Calculus II For Dummies, 2nd Edition (2012)

Part VI. The Part of Tens

Chapter 17. Ten Tips to Take to the Test

In This Chapter

Staying calm when the test is passed out

Remembering those dxs and + Cs

Getting unstuck

I’ve never met anyone who loved taking a math test. The pressure is on, the time is short, and that formula that you can’t quite remember is out of reach. Unfortunately, exams are a part of every student’s life. Here are my top ten suggestions to make test-taking just a little bit easier.

Breathe

This is always good advice — after all, where would you be if you weren’t breathing? Well, not a very nice place at all.

A lot of what you may feel when facing a test — for example, butterflies in your stomach, sweaty palms, or trembling — is simply a physical reaction to stress that’s caused by adrenalin. Your body is preparing you for a fight-or-flight response, but with a test, you have nothing to fight and nowhere to fly.

A little deep breathing is a simple physical exertion that can help dissipate the adrenalin and calm you down. So while you’re waiting for the professor to arrive and hand out the exams, take a few deep breaths in and out. If you like, picture serenity and deep knowledge of all things mathematical entering your body on the in-breath, and all the bad stuff exiting on the out-breath.

Start by Reading through the Exam

When you receive your exam, take a minute to read through it so you know what you’re up against. This practice starts your brain working (consciously or not) on the problems.

While you’re reading, see whether you can find a problem that looks easier to you than the others (see the next section).

Solve the Easiest Problem First

After the initial read-through, turn to the page with the easiest problem and solve it. This warm-up gets your brain working and usually reduces your anxiety.

Don’t Forget to Write dx and + C

Remember to include those pesky little dxs in every integration statement. They need to be there, and some professors take it very personally when you don’t include them. You have absolutely no reason to lose points over something so trivial.

And don’t forget that the solution to every indefinite integral ends with + C (or whatever constant you choose). No exceptions! As with the dxs, omitting this constant can cost you points on an exam, so get in the habit of including it.

Take the Easy Way Out Whenever Possible

In Chapters 4 through 8, I introduce the integration techniques in the order of difficulty. Before you jump in to your calculation, take a moment to walk through all the methods you know, from easiest to hardest.

Always check first to see whether you know a simple formula: For example,

may cause you to panic until you remember that the answer is simply arcsec x + C. If no formula exists, think through whether a simple variable substitution is possible. What about integration by parts? Your last resorts are always trig substitution and integration with partial fractions.

When you’re working on solving area problems, stay open to the possibility that calculus may not be necessary. For example, you don’t need calculus to find the area under a straight line or semicircle. So before you start integrating, step back for a moment to see whether you can spot an easier way.

If You Get Stuck, Scribble

When you look at a problem and you just don’t know which way to go, grab a piece of scratch paper and scribble everything you can think of, without trying to make sense of it.

Use algebra, trig identities, and variable substitutions of all kinds. Write series in both sigma notation and expanded notation. Draw pictures and graphs. Write it all down, even the ideas that seem worthless.

You may find that this process jogs your brain. Even copying the problem — equations, graphs, and all — can sometimes help you to notice something important that you missed in your first reading of the question.

If You Really Get Stuck, Move On

I see no sense in beating your head against a brick wall, unless you like getting brick dust in your hair. Likewise, I see no sense in spending the whole exam frozen in front of one problem.

So after you scribble and scribble some more (see the previous section) and you’re still getting nowhere with a problem, move on. You may as well make the most of the time you’re given by solving the problems that you can solve. What’s more, many problems seem easier on the second try. And working on other areas of the test may remind you of some important information that you’d forgotten.

Check Your Answers

Toward the end of the test, especially if you’re stuck, take a moment to check some of the problems that you already completed. Does what you’ve written still make sense? If you see any missing dxs or + Cs, fill them in. Make sure you didn’t drop any minus signs. Most important, do a reality check of your answer compared with the original problem to see whether it makes sense.

For example, suppose that you’re integrating to find an area someplace inside a 2 x 2 region on a graph, and your answer is 7 trillion. Obviously, something went wrong. If you have time to find out what happened, trace back over your steps.

Although fixing a problem on an exam can be tedious, it usually takes less time than starting (and maybe not finishing) a brand-new problem from scratch.

If an Answer Doesn’t Make Sense, Acknowledge It

Suppose you’re integrating to find an area someplace inside a 2 x 2 region on a graph, and your answer is 7 trillion. Obviously, something went wrong. If you have time, try to find out what went wrong and fix the problem (see the preceding section). However, if you don’t have time to find out what happened, write a note to the professor acknowledging the problem.

Writing such a note lets your professor know that your conceptual understanding of the problem is okay — that is, you get the idea that integration means area. So if it turns out that your calculation got messed up because of a minor mistake like a lost decimal point, you’ll probably lose only a couple of points.

Repeat the Mantra “I’m Doing My Best,” and Then Do Your Best

All you can do is your best, and even the best math student occasionally forgets a formula or stares at an exam question and goes “Huh?”

When these moments arrive, and they will, you can do a shame spiral about all the studying you shoulda, coulda, woulda done. But there’s no cheese down that tunnel. You can also drop your pencil, leave the room, quit school, fly to Tibet, and join a monastery. This plan of action is also not recommended unless you’re fluent in Tibetan (which is way harder than calculus!).

Instead, breathe (see the section on breathing earlier in this chapter) and gently remind yourself “I’m doing my best.” And then do your best with what you have. Perfection is not of this world, but if you can cut yourself a bit of slack when you’re under pressure, you’ll probably end up doing better than you would’ve otherwise.