Phase 1 – Learning Phase
In this phase, you should
(a) Attempt the problem. Don’t jump to the solution immediately. Try at least 5-20 minutes. 5 minutes, if you don’t understand question properly and 20 minutes if you are getting ideas or almost solve it. So average time spent on each question should be around 10-15 minutes. If you have solutions, refer them otherwise mark them and refer solutions later.
(b) Mark levels. After you have gone through the solutions, you need to decide the level of the question and mark it with each question. There can be 4 levels.
Easy : Problem is easy if you are able to solve (without even looking at the solution) it in less than 5 minutes.Average : Problem is average if you are able to solve it by just glancing the solution. You look at the solution for less than 1 minute and get the idea. Or you could do it yourself by trying hard and spend more time to solve it.Difficult : Problem is difficult if you are not able to do it yourself (after spending lot of time) and to understand the solution you have to spend more time on each step and finding little hard to understand the steps. But finally able to understand solution very well.Very-Difficult : Mark a problem a very-difficult if either you are not able to understand the question or question is clear but finding almost impossible to understand the solution or you find either question is wrong or solution is wrong. Don’t waste time on such questions. May be you can tackle them later when you get time. But at this stage they are useless and pull your confidence down.Once leveling is done, this phase is over. This is a Learning phase as you are learning ideas/tricks to solve question which you cannot do yourself.
Phase 2 : Retaining Phase
In this phase you have to appear for a test. The questions of the test would be the average and difficult questions you marked in phase – 1. Just count how many questions you marked average or difficult. If supposed they are x, then time for the test should be 60x/25 minutes. If time is more than 210 minutes, then you can divide questions in two parts equally and take 2 tests.
You have to take test very seriously. It should be like the tests you appear at the center. Taking these tests will improve your following abilities:
Speed : As you know ideas of most of the questions, try to be little fast in solving these questions, specially the one you know who to solve. This will improve your speed to write fast.
Accuracy/perfection : Try to be accurate as much as possible. No room for calculate mistakes. If you realize that you are doing mistakes in more than 5% of the questions, focus on it and before you sit for the test, give a strong suggestion “NO MISTAKES !!”. If you make it a target that you have to be perfect, after few tests you will start seeing the results.
Concentration :There is a difference of concentration when you normally study or when you appear for a test. While doing a test, your level of concentration is much higher. So these tests will help you in improving your concentration on a regular basis. So when you are doing these tests, make an environment that should resemble the environment you face at test center (I know it is possible up to a limit, but try to do as much as you can). Don’t answer phone, don’t respond to door bell, don’t get up for water, don’t give your ears to what others are talking in house, no music and no day-dreaming (living in your thoughts).
Sitting habit : In today’s world everybody is so restless. You know why? Lots of happenings around us. So it is very difficult to be just on one thing for a long time like sitting on a table and chair and study for hours. If you practice FPA, it will help you in improving your potential to sit and study for long hours.
Phase 3 : Strengthening Phase
After finishing phase 2 where you appeared for a test based on the selected questions, you need to review your performance. If you could not solve more than 85%-90% of the questions, you need to repeat what you did in Phase 2 to strengthen your preparation. This is phase 3, where you take the test again. Do it after a gap of 4-5 days. You can even change some ratings before you take the test like you can re-mark some average questions as easy or difficult questions as average or average as difficult. This phase will further improve your preparation and grip on the topic.
You can even skip this phase if either topic is not important or you are short of time.
Phase 4 : Finishing Phase
Finishing Phase is very important phase as it does the last act. This is the fourth and last phase where you revise all questions orally. This phase should come after 4-8 days of the strengthening phase.
Suppose there are 50 marked questions (average and difficult) that you want to revise them. Keep 30 second for each question. So for 50 questions, you can take 25 minutes. Go through each question and try to recall the trick/steps/concepts you applied to solve that question. If you are not able to recall in 15 seconds, mark the question and go to next question. You don’t need to use pen in this phase. Just recalling tricks/concepts from your mind orally. Repeat this for all the questions. After all the questions are finished, refer solutions to see the marked questions and try to learn their ideas.
