Checking work during a math test is a highly effective strategy that is, unfortunately, overlooked by many students and not addressed by all instructors. But checking work is a simple way to improve your test scores and, ultimately, your overall success in the class. There are a number of approaches you can take to check your work in a productive way.
General Best Practices
When solving any math problem, show every step and always write neatly. That way, if you discover an error later, it will be easier to pinpoint. After completing a problem, glance over your work for careless errors, such as putting a decimal in the wrong location or omitting a digit. Re-input any calculator entries -- it is unlikely that you’ll mistakenly push an incorrect button twice in a row -- and it would be regrettable to lose points on an exam for such an innocent error.
Determine Whether Your Answer Makes Sense
Upon finishing a problem, re-read the original question. Make a mental estimate of a reasonable answer. For instance, in 498.2 - 503.14, your answer should be negative and near zero. But if you obtain a positive number, you've made a mistake somewhere. When dealing with word problems, analyze whether your answers make sense in the context of the problem. For example, suppose you need to predict the amount of money in a savings account after earning interest for a number of years, but your answer is less than the original amount in the account. This cannot be correct because accruing interest over time results in more money, not less.
Solve Problems a Second Time
Without looking at the work you did the first time, completely re-do each problem from scratch and see if you get the same result. If you don't, you made a mistake one time or the other. Analyze your steps for an error, or try again a third time. If possible, when re-solving a problem, use a method different from the one you used initially. For instance, suppose you originally added 3/4 + 4/5 by finding a common denominator and then adding the fractions. When solving the second time, convert the fractions to decimals and add them that way.
When solving a multiple choice problem, you may sometimes obtain an answer that isn’t listed. If you’ve already looked for careless errors and re-worked the problem using a different method, but obtain the same unlisted answer, you may be able to find the correct answer by taking each of the given answer choices and testing them against the original problem. For instance, suppose in solving x + 6 = -2, you obtain an answer of x = 4, but the only three given answer choices are x = -4, x = -8 and x = 8. Check which answer choice works by substituting each one for x in the original equation and simplifying -- when you get a result that forms a valid mathematical sentence, you’ve found the correct answer. In this case, x = -8 is correct, because testing yields -8 + 6 = -2, a true statement.
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