Up Your Score (48 page)

First, you should figure out the ratio, by dividing the second number by the first:

Then just follow the formula:

a
_n
= (½)(½)
⁷

a
_n
= 1/256

Of course, the ETS is not going to be so nice as to say, “Hey, just plug numbers in!” No. The Serpent will probably sneak geometric sequences through the back door. Since they’re frequently used to describe population growth, he’ll probably ask something like this:

Example: A town now has a population of 100. A big company is to be moving in and the town’s population is expected to double every six years. What will be the population of the town after ten years?

(A) 215

(B) 252

(C) 304

(D) 317

(E) 400

The tricky part of this problem is figuring out what the
r
^(
n–1
)
expression equals. The a
₁
is obviously 100—this is
the population that we’re starting out with. Since the population
doubles
every six years, then
r
, the rate, should be 2. So what’s (
n–1
)? Don’t be tempted to subtract 1 from 10 and get 9. It wouldn’t make sense because the population only doubles every six years, not every year.

So that’s when you should ask yourself, “If six years is one cycle, then by the time we go through the tenth year, how much of the cycle have we gone through?” If we divide 10 by 6, we get the answer: 5/3. We have gone through one and two thirds of the 6-year cycle of doubling.

Now you know all the numbers:

a
_n
= (100)(2
^5/3
) = 317.4802.

Since we can’t have 0.48 of a person, we round down. The population will be 317.

Answer: (D).

Probability is one of those things you learn in school that is actually helpful in life. After you learn about it, you’ll never want to go to Vegas again.

Probability of an event:

The mathematical probability of an event that is certain to happen is equal to one. The mathematical probability of an impossible event is zero.

A fair die is rolled. (All dice are “fair” in SAT-land. It just means that all the numbers have an equal chance of being rolled.) What is the probability that the result is greater than 4?

Well, there are only two numbers that could make this event happen: 5 and 6. Meanwhile, you can actually roll any one of 6 numbers. So,

A scatterplot is basically a graph without lines. Instead, dots are placed for the information that’s available. The
best fit line
is exactly what it says—a line that best fits the graphed dots. The SAT won’t ask you to draw this line, or figure out what the equation for it is. Instead, all you will have to do is know whether its slope is positive or negative. Sometimes the Serpent will tell you to get information from a scatterplot without asking for the best fit line. In this case, just treat every dot as a separate piece of information. These kinds of questions aren’t that common on the SAT, but you should know how to handle them just in case.

Example: Five students were in a pie-eating contest, and the results were plotted in a graph of time versus pies eaten, as shown in Figure 1. Of the five students
A, B, C, D,
and
E,
which one ate the most pies per hour?

(A) A

(B) B

(C) C

(D) D

(E) E

Notice first that the question asks for the most pies
per hour,
not the most pies overall. So, our goal is to find the most pies/hour. Since pies is the
y
-coordinate and time is the
x
-coordinate, the question is really asking you to find the
slope
of the imaginary lines that run from the origin to the point. If you draw these lines, you should be able to see that the line from the origin to
A
has the steepest slope.

Answer: (A)

The SAT has math questions for which you produce the answer. No more stinking multiple choice—here’s a chance for some creativity!

Note: Since the ETS doesn’t offer you a multiple choice option, they don’t take points off your score for wrong answers on grid-in questions. (They’re probably just trying to cover up the fact that they screwed up!)

On the test, these problems will be called “Student Produced Answers.” However, the ETS informally calls them “grid-in problems,” and many of the questions will ask you to “grid” a number. Well, get this:
The ETS screwed up!
Let’s say that again; it feels good.
The ETS screwed up!
You see, in every dictionary we’ve looked at, the word
grid
is used only as a noun. It doesn’t exist as a verb! The ETS made up a word! We think it’s pretty downright disgusting that the ETS will nail you if you don’t know the meaning of the word
supercilious,
yet it has no qualms about making up its own word.
The ETS screwed up!

Don’t be thrown off by these problems: They test you on the same subject matter the rest of the test covers. Plus, you don’t lose any points if you answer these questions wrong!

In fact, because the content is the same as the rest of the test, there aren’t any special hints we can give you. The only tricky part of this section is knowing how to fill in the answers. There are directions for this on every test, but because you probably won’t have time to read them, we’ve provided a summary.

First of all, take a look at a sample of the grid that will appear on your answer sheet. Notice that at the top is space to write in your answer. However, this is not required—the computer scores only what’s in the ovals. So don’t bother to write in the answer unless you’re afraid you’ll get confused otherwise.

You can start your answer in any column. Either of these positions is correct:

Both fractions and decimals are accepted. If the answer is ¼, you can use either ¼ or .25. But remember to make decimals as accurate as possible. For instance, ⅔ can be filled in as .666 or .667, but not .66 or .67. Because of this we think it’s easier to stick with fractions.

Important:
You can’t state your answer in mixed fractions. For instance, 21/2 would look like 2½ (twenty-one halves). So you have to use 5/2 or 2.5.

For some reason, there is a decimal point in the last column: Ignore it. There is no possible answer that would use it.

If for some reason you forget, the largest possible answer on the grid is 9,999; the smallest answer is 0. There are no negative answers. If you get a negative number or a five-digit answer, try the problem again.

Here are two real SAT questions to whet your appetite (have you ever seen
whet
used in a sentence without
appetite
?).

1.
If
(
a
/6) (12
b
) = 1, what is the value of
ab
?

Answer: