This is the first of a few tips in which we’ll be going over pronouns. A pronoun (he, she, we, it…) must have a uniquely determined antecedent. That is, there must be a noun of the same number and gender in the same sentence for it to refer back to. If there is no such noun, or if there is more than one such noun, the pronoun is being used incorrectly.

When Correcting Sentences or finding Sentence Errors, be on the lookout for ambiguous pronouns; that is, a pronoun that does not clearly match with a specific antecedent.

Take a look at the following illustrations:

Gerald, Matilda, and Nicole were dining when, choking on a bone, she toppled off the kitchen chair.

Well, who fell off the kitchen chair? We can surmise it was either Matilda or Nicole since the pronoun “she” is female, but we have no means of determining which of the two fell. A better written sentence might look something like this—

Gerald, Matilda, and Nicole were dining when Nicole toppled off the kitchen chair after choking on a bone.

Now we can clearly identify that it was Nicole who was so unfortunate. In addition to the ambiguous case of “whodunit,” in which you must choose between multiple people, there is also the case of “whichdunit,” where it is impossible to tell whether the pronoun refers back to people or objects. For example:

It is difficult for many young people to understand that citizens were once not allowed to read certain books, but they have since become available.

Since ‘they’ could refer back to ‘books,’ ‘citizens,’ or ‘people,’ it is ambiguous. The sentence should either be rewritten with a specific noun in place of the pronoun, or it should employ “which” or “that” (not allowed to read certain books which have since become available).

A pronoun must have exactly one antecedent of the same number and gender as itself. If it has more than one, it becomes ambiguous and therefore erroneous.

QUICK TIP: Watch for sentences that have multiple subjects and nouns but only one pronoun.

A common pitfall among test-takers on the Critical Reading portion is the habit of choosing answers that are only partially correct. This occurs most commonly on general questions—questions that address a passage’s overall tone or point, its author’s overall tactics, opinion or tone… you get the picture. The way to make sure you answer these questions correctly is to find a specific sentence to show why each part of your answer is right. Students get this type of question wrong because they make a decision based on their overall impression of the passage, rather than the details of the passage. This is particularly true when the answer choices are two-part.

For example, let’s say we read a passage about the humanitarian efforts of Bill Gates. We might be asked a question like this:

Which of the following best characterizes Bill Gates?

(A) philanthropic and wealthy
(B) humanitarian and reclusive
(C) rebellious and practical
(D) genius and exacting
(E) passionate and mystical

While many of these words are accurate on their own—philanthropic, wealthy, humanitarian, practical, (arguably genius) and passionate, only one answer pair possesses two true adjectives for Bill Gates— (A) philanthropic and wealthy. Don’t get distracted by all the possible words that might fit; make sure you find support in the passage for each part of your chosen answer choice. An answer cannot be “half-right,” only all wrong or all right!

As if the SAT Critical Reading sections didn’t already have enough tricks up their sleeve, they introduce new question types just for the dual passage sections! (This is when you have two longer passages labeled “Passage 1” and “Passage 2” lined up vertically.) The most challenging question type for the dual passages is the comparative question. There will be several of these on each SAT, so make sure you know how to identify them and are ready for them!

You will be presented with two passages that are somewhat related to each other, each focusing on varying aspects of the same subject. These passages will rarely present completely opposite points of views. (For instance, the first author in a sample set of dual passages argued that dolphins are incredibly intelligent, while the second argued that there are different ways of defining intelligence. Note, the second author does NOT argue that dolphins are not intelligent, but comes at the argument from a different angle altogether.)

The authors will talk about some of the same things, but there will also be things that only one of them talks about. Within the ideas they both touch upon, there will be things about which they both agree, and things about which they disagree.

There are several types of comparative questions. Comparative questions can ask about what is mentioned in just one passage (“difference” questions). They can ask about what both authors mention (“both” questions). They can ask about what both passages assert (also “both” questions). They can ask about what the authors disagree about (also “difference” questions). Finally, they can ask what one author would say to the other (author-vs.-author questions).

Some students find these comparative questions more difficult because they ask one to synthesize information from two different passages and to perform critical analysis across authors. Don’t worry! Simply be on the lookout for the “comparative” questions and say to yourself; “What is this question asking me? Where would it fall on the Venn diagram?

QUICK TIP: When you encounter a “both” question, inquiring about what both passage assert, remember—since the authors of dual passages always agree about some things and disagree about others, questions of this variety tend to have boring answers. After all, what they both assert will be their common ground, despite their disagreements.

Ever see those weird symbol questions on the SAT? Something to the tune of “if xΩ = 2x-1, then what is the value of 3Ω?” You freeze and think to yourself—we haven’t covered horseshoes yet in precalc!

1) The “weird symbols” questions are really functions in disguise. Whenever you see a weird symbol, its corresponding relationship (here, 2x-1) will ALWAYS be defined immediately after. So don’t worry if you haven’t covered horseshoes yet. In fact, most of the time you can substitute f(x) for the weird symbol. The question above could be rewritten as, “if f(x)=2x-1, what is f(3)?” So take these questions and treat them exactly like functions. Just the same as a function could be called “f(x), g(x) or h(x),” why couldn’t it be called xΩ?

2) The horseshoe, spade, weird brackets, smiley face, triangle and whatever other strange symbols that show up on the exam have no actual defined mathematical meaning. No theoretical mathematician knows what xΩ is either! That’s why it will always be defined for you.

