The SAT will frequently trip you up with what may seem the most simple numbers of all—0, 1 and 2.  In the context of Arithmetic Questions on the SAT, these numbers are deceptively simple, but all have specific special properties.  Memorize these few facts about 0, 1 and 2 and be prepared for their tricks.

Facts About 0

1. Any number multiplied by 0 equals 0.

example –>  6 x 0 = 0

2. You may NOT divide a number by 0.

example –> 6/0 is undefined

*Similarly, 1/(x-3) is undefined when x=3.  Therefore, x=3 could not be a solution to a question containing this expression.

3. 0 to any power is 0.

example –> 0^2 = 0,  0^1.5 = 0, 0^78 = 0, etc.

4. Any number to the power of 0 is 1.

example –> 1^0 = 1,  147^0 = 1,  1,000,000^0 = 1, etc.

Facts About 1

1. Any number multiplied by 1 is that number.

example –> 147 x 1 =147,  132.667 x 1 = 132.667, (a/b) x 1 = 0

*Be on the lookout for ones in disguise, usually in fraction form, i.e. 3/3, (x-2)/(x-2) or b/b.

2. One to any power is still 1.

example –> 1^3 = 1, 1^2.3 = 1, 1^-3 = 1, etc.

3. Any number to the power of 1 is that number.

example –> 147^1 = 147, 0^1 = 0, (x-b)^1 = x-b

4. 1 is NOT a prime number.

A prime must have only two distinct factors.  While 1 has only two factors (1 and 1), they are not distinct (different) from each other; therefore, 1 is NOT prime.

Facts About 2

1. Any integer multiplied by 2 will be even.

example –> 3×2=6, 1×2=2, 0×2=0 (0 is even)

2. 2 is a prime number.

It is the lowest prime number and the only even prime number.

On occasion you will encounter a two-blank Sentence Completion question on the SAT in which the two blanks are interdependent, meaning you cannot predict what one is without making an assumption about the other.

Try this question:

Less ___________ than her predecessor, Queen Elizabeth’s ______________ made her remarkably more popular.

Hmmm, we could substitute many different word pairs for this:
close-minded: tolerance
miserly: generosity
boorish: charm

However many pairs we come up with, they will always be opposites, won’t they?  Queen Elizabeth has become popular by doing something different from her predecessor.  So when you take a look at the answer choices, without even plugging them into the sentence, you can quickly eliminate at least two or three choices by crossing out those that are not opposite pairs.

QUICK TIP: Remember to look for the relationship between double-blanks.  Should they be the same or opposites?  Then eliminate answer pairs that don’t fit the proper relationship before you start plugging words into the sentence.  This will save you a lot of time!

Sarah Fine, an advisor to Lumina Prep, recently authored an interesting article on alternative education models in WireTap Magazine. In the article, she profiles The Big Picture Learning Company and their unique approach to structuring education around a deep connection to the real world. Big Picture promotes the “radical” notion that kids learn best when they are doing something they love to do.

If you are interested in the future of education and how different models might serve different children, you can read the full article at: http://www.wiretapmag.org/education/44669/

In 2005, the SAT I was reconfigured and the SAT Writing portion was added for the first time.  The Writing portion is an area your parents and even older siblings will know almost nothing about.  Make sure to know what you’re in for!

The SAT I has three Writing sections—two of them are multiple choice, and the other is an impromptu essay.

The Essay will always be Section 1.  You will be given a short prompt – usually a yes-or-no question about ethics – and then asked to write a two-page response.  You will have 25 minutes.  It’s important to be in “essay writing mode” when you first show up for the test, and then be able to switch gears afterward for the other sections.

There are three types of questions in the first multiple choice section:

(1)    Sentence Improvement (questions 1-11),
(2)    Error Identification (questions 12-29), and
(3)    Paragraph Improvement (questions 30-35).

All three test your understanding of standard English grammar.  You will be asked to identify grammatical errors, re-phrase sentences or phrases, and edit a short passage for both grammar and clarity.

At the end of the test, you will see section 10, which is a 10-minute, 14-question multiple choice section involving only sentence improvement questions.

Obviously, sentence improvement questions are the primary focus of the test, so they should be your primary focus for studying.  Fortunately, sentence improvement questions are also the easiest to prepare for!  In fact, the concepts tested in sentence improvement also appear in the other types of questions, so by studying one, you’re really preparing for every multiple choice question.

