Word problems never cease to be intimidating, whether in math class or on standardized tests.  You probably find yourself thinking, “If this is math class, then why are there all these words in the question?  If they want me to do the math, why don’t they write out the problem properly?!”

While that is a question best left to pedagogical studies, we can give you a way to decipher those problems on the SAT and “translate” them into the mathematical expressions you find so familiar.

Luckily, just like an encrypted code, each key word in a word problem represents a symbol or operation in a number expression.  Take a look at the table below.

English equivalents of math symbols

Now, let’s translate almost word for word the problem below, strictly adhering to the chart!

EXAMPLE:
If 25 percent of 60 percent of a positive number is equal to 30 percent of p percent of the same number, what is the value of p?

TRANSLATION:
If 25 percent (25 over 100) of (multiply) 60 percent (60 over 100) of (multiply) a positive number (positive x) is equal to (equals sign) 30 percent (30 over 100) of (multiply) p percent (p over 100) of the same number (positive x)…

Without the words, that would look something like this–>

Wow!  This is much more manageable than the word problem we were given a moment ago.

QUICK TIP:  Practice “translating” word problems according to the chart above.  You’ll be surprised at how easily you can break down the problems.  Don’t forget to look for that little word “of,” in particular!

This quick tip for Sentence Completions will go a long way toward raising your Critical Reading score.  The tip is: don’t look at the answers.

What?, you may ask.  I obviously have to choose the correct solution from amongst the answer choices; how could I not look at them?

The key here is looking at the answer choices at the correct time—that is, after you’ve read the sentence, after you’ve looked for keywords and clues, and after you’ve formulated in your head some approximation of what the answer should be.  Not until you’ve completed all those steps should you look at the answers.

In fact, make your first step covering the choices with your hand.  Four of those choices on Sentence Completion questions are only there to distract and tempt you.  Don’t give in to that temptation!

Let’s simulate covering the answer choices with our hand by leaving them out here.

“Even though she was ___________, Cindy was unable to score points at the basketball game.”

We see the key phrase, “even though” indicating a directional shift from Cindy’s ability to score points.  This leads us to conclude that Cindy should have been able to make a few baskets.  Why?  She is probably either good at basketball, or possesses other helpful characteristics, like being tall or fast.  Now that we have an idea of what to look for (a synonym for talented or tall or fast), let’s look at the answer choices.

(A) debonair
(B) lanky
(C) capricious
(D) magnanimous
(E) fastidious

Compare your word or phrase to the answer choices.  Those that are not synonyms or near-synonyms should be eliminated.  Be ruthless.  Only one answer choice is correct, so all of its competitors must be eliminated.

If we quickly skim our options, we see that only (B) lanky is related to our predictions, making it the correct answer choice.  (Lanky means tall and skinny.)  If we had not predicted, we would perhaps have been tempted by (E) fastidious, meaning to have high standards.  Surely if someone has high standards, they would be expected to win a game?  But Cindy having high standards does not necessarily give her the tools to achieve her goal, the same way that height or skill would.

QUICK TIP:  Cover Sentence Completion question choices with your hand, and don’t look at them until you’ve made a prediction to fill in the blank yourself.

Some of our readers may know of our work with African Leadership Academy in South Africa. We were excited to see one of its students interviewed on The Daily Show with Jon Stewart the other night and we felt compelled to share the remarkable story of William Kamkwamba, who at the age of 14 built a windmill for his village in Malawi. You can read more on his website at http://williamkamkwamba.typepad.com/williamkamkwamba/ or just watch the interview in the video below.

Although he mentioned studying for the SAT, he surely doesn’t need the help. In any case, Lumina Prep is honored to be part of the story thorough our affiliations with African Leadership Academy.

About African Leadership Academy:
African Leadership Academy (ALA) is an elite, residential secondary institution located on the outskirts of Johannesburg, South Africa for outstanding 15-18 year old youth from all 54 African nations and around the world. ALA was founded in 2004 by Fred Swaniker, Chris Bradford, Peter Mombaur, and Acha Leke with the mission to “transform Africa by developing and supporting future generations of African leaders—ethical and innovative leaders who will usher the continent into a peaceful and prosperous future. To achieve this goal, ALA teaches a unique two- year curriculum in African studies, leadership and entrepreneurship as well as the usual academic core subjects. ALA officially opened in September 2008 with an inaugural class of 97 students from 29 countries worldwide.

