot of efforts. This becomes even more important since you have to also study class 12th syllabus.

Your willingness to focus

Since a full year is wasted, you have to ensure that you will spend twice the amount of time than your friends. The syllabus of 12th itself is very comprehensive. Calculus takes major part of 12th syllabus. Topics such as application of derivatives, indefinite and definite integration, differential equation and its applications are huge chapters. Moreover, 3D and Vectors are other areas where students face problems. 3D requires visualizing the shapes and curves in 3 dimensions which is difficult to draw on paper.

How much hours of study is required

Double of what you would do otherwise. Realistically, studying on your own at least 4-6 hours a day should be good enough. Add to this your school and coaching hours which is about 8-10 hrs. This is a ballpark estimate. You have to decide for yourself depending upon your level of knowledge and size of your ambition.

Finally, remember that this one year of effort can make your life much easier. You will have lot more time to do what you want to do now apart from study. IIT campuses are fun places with little bit of before-exam study hours unless of course you want to change the world with your engineering skills.

~ Pankaj Priyadarshi

How to analyse your mock tests for JEE Advanced

Now is the time to practice mock tests for the upcoming JEE Advanced. Take at least 2 full tests (of 2 papers each) in a week. Since you have about 5 weeks, you should be able to complete 5 sets, i.e. 10 mock test papers of 3 hours duration. You should take the tests in a very similar environment and practice all that will actually happen in your test centre. Here are some important things to consider when you take mock tests.

  1. Follow the timeline strictly. Don’t give excuse that I was doing something in between the test for 30 minutes so I will take extra 30 minutes at the end of 3 hrs to compensate for it. Never do it. You are not given this option in actual test. Adhere to timeline.
  2. If you forget a formula, don’t rush to open your book and check. This is again an option not given in the actual test. Try to remember if you are keen to solve the problem or derive it though I will not suggest deriving it unless it is easier to derive. Derivation in actual test kills enormous amount of time.
  3. Do not dilly dally with things on your table such as playing with pen, checking your smart phone, attending calls etc? Switch off your gadgets and cut off from the world for 3 hrs. It is not going to change in 3 hrs, I assure you.
  4. Do not leave a test in between. Do not get frustrated by a few questions and skip the test thinking that I will take the next test. Work through the test for 3 hrs and then close.
  5. Use the OMR sheets. There are plenty available in the market. Darken the right answer and don’t change if you have done it by mistake. Get it right the first time.

 

How to analyse your test

Once you have taken the test, you have to analyse your performance. Here is what you should do to make your analysis more effective and hence more helpful. Divide the questions into 3 categories; “Right”, “Wrong”, and ‘Not attempted”.

For right questions, you don’t need to worry. They are right because you know how to solve such questions and have command over the topics related to them.

Analysis of “Wrong” questions

For wrong questions, note down why they are wrong. Since you attempted to those questions, there must be reason why you couldn’t solve it. The reasons could be one of the following:

  1. You made silly mistake. By the way, these silly mistakes are not silly. They cost you a fortune and make or break your chances to IIT. Avoid silly mistakes like plague. Most of the students do not take these silly mistakes seriously but that is what makes the difference. Once again, “avoid silly mistakes”. Write this on a paper, paste it in your study room and follow it. Remember that one silly mistake costs you 5 marks. This means you lost 4 marks which you could have scored by avoiding the silly mistake and you lost 1 mark for wrong answer.
  2. You did not know how to proceed after a certain point. Where you got stuck? Fine out precisely what you did not know. For example, while solving probability, did you confuse between conditional probability and Bayes’ theorem? Did you misunderstand point of inflection in calculus? Asking these questions will point precisely where your weak area lies. Note down these areas and focus on them. Look at these points in the same day. Do not postpone.

Analysis of “not attempted” questions

For “not attempted” question, you should ask yourself why you did not attempt the question. The reasons will be limited. You may not have known the concept behind the problem. You may know how to proceed but couldn’t recall a formula that was supposed to be used. Note down these points and work to improve.

~ Pankaj Priyadarshi