SAT Prep Black Book: The Most Effective SAT Strategies Ever Published (48 page)

Some students are tempted to choose 4 as the answer to this question, because it kind of looks like the right-hand
x
-intercept of the graph might be at
x
= 4. But if you look carefully, you’ll see it’s at a position much closer to
x
= 5. Remember how important it is to pay attention to details!

If we read carefully, look at the graph carefully, and remember to think in terms of things like intercepts, we can answer this question in about 10 seconds, without even picking up a pencil.

A lot of test-takers drop the ball on this question because they don’t look for the ways to simplify the algebraic expressions involved, or they try to assign values to
n
and
k
without making sure that those values satisfy the original requirements of the given equation.

I would start off by simplifying the expression on the left-hand side of the equation, dividing
by
n
/
n
and ‘eliminating’ an
n
from the top of first fraction and the bottom of the second fraction. Then it’s a little easier to see that the whole thing could be combined to this:

n
/(
n
2
- 1)

(Notice that (
n
- 1) can be multiplied by (
n
+ 1) to create the difference of squares (
n
2
- 1). This is something we’d want to be able to do in our heads, without needing to foil it out manually.)

So now our equation looks like this:

n
/(
n
2
- 1) = 5/
k

This means that
n
corresponds to 5, and (
n
2
- 1) corresponds to
k
.

If
n
is 5, then (
n
2
- 1) is 24, so the answer is (C).

In our wrong answers, we see the value of
n
, which helps reassure us that we attacked the question correctly, because it suggests that the College Board is hoping some test-takers will correctly realize that
n
is 5 but then forget the question was asking for
k
. We also see a series that goes 24, 25, 26, which might seem odd at first, because normally we’d expect the right answer to be in the middle of a series like that. But there’s a certain logic to it here, because in order to arrive at 24 we have to square 5 and subtract 1; in this case, the wrong answers reflect squaring 5 and
adding
1, and squaring 5 while forgetting to add or subtract. We can see there’s a certain symmetry the College Board is going for here, in trying to give test-takers a variety of ways to mess this question up. And that can reassure us that squaring 5 and then subtracting 1 was, indeed, the right way to go.

We’ve just looked at a whole bunch of SAT Math questions, and we never really broke a sweat!  We did this by sticking to our simple process, and by looking for quick and easy answers. As we saw, the hardest part of each problem was the setup. The actual calculations didn’t present much of a problem, as long as we had our basic concepts in order.

On the next page, you’ll see a brief, one-page summary of the main ideas to keep in mind on the SAT Math section. After that, we’ll dive into the SAT W
riting section. You’ll see that the Writing section, like the SAT Math section, is a lot easier to attack if you’re familiar with a core set of basic principles.

If you’d like to see videos of some sample solutions like the ones in this book, please visit
http://www.SATprepVideos.com
.
A selection of free videos is available for readers of this book.

This is a one-page summary of the major relevant concepts. Use it to evaluate your comprehension
or jog your memory. For a more in-depth treatment of these ideas, see the rest of the section.

The
Big Secret:
SAT Math tests very simple things in very strange ways.

The concepts
in the SAT Math section must be limited because of standardization. No trig or advanced stats—just
arithmetic, algebra, and geometry.
Refer to the SAT Math Toolbox if necessary.

Focus on the
definitions and properties of the concepts in each question
, not on formulas.

All SAT Math is
“easy,” and each question can be done in
30 seconds or less
if you find the fastest solution. If your solution is very complicated, you’re probably doing the question wrong.

Look for shortcuts, things that cancel out, equivalent terms, etc.
Leave expressions as fractions and radicals, instead of decimals, for easier canceling and substitution.

Diagrams
are assumed to be to scale unless the question says otherwise. Taking a close look can often help to eliminate wrong answers or even point to the right one without doing any math.

Diagrams that aren't drawn to scale
often yield important information if you redraw them to scale.

Every
question contains all the information you need to answer it (unless “not enough information” is an answer choice, in which case there may not be enough information), even if it doesn't seem like that.
If you understand every word in the question, then you know enough to mark the right answer.

Some common wrong answer patterns include choices that are:

o
half or double the right answer

o
in a series with the right answer

o
a number that you have to find “on the way” to the answer

o
similar in appearance to the right answer

I recommend a step-by-step process called the Math Path
for questions that are hard to figure out:

o
Read the question carefully and consider the words.
This is the most important step.

o
Consider any diagrams—
scale, missing dimensions
, etc.

o
Consider answer choices (if there are any)—relationships with each other and with question.

o
What areas of math are involved?
What can the SAT test in those areas?
(Math Toolbox.)

o
In light of steps 1 - 4, look for a solution that would take 30 seconds or less, ideally.

o
Solve the problem.

o
Check your work
with the answer choices. “Carelessness” costs more people more points than any other single thing does.