Sometimes remembering the definitions of math terms is all you need to answer a question on the Arithmetic portions of the SAT Math sections.

Here’s a quick review of basic (but important!) math terms:

WHOLE NUMBERS: a whole number can’t be a fraction of a number, a percentage, or have a decimal. Whole numbers are always positive, and are all also called the “counting numbers,” because they include the first numbers we ever learn to count as children (1, 2, 3… 147… a million…). 0 is a whole number.

INTEGERS: all whole numbers and their negatives, from negative infinity to positive infinity (-3, -2, -1, 0, 1, 2…).

RATIONAL NUMBERS: includes all integers, as well as terminating or repeating decimals, such as 1.125, or 2.7777777… These numbers could all be expressed as a fraction.

IRRATIONAL NUMBERS: decimals that never end and never repeat, such as pi or e.  These numbers cannot be written as fractions or integers.

REAL NUMBERS: includes all rational numbers as well as irrational numbers.  Excludes i.

QUICK TIP for SAT Math Arithmetic: In a Venn diagram, whole numbers are the smallest group, completely inside integers.  Integers and fractions are inside rational numbers.  Rational and irrational numbers are inside real numbers. Imaginary numbers are separate from everything.

Remember these definitions and you’ll be ready to learn more strategies for approaching Arithmetic questions on the SAT Math sections.

In future posts, we’ll deal with specific types of passages and questions. for our first tip, however, we’ll talk about how to approach Critical Reading on the SAT in general.

Sometimes you can get so caught up with strategies and tricks for answering questions, you can forget that strategy starts much earlier—in reading the passages themselves.  Here you can find how to minimize your time reading the passage, but maximize points on questions!

You’ve probably run into people who approach the SAT Critical Reading sections by slowly and carefully reading the passage, approaching each question as it is asked, and then going back to review the section from which the question came and  proceeding to answer the question.

You may also have met those who speedily jump straight to the questions, and only read a portion of the passage if a question refers back to it.

In fact, you yourself are probably one of these two types of people.  Do you see any flaws with either approach?

Our brains are wired to only remember the most recent idea that we’ve read—as in the last 20 seconds or so.  By the time you’ve conscientiously read the passage and read the questions, you’ve already forgotten most of what you’ve read and must spend precious minutes reviewing in order to answer each question!  However, if you skip the passage and only read it in pieces, you’ll have a very difficult time maintaining continuity of thought and flow in your head.  On top of that, there may be relevant pieces of that passage that you never read at all because they weren’t included in the specific line numbers mentioned in the question!  In other words, you have a choice between wasting time, and getting things wrong – a true fool’s choice.  So what to do?

Follow Lumina Prep’s SAT Critical Reading strategy to minimize time and maximize points:

- First, read the introductory blurb in italics to get an idea of the context of the passage.

- Second, divide the questions into two groups: specific (those including line number references) and general (those discussing the overall purpose or intent of the passage).

- Third, read the passage paragraph by paragraph, answering all questions for each paragraph as you deal with that paragraph.

- Fourth, read the rest of the passage, if any of it remains unread.

- Finally, answer the general questions.

QUICK TIP:

It will take you a few passages to get the hang of this at first; don’t get discouraged, you’ll see your score improve quickly!  Try following the reading strategy at home on as many passages as you can.  Remember, practice makes perfect!

Algebra is a core subject area of the SAT math section. Master the basics and you will be well positioned for the test.  The first rule of algebra is to ALWAYS BALANCE the equation, meaning “whatever-you-do-to-one-side,” do to the other!  It is important though to not only perform the same operation to both sides of an equation, but to every term as well.

Here’s an example:  3x-7=15.  Simple, right?

Just divide both sides by 3 in order to isolate the variable (get the x on its own), and you get x-7=5.  Perform reverse PEMDAS, add 7 and we find that x=12. Ta-da, done.

But we forgot that we must divide every single TERM by 3, not just both sides of the equation.  So we really end up with x- (7/3) = 5.  Now we’ve made ourselves a fraction, something even more complicated than before, and answer is 7 1/3, or 22/3 –something very different from x=12.

In this particular example, it’d be simplest to start with reverse PEMDAS and add 7, getting 3x=22, and then divide by 3.  But remember the rule of thumb, if you’re manipulating an equation, change every term, not just one term on both sides of the equals sign.

