How to Succeed at Math Competitions
How to Succeed at Math Competitions
By: Gordon Lee
You’re about to begin a fast-paced math competition. You glance at the clock, and notice there’s a minute until the timer begins. Perspiration drips down your back, and your heart pumps a little faster. You recite last minute formulas in an attempt to prime yourself for the upcoming behemoth. Suddenly, the proctor calls out, “3...2...1...begin.”
Fast-paced math competitions can be stressful and adrenaline-inducing, but can also be very rewarding, given that you do well during the contest. To do well in a math competition, there are three simple words to remember: practice, practice, practice. There is no magic way to become better at mathematics; it takes hard work, diligence, and persistence.
Practice:
To prepare for a math competition, you must learn all the material that are tested in the competitions. This includes algebra, geometry, counting, and number theory. To aid in calculations, it is recommended that you practice mental math. (To improve this skill, refer to Secrets of Mental Math, by Arthur Benjamin).
There are a few concepts that should be memorized, which includes, but is not limited to, squares from 1-30, the formula for finding the number of diagonal in a polygon, volume formulas for spheres, cylinders, and cones, factorials up to 10!, difference of squares, power of a point, etc. (I didn’t mention it in the list, but you should also be able to recite the alphabet). The best way to hone these skills is to practice using previous years’ tests, as those will most likely have many questions which require the use of these memorized concepts.
When engaging in practice problems, use the solutions key sparingly; it is only a guidance. You learn much better by solving the problems on your own. Studies have shown that your brain is able to pick up mathematical concepts and synthesize them to solve similar problems if you are able to work through and solve math problems. Believe it or not, that is why you are able to remember the answer to 2+2, and similar problems.
The more you practice for a certain kind of problem, the faster you will be able to solve it. For example, if I asked you to solve “What is the probably that the sum of 2 fair 6-sided die is 8,” and this were the very first time you were to attempt a problem of this nature, it would probably take you a while, as you are unfamiliar with this concept. As time progresses, however, and you practice this type of question, you will continue to become better and faster at these types of problems.
Test-Taking Strategies:
Know which math competition you are preparing for, since different competitions call for different methods. For example, There is a slight benefit to leaving answer blank on the American Math Competition (AMC) 10&12 as opposed to the wrong answer, whereas you should never leave and answer blank on competitions such as the MIC or Blaine. The reason for this is that wrong answers on the AMC gives 0 points, while a blank answer rewards 1.5 points. On the MIC and Blaine, both wrong answers and blank answers earn you 0 points, so it beneficial to make an educated guess.
Let’s investigate the scoring system of the AMC more meticulously. A correct answer rewards 6 points, a blank answer 1.5, and a wrong answer 0. Since there are 5 plausible answer choices, the expected value of randomly guessing an answer is 1.2 points. In other words, if you have no idea which answer choice is correct, leave it blank. If, however, you are able to eliminate a single answer choice, your expected value is increased to 1.5; equivalent to leaving it blank. You might as well guess. If you are able to eliminate 2 or more answer choices, there should be no hesitation in making an educated guess, since the expected value would be 2 or more.
For the MIC, you do not have the luxury of having answer choices in front of to guess among; your answers must come from your brain. To maximize your score, you must tone your time-management skills (this comes with practice as well). Never spend too much time on any one problem; skip problems that are taking too long, and circle the question number on your answer sheet. This ensures that you do not accidentally write in the answer for the next problem into the space for the question you in fact skipped, and also allows you to spot it quickly to work on later on if you have finished all the ones you are able to solve.
It is very important to double-check your work. It is a terrible feeling to know that you are able to solve a specific problem, only to find that you miscalculated, and ended up with the wrong answer. Going over your work may also help you finish problems you forget how to do earlier, either because a similar problem occurred later on in the test, or it just suddenly came to you.
The Day Before the Test:
You must keep your body well-rested and fit to do well in the competition. Drink plenty of water, sleep early, and have a healthy breakfast. Though this may sound ridiculous, it has been proven by many trusted health clinics that healthy breakfasts help maintain a stable metabolism throughout the day, and help reduce hunger later on in the day.
Your body is not the only thing that should be well-rested; your brain deserves a break from studying as well. Relax your mind, and remain in a serene atmosphere. This means no studying the day before the test. I repeat: no studying right before the test. Not only will it not help, but it will also cause unnecessary stress. Studies by psychologists have determined that by stressing your mind out right before the test, you will hardly remember anything you study at the last minute, and instead only cause anxiety. I’m sure your teachers told you the same thing back when you were pulling all-nighters to study for the test, which most likely hurt your grade.
Overall, rigorous training, skill sharpening, and good study habits are extremely helpful in boosting your score in math competitions. Begin to develop these good habits, such as practicing everyday for upcoming competitions (just 30 minutes a day would be great), and developing any skills that leave something to be desired. If you follow these steps, you can heighten your potential, maximizing your chances of receiving a trophy. Good luck!