How Many Times Should You Take the SAT?

I dealt with this question in my Sept. 13th post “The College Hunt.”  Before ScoreChoice was implemented, this was a much simpler question, yet I still heard/read all sorts of conflicting advice.  I hope that some common sense will help out.

First, let me get some history out of the way.  Before ScoreChoice, it was definitely NOT a good idea to take the SAT more than twice, except under special circumstances.  Plenty of college advisers gave advice to the contrary; you can still find some of that wrong advice on the web.  So how can I say so confidently that these experts were wrong?  Because I consulted some very knowledgeable experts whose opinions I trusted.  One was a college admissions expert who personally visited every major campus in the U.S.

Students in McClurg

Image by Sewanee: The University of the South via Flickr

After all, college admissions are decided by college admissions officers (duh!).  So, if you’re a guidance counselor and you want to be sure you have correct information about the admissions process, consult those officers, and not just fellow counselors, journals, etc.

But as I mentioned in my earlier post, ScoreChoice changes things.  If you get to choose which scores to send to a college, you can take the SAT as many times as you want and an admissions office won’t know it (or care).  But things can get dicey when you’re applying to several colleges, only some of which accept ScoreChoice.

I imagine that many schools that do reject ScoreChoice (i.e. require you to send all scores) are more forgiving of multiple-SAT-takers than they used to be.  After all, they know you might want to take the test 3 – 5 times to help yourself get into other schools that do allow ScoreChoice.  Notice that I used the words “I imagine.”  I DO NOT have sufficient information to make a definitive statement about this.  It just makes sense to me that some admissions officers will be more progressive in light of the new rules, while others cling to their old ways and penalize students who take the SAT more than twice.

So what’s a poor student to do?  I could present a load of links to web articles with conflicting information, but I’ll refrain (for one thing, over half of the articles I found have no dates, so one can’t even tell whether or not they were written before ScoreChoice was permitted).  Fortunately, there is a truly simple, logical solution:  Decide where you want to apply early on (sophomore year isn’t too soon), and contact the admissions offices about their policies (you can do this by phone, or in person if you visit a campus).  Surprise – almost all admissions officers will be happy to give you this information!

And then, when you have definitive information, you can formulate your best application strategy.  Suppose you plan to apply to 6 schools, and 4 of them accept ScoreChoice.  You call the admissions offices at the other 2 colleges, and are informed that one doesn’t mind if you take lots of SATS, but the other frowns on the practice.  But the college with the strictest policy is also your first choice!  Well, one possibility would be to take one SAT in the spring of your junior year, and another in October of your senior year.  Then you could apply Early Decision to your top choice, take the SAT again in November and/or December, and apply for standard admission at the other schools.

So get the facts, and get ’em early.


Function Fun

Okay, maybe functions aren’t fun.  But succeeding on the hard questions isn’t exactly a downer.  So let’s look into them a little more:

There are two ways to symbolize functions on the SAT.  One is the way you learned in school:

f(x) = 3x + 2

Another way is to use a made-up symbol.

Let x* = 3x + 2

Both equations means the same thing.  So f(5) = 15 + 2 = 17, and 5* = 17 too.

Some SAT functions are a little strange:

Let a ^ b = true if a is a multiple of b; otherwise a ^ b = false.  Here, you input two mathematical values, but the output isn’t a number or variable – it’s just “true” or “false.”  10 ^ 2 = true, since 10 is a multiple of 2, but 10 ^ 3 is false.

f(x) = 5 simply means that the output is 5, regardless of what x is.  It’s a pretty trivial function, but it’s good for confusing students.

Drawn in Autosketch + pasting in words from Excel

Image via Wikipedia








Q. If f(x,y) = 2x + 3y, what is f(2y,2x)?


This confuses a lot of students.  Huh – isn’t x supposed to be on the left?  What’s going on here is something I call “windows and variables.”  The definition of a function contains windows, or “supervariables.”  Here, the definition is f(x,y) = 2x + 3y.  The function is only defined once.  Every other time you see it will be an example, which can contain numbers or variablesf(2,5) is easy – it’s just 2(2) + 3(5).  In other words, you plug the number 2 into the x window, and the number 5 into the y window.  The example f(2y,2x) contains the variables x and y, which have nothing to do with the windows x and y.  All you need to do is plug the variable 2y into the x window, and the variable 2x into the y window.  So f(2y,2x) = 2(2y) + 3(2x) = 4y + 6x.

