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Introduction to the SAT Math Test

Page 1

Introduction to the SAT Math TestHow SAT Math Is Different from Classroom Math
Most students are surprised to find out just how basic SAT math is: arithmetic, geometry, algebra, and a smattering of elementary logic and probability. Yes, the SAT Math Test for the first time now includes a bit of algebra II—not much—but most of the concepts tested were familiar to you by ninth grade, if not earlier. You won't need the quadratic formula, or any trigonometry; and you won't need to prove any geometry theorem. Indeed, one of the problems many students face on the SAT Math Test is remembering their basic math from junior high school.

As I'll remind you frequently in the math articles, you already know all of the math covered on the SAT. The trick is learning how to reason in new ways with fairly basic math concepts.

The SAT Math Test consists of 54 questions in three sections. Forty-four of the questions are regular, multiple-choice questions. Ten of the questions are more like the math problems you solve in school. These questions do not provide choices; you must work out the answer to these "student response" questions and "grid-in" your result into special boxes on your answer sheet. Unlike your math tests in school, however, you will not receive any "partial credit" for your work.

More Good News: They Provide Most of the Formulas You Need
Here are the instructions you'll find on each section of the SAT Math Test:

Directions: You may use any available space in your booklet for scratch work, but only your answer sheet will be graded. When you have determined the answer to a question, fill in the corresponding oval on your answer sheet.

Notes:

1. You may use a calculator. All numbers used are real numbers. All figures lie in a plane unless otherwise indicated.
2. Figures that accompany problems are intended to provide information useful in solving the problems. They are drawn as accurately as possible EXCEPT when a specific problem states that the figure is not drawn to scale.

You probably know most or all of these formulas already, but spend a minute to review this information so you do not waste precious seconds on the actual exam doing so. The only important facts in the instructions are the formulas; the "notes" will not change significantly.

The Bad News: The SAT Math Test Camouflages Simple Concepts
If the math on the SAT is so basic and it is you may be wondering how anyone can find it difficult. One of the big reasons that students have trouble on the SAT Math Test is that the test writers do an excellent job of transforming very simple math concepts so that these concepts are barely recognizable. But the real reason students have trouble is that the SAT tests their knowledge very differently from the way you're used to being tested in school.

Never let an unfamiliar term on an SAT math problem bamboozle you. The test writers often stumble in their efforts to remove ambiguities from problems that only a mathematics professor would quibble with—creating needless confusion for hundreds of thousands of SAT students. One of my favorite terms in this regard is "non-overlapping," which just refers to figures that share at most a line in common.

Page 2 SAT Math Is Way Different from School Math
The SAT Math Test is remarkably different from the kind of math tests you're used to taking in school. As I said in The SAT Is Not Like Your School Tests: if you take the SAT Math Test the way you're used to taking math tests in school, you're in for a rude surprise. Consider the following differences:

• The SAT Math Test is a multiple-choice test; you receive no partial credit for your work if the solution isn't correct. In school if your math solution is "mostly correct," you will probably receive close to full credit even if your exact answer is off the mark. Not on the SAT. On the SAT, if you're even a bit off the answer—for whatever reason—you'll lose full credit for that question. This difference is huge, and will completely reverse your priorities from being quick and clever (but sometimes sloppy) on school tests, to being ruthlessly, obsessively accurate on the SAT.
• SAT math questions are all worth the same amount. Again, this will completely upend your usual priority on school math tests to spend the most amount of time on the most difficult questions. On a school test you can't afford to miss a difficult question (because it's usually worth a lot of points). On the SAT Math Test, you can't afford to miss an easy question.
• SAT math questions are in order of difficulty. On school math tests this is often the case, but remember that the later questions on those tests are worth more. You have been trained, in other words, to sprint in the early part of a test so that you can spend enough time on the questions that count more near the end. On the SAT, you should do exactly the reverse: go slowly on the easy and medium questions in the early part, and then sprint on the hardest questions at the end.
• The SAT Math Test covers a hodgepodge of material. Yet again, this aspect will require a much, much larger adjustment of their problem-solving methods than most students realize. When you're studying a math topic in school—say, solving simultaneous equations—you can expect that your quiz or test on that material will involve just simultaneous equations. Granted, sometimes your math teacher may make a test cumulative, but even then the test will cover relatively recent material. On the SAT, one question can be on percentages that you studied back in junior high, followed by an algebra II question on material you may have studied last year, bouncing back to geometry you covered a year or two ago, and continuing all over the place. The SAT Math Test requires that you orient yourself instantaneously to each new question, and then leap nimbly to the next question, reorienting yourself all over again.

