How to Take a Math Test or Quiz

Summary: Tests are different from homework because there’s a time limit, because you can’t take breaks or (usually) refer to your textbook, and because you have many types of problems to solve. Here are some strategies to help you do your best.

See also: How to Succeed in Math
How to Study Math

Before the Test

You’ve got a big athletic meet coming up, or you’re playing in a concert, or you’re making an important presentation at work, or hosting an anniversary party for your parents. What do you do to ensure success? You prepare, of course. (Well, duh!)

The biggest part of preparing for a test is to study effectively right through the course. (Some study tips are on a separate page.) Don’t wait until the test is looming and then try to learn everything you didn’t really understand.

But there are a couple of things you can do in the nights (not the night, the nights) before the test.

Work a variety of problems.

If you’ve been doing the homework right along, and getting questions answered before they fester, you should be in pretty good shape.

But one thing is different between the homework and a test: In the homework, you know pretty much what type of problem each one is, because you just studied that type. That’s usually true on a quiz, too. But on an exam, several weeks’ worth of problem types are mixed together. You need to practice approaching problems where you don’t know up front what type they are.

How can you do this? If you’re lucky, your textbook has a section of review problems, or a practice exam, with problem types all mixed. If not, ask a classmate or your study buddy to throw problems at you, and practice recognizing the different types.

See also: How to Work a Math Problem

Don’t bother cramming.

Many students try to learn all the material in a marathon session the night before the test. While this may be partially effective where you have a lot of rote memory work, most of math is not memory work but recognizing patterns and selecting and applying useful techniques to problems.

In other words, you’re being tested mostly on skills, not on memorized facts. The only way to learn any skill is to practice, and in math that means working some problems almost every day. Most successful math students find that the best approach is to do the homework on time, and then just do a quick final review the night before the exam.

If you don’t know the material sooner than the night before the exam, odds are you’re not going to learn it then.

Make a crib sheet.

Try to reduce everything to one sheet of paper, and not by writing so small you need a microscope to read it. There’s surprisingly little to memorize in math, so your crib sheet doesn’t need to be very elaborate. Most of what you’ll need to know is not facts or formulas but techniques.

Why go through the exercise? Well, of course if your instructor lets you use a crib sheet during tests the answer is obvious. But even if you can’t use the crib sheet during the test, the act of making it up will organize the material in your mind and help you to retain it.

Overcome test anxiety.

To a certain extent it’s normal to be nervous about taking tests, even if you’re a very good student. While mild anxiety can be a motivating factor, high anxiety triggers your flight response and makes you avoid the subject — which makes the anxiety worse.

Being thoroughly prepared for a test won’t necessarily make the anxiety go away, but it can help you master the anxiety. Chapter 3 of Noltling’s book has some great tips for dealing with math anxiety, particularly before tests.

See also: Overcoming Test-Taking Anxiety in Graduate School: Practical Strategies for Success. Don’t be put off by the “Graduate School” label! The tips here apply to taking tests at any level.

During the Test

Do a “brain dump”.

If your instructor doesn’t allow crib sheets, immediately write any key formulas on an empty section of the test paper. Then you’ll have them available before the pressure of solving problems has driven them out of your head.

Work carefully.

Don’t lose points through careless errors. Check each step as you go — does it really follow correctly from the previous step? Watch for things like dropped minus signs or missed exponents. Check the numbers you type in your calculator against the numbers in the problem.

See also: Careless mistakes keep killing me.

Show your work clearly and in order.

Discipline yourself to show all the steps in your solution. And show them one after the other, not little bits of math written here, there, and everywhere.

First and most important, showing all the steps makes it easier for you to check your work as you go along. It’s awfully easy to make a careless mistake if you’re writing down one step out of three. If you write down all the steps, one after the other, you’re more likely to get each one right the first time and more likely to find any mistakes when you check your work.

Second, showing your work is good strategy for grading. Most instructors won’t give full credit for a bare answer unless the problem was extremely simple. And if you’ve made some truly minor error (like adding 8 and 6 and getting 12), if your work is clear most instructors will give you substantial partial credit.

Pick the low-hanging fruit first.

This doesn’t work for everyone, but some students find it effective to scan the whole test, looking for easy problems. If you can do it quickly, you may want to look for any easy problems and solve them first. This will build your confidence, and you won’t miss easy points through getting hung up on hard problems.