Note that
we
think about the question holistically before we actually start solving it.

Ignore the order of difficulty
, which is based on people who don’t know what they’re doing. You can make careless mistakes on any question, and every question has a simple, direct solution.

See the example solutions in this Black Book
for demonstrations of these ideas.

“You only fail if you stop writing.”
- Ray Bradbury

The SAT Essay is supposed to evaluate your ability to produce what the College Board calls “good writing.” The College Board’s intention here is commendable, but the essay test it has come up with is an awful tool for measuring writing ability. In other words, while a good writer might score well on this writing exercise, it’s very possible to score well without being a good writer at all, and some hallmarks of good writing might actually hurt you. In fact, in a widely publicized
New York Times
article from 2005, Dr. Les Perelman, a director of undergraduate writing at MIT, described the writing skills necessary for a good SAT score as “exactly what we don’t want to teach our kids.”
[1]

To score well on the SAT Essay, all you have to do is completely ignore the official scoring rubric on page 105 of the College Board’s
The Official SAT Study Guide
and just imitate (almost copy) the features of the high-scoring sample essays from the
Study Guide
. In the coming pages, you’ll see what really sets apart a high-scoring essay, and exactly how to construct one of your very own.

(While you should do your best to imitate high-scoring sample essays and copy their techniques, you should NEVER plagiarize ANYTHING, ever. I’m not suggesting that you recycle any passage from anyone else’s work as your
own. For one thing, since SAT Essay topics aren’t repeated, it’s unlikely that an exact passage from a high-scoring sample essay will help you much; more importantly, though, passing off another person’s work as your own is one of the most intellectually  reprehensible things anyone can do. So don’t do it.)

Believe it or not, even essay tests have rules. You have to learn them if you want to do well. But be careful! The SAT Scoring Guide that appears on page 105 of the College Board Publication
The Official SAT Study Guide
isn’t very useful if you’re trying to figure out exactly what to do on the test.

It might sound strange to say this, but most of the College Board’s advice on how to write t
he SAT essay is very, very bad, in the sense that many people who make an effort to follow it still end up with lower scores on the SAT Essay than they would like. Instead of following the rules that the College Board states explicitly, we’ll do something much smarter—we’ll figure out the rules that are implicitly revealed in the high- and low-scoring sample responses provided by the College Board in
The Official SAT Study Guide
. Remember that these are the rules revealed by actual high- and low-scoring sample essays released by the College Board. As such, they may be very different from the stated rules that you’ll find on page 105, and elsewhere, in the College Board’s Blue Book, the
Official SAT Study Guide
. Here are the real rules:

The prompts that appear on the SAT Essay are all open-ended and fairly vague about what they want you to write. This gives you a wide degree of latitude in deciding which side of an argument to defend, and in supporting your position, which can be a good thing if you don’t let it overwhelm you.

When you plan your answer, you don’t have to worry about being politically correct or trying not to offend your reader. As an example, take a look at page 197 of the College Board publication
The Official SAT Study Guide
. You’ll see a perfect-scoring essay that talks favorably about how the Confederate Army was “defending its way of life” during the Civil War when it fought to defend slavery.

Now, nobody is suggesting that you go out of your way to discuss something controversial or offensive. All I’m trying to point out is that there’s no need to be worried that you might say the wrong thing. As the essay on page 197 demonstrates, the graders are interested in how well you develop an argument that answers the question in the prompt—they don’t really care what the argument actually is.

When you’re looking for examples to support your argument, the SAT allows you to draw from anything at all. Some
high-scoring essay-writers choose to draw examples from history and literature, but some of them draw examples from their own lives. In fact, the high-scoring essay on page 200 of
The Official SAT Study Guide
uses two personal examples that are almost certainly made up.

Many test-takers are surprised to learn that you don’t get extra consideration for using more academic examples, but
it makes sense if you put yourself in the College Board’s shoes. The College Board is always nervous about being accused of elitism; if the SAT Essay rewarded historical and literary examples over personal ones, then people might complain that the scoring process was too heavily influenced by the quality of a test-taker’s education rather than by innate writing ability. So the College Board accepts non-academic examples in an effort to avoid this kind of criticism.