One of the biggest differences of all is that the SAT Math Test is what the test writers call a "reasoning test." Unlike an achievement test—like the SAT II Math Ic and IIc Tests—the SAT Math Test rewards students who see past what the problems seem to be asking to what the problems are actually testing. On the SAT Math Test, for example, a problem may seem to require that you solve for x, when in fact you don't need to solve for x at all. In fact, trying to solve for x on some problems will send you on a wild goose chase away from the solution.

Not all of these differences make the SAT more difficult; indeed, some of these differences will give you powerful leverage. But these differences will require a complete overhaul in the way you approach solving math questions.

SAT Math Questions Are Arranged in Order of Difficulty
Each math section is arranged in order of difficulty. Here's the question layout of the entire SAT Math Test:

You won't see warning signs in your booklet like this: Warning! You are about to leave the medium questions—hard questions coming up! The only clue you'll have regarding the difficulty of a question is where in its section it appears, so you'll have to keep an eye open for the question number at all times.

The only exception to this rule about order of difficulty (danger) occurs on compound questions. Your SAT Math Test may have two or three consecutive questions based on the same information. If so, the second and third ones will be medium to hard—regardless of where these questions appear in the section.

Normally, for example, questions 10 and 11—smack in the middle of a 20-question section would be medium questions. If this were a pair of questions on the same information, however, the first question would be medium and the second question would be difficult. If it were a trio of questions on the same information—say, 10, 11, and 12—the first question would be easy, the second question would be medium, and the last question would be difficult. Not a big deal since these compound questions appear maybe once every SAT, but worth watching out for.

Stay alert! Every once in a while, a difficult question gets dropped into the medium "area." You won't, however, find an easy question in the difficult area at the end of a section.

Page 3 Here's How You'll Improve Your Math Score
I'll show you everything you need to know to achieve your maximum SAT math score in the minimum time.

Of course I'll show you all of the math you need to know for the test (it's surprisingly little). But I'll also show you the most common tough SAT problems of the past twenty-five years—these problems show up over and over—and how to solve each one in a snap.

I'll show you the true secret behind solving SAT math problems, and four specific master math moves that can solve just about any SAT math problem they may throw at you—sometimes in mere seconds. Every SAT has its little surprises, so I'll show you the best way to rescue problems that you can't solve, and the best way to bail out of difficult situations.

I'll show you how to make the best use of your limited time—and what to do if you run out of it. Finally, I'll show you how to catch errors that you make (it's not the way you think), and how to avoid most errors in the first place.

Have a Calculator Handy for Emergencies, but Try Not to Use It
The instructions say that you can use a calculator on the SAT Math Test, but relying on a calculator on the actual exam is not recommended for the following reasons.

• Using your calculator wastes time. Unless you're ambidextrous, stopping to use a calculator means juggling with your pencil, punching numbers into the calculator, and then readjusting your pencil to resume writing—and that's just for a single step of a problem.
• It's easy to get confused with order of operations on a calculator, or with multi-step calculations; heck, even punching in the numbers incorrectly is a source of error. If you make a mistake, it won't be clear where you went wrong and you won't have any written record you can review.
• Most risky of all, when you use a calculator you take your eyes off the problem and you stop thinking. It's easy to get caught up in the calculation and forget what you were solving for.

Besides, you shouldn't need your calculator: if you think you need it for a tough or lengthy calculation, you probably missed the point of the question.

Still, you should have a calculator with you in case your brain freezes in the exam room on the Big Day and you can't remember what 9 times 8 equals—it happens! Calculators are not supplied so bring one you're familiar with, not a calculator you borrowed from someone at the last minute. The last thing you need when you're taking the SAT is to be fumbling around with your best friend's super-calculator.

Most four-function, scientific, or graphing calculators are fine. The calculator needs to solve only simple calculations, so avoid anything too complicated; the simpler the model, the better. Hand-held minicomputers, laptop computers, and pocket organizers (such as those with typewriter-style keypads) are not allowed.

A Few Important Words about the Open-Ended Questions
Ten of the 54 questions on the SAT Math Test will consist of what the test writers call "student-produced response" questions. The open-ended questions do not have choices, so you will have to grid-in your exact answer.

