SAT Math Resources

1. Introduction to Math Section of SAT

SAT math spans two question types, three timed sections, and four major math topics—that’s a lot of stuff. This section covers all of it—the basic facts, the crucial score-building strategies, and, that’s right, all the math tested on the new SAT. So, read this chapter, become an SAT Math guru, and then find yourself a mountain somewhere in Tibet. Up there you can give cryptic advice to awed high school students who’ve climb thousands of feet to see you, risking their own deaths at the hands of avalanches and abominable snowmen. Or forego this life of reverence and head off to the college of your choice.

2. The New SAT Math

There are four major changes that make the new SAT Math new. Three of those changes are good news: There are fewer math questions on the test, the entire math section is five minutes shorter, and those pesky Quantitative Comparisons have been eliminated. But the last change probably won’t light a smile on your face: SAT Math now covers some topics in Algebra II. What does this all add up to (pardon the pathetic pun)? The math covered by the new SAT is more difficult. Yeah, it sucks.

But the truth is that the new Math isn’t really all that much harder, and it’ll still be stuff you’ve probably already seen in your high school math classes. Whether you’ve seen it before or not, we’ve got it covered in this book:

• Numbers and Operations

• Algebra (I and II)

• Geometry

• Data Analysis, Statistics, and Probability

On the test, questions covering these four major math topics are spread across three timed sections and 54 total questions.

• • 25-minute section with 20 questions: all questions are Multiple-Choice.

  • 25-minute section with 18 questions: 8 Multiple-Choice and 10 Grid-Ins.

  • 20-minute section with 16 questions: all questions are Multiple-Choice.

3. The Math Reference Area

The math section on the SAT provides a reference area with the basic geometric formulas and information.

You might think that the SAT gives you this reference area because it asks lots of questions on these topics. Well, you’re right. But the reference area is also a trap. Imagine a lazy student out there named Mike. Mike says to himself, “Why should I study all those formulas if they’re just sitting there in the reference area?” Then he goes and takes a nap. On the day of the test, he’s sitting there in his seat, sweating under the pressure, flipping maniacally back and forth between the reference area and the test questions, losing time and focus with every flip of the page.

Don’t be like Mike. And don’t just memorize the formulas. Figure out what they mean. The mathematical facts and rules in the reference area are the foundation for almost every geometry question on the test. Know all the formulas in the reference area as if they were tattooed on your body, as if they’re part of you. You’ll save time. You’ll raise your score. You’ll have funky mathematical tattoos.

4. Order of Difficulty

In each group of questions types, questions are ordered by difficulty. The first third of the questions are generally easy, the second third are a little harder, and the last third are difficult. So in the sections that are entirely Multiple-Choice the first third of the section will be easy, the scond third medium, and the last third hard. In the section that has both Multiple-Choice and Grid-ins, the pattern will start over for each group of questions. Knowing where you are in the order of difficulty can help you in a variety of ways:

• • On Individual Questions. If you think you’ve got the answer to an easy question, don’t second-guess yourself: You probably do. If you’re looking at a difficult question, though, you might want to check your answer just to make sure you haven’t fallen into a trap.

  • Overall Strategy. Unless you’re going for a 700 or above, you don’t have to worry about answering every question on the test. You can use the order of difficulty to help you focus on answering the questions that you can. You should, for instance, answer every question in the first half of a timed math section. But if you’re worried about time, you can probably get by without spending any real time at all on the final two questions.

  • Pacing. You can also use the order of difficulty to manage your pacing. When you’re given 25 minutes to answer 20 math questions in a timed section, you shouldn’t just think to yourself that for every five minutes you should answer four questions. It takes more time to answer difficult problems than it does to answer easy problems. So in the early questions, you should be going faster than four questions answered per five minutes so you can save up time to figure out the harder problems.

5. Better, Smarter, Faster

Time management separates the students who kick major hindquarters on the Math section from those who merely do okay. If you take two students of equal skill in math, but give one a few extra minutes on an SAT Math section, who’s gonna get a better score? The kid with more time.

You might be thinking, “Yeah, but no one’s going to get more time.” While no proctor is going to come along and give half the room 28 minutes on a section and hold the other half to 25, there is one person who can give you more time on a Math section: you!