QUICK TIP: One way to avoid careless errors and keep track of your work is to work vertically, and mark ALL YOUR WORK.  Re-copy the entire equation at each step.

The Lumina SAT blog will spend plenty of time reviewing strategies for the test itself, but we thought some practical tips for test day would be helpful as well.

What to Bring on SAT test day:

* At least two #2 pencils (non-mechanical)
* A snack and water (you will not be able to eat during the test but bring a snack to munch on during the breaks)
* Graphing calculator and extra batteries
* A watch (not your phone, as you won’t be able to have that out during the exam)
* Valid photo identification—your school I.D. is fine, as long as it has your photo

Other tips: keep your routine

Don’t break your sleep routine the two nights before the test.  If you normally go to sleep at a certain time, keep it up, even if you think it’s too late or too early.

The key here is routine: if you normally drink coffee, tea or Mountain Dew in the morning, do the same on test day.  But if you don’t, consuming three espresso shots will only make you jittery (not to mention putting serious stress on your bladder!).

Try not to study the morning of or the night before the test.  Preparation is best done over the long haul, and you need focus and relaxation—not more vocabulary words swimming in your head.  There’s very little that can be gained by continuing to cram the evening before the SAT, so take that time to get some sleep, do something fun or focus on other things in your life.

If you keep to your routine and come in to the test well rested, you’ll be ready to do your best!

Because the SAT and ACT are such important pieces of the college admissions process, advice about the tests seems to take on a life of its own. We often speak with parents or students who have some misconceived notions about the tests and their associated strategies. Mark recently updated a presentation on the subject and shares his slides below.

I recently sat down to interview Evan Forster, college and graduate consultant at Forster-Thomas inc. and author of The MBA Reality Check (Penguin / Prentice Hall, due out April 6, 2010).  Here are his views….

(1) How many schools should the typical student apply to?

In my opinion, a great number is eight. Two reach schools, four targets, and two safeties. The two reach are your dream schools, where chances of acceptance is low. Your four target schools are “even money” (a 50% chance). Your two safeties are a sure thing. But here’s the most important part—all eight schools should be places where you would be excited to go: they meet your academic, geographical, extracurricular, and cultural criteria (whatever they be), and most importantly, you should be excited to go there.

It simply doesn’t matter where you get in if you won’t be happy for the next four years. It’s got to be your choice, not what your parents, teachers, or guidance counselors are excited about. For example, if you’re into school spirit and the big Friday night, you won’t thrive at an artsy school like Bennington—not matter how highly ranked it is. The highest-ranked school you get into is not necessarily the one you’ll be happiest at. Take it from me: I ended up going to preppy Northwestern when I may have been happier in the lower-ranked but much more “downtown” NYU.

(2) Should students always try to apply early?  Does the answer depend on whether the student is applying early action or early decision?

I say yes: Early Decision can give you an edge, because you’re telling the school that you absolutely will go. So, unless you’re very dependent on financial aid, apply Early Decision. Of course, by the time the Early Decision deadline rolls around, you should be completely certain that you will be happy at that institution. Early Decision means you have legally bound yourself to attend if accepted. There’s no do-overs.

You’re wasting the edge that Early Decision gives you, however, if you choose a ‘far reach’ as your Early Decision school. Your stats should fall somewhere in at least the middle 50 percent, if not slightly higher. All too often, students come to me hoping to get into the University of Pennsylvania, for example, when their chances are less than none. They say, ‘Well, I just want to give it a shot.’ But there are many competitive schools you might want to attend that, while still a reach for you, are within the realm of reality—but now you’ve thrown away the edge that Early Decision gives you by shooting for the stars when you could have had the moon.

Early Action is a whole other game; you still get an edge but you’re not locked in. However, make sure you know the Early Action rules of any particular school. Some schools have “single choice” Early Action programs; you’re not allowed to apply to any other schools, whether Early Action or Early Decision.

Note: For low-income students, I always caution against Early Decision. Remember, if you get into that school, you’re locked in—even if they give you a really bad financial aid package. You might have gotten a full ride somewhere else.  (Note that I have known ED schools to renegotiate, so be sure to look before you leap!)

(3) Should a student try to distribute his SAT subject tests among very different topics?  In other words, does it look bad to do subject tests only in math and science?