One of the most common question types you will see in Critical Reading on the SAT goes something like this:

The author’s tone in the final sentence is best described as

(A) shocked
(B) resigned
(C) ambivalent
(D) somewhat encouraged
(E) perplexed

Hmm, pretty difficult to answer out of context, huh?  In fact, even without an accompanying passage, we still eliminate incorrect answer choices!  How?  Questions regarding the author’s tone or attitude come up in almost every CR section on the SAT, and the answers always have something in common.  Authors will never be one of these three things: confused, uncaring or over-emotional.

CR authors tend to be scientists, historians, attorneys, artists, anthropologists or great writers—as authorities in their own fields, they would not express confusion.  So we can immediately cross off choice E, perplexed.  Authors are never uncaring—they are always invested in topic of the passage at hand.  If an author didn’t care about a subject, he wouldn’t bother writing about it!  Let’s cross off choice C.  Lastly, an author will never be over-emotional; she’s a professional, with a careful, practiced opinion.  Eliminate choice A, shocked.

We are left with choices B and D, and we haven’t even read the passage!  (In the practice test from which this question was taken, the correct choice was D, for those of you who were curious!).

QUICK TIP:  Avoid answer choices that are synonyms for over-emotional, uncaring or confused, such as:
Over-emotional: outraged, resentful, unshakably confident, derisive
Uncaring: ambivalent, apathetic, indifferent
Confused: perplexed, baffled, bewildered

When preparing for Algebra questions on the SAT, remember that ETS hates negative powers.  Whenever you see something like x^-2 in an expression, know that you must get rid of the negative exponent in order to solve the problem.  However, you can’t just delete sections of a question to suit your fancy!  In order to “get rid” of something in an expression, you must either simplify, or change the format of that piece.  Remember, negative exponents can be re-written as positive exponents by putting them in the denominator.  X^-2 becomes 1/x^2.  Voila, we have turned our negative power into a positive one.  This rule goes for all negative exponents: x^-n = 1/x^n.  We haven’t really changed the overall quantitative value of the expression, just its format.

Converting negative exponents will quickly set you up to start simplifying.  For example:

(x^2)(x^-4)=
(A)    1/x^8
(B)    1/x^2
(C)    X^8
(D)    –(x^2)
(E)    -4x^2

Let’s try a combination of converting negative powers and simplifying:  (x^2) (x^-4) =  (x^2) x (1/x^4), becoming (x^2)/(x^4).  Two exponents dividing each other with the same base but different powers?  That’s your clue to subtract the powers and simplify the expression to x^-2.  Go one more round of converting negative powers, and we’re left with 1/x^2, choice B.

Alternatively, you can also recognize that the initial expression (x^2)(x^-4) has two exponents being multiplied with the same base and different powers—in this case you add the powers, getting x^-2.  Triumphant, you look at the answer choices, only to find no options with a negative power!  Again, convert it to a positive one, 1/x^2, and choice B becomes apparent.

QUICK TIP: Always convert negative exponents to positive ones.

Like most things, time management is best practiced BEFORE test day. Practice with as many mock exams as possible. Try completing them on your own time first and gauging whether you tend to work quickly or slowly. Then practice the exams with the time limits mandated for each section—do you run out of time, or do you finish early but make careless mistakes? Develop your “inner clock” to measure your pacing.

Practice exams also familiarize you with the directions for each section and each type of question. You don’t get any points for reading directions or passages, only for choosing correct answers. So get to the point where you can skip the directions and head straight for the points—in the questions!

You may have heard “practice makes perfect;” in reality, it’s “perfect practice makes perfect.” When you complete the mock exams, simulate the test environment as closely as possible. No distractions, a clear space to work and a long stretch of time in which to concentrate. “But I’ve been studying for weeks!” doesn’t hold very much water if your weekly sessions were held in front of Saturday football!

During the exam
If you have extra time during the exam on test day itself, use that time to go back over questions, particularly the ones near the beginning of the sections. Double-checking the easier questions is quick and helps you avoid dumb mistakes and careless errors and gives you the points you deserve!

Always mark your answers in the test booklet. You may find it easier to transfer a page of answers to the answer grid all at once. Just make sure to say to yourself “4-D,” “5-A,” “6-A,” etc. when you do so. Keep careful track of any questions you skipped in order to avoid gridding errors. You don’t want to get to the end of a section and realize you’re bubbling in question 27 from the test booklet next to question 24 on the scoring sheet, and then have to search back for where you went wrong!