Math Shortcuts

On the SAT Math, how much time you spend on a problem depends less on how much math you know and more on how you approach the problem. Take a look at the following example:

One student, we’ll call him Bob, might solve this problem algebraically: Plug 4 into the formula for the area of a square and then the area of a circle. Area of a square so the area of this square = Area of a circle =

so the area of this circle must be . is obviously bigger than 16, so the circle must have a larger area than the square.

But another student, we’ll call her Melanie, might choose a faster approach by quickly sketching the square and circle superimposed.

Bob and Melanie know the same amount of math, but because Melanie took the faster approach, she gave herself more time to work on other questions, a distinct advantage. A few more questions like this one, and Melanie will score considerably higher than Bob, even though the two of them know basically the same amount of math.

What Melanie did, essentially, was find a shortcut. Though she knew the same math that Bob did, Melanie found a way to answer the question more quickly. This doesn’t make Melanie better at math, but it does make her a little bit better at taking the SAT.

The important question is, How can you learn to be more like Melanie? You need to do two things:

• • Be prepared. You’re not going to find a shortcut for a problem unless you know how to work it out the “long” way. An ability to find shortcuts is an expression of how comfortable you are with the math you know. Familiarity breeds shortcuts. The more you practice, and the more you look over the practice tests you take, the better you’ll become at finding shortcuts.

  • Be on the lookout. Be aware that there are shortcuts out there just waiting to be found. If you can invest a second to survey the question and think about a faster way, you’ll be well served.

This is not to say that you should go into every question searching for a shortcut. A shortcut won’t always exist. If you’re on some blind quest for a shortcut, it might end up taking longer than the obvious long route to solving the problem.

Shortcuts are more common on SAT questions that cover particular SAT math. As we teach you the math you need to rock the SAT, we also point out the shortcuts you need to really rock the SAT Math.

6. SAT Calculator Smarts

By all means, use a calculator on the test. Bring the biggest, baddest calculator you’ve got, as long as it fits these specifications from the SAT:

• • It isn’t a hand-held minicomputer or laptop computer.

  • It has no electronic writing pad or pen-input device.

  • It isn’t a pocket organizer (PDA).

  • It doesn’t have a QWERTY keyboard.

  • It doesn’t use paper tape.

  • It doesn’t make unusual noises (translation: any noises).

  • It doesn’t reqire an electrical outlet.

Any four-function, scientific, or graphing calculator is accepted as long as it doesn’t break any of the above rules.

But just because you’ve got an awesome shiny hammer doesn’t mean you should try to use it to pound in thumbtacks. Your calculator will help you on the SAT, but only if you use it intelligently.

Every question on the SAT can be solved without using a calculator, so you never need to start pushing buttons. In fact, on algebra questions involving variables, calculators are absolutely useless. So instead of reaching instinctively for your calculator every time, you should come up with a problem-solving plan for each question. Make sure you understand what the question requires and then decide whether to stick to your no. 2 pencil or to wield your formidable digital axe.

To see an example of what we mean, take a look at the following problem:

Then, factor the numerator to its simplest form:

Now it’s obvious that if you plug the 3 in for x, you get , which equals .364.

7. Practical Calculator Rules

There are a few general rules of calculator use on the SAT that it pays to follow:

• • Use a calculator for brute-force tasks, such as dealing with decimals.

  • If you have to deal with a long string of numbers, do not jump to use your calculator. Instead, look for a way to cancel out some of the terms and simplify. A way will usually exist.

  • Avoid using your calculator on fraction problems and on algebra questions with variables.

  • Know your calculator before the test. Be comfortable and familiar with it so you don’t waste time fiddling with buttons during the test. This is particularly true of graphing calculators, which have more buttons than 50 Cent has tattoos.

  • Make sure your batteries are in good shape. Yes, we sound like your parents. But if your batteries run out during the test, you’ll probably have to retake the test and tell your sad story to your entire extended family. That would be ugly.

Above all else, remember: Your calculator is a tool. You wouldn’t wildly swing a hammer around, but some students seem to think they can just whip out their calculator and it will magically solve their problems. Those students seldom do all that well on the SAT Math section.