Another way to think of this is that f(x,y) = 2x + 3y means “start with 2 values, and end up with twice the left value plus 3 times the right value.”

What about graphing functions?  Here’s the trick: don’t try to understand what the graph means.  Not many people have any idea what a graph means, unless it’s explained slowly and it’s truly simple to begin with.  So just consider one point at a time.  So if you’re shown a graph of f(x) and asked which answer shows the graph of f(x+2), just find a point on the first graph.  Suppose it contains the point (1,3).  Then you know that f(1) = 3, even though you don’t know what the function is.  And since f(x+2) uses the same function, f(1) still equals 3, so the correct graph will include the point (-1,3) (since f(x+2) will be f(1) when x = -1).  If more than one graph in the answers includes that point, just move on to another point.


The following is typical of the most challenging function questions on the SAT:

Q. Let f(x) = 3x + 1

If 2f(a) = f(3a), what is the value of a?

This might look scary to you, but it’s actually not very hard!  The illusion of difficulty comes from your unfamiliarity with the symbol f( ), so you should get rid of it as soon as possible.

Recall that 2f(x) just means 2 [f(x)].  And here, f(a) means “start with a, and end up with 3 times a plus 1.  So now you can translate the equation into

2(3a + 1) = 3(3a) + 1

And that’s just a plain old algebraic equation.  If this is a multiple choice question, you can just try the answers (substitute for a) until you find the one that works.  Or just solve:

2(3a + 1) = 3(3a) + 1

6a + 2 = 9a + 1

2 = 3a + 1

1 = 3a

1/3 = a

Now let’s check:  substitute 1/3 for a

2(1 + 1) = 3(1) + 1

2 X 2 = 3 + 1

4 = 4 Cool.

Function Fear

Of all the topics on the math section, my students seem to have the most trouble with functions.  Did your heart rate increase when you read the word “function”?  Okay – maybe not.  But a lot of students get frazzled by function questions, so here’s some help:

Actress demonstrating initial reactions of fea...

Image via Wikipedia

Let’s start with the psychology.  I like to ask my students “what was the first grade in which you ever leaned a math function”?  Their answers typically run from 7th to 11th grade.  Wrong!  You learned your first function in 1st grade.  Addition and subtraction are functions, as are many other concepts you learned throughout grade school.

A mathematical function is simply a set of instructions that tells you what to do with one or more values.  Addition is actually a hard one, since you have to memorize all of those combinations (you’re not born knowing what 8 + 3 is).


First grade teachers like to make things simple.  They just show you a chart that says something like 8 + 0 = 8, 8 + 1 = 9, 8 + 2 = 10, etc.  But high school teachers can’t make things that simple, because they know you’d laugh at them.  So they show you something like

f(x,y) = x + y

…and say “here’s an easy one.”  Who’s laughing now?

But wait…the only thing that’s new there is f( ).  Your teacher tells you that f( ) means “eff of.”  But I don’t know what “eff of” means either.  So I say that it means “start with.”

So f(x,y) = x + y means “start with x and y, and end up with their sum.”

And f(3,4) means “start with 3 and 4, and end up with their sum,” which is obviously 7.

Let’s look at one more:

f(x) = 2x + 4 means “start with x, and end up with twice x plus 4.”

f( ) looks scarier than + or √, because it looks like 3 symbols.  Just think of it as one symbol.

Okay, that was pretty elementary stuff.  But my point is that overcoming “function fear” is the first step toward mastering function problems.  More tips on functions will follow shortly.

Prepare For The PSAT

The PSAT will be administered on October 12th and October 15, depending on your school.  If you haven’t already registered, do so right away (for many schools, Sept. 21st is the deadline).

If you’re not already taking a PSAT prep course, should you start one this late?  Naturally, that’s up to you.  You won’t be able to fit a full-length course into the time remaining, but you could take a few lessons with a private tutor if you wish.  You might continue towards an upcoming SAT (see my earlier post: “The College Hunt”).  But if you don’t plan to take formal lessons for the PSAT, you still shouldn’t go in blind.  At the very least, obtain a copy of the Official Student Guide to the PSAT/NMSQT from your guidance office, and familiarize yourself with the exam.  You should definitely take the practice test that’s included.