These questions will require us to modify some of the techniques you'll be learning shortly—our four "math moves"—but the important thing is to become comfortable with bubbling-in your answer in the special grids.

I'll give you some practice bubbling-in on your answer sheet shortly, but first here are the main points to keep in mind regarding these questions:

• Before filling in the ovals on a question, it's a good idea to write your solution to each problem in the space provided on the answer sheet above the bubbles. Doing so takes only a couple of seconds and reduces the chances of filling-in the wrong bubbles.
• Some questions have more than one correct answer. If so, you can bubble in anyone of the possible answers; the choice is up to you.
• All answers are non-negative. If you get a negative answer to an open-ended question, you've made a mistake. (The answer to any open-ended question must also be no greater than 9999, which is the maximum number that the answer sheet will allow for these questions.) In other words, the answer to an open-ended question on the SAT Math Test must range from 0 to 9999 inclusive.
• The answer sheet gives you the option of filling in the answer to a question as a fraction or as a decimal. Choose whichever way seems most natural to the problem you've just solved.
• Mixed numbers (like 1½) are not allowed, so either convert any mixed number to a fraction (3/2) or convert it to a decimal (1.5) before filling in the bubbles.
• The answer sheet has room for four-digit answers. If your answer has fewer than four digits, you can start bubbling your answer into any column that space allows. For example, the two-digit number 28 could be bubbled into the first and second, second and third, or third and fourth columns.
• Ignore the decimal point for integer answers.
• If you're entering a decimal answer with a repeating digit (such as 2/3, which equals 0.6666. . .), you should enter the decimal point (ignoring the zero to the left of the decimal point) and the first three digits to the right. You can round the answer or not (.666 or .667 are equally acceptable versions of 2/3; .66 or .67 are not); it's up to you. Of course, simply entering in the fraction version of such answers may be easier than wondering which digits to include or how you should round them.

Be especially careful—but then you're always careful, aren't you—on the open-ended questions. If you're off on a question by even a one-thousandth, you will receive no credit for your answer.

Page 4 Answer Sheet Practice for the Open-Ended Questions
In the space provided below, fill in the ovals for the following sample answers to the open-ended questions.

You'll find the correct version or versions of each answer at the end of this article

My Job—Your Job
My job is to provide you with all the skills and knowledge you need to achieve your maximum possible SAT math score, but you have to master these things. Hey, I'm just your coach, remember—you've got to do most of the work. Fortunately, the work won't seem that hard when you see how quickly your SAT math score starts improving.

It doesn't matter whether you're a whiz at math or whether math's your worst subject: I'll show you how to improve your score. The key point to keep in mind now is that you'll be learning a whole new way to take the SAT Math Test. Your most important job is changing the way you approach and solve math problems. I'll show you how, but you've got to do the changing.

As we discussed in Prepare for the SAT—but Practice Alone Is Not Enough, To Change Your SAT Score, You'll Have to Change the Way You Take the Test, Changing the Way You Take the SAT, Knowing What to Do on the SAT—and Being Able to Do It, changing old habits isn't easy—especially if you're already good or even great at math. (If math's not your thing than you'll be eager to change.) Remember Michael Jordan's advice: if you practice eight hours a day incorrectly, you get very good at doing the wrong thing. When you solve practice SAT math problems here or on your own, the crucial thing is not—repeat: not—merely getting the answer. I can't stress that point enough. The entire point of practicing for the SAT Math Test is rehearsing the techniques you're about to learn. These problem-solving and test-taking techniques are the key to your improvement.

Remember: to change your math score, you've got to change the way you take the test. If you want to change your math score dramatically, you've got to change what you're doing dramatically.

I'll Cover Techniques before Content but You May Need to Reverse the Order
The content of the SAT Math Test is relatively simple, and won't require much time to review. Changing your problem-solving and test-taking habits, on the other hand, will require stronger measures, so we'll start there.

• If you're a strong math student, immediately begin with the techniques (the experience sets). Then review the most common SAT math problems before returning to review any math concepts you may need brushing up on.
• If you're good at math but it's not your strongest subject, simply follow the articles as they are organized (techniques, math review, most common SAT math problems).
• If you don't feel comfortable with math, begin with the math review and most common SAT math problems before returning to the techniques.

Page 5 Solutions for the Answer Sheet Practice Drill
Here are the acceptable ways of bubbling-in the sample answers. When more than one version was possible, I have provided each one.