Which reminds me …

Don’t get hung up on one problem.

You should have a rough idea of how much time to spend on each problem, just by dividing the time for the test by the number of questions. If you seem to be spending too much time on one question, leave it and move to questions you can answer more easily. If you have time at the end, you can come back to it, and with a fresh look you may suddenly see how to solve it.

With word problems, you may get partial credit if you get to the point of setting up a correct equation. If you feel you are spending too much time on this problem, and the equation is going to be hard to solve, you can come back to it after doing your best on the other problems.

See also: The test is too long; if I’d had more time I could have done really well.

Answer the actual question.

Does the problem ask for the dimensions of a box? You had better have three numbers (length, width, height) in your answer. Does it ask for a percent? A decimal is not your final answer. Does the problem ask how old the woman was? Verify that your x really did stand for the woman’s age and not her daughter’s age.

Students lose lots of points on every test because they answered the question in their heads instead of the one on the paper. Work the problem to the end, and put your answer in the right form. Then reread the question to check that you actually answered it.

Give just one answer.

Don’t give two conflicting answers and expect your teacher to pick one — you may not be happy with the results. If you give one answer you may be wrong, but if you give two you will be wrong.

Is it right, or at least reasonable?

If you’ve solved a word problem, put your answer back in the problem and see that it works. If you had an equation to solve, put your answer(s) back in the equation and see that they work.

Some problems can’t be checked that way, but with every problem you should ask, “Is this answer reasonable?” If all the numbers are under 100, is an average of 152 reasonable? If a rectangle’s area is 50 sq.ft. is 680 feet reasonable for the length of one side? Unreasonable answers tell you to go back and find your mistake.

Watch your stress level.

Stress affects your body and your thinking processes negatively. Pay attention to how you are feeling, and if you find yourself getting stressed, do something about it. Different techniques are right for different students. You should use whatever technique works for you, but here are some suggestions:

• Close your eyes, take a deep breath, and let it out slowly. Repeat.
• One at a time, deliberately tense each muscle group and then release it.
• Drink some water.
• Visualize a favorite place, mentally run through a favorite tune, etc.
• Stretch. Change your posture.

If you frequently get extremely stressed during tests, you may want to visit the counseling center for some customized suggestions on handling the stress. If that’s not an option, there are many resources on the Web. Here’s a sampling:

• The Mayo Clinic’s Test Anxiety: Can It Be Treated? offers plain-English suggestions to students.
• Managing Test Anxiety: Ideas for Students, (PDF) by Jim Wright, has a lot of practical suggestions.
• Test Anxiety and How to Control It. Don’t put too much stock in the true-false test — everybody can say yes to one or more of those. But the suggestions are good, and I like the exercise that follows.
• Reducing Test Anxiety from ETS aims at anxiety about standardized tests — start at page 5.

Take all the time available.

Many students like to leave a test early. Either it’s a painful experience and they just want it over, or they enjoy thinking how good they are because they finished early. Regardless of your motive, leaving too early is a mistake.

Use that extra time to go back over your work. Are all answers reasonable? Did you actually answer each question as written, and is your answer in the right form? Did you answer all parts of every question? Check your work on each problem, and correct any mistakes.

Only after you’re truly sure you’re turning in your best work should you leave the test early.

If it ain’t broke, don’t fix it.

Sometimes students will look at a problem that they have worked, suddenly decide that their answer is wrong, and change it. If you do that, check your change just as carefully as you checked the original.

If you’re like most people, at some point in your career you probably had a right answer but changed it to a wrong answer. Don’t do that again!

After the Test

When you get your graded paper back, of course you’ll look at the grade. But also look at the problems that you got wrong. Do you understand why you got each one wrong? Ask yourself that as honestly as you can, and make a plan for corrective action.

If it was a careless mistake, what caused it? Did you skip steps? Did you fail to check your work? Did you work too quickly? Figure out how you mess up, and write down the countermeasure you need to take, then begin forming that habit.

Did you not understand the math involved? Ask for help from your instructor. Visit the tutoring center. Ask your study buddy for help. Go back and rework all the examples in the textbook. Odds are good that you will need to know this to understand later material in the course — plus of course you’ll probably need to know it for the final exam.