You can buy a PSAT prep book, or look for free resources on the web.  A quick Google search yielded these:

PSAT Study Guide from the Study Guide Zone

ePrep articles

PSAT* Online Course from Test Prep Review


Image via Wikipedia

Of course, you can read the SAT Tips posts in this blog, but I’ve only written a few so far.  Here are some other blogs:

Phillip McCaffrey’s blog – lots of video tips

Reading and Writing Tips for the SAT and ACT

SAT Tutor’s blog

Why should you study for the PSAT?  If you do very well, you could become a National Merit Scholarship semifinalist (or better).  But even if you think you have no chance at the NMS, you’ll feel a lot better about the upcoming SAT if you don’t get a lousy score.  Also, you’ll have a better idea what your strengths and weaknesses are if you’ve prepared for the PSAT, and that will help you form a strategy for the SAT.

How To Solve “Shaded Region” Questions

Relax – no one else knows the formula for that oddly shaped shaded region either!  Shaded region questions nearly always involve subtraction.  Usually, all you have to do is subtract the white area from the area of the whole figure are to get the gray.

Suppose you’re told that the length of a side of the larger square is 25, and the smaller square has sides of length 10.  What is the area of the shaded region?

Simply use these 4 steps:  English, Formulas, Substitute, Solve.

Step 1 (English)  large square – small square = shaded region

Step 2 (Formulas)  S2 – s2 = answer

Step 3 (Substitute) 252 – 102 = answer

Step 4 (Solve) 625 – 100 = 525


If you use these steps, most of these problems will be fairly easy.  Need to subtract a semicircle?  No problem; just use (πr2)/2.

Let’s do a trickier one:

Okay, the large and medium squares still have sides of 25 and 10, respectively.  Suppose the small square has sides of length 3.  What is the area of the unshaded region?

Step 1 (English)  large square – medium square + small square = unshaded region

Step 2 (Formulas)  l2 – m2 + s2 = answer

Step 3 (Substitute) 252 – 102 + 32 = answer

Step 4 (Solve) 625 – 100 + 9 = 534

If you didn’t see Step 1 right away, that’s okay.  It’s easier if you break things down into simpler steps anyhow.  Just find the area of the shaded region first (medium square  – small square), and then subtract that from the large square (whole – gray = white).

Unfair Test?

This post is going to be one of my rants, and a geeky one at that, so if you’re looking for SAT tips, please be patient and wait for another article.

The College Board recently announced that SAT scores dropped (again), and numerous articles have appeared on the Web and in print.  The one that caught my eye was in Newsday, and it ironically appeared next to a photo of a just-launched long-distance rocket.  “Shouldn’t that rocket be crashing?” I wondered, until I realized that the photo belonged to an article about NASA’s new rocket.

Anyhow, after the usual moaning and hand-wringing about students’ lack of preparedness for success in college, I came across this:

Anti-testing advocates seized upon the latest dip in SAT scores as further evidence that schools have spent too much class time prepping for standardized exams and not enough time on instruction.

 “We feel that schooling on average has been dumbed down by a fixation on testing,” said Bob Schaeffer, public education director for FairTest, a Massachusetts-based advocacy group.

First, let me make clear that I like FairTest.  As their name implies, they put pressure on private and public institutions who administer the bevy of tests that permeate our lives, in the interest of keeping them fair.

But hold on!  If the scores went down, how exactly does one conclude that the problem is that students spent too much time studying for them?  If students ignore their subjects and study for the SAT’s too much, shouldn’t they be acing the SAT’s and then flunking out of college?  Methinks that FairTest would have complained just as much if the scores went up.

What exactly does the dip in scores mean?  Are we becoming a nation of illiterates (Reading scores dropped the most)?  The drop in scores from last year was 4 points out of 1800 (scores range from 600 to 2400 for the three sections combined).  Is a 4-point drop meaningful?  The scores for each section are multiples of 10 – you can score 560 or 570, but nothing in between.

4 points might seem like a measly difference, but I’m willing to concede that it means something, if for no other reason than the scores have dropped steadily for several years.  But does that really mean we’re getting dumber?  Is there lead in my favorite breakfast cereal?

