Cracking the SAT subject test in math 2, 2nd edition

Cracking the SAT Subject Test in Math 2, 2nd Edition finding fractional equivalents At the beginning of each chapter in this book, you may see additional definitions that pertain to the material in th[.]

At the beginning of each chapter in this book, you may see additional definitions that pertain to the material in that chapter Every time you see such definitions listed, be sure that you know them well One way to memorize the definitions is to make flash cards for them

DOING ARITHMETIC

This chapter deals with the basic manipulations of numbers: averages, word problems, exponents, and so on Most of these operations can be greatly simplified by the use of a calculator, so you should practice them with your calculator in order to increase your speed and efficiency Remember the points about calculator use from Chapter 2, however If you use your calculator incorrectly, you’ll get questions wrong If you use

it on every question without thinking, it will slow you down Keep your calculator near at hand, but think before you use it

Order of Operations

You remember the Order of Operations, right? You might remember this

as PEMDAS (or Please Excuse My Dear Aunt Sally) or BEMDAS This is the order you must use to correctly solve an arithmetic problem PEMDAS stands for Parentheses (or Brackets, in the case of BEMDAS), Exponents (and roots), Multiplication and Division, Addition and Subtraction When using PEMDAS, it’s important to remember that exponents and roots should be calculated from left to right, just as multiplication, division, addition and subtraction should be You can think of PEMDAS in the following way:

PEMDAS

Parentheses

Exponents and roots

Multiplication and Division

Addition and Subtraction

Most graphing calculators can display calculations the way that they would be written

by hand (for example, using a horizontal bar with a numerator above and a denominator below to represent a fraction) This feature is called Pretty Print For some calculators, such

as the TI-84, it is necessary to download an application to enable this feature For other calculators, you need to enable Pretty Print in the settings Either way, we recommend enabling this for the SAT Subject Test in Math 2: doing so makes it easier to check if you’ve

made a mistake, which is valuable!

PEMDAS and Your Calculator

The safest way to do multi-step problems like this on a calculator is one step at a time

On scientific and graphing calculators, it’s possible to type complex expressions into your calculator all at once and let your calculator do the work of grinding out a number But in order for your calculator to produce the right answer, the expression must be entered in exactly the right way—and that takes an understanding of the order of operations For example, the expression would have to be typed into some calculators this way:

(2 √(3 ^ 3 − 2))/5 =

On other calculators, it would have to look like the following:

(2(3^3 − 2)^(1/2))/5 =

Any mistake in either pattern would produce an incorrect answer On other calculators, the equation might have to be entered in still another way If you intend to make your calculator do your work for you, check

your calculator’s operating manual, and practice In general, use lots of parentheses to make sure the calculator does the arithmetic in the right order If you use too many parentheses, the calculator will still give you the right answer, but if you don’t use enough, you may get the wrong answer And remember, the safest way to use your calculator is one step

at a time

DRILL 1: PEMDAS AND YOUR CALCULATOR

Check your PEMDAS skills by working through the following complicated calculations with your calculator The answers can be found in Part IV

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