You should be able to recall ideas of 90% of the problems. If it is less, you need to repeat this phase after few days.
Now this could be hard to follow and time consuming, so I suggest a modified version of this:
Phase 1: Learning phase
This remains the same as above. Instead of marking the questions into multiple levels, you can just mark the questions that you think require repetition. (For very-difficult problems, follow as suggested in the original approach.) Mark the questions using a pencil, as you'll need to modify the markings as you go along.
Phase 2: Retaining/Strengthening phase
Timed test is not always necessary. Sometimes do a timed test, sometimes untimed - whatever suits you. Do only the marked problems. Modify markings: If you are able to solve a marked problem easily, unmark it. The next time you practice, you should not do this problem again.
Phase 3: Finishing phase
Same as before
Note that it is the learning phase that takes most time: If learning phase takes 20 hours, the other two phases can be completed in less than 10 hours.
More about the learning phase:
Do the following for each problem:
1) Read and understand the problem completely. Try to understand the intuition - draw a figure or visualise the scenario.
2) Try to figure out what equations / concepts are related to the problem. You may start by listing all the ideas and formulas discussed in a chapter, and after you have understood the problem, scan through the list and for each item in the list, ask yourself if it is connected to the problem at hand. Later, you should not use the list and should be able to recall the required results from memory: It is significantly harder to recall from memory than using a checklist, since your brain does a random search instead of the linear search using a list.
3) For each item (whether from the list or from memory), try to use it for the problem at hand. See if you can use it to solve the problem. Many a times, you will not be able to solve the problem using a single idea:
May be you have some information A, but the formula requires information B and gives some other information C - which is the solution. Then, for the remaining formulas, you should not only try to go directly from A to C, but also see if you can get from A to B, because then this result will get you from B to C.
Similarly, it may take you from A to B, while you need C. Then in the remaining formulas, you should check for B to C in addition to from A to C directly.
4) At the end of the above process, you would either have solved the problem successfully, or you wouldn't have. But in any case, you would have a reasonable insight into the problem. If you couldn't solve it, you must go through the solution: Go through the solution only when you have tried all the formulas from the list, and you do not see any obvious ways to continue. (If you have tried all the formulas and have some ideas that may work, don't read the solution. Continue to try those ideas unless you have tried all of them.)
Understand all the ideas used in the solution. Now most students proceed on to the next problem after this. THIS IS THE MISTAKE. You need to spend some time to analyse the solution.
- If you weren't able to solve the problem, see where you got stuck. You must have been short of some information, which the solution got in some way. Observe this carefully.
- If you solved the problem but the answer was wrong, see why the formula you used gave the incorrect answer: Many a times, formulas are valid under certain conditions and students tend to use them when they are not applicable. Make sure you are able to find the flaw. Otherwise, discuss with friends or teachers (or post it on some online forum like Quora).
When you analyse the solution this way, you get to know the concepts in more detail, and know when to use them when you see a similar scenario in the future.
This is the complete process for solving a problem. This may take significant time for some problems, and may require lesser time for other problems (mostly depends on the no. of relevant formulas from the list). But the good thing is that you don't need to sit with the book all this while. Many of these steps like analysing the problem, thinking about what ideas may be useful for a problem, analysing the solution, you can do while you are doing other less constructive work.
Again, you may need to modify this a bit if it takes too long, but you will have to follow this roughly to develop your problem solving skills.
I would not suggest skipping less important topics. Study (and practice) everything at least once, and then focus more on the important topics. If you skip topics, you might not be able to solve a very simple question in the exam from a not-so-important topic. Or some problem may require a small idea from unimportant topic, which you will not be able to do.
Pick few good books that have many problems. Solve these problems: both subjective and multiple-choice.
Subjective problems help you build your concepts, while practising MCQs will help you learn smart tricks that are useful in the exam. While practising MCQs, try to develop this skill of smart thinking: without actually solving the problem, see if you can eliminate few options quickly, or get the correct answer directly.
Post Originally Shared From: quora.com