Using a calculator effectively on the test can really help you on the SAT Math Section. Here’s a few tips to make the most of using a calculator on the SAT.

-    Have the quadratic formula programmed into your calculator.

-    Have the distance formula in both 2- and 3-dimensions programmed into your calculator.

-    Don’t let the proctor wipe the memory of your calculator or take your graphing calculator away.  The TI-83, TI-84, TI-89 and TI-90 are all allowed on the test and may have programs stored in their memory.

-    You may NOT have your calculator out during the Writing or Critical Reading portions of the test, so don’t count on storing a dictionary or grammar rules in your calculator.

-    If your graphing calculator is new, practice with it before the exam.  Test day is not the time to be searching for the cube root function!

-    Recognize that every problem on the SAT I can be completed completely without a calculator.  Choose when to use your calculator—don’t reach for it on every problem.  When you’re required to multiple 3-digit numbers, by all means go ahead.  But using your calculator to find “8^2” or “49 – 30” can just suck up your time.  Make sure your calculator is a help, not a hindrance.

-    Most importantly, remember that your calculator doesn’t have any common sense—it won’t tell you that the average of 3 and 26 can’t possibly be 27, or that 212 can’t be someone’s age.  It won’t remind you that the question asked for a negative root, when your screen showed only positive 4.

For those of you who hate math, never fear.  Read on and let us take the mystique out of the SAT Math section.  SAT Math is broken down into three sections, with 44 multiple-choice questions and 10 grid-in (or “open response”) questions.

The SAT does not test beyond traditional high school sophomore math.

Believe it.

There is no trigonometry and no calculus.  There are no proofs and no imaginary numbers. There will be questions that concern arithmetic, algebra, geometry, probability & statistics, sequences, ratios, and the interpretation of figures.  It’s all, or at least mostly, stuff you’ve seen before.  It’s just asked about in strange ways.

Remember that even kids taking college Calc II in high school are not scoring perfect 800s on SAT Math.  This is because the SAT phrases questions in weird ways and attempts to trick you by asking things you’d never be asked in a classroom setting.  For instance, a problem may require you to solve for 6w.  I guarantee your high school math teacher has never asked you for 6w.  No, he’d ask you to solve for w.  In addition to understanding the material, the SAT can be an exercise in understanding their tricks and reading directions and problems very, very carefully.

However, there is a wonderful boon on SAT Math.  You’ve been given 44 out of 54 answers!  They’re all there in the test booklet—in the form of multiple-choice.  When it comes to the multiple choice questions, you want to use the principle that one of those five answer choices must be right.  This little fact is really wonderful.  There is an uncountable infinity of numbers out there in the world, but only 5 of them will be answer choices on a given problem.

In order to further increase your chances of getting a problem correct, you must get into the habit of eliminating incorrect answers just as much as looking for right answers.  You should guess on the SAT whenever you can eliminate at least one answer choice as wrong.  That might turn out to be a lot of guessing, but even with the small penalty for guessing wrong, you’ll do better if you guess when you can eliminate at least one answer choice.

We’ll talk about more of these tricks and traps to watch out for in future posts.  For now, rest assured that you’ve already learned everything you need to know in math class to be prepared academically for the SAT.  Now a little review and a few tips should have you fine-tuned in no time!

Many of you may hear your parents refer to the Verbal section of the SAT.  Imagine your confusion when you flip through a sample SAT and can find no such section.  In 2005, the SAT I was adjusted by the College Board, and the Verbal section renamed Critical Reading. Here we’ll give you a quick run-through of what to expect (it’ll be up to you to correct your parents every time they start bringing up your “Verbal” score).

The Critical Reading portion of the exam consists of three main types of questions:

Sentence Completions: You will be asked to pick a word (or pair of words) from a list of five answer choices to fill a blank (or pair of blanks) in the sentence.  ETS’ instructions suggest that you “choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole.”  Sentence completion questions primarily test your vocabulary.  There are 19 Sentence Completions on the SAT.

Short Critical Reading:  These questions will require you to analyze the text of short passages, usually one or two paragraphs that together contain about five or six sentences.  The passages may be dependent or unrelated.  There are 8 short critical reading questions.

Long Critical Reading: These questions will also require you to paraphrase and analyze the text and make inferences and deductions, only the passages will be between half a page and a whole page of text.  There are 40 long critical reading questions on the SAT.

In sum, there are 67 Critical Reading questions over 3 sections and your total score for all three sections (each containing each type of question) is out of 800.