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How to Tackle Math Olympiad Questions

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How to Tackle Math Olympiad Questions
  How to tackle Math Olympiad questions – Part 1   Math Olympiad papers can seem rather daunting, isn’t it? And rightly so –   a well set Olympiad question will test your fundamentals and analytical skills, and challenge your way of thinking. Irrespective of the fact that most of the so- called “Math Olympiads” conducted by  various  businesses in our country are nowhere near international standards, the questions in even those are generally “tougher” than the ones you face generally  in school tests or exams. In solving these types of questions, you generally need to be able to think quickly on your feet  –   one factor that makes these questions harder is that the time available to you is limited. A second factor is that you may have negative marking for wrong answer, so sometimes it would seem  better to leave the question rather than putting in an answer you are not sure about. To add to the confusion, sometimes it is possible that more than one answer is correct. So how do you tackle this. The first step is of course (to reiterate a point made in an earlier article we wrote) is “Don’t Panic”. Take a deep breath, re lax, read the questions and do your best. In this article we talk about some general practices you should follow. In the next part of this article, we’ll talk about some specific mathematical techniques that  could help you tackle such exams better. The first step is make sure all your resources are there with you  –   pencils, erasers, spare paper for computations (if allowed). It seems trivial, but these are things that you don’t want to worry about once the test starts.  Now, start reading the paper. There’s no standards here  –   different  people do it in different ways. Some people start from a fixed location, typically the beginning of the paper, but some folks even like to start at the end (the theory being that the examiners would have gotten tired of finding tough questions, and would start putting easier questions towards the end  –   of course, no sensible examiner would set papers that way). Some other folks like to look for questions in topics they are familiar in, and try those first. Whatever approach you are comfortable with is fine. The most important thing, and this is where a lot of people make their mistake  –    read the question completely and carefully . Spend as much time you need on this part. Any mistake you make here will ensure you get the wrong answer. Let me repeat this  –   read the question carefully and completely. Find out what the question is really all about. Take careful note of all the values and data provided in the quesion. Then, and only then, should you start trying to find the answer. And once you have solved it, or think you have  –   check that your answer indeed is what the question is asking for (If, for example, the question asked for speed of a car, and you have 121 seconds as your answer  –   something has gone wrong) Second, keep track of the time. Keep a general idea of how much time you have per question. It need not be exact  –   for example, if you have 2 hours and there are 50 questions, just think that you’ll have about 2 minutes per question. Of course, you may do some questions fa ster, but keep this general timeframe in mind per question. If you are completely confident of a question, you could take a little more time (say 3 minutes) on it, but generally try not to spend more than the  computed time per question. In fact, ideally you should target leaving the last 10 minutes for a quick revision.  Now, if you haven’t attempted all the questions when you find there are 10 or so minutes left then it’s time to start picking and choosing from the remaining questions. Run through them quickly to see which ones look easiest for you to solve. Then try those. The next tip is on using your spare paper effectively. It can get very messy quickly, so you should mark off specific areas for questions for which you need to use the spare paper for computation. You could use a grid kind of structure if that helps  –   but the aim is to use it effectively and neatly. And make sure that for questions where you use it, copy all the values correctly to the spare sheet. Double check it, and triple check. Do the same thing while copying the answer back. In the next part of this series, we’ll look at techniques specific to mathematics to help  you do  better in Olympiads Comments: 5 Leave a reply »  March 26th, 2012 at 2:00 pm | Reply »  #909 The use of technology (calculator to be specific), in my opinion, should be used as a tool to engage students in the lessons that are being taught. I do not think the use of technology necessary promotes mastery of concepts taught, in many cases I think it demonstrates the students and teachers ability to learn and teach how to manipulate a calculator to choose the best solution on a multiple-choice exam. This is evident in talking to two of our peers who observe hundreds of students at our local community college who are unable to compute their way through College Algebra and spend hours tutoring students who mastered a standardized test but are unable to compute a given problem without a calculator.The other technologies that are used in the classroom could be measured through project outcomes and graded based on a rubric which highlights what skills are to be mastered and demonstrated through the use of some type of technology. The use of a calculator is good if the student already mastered the four fundamental operations…primary schools must see to it that the child had enough knowledge of the  basic operations before allowing him/her to use the calculator…this is just my opinion  because I had seen some of my classmates who were so dependent on calculator that they cannot work on small numbers without calculators…I just pity them…    How to tackle Math Olympiad questions – 2   In the last article we talked about some general practices that will stand you in good stead while taking part in the Maths Olympiad (or any exam/test in general). In this edition, we’ll talk about various additional techniques that could help you perform better in Math Olympiads. Most of the time the questions in such competition are of the objective type question. This can make things simpler for you (on the other hand, depending on the ingenuity of the question setter, it can also make it harder for you). The way it makes it easier for you is in two ways    One is that you can easily check if the answer you compute is part of the options provided to you    The second is that sometimes, just sometimes, you can do some amount of guessing to eitherget the right answer, or narrow down your possibilities For example, take the following question taken from  Question : The number 11449 can represented by a 107 x 107 square grid. Out of the following numbers, which number can not be represented on the square grid? a. 14641 b. 90601 c. 9216 d. 16122 Here, you could work out the square root of all the numbers and try to figure out the answer, but a quicker way may be to notice that a square number cannot end in 2. In addition, the question reads ”which number”, which implies there is only one choice that is true.  So the answer here is obviously d)  –  16122 Similarly, in a lot of these cases, you can eliminate at least one of the choices  –  there can be many variants that you could identify by just looking at the question. Ask yourself some mental questions like “Can the answer be an odd number?” etc. Of course, each mental question you ask yourself   will be specific to that question. Sometimes, a question can seem rather hard at a quick glance, but if you read it once more slowly, you can probably see past the apparent complexity into a simple solution. Consider the question (also taken from  Question :    Archana’s roll number is a two digit number. Her friend Balvinder’s roll number has the  same digits as Archana’s roll number, but with digits interchanged. If they add their roll number,  and divide the sum by 11. Find the remainder of this division.    a. 1 b. 2   c. 0 d. Can not be determined without knowing the roll number   At first glance, it may seem really hard  –  how can you know without really trying? Here you can use one of two methods. One is not really what I would call mathematical, but if you are pressed for time, you could easily use it for such question. And what’s that t echnique? It’s simple –   all you do is try it out on a couple of example numbers. Imagine that Archana’s roll  number is 61. Then Balvinder’s roll number would be 16. Add 61 and 16, and you get 77. The remainder  when 77 is divided by 11 is 0. However, you also need to know how to solve this directly (after all, you are here because you want to learn mathematics). The way to do that is to think of it as follows Archana’s number has two digits –  say they are “ab”   where a and b could be any of 0,1,2,3,4,5,6,7,8 or 9. You can represent it mathematically as 10a + b   Then Balvinder’s number would be “ba” –  mathematically you would say 10b + a Add them up 10a + b + 10b + a = 11a + 11b = 11(a+b)  This is of course divisible by 11 leaving a remainder of 0. Simple, an d more satisfying to do it this way, isn’t it?  So you should always keep in mind that no matter how hard the question looks, it is very likely that you have already been taught the tricks to solving it. There may be a few questions that may use concepts yo u haven’t been taught yet (to identify the really advanced students), but   there’s not much you can do about that. For a majority of the questions though, you already know all the techniques you need to solve them. It’s just a question of identifying them a nd applying them. You should also know your strengths and use them appropriately. For instance, you may be very good with spatial questions and at visual data  –  then go for the geometry or figure related questions first. If numbers dance in your head, go for the arithmetic questions. Get them out of the way, and then move on to the other sections.
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