## Cracking the SAT

# Part III

# How to Crack the Math Section

# Chapter 11

# Fun with Fundamentals

Although we’ll show you which mathematical concepts are most important to know for the SAT, this book relies on your knowledge of basic math concepts. If you’re a little rusty, this chapter is for you. Read on for a quick review of the math fundamentals you’ll need to know before you continue.

## THE BUILDING BLOCKS

As you go through this book you might discover that you’re having trouble with stuff you thought you already knew—like fractions, or square roots. If this happens, it’s probably a good idea to review the fundamentals. That’s where this chapter comes in. Our drills and examples will refresh your memory if you’ve gotten rusty, but if you have serious difficulty with the following chapters, even after reviewing the material in this chapter, then you should consider getting extra help. For this purpose, we recommend our own *Math Workout for the SAT,* which is designed to give you a thorough review of all the fundamental math concepts that you’ll need to know on the SAT. Always keep in mind that the math tested on the SAT is different from the math taught in school. If you want to raise your score, don’t waste time studying math that ETS never tests.

Let’s talk first about what you should expect to see on the test.

## THE MATH BREAKDOWN

Three of the nine scored sections on the SAT are Math sections. Two of the scored Math sections will last 25 minutes each; the third will last 20 minutes.

The math questions on your SAT will be drawn from the following four categories:

1. Arithmetic

2. Basic Algebra I and II

3. Geometry

4. Basic probability/statistics

That’s it! Although there are some smaller, miscellaneous topics that will occasionally appear on the SAT (logic, visual perception, permutations/combinations), they are very, very rare: don’t expect to see more than 1 or 2 of those questions on the test.

The math questions on the SAT are almost entirely arithmetic, basic algebra, or geometry.

The math questions on your SAT will appear in two different formats:

1. Regular multiple-choice questions

2. Grid-Ins

The Grid-Ins will only appear in one of the scored 25-minute sections. All other math questions will be normal multiple-choice questions.

## THE INSTRUCTIONS

Each of the three scored Math sections on your SAT will begin with the same set of instructions. We’ve reprinted these instructions, just as they appear on the SAT, in the Math sections of the practice tests in this book. These instructions include a few formulas and other information that you may need to know in order to answer some of the questions. You should learn these formulas ahead of time so you don’t have to waste valuable time referring to them during the test.

Still, if you do suddenly blank out on one of the formulas while taking the test, you can always refresh your memory by glancing back at the instructions. Be sure to familiarize yourself with them thoroughly ahead of time, so you’ll know which formulas are there.

## BASIC PRINCIPLES OF SAT NUMBERS

Before moving on, you should be certain that you are familiar with some basic terms and concepts that you’ll need to know for the Math sections of the SAT. This material isn’t at all difficult, but you must know it cold. If you don’t, you’ll waste valuable time on the test and lose points that you easily could have earned.

### Positive and Negative

There are three rules regarding the multiplication of positive and negative numbers.

1. positive × positive = positive

2. negative × negative = positive

3. positive × negative = negative

### Integers

Integers are the numbers that most of us are accustomed to thinking of simply as “numbers.” Integers are numbers that have no fractional or decimal part. They can be either positive or negative. The positive integers are

1, 2, 3, 4, 5, 6, 7, and so on

The negative integers are

–1, –2, –3, –4, –5, –6, –7, and so on

Zero (0) is also an integer, but it is neither positive nor negative.

Note that positive integers get bigger as they move away from 0, while negative integers get smaller. In other words, 2 is bigger than 1, but –2 is smaller than –1.

This number line should give you a clear idea of how negative numbers work. On the number line below, as you go to the right, the numbers get larger. As you go to the left, the numbers get smaller (–4 is smaller than –3, which is smaller than –2, and so on).

You should also remember the types of numbers that are *not* integers. Here are some examples:

Basically, integers are numbers that have *no* fractions or decimals. So if you see a number with a fraction or non-zero decimal, it’s *not* an integer.

### Odd and Even

Even numbers are integers that can be divided by 2 leaving no remainder. Here are some examples of even numbers:

–4, –2, 0, 2, 4, 6, 8, 10, and so on

You can always tell at a glance whether a number is even: It is even if its final digit is even (divisible by 2). Thus 999,999,999,994 is an even number because 4, the final digit, is an even number.

Odd numbers are integers that have a remainder when divided by 2. Here are some examples of odd numbers:

–5, –3, –1, 1, 3, 5, 7, 9, and so on

You can always tell at a glance whether a number is odd: It is odd if its final digit is odd. Thus, 444,444,444,449 is an odd number because 9, the final digit, is an odd number.

**Pick a Number, Any Number…**

If you aren’t sure about one of these rules, it’s safer to try an example than guess. Say you need to know what kind of number you get when you add an odd number and an even number to solve a problem but you can’t remember the rule. Just try an example like 2 + 5 = 7 and you’ll know that even + odd = odd.