I think it’s hard to conclude just what is responsible for the dip.  It has been suggested that more below-average students are taking the SAT’s than did in earlier years.  Another theory is that more students for whom English is their second language are pulling the scores down.  Perhaps there are other factors.

I believe we should look for positive strategies, rather than expending our time finger-pointing and overanalyzing.  Tests are a necessary part of the educational process, and that means we have to spend time studying them.  Sure, we shouldn’t overdo it.  But as parents and students, we should recognize that we must adapt to a changing world.  Reading used to be considered fun; now it’s geeky.  And students can’t be expected to give up XBox and FaceBook.  But students must also realize how easy these and other modern distractions make it to neglect activities that are vital to their future.  And parents must be vigilant in reminding their teenagers of this, and taking an active role overseeing their childrens’ activities.

Study hard, get a good job, and you can afford next year’s iPad.  Now that’s fair.

All About Metaphors

This post is not for everyone.  If you’re confident that you can understand any metaphors on the SAT, skip this.  If you’re not sure, give it a quick read.  And if you’re thinking “what’s a metaphor?” you should turn off your iPod and read carefully.

Those pesky SAT writers love to test you with metaphors.  Some are easy to recognize, but others are quite subtle.  Many of my students can tell me what a metaphor is, but are surprised by how often they overlook them in Critical Reading passages.

Let’s start with the basics.  According to, a metaphor is “a figure of speech in which a term or phrase is applied to something to which it is not literally applicable in order to suggest a resemblance.”  Got that?  Don’t worry…

If a writer wants to compare one thing to another, he can use several methods.  One way is a simile, which usually includes the word “like” or “as.”  If I read “she’s as beautiful as an angel,” I know what that means.  She may not have wings, but she sure is gorgeous.  Similes are easy to understand.

Metaphors can be trickier.  “She has the face of an angel” isn’t too hard; it also means she’s pretty.  But consider “her eyes are glowing jewels.”  Does light actually come out of her eye sockets?  Can you string her eyes on a necklace?

The point is that metaphors don’t mean exactly what they say.  A simile states “A is like B,” and it means exactly that.  A metaphor also means “A is like B,” but it reads “A is B.”  B doesn’t even have to exist: “Lawrence has the heart of a dragon.”

That, in a nutshell, is the key feature of a metaphor.  When an author uses a metaphor that reads “A is B,” he’s not talking about B.  B is just a reference for comparison.

Sometimes you’ll find extended metaphors on SAT passages.  There is a specific definition of “extended metaphor,” but for practical purposes you can just think of an extended metaphor as one that goes on for more than one sentence.  Consider the following paragraph:

The MightyCorp manufacturing company is a great solar system.  The workers may draw light from the sun, but they each follow their own path.  Comets may leave the system, but they return from time to time, and are often visible to many.

Q) By stating that “The MightyCorp manufacturing company is a great solar system,” the author implies that

a) Many manufacturers are interested in astronomy.

b) The company will make great strides in the future.

c) MightyCorp is a productive place to work.

d) Comets can be as viewable as businesses.

e) MightyCorp is organized as a hierarchy.

Okay, I know that doesn’t have the “look and feel” of the actual SAT, but it was fun to write.  Now let’s answer the question.  Remember what we just talked about regarding metaphors – there is no solar system in the passage!  No sun, no planets, no asteroids.  The writer is only comparing a business to a solar system.  So you know right away that (a) and (d) are incorrect.  Those are the answers that students who don’t understand metaphors will go for.

Solar System Planets.

Image via Wikipedia

Answer (b) must be wrong, because there was no mention of the future.  Since there’s no mention of productivity, (c) is out, and you know the answer is (e), even if you don’t know what a hierarchy is (“any system of persons or things ranked one above another” – again, from

Of course, once you are comfortable with metaphors, the best way to answer a question is in your own words, before you look at the answers.  Even if you say “that company is like a solar system, with things like suns and planets,” you’ll still choose (e) readily.

Now, if you’re still having trouble with metaphors, you might be getting discouraged.  Perhaps you’re thinking “I’m just not as smart as the kids who get it.”  More likely, you simply don’t read as much as the kids who get it.  Try to read as often as you can.  Even if you just read the sports or entertainment page of the newspaper (or Google News) each day, you’ll do better on the SAT, and have an easier time in college.

And as you travel the escalator of knowledge, remember to oil the gears!