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One of the most common complaints of students during Mathematics examinations is that they often run out of time; in that case, advice on how to solve math problems more quickly will help them finish timed exams. Math is a complicated discipline, and while some problems are routine and straightforward, some problems require zigzag mazes and long expositions of solutions before an answer can be found. Many teachers, while willing to give plenty of help to their students so that they can be faster in Math, do not have the time to do so. In that case, it is up to the student to figure out techniques on how to solve math problems more quickly than they did before. Here are five effective means to do so:
(1) Read the question. In any Math problem, there is a paramount need to read the question carefully, from beginning to end, so that the student can take down all given facts and keep sight at the unknown. Many students slow down in Math problems, especially on long ones, because they may be slacking in the way they read the question; in many other cases, students do not bother to read the problem at all. While reading the question intently, you develop at least a 'blueprint' of the solution in your head. Your subconscious processes prior knowledge and chooses those which become most applicable to the problem at hand. You recall similar problems, formulae, and theorems that could help you in solving the problem. Knowing all of these before beginning to solve will help your solving run on a smoother path.
(2) Set up easily solvable equations. After reading the question you should be able to translate all the given data into mathematical equations. Also, keep in mind to select proper notation for your equations. Refrain from using the same letter to represent different unknowns (although letters with different cases, such as R and r, are permissible) to avoid confusion and to proceed more quickly. There is also an art in choosing notation; for instance, in adding seven consecutive integers, it is easier to have
x - 3, x - 2, x - 1, x, x + 1, x + 2, and x + 3 as the unknowns,
instead of x, x + 1, x + 2, x + 3, x + 4, x + 5, and x + 6.
Try adding both sets. Which one is easier to add?
(3) Think of useful shortcuts. Any formula or procedure that could shorten the solution is a shortcut. However, there are two things to remember when relying on shortcuts. First, unless you want to make sure, it is not mandatory to put on paper what you can solve on your head, although that requires plenty of mental dexterity obtained through continuous practice. Second, many shortcuts are applicable only to specific situations, so before using a shortcut, make sure that it is relevant to the problem at hand.
(4) Memorize arithmetic computations that deserve memorization. These include: powers of bases 2, 3, 4, 5, and 6 (up to the 5th power, at least); multiplication tricks (multiplying by 11, or multiplying numbers with zeroes in the end); and some subtraction tricks (like 10000 - 443 = 9999 - 442). There are plenty of tricks available; if you practice them at your spare time, then you have an edge in speed and agility over your peers.
(5) Simplify and factor as much as possible. Simplifying fractions into lowest terms and rationalizing radical expressions can make your numbers on paper more organized and easier to handle arithmetically. Factoring could also break down complicated expressions and could reveal some of their properties that are not easily accessible in their long, original form.
Finally, the bit of advice that could unite all of these is: Practice. Practicing will make you save plenty of information common situations where these methods on how to solve math problems more quickly could figure, so the next time you encounter that situation, you'll be ready.