It’s also okay to make up facts, or to make mistakes in your presentation of historical or literary details if you decide to use academic examples. This isn’t like a history test in school, where the
teacher would probably take points off for historical inaccuracies in addition to poor writing. On the SAT Essay, the accuracy of the facts simply doesn’t matter. (This is one of the things that Dr. Perelman was referring to when he complained that the test rewards the wrong things.) All that matters is that the examples you cite
would
support your thesis if they were true. Whether they actually
are
true is irrelevant.

Again, the reasoning behind this bizarre policy starts to make a little sense when we think about it from the College Board’s standpoint. Since they have to standardize the grading of the essay, if they
were going to penalize you for writing something false, they would have to fact-check every single statement in every single essay, which would take a ton of time and money, particularly since writers can cite personal examples. So the only real solution for the College Board is to avoid doing any kind of fact-checking at all. Instead, the graders are simply looking to determine whether your examples would support the thesis if they were true.

This means that the SAT Essay allows you to make up any facts you want, as long as they would support the thesis if they were true.

The high-scoring essays that appear in
The Official SAT Study Guide
have many mistakes that would qualify as errors for the Identifying Sentence Errors portion of the Writing Section. For example, the high-scoring essay on page 120 of the College Board’s book improperly shifts from the present tense to the past tense, uses the incorrect word
alright
, and incorrectly starts a sentence with the conjunction
however
. So you can get away with a few grammatical mistakes and still make a perfect score.

All the high-scoring sample essays included in
The Official SAT Study Guide
are fairly long and well-developed, while the low-scoring sample essays are much shorter. But be careful—an essay’s score seems to correlate with its length, but that doesn’t mean that writing garbage just to fill up space is a good idea. What it means is that if you’ve written a short essay, your chances of scoring high seem to be just about zero.

For proof of this, check out the sample essay on page 210 of
The Official SAT Study Guide
. You’ll notice that it’s one of the better-written sample essays provided by the College Board, at least in terms of grammar, diction, and style, and that it does a better job of following the scoring guide on page 105 than the other sample essays do. You’ll also notice that it received a 3 out of 6 because it’s too short.

On page 105 of the Blue Book, the College Board says it looks for a “varied, accurate, and apt vocabulary” in high-scoring essays. But the essays that receive the highest possible scores demonstrate very little in the way of vocabulary skills. The biggest word in the sample high-scoring essay on page 120 is
dumbfounded
, and, as already mentioned, that essay also uses the non-word
alright
. The other high-scoring essays have similarly unimpressive vocabularies.

I often see essays in which test-takers have tried to use
big words they didn’t actually understand in an effort to impress the reader. But the reader truly doesn’t care about your vocabulary; the reader only cares how well you support your position and how long the essay is, as we see from the grades that real essays get. Be aware, though, that poorly used vocabulary words can hurt you if the reader notices them. The safest way to avoid any potential difficulties is simply to stick to words you actually know, since trying to use words you’re not certain of can’t help, and might hurt.

The high-scoring essays in
The Official SAT Study Guide
use a variety of formats. Some seem to use variations on the standard five-paragraph essay; all of them use an opening paragraph and a closing paragraph, both of varying lengths. So, in theory, just about any format seems acceptable.

Most of the top-scoring essays I’ve seen, though, have followed something similar to the 5-paragraph format: intro paragraph, three example paragraphs, conclusion paragraph. The number of example paragraphs might vary, and sometimes there isn’t a conclusion paragraph, but in general the top-
scoring essays seem to favor this 5-paragraph format. It’s the format I use, and the one I advise all of my students to use.

Whether you use the 5-paragraph format or not (again, I highly recommend it), make sure you have a clearly stated thesis in the essay. One of the things that graders really seem to pay attention to is how well you support your position (which makes sense, right?). If they can’t find a clearly articulated statement of your position right away, it becomes more difficult for them to tell if you did a good job of supporting that position. So make it easy on them and include a clear thesis.

I’d also recommend putting that thesis as the first sentence in your essay, even though that’s not the common place for a thesis in the standard 5-paragraph essay format. For an example of an essay that does this, check out the essay on page 197 of
The Official SAT Study Guide
again. Note that the prompt asks, “Is deception ever justified?” The first sentence of the essay on 197, which got a perfect score, is “Deception is sometimes justified”—a clear statement of the thesis for the rest of the essay to support.

I think readers react well to a thesis in this position because it makes it very clear what you’re trying to prove, which makes it easy for them to determine whether you go on to prove it or not. (Of course, in order to get a good score, you do need to support the thesis in the rest of the essay. Stating it clearly is just an important first step.)