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Posts Tagged ‘ Math ’ |
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DPP: Permutation and CombinationWednesday, January 19th, 2011 by pradeepA person writes letters to six friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that (a) at least two of them are in the wrong envelopes? (b) all the letters are in the wrong envelopes? Solution
Tools for measuring IIT JEE preparation: Self AssessmentTuesday, December 21st, 2010 by adminSelf Assessment: Assess and mark yourself on a scale of 1 to 5 on your level of preparedness for each topic, where 5 is very good and 1 is very bad
You should give yourself a score of 5 when you are among the top 5% in your peer group. You should give yourself a score of 1 when you are among the bottom 50% in your peer group.
In order to get a good rank in IITJEE, you should target a score of 5 in every topic. You may notice that the topics where you have scored 3 or less are the ones where you have not completed the activities as per the plan. Prepare a new plan to study the topics, where you have scored 3 or less. Identify sub-topics, concepts which are causing problems. Different subjects, different skills – how to study Math, Physics and ChemistryMonday, December 20th, 2010 by adminMath Math is the study of quantity, structure, space, and change. It is a tool we use to solve real-life problems. So, proficiency in math is measured by our ability to use it to solve difficult problems. Students who are weak in math, typically, study without writing and practicing with pen and paper. They may be spending a lot of time in reading, remembering or trying to understand the problems. Mathematics requires us to practice solving problems with pen and paper. Only by attempting problems in various ways do we become proficient in applying the quickest method in the shortest time. So, students who like to study by practising with pen and paper, automatically tend to excel in mathematics. Physics Physics is the study of matter and its motion through space-time and all that derives from these, such as energy and force. Physics requires thorough understanding of concepts. Proficiency in physics is measured by our ability to reconstruct or model the physical world through the various laws it follows, and predict the outcome of a given situation. Application of formula to solve problems requires modeling the problem into solvable mathematical equations. Typically, the mathematics involved in solving the problems is very simple. Most students get stuck in the modeling of the problem. They don’t know the method of applying the formula to arrive at a mathematical model to solve the equation. If one does not understand the problem and application of the formulae, no amount of practice will help. Even if one has a perfect memory of the formula and quantities involved, it would not be possible to solve the problem. Just knowing and remembering the concepts as written in the books may not be enough. Students who are weak in Physics, do not spend time in reading and understanding the concepts. They may be spending a lot of time in reading, remembering and practicing the problems. Physics requires reading, thinking, visualizing, integrating and understanding. Students who spend time in reading and understanding concepts, do well in physics. Chemistry Chemistry is the science concerned with the composition, behavior, structure, and properties of matter, as well as the changes it undergoes during chemical reactions. It is the study of various atoms, molecules, crystals and other aggregates of matter whether in isolation or combination, which incorporates the concepts of energy and entropy. Physical chemistry requires thorough understanding of concepts to solve problems. Inorganic chemistry requires knowledge of properties and reactions. Organic chemistry requires understanding as well as knowledge of the compounds and their reactions. All in all, we find that there is a lot more to learn in chemistry than physics and maths combined. Students who are weak in chemistry do not read and remember. They may be spending time in trying to understand the system or practicing the problems. Chemistry requires reading, integrating, learning and revising. Students who spend time in reading and learning naturally do well in chemistry. Proficiency in physics is measured by our ability to reconstruct or model the physical world through the various laws it follows, and predict the outcome of a given situation. 3 key skills – Remembering, Understanding and PracticeMonday, December 20th, 2010 by adminWe have different styles of study. Some like to read and remember, some others like to read and understand the phenomenon and still others like to practice by writing and solving. If we want to do well in IIT JEE, we should have skills in all three areas:
Every subject requires all three skills. Reading and memorizing Whatever we read gets retained in the head as memory. We can recall from our memory when we are needed to do so. It has been observed that we tend to remember better if we have written something ourselves. We are required to reproduce these things at will while solving problems. We have to learn the formulae. One can understand their source by going through the derivations, wherever possible. However, eventually, what matters is that we know the formula. We can learn/remember all formulae by reading, writing, and revising them again and again. It helps to have a compendium of all formulae. For example, if we don’t understand the derivation of formulae in mathematics, we won’t be able to apply formulae effectively. However, while solving problems, one does not have the luxury of time to derive it. So, it must be pulled out of our memory instantaneously. Conceptual understanding It is critical to understand the conceptual framework of a subject. It is important to understand the flow of the logic in the argument being put by the narrator. The examples and illustrations used should fit well into our understanding. We observe various phenomena around us in everyday life. Physics and chemistry attempt to explain the reason behind these phenomena through various concepts, laws, deductions etc. We should gain a thorough understanding of the system / concept being explained, before attempting to learn any formulae or solve any problems. This can be done, with the help of examples. Apply the concept to different real life situations and predict the outcome. If the understanding is correct, the outcomes predicted will be right. Conceptual, theoretical questions are a great way to check ones learning of concepts. Practice After writing down the formulae required and applying the concepts, we still have to solve the mathematical equations. Solving problems is a skill. If there is no limit to the time available, a lot of students may end up solving all the problems in a test. However, the key is to solve maximum number of problems in a given amount of time, which is the duration of the test. The best performer manages to solve maximum number of problems in the given time. This needs practice. In a competition, we don’t want to lose time in experimenting, deriving etc. If we have practiced enough, we would know the exact manner in which a problem can be solved. This saves time in solving a problem and gives s extra time to solve others. Therefore, to score high in a competition, practice is a must. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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