The answer is a big old “no.” This question has its roots in the same old myth that has been haunting college applicants since my father applied. According to one former Dartmouth admissions counselor, “We want to see a kid who is strong in a specific area. That’s what makes him a compelling candidate, much more so than a student who is ‘pretty good’ across the board. Better to have strengths and edges.”

Good schools are looking for a well-rounded class, not well-rounded applicants. Science, engineering, and business majors have such specific course requirements that there is not much room left to take many liberal arts classes outside the core curriculum. So if math and science are your thing, focus on those SAT II’s. If language arts is your strong suit, be the person who brings that expertise to the student body.

(4) What’s up with Score Choice?  Is it worth bothering with?

Right now, Score Choice is a hot mess, and not all it’s cracked up to be. Score Choice, a fee-based (as in pay mo’ money) method by which you can instruct College Board to disclose only selected overall SAT scores, is intended to relieve stress by decreasing the risk of taking the test multiple times. Score Choice allows you to reveal only the SAT scores you are most proud of. In theory, you can effectively ditch your bad scores. However, you have to hide an entire test taken on a specific date; you can’t only hide a specific date’s poor math score, for example.

Score Choice is almost always going to be a waste of money, however, because it’s not even necessary.

Most schools practice something called “super scoring”—that means they look at all the SAT tests you’ve taken, pick the highest individual math, critical reasoning, and writing scores from your different test dates to create a “single” super score. (In fact, for many select schools, this arithmetic is done before an admissions officer ever even sees your application. The best three scores have already been calculated by the time the admissions officer sees your packet.) The Super Score is what they use when considering the standardized-test aspect of your candidacy. For those schools, Score Choice is meaningless—and, in my opinion, and that of many of my colleagues, a simple revenue-enhancer for the College Board. (For example, when I recently met with a Cornell admissions officer, he rolled his eyes when I mentioned Score Choice. “What’s the point?” he asked. “We super-score anyway.”)

So, what about the schools that don’t super-score?  Does Score Choice work for them? Not necessarily. Many schools’ applications require that you allow them to see all of your test results, whether you shelled out for Score Choice or not

That’s why Score Choice is a big hot mess. Thanks, College Board, for throwing this wrench into the gears and increasing everybody’s stress level. Isn’t that what you were trying to avoid in the first place?

(By the way, as of September 2009, Harvard and the University of Chicago were the only two highly selective schools that accepted Score Choice.)

(5) If a student’s SAT scores are below the average for a given school, should she refrain from applying?

Absolutely not! By definition, every school’s population has to have a “bottom 10 percent” (it’s impossible to count to 10 without starting at 1). So how do you get into a school if you’re in the bottom 10 percent? That’s where “fit” comes in: Schools will sometimes take stats-weak applicants if they perfectly fit the profile otherwise. For example, if you’re an award-winning creative writer but you’re not an A student, you may be more competitive than you think at a top writing-intensive school like Sarah Lawrence. In other words, you have to really stand out in another area of your candidacy. After all, who do you think plays football at Harvard?

(6) If a student’s SAT scores are above the average for a given school, should she refrain from applying?

No, you need at least a couple of safety schools. And if you are a perfect match, such as that writer applying to Sarah Lawrence—which doesn’t even require the SAT, by the way—then SAT scores may not matter much to you.

(7) What is the maximum number of times a student should take the SAT?

Three seems to be the magic number. It’s not uncommon for the best of my students to bomb the SAT on the first time out. Like any competitive situation, the first time you find yourself faced with actual event, your nerves take over and you don’t give your top performance. The second time is generally when most students do their best. You are familiar with the lay of the land—the timing of the sections, the actual test center environment, the unknown.

If you’ve done all you can, really studied to the best of your ability, and can honestly say “I gave it my all,” then chances are you’re not going to significantly raise your score to make studying all over again worth it. Your time is better spent working on your essays and doing well in school.  But if you didn’t do as well as you possibly could have, and found yourself making a lot of excuses—out loud or in your own head—like “my SAT tutor sucked,” “I didn’t have time because of my job,“ or just plain know that you really could’ve worked harder—and now you actually will—then yes, you are a candidate for taking the SAT a third time.

(8) Is the PSAT an important test for admissions?

Not to the admissions office, but it will give you a rough indication of which areas you need to bolster. It also determines National Merit Scholarships.

(9) What’s the most important thing most students fail to do when it comes to applying?