3) Sometimes the SAT is testing your ability to draw visual parallels . For instance, take the following question:

Because there is no triangle in real mathematics, only in SAT land, the SAT wants to see if you reason—“hmm, in the example, the lower left-hand number (a) was multiplied by the top number (b) and then the lower right-hand number (c) gets subtracted from that product. Maybe I should do the same thing to the numbers in the question! In which case, (7(3)-2) = 21-2 = 19.

QUICK TIP: When you see strange symbols, don’t freak out, treat them as functions, and be on the lookout for visual parallels in how the variables are spatially laid out.

Some SAT Algebra questions will not only have one variable, but two or three for you to keep in mind. On occasion you’ll be given a set of equations, a “system” of equations, and asked to solve for one or all of the many variables in that system. You will also encounter questions like these that will give you a fifth option, choice E: This question cannot be solved with the information given. Remember this general rule of thumb: you must have the SAME NUMBER of equations as unknowns. If there are three variables and only two equations provided, chances are you will not be able to solve the problem. If there are two variables AND two equations given, chances are you will be able to solve it.

However, the SAT has a few tricks up its sleeve—here are two of the most common ones:

2x-y=14, and 4x-2y=28.

Two equations, two variables—should be simple, right? Let’s try our first tactic, substitution, and see what happens. Solve the first equation for y, and we get 2x-14=y. Fantastic—plug that expression in for y in the second equation. 4x-2(2x-14)=28. Distribute: 4x-4x+28=28. Reverse PEMDAS, and we’re left with… 0=0.

Well, while 0=0 is certainly true, it isn’t very helpful! Where was the trick? 2x-y=14 and 4x-2y=28 are the same equation. The second is simply the first multiplied by two. None of the relationships have changed between the variables and thus no new information is provided. This is really a two-variable, one-equation problem—it can’t be solved with the information provided.
Here’s a second trick, one that may make you give up before you even examine the numbers.

2m+z+5p=10, and 2m-z+3p=6. Find the value of p.

Shoot, only two equations, but three variables; it must be unsolvable… Let’s try another technique before we write this one off and move on. This problem requires a little bit of heavy lifting in the world of systems of equations: linear combination (combining multiple equations by either addition, subtraction, multiplication or division in order to cancel out variables). In this case, subtract the second equation from the first (setting up the problem vertically):

2m+z+5p=10
+ 2m-z+3p=6
0 + 0 +8p = 16 becomes 8p=16. Divide both sides by 8, and p=2.

Using linear combination, you were able to cancel out two variables, leaving you with 8p=16, a one-variable, one-equation problem!

QUICK TIP: Use the general rule of thumb that you must have the same number of equations as unknowns, but keep in mind the two ways the SAT can disguise these problems!

You may already be familiar with idioms from your study of a foreign language. It’s typically a phrase that, when translated or taken literally, makes no sense. We have idioms in English as well. However, the idioms tested on the Writing portion of the SAT are of a very different sort.

Idioms are special phrases or expressions that determine whether a certain word is allowed or required to follow another word. For instance, you should only say ‘on the one hand’ if you also say later ‘on the other hand.’ You can never say ‘either’ without also saying ‘or.’ It makes sense to say: “John is either at the library or napping.” It doesn’t make sense to say: “John is either at the library.”

In addition to these “phrase pairings,” the SAT loves prepositional idioms. There are certain verbs that can only be paired with specific prepositions. For example, you can be “preoccupied with a book”, but never “preoccupied at a book”, or “for a book.” You could believe in a dream, capitalism or ghosts, but you wouldn’t believe at ghosts or with ghosts or about ghosts.

There is very little formalized logic behind certain verb-preposition pairings. Idioms in any form are expected to be learned by instinct, as a native speaker with a feel for the language and what is “right,” rather than according to strict grammar rules. Your best approach is to start making a list of idioms, either from your reading, practice SATs or the internet and memorize them. Review the list and get a feel for what is acceptable and what is not.

QUICK TIP: Here’s a short list to get you started!

You may be familiar with the concept of parallelism from your English class, but in case you’re not, here’s a quick overview. Parallelism is one of the most common concepts tested on the Writing section of the SAT, and one of the easiest errors to spot, once you know what to look for.

You’ll find parallelism errors in one of three places: lists, grammatical comparisons and factual comparisons. The rule of thumb in parallelism is: the items in a comparison or list must be of the same type, both grammatically and physically.

You’ll probably catch the mistake in this sentence: I enjoy biking, skiing, and to go on vacation. “To go” is in infinitive form, while the other activities are gerunds—they must all be gerunds, according to parallelism. I enjoy biking, skiing and vacationing would be correct. Or even I enjoy biking, skiing and going on vacation would be acceptable.

Your grammar ear is pretty adept at picking up these mistakes. However, the place where the SAT tends to stash its difficult parallelism errors is factual comparisons.

Unlike the other parallelism errors, faulty comparisons do not involve grammatical errors. Instead, a faulty comparison tries to contrast objects of different sorts. It is wrong to say: “My cat is faster than Amy.”

Instead one should say, “My cat is faster than Amy’s horse.” Or one could more tersely say “my cat is faster than Amy’s.” (The possessive grammatically implies the cat).

This type of error can be very difficult to pick up because your brain unconsciously makes the correction as you read. Because your mind reads for content and understanding, not grammar, you’ll have no problem understanding the meaning of the sentence, evens as the grammatical error passes you by.

QUICK TIP: Be on the lookout for comparisons. Your brain’s leniency toward bad grammar means that you need to read word for word, tracing your finger under the words if necessary.

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.

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.