The biggest mistake a student makes is saying what they think a school wants to hear instead of figuring out what he or she wants to say—what makes you you. Don’t try to second-guess what you think the admissions committee wants to hear. As I’ve said, they want a well-rounded class filled with diversity—diversity of all kinds, including the way you think and what you believe.

By being strategic and trying to figure out how you can sound like the symbol of the class profile, you’re sanding off any edges in your voice/candidacy that make you memorable and interesting. If you want to be remembered, don’t do an impersonation of someone else—like the guy you think they are looking for.  At best, you’ll be remembered for your impersonation, and at worst, you’ll be remembered as an impersonator. None of these is preferable to being remembered as someone with his or her own opinion and voice, someone comfortable in his or her own skin—someone who will be a leader or scholar of consequence.

(10) Are admissions officers impressed by the 500, 600, 700, and 800 “psychological thresholds”?  In other words, is the psychological difference between a 580 and a 590 smaller than the psychological difference between a 590 and a 600?

Higher scores are always better. Certainly “psychological thresholds” make a difference when you’re talking about a large spread, such as that between a 500 and a 550, or the hundred-point spread between a 600 and a 700. But is it worth chasing an extra ten points? Not if that takes away from studying from your chemistry AP. Too often, students and their parents get wrapped up in what I call “chasing a number.”

Think of it as a cost-benefit analysis—what’s the cost for the benefit you’re getting? If you’ve already got all your SAT II’s out of the way, and you want to raise your SAT I from a 1950 to a 2000, then go for it. If you’re still studying for your subject tests or need to concentrate on raising your GPA, however, it’s not a good use of your time to chase that 2000.

In my opinion, in either of these situations, you should be spending your free time beefing up your leadership profile, or at the very least, watching Glee. After all, everyone needs to recharge his or her batteries with a little down time. Forgo the extra 50 points unless you know you can raise your score or if you’ve got all the time in the world to achieve it.

(11) Are admissions officers impressed by the 2000 “psychological threshold”?  That is, is the difference between a 1980 and a 1990 smaller than the difference between a 1990 and a 2000?

At first glance, yes. Upon closer examination, here’s what good admissions officers do. They break it down by section. If you have a real imbalance in your scores, you may want to address that by retaking the test and beefing up your weakest section.

Still, I get this question all the time. The other day, a father asked me if his daughter should try to increase her overall score by 100 points, from 1760 to 1860. I told him, if the 100 points is going to come by raising her 530 math score to a 630, in line with her other two sections, then great. Go for it.

This also of course depends on the school you’re applying to and your area of academic interest. If you’re applying to an engineering program, for example, your math score may be more important than your critical reasoning. On the other hand, if you already have a really strong math score, it’s certainly going to distinguish you to a Carnegie Mellon if you can also demonstrate strong verbal skills.

Date:  March 24, 2009

The Opportunity Network announced today that it has partnered with Lumina Prep to prepare its students for the October 2009 SAT.  “Since Lumina Prep’s online program is individually customized for each student, it is perfect for students with a variety of schedules and educational objectives.  The weekly status updates also give me another touch point with my students and help me monitor their progress,” said Rajib Guha, Director of College Initiatives at The Opportunity Network.

About The Opportunity Network:

The Opportunity Network (www.nyopportunitynetwork.org) seeks to equal the playing field for high-achieving, underserved high school and college students by creating access for them to career opportunities, professional networks and college. We believe influential networks are essential ingredients for success not emphasized in career development programs for youth, so we take an innovative approach by underscoring the power of personal connections and professional relationships as vital complements to skills and experience.

Through unique interaction with executives, intensive networking training, coursework in careers, internships and college counseling, our students dramatically change the course of their futures.

About Lumina Prep:

Lumina Prep (www.luminaprep.com) is a tutoring and online SAT prep company founded by Ivy League educated tutors to make the techniques and benefits of private tutoring available to a broader set of students.  Mark Alfano, Lumina Prep’s Chief Learning Officer, is a private tutor in New York City and previously taught at The Princeton Review.  He is pursuing a Ph.D. in philosophy and graduated with honors from Princeton University.

Lumina Prep has worked with domestic and international partners to prepare students for the SAT.  The company has students in the USA, Turkey, Switzerland, South Africa, and Singapore.

Contact: Edward Alfano, CEO

E-mail: edward.alfano@luminaprep.com