Pattern Problems

Link of the Day

How important is history?  Should people take more responsibility for solving problems that affect their communities or the nation in general?  That second question is a previous SAT essay question.  Before you answer it, read here and here about how the people of Mali reacted to a threat against manuscripts as old as the 13th century.  What important themes do you see in these articles that would be easy to write about as a current event example?  Write down details and facts that could help to support an opinion on a broad topic.

Arithmetic: Pattern Problems

Read the following SAT test question and then select the correct answer. 

Work each math problem by reading the question carefully and identifying the bottom line.  Then assess your options and choose the most efficient method to attack the problem.  When you have an answer, loop back to make sure that you finished all of the steps to match your bottom line.

If it is now 4:00 p.m. Saturday, in 253 hours from now, what time and day will it be? (Assume no daylight saving time changes in the period.)

Bottom Line: 253 hours from now = ?

Assess your Options: You could try to count the hours elapsed from the answer choices, but that will be time consuming if you don’t guess the right one first and end up working the problem five times.  Instead, use logic to methodically work through this problem.

Attack the Problem:  You are given 253 hours, but you know that there will also be a change in the day.  There are only 24 hours in a day.  Find out how many days there are in this time period by dividing.  Now, this problem is similar to the pattern problems in your Knowsys book.  You want to know how many days and hours have passed.  Instead of dividing with your calculator, use long division to find out how many days pass and how many hours remain. 253 ÷ 24 is 10 with a remainder of 13.  That means that there are 10 days and 13 hours that pass.

Continue to think about this logically.  If it is 4:00 p.m. on Saturday and a week passes, it will be the same day.  So 7 days will get you back to the same place.  Then you have 3 of your 10 days still to go.  Count 3 days from Saturday, (Sun, Mon, Tues), and you are now at 4:00 p.m. on Tuesday.

That accounts for all of the days that have passed, but you still have 13 hours.  If you add 12 hours to 4:00 p.m., it becomes 4:00 a.m. on the next day, Wednesday.  Add 1 more hour and you get 5:00 a.m. on Wednesday. 

Loop Back:  You accounted for all of the 253 hours by counting out 10 days and 13 hours.  Look down at your answer choices.

(A) 5:00 a.m. Saturday

(B) 1:00 a.m. Sunday

(C) 5:00 p.m. Tuesday

(D) 1:00 a.m. Wednesday

(E) 5:00 a.m. Wednesday

The correct answer is (E).

On sat.collegeboard.org, 49% of the responses were correct.

For more help with SAT math, visit www.myknowsys.com!

Pronouns

Writing: Improving Sentences

Part or all of the following sentence is underlined; beneath the sentence are five ways of phrasing the underlined material. Select the option that produces the best sentence. If you think the original phrasing produces a better sentence than any of the alternatives, select choice A.  

Read the entire original sentence to yourself, listening for errors.  Then evaluate the underlined portion using the Big 8 Grammar Rules.

About 35 percent of the world’s orange juice is produced by Florida, comparing it with nearly 50 percent produced by Brazil, the world’s largest orange producer.

There are two things that you should immediately notice about the underlined portion of the sentence.  The first is that one of the underlined words ends in “-ing,” but does not have any reason to do so.  The second is that you have an unassociated “it.”  The “it” is intended to refer to the percent of juice, but “it” seems to refer to Florida within the context of the sentence.  Your Knowsys book specifically tells you to watch for both of these things and avoid them.  Look down at your answer choices.

(A) comparing it with

(B) but

(C) whereas

(D) although

(E) compared with

(A) You already found two problems with the original sentence.  This choice always matches the original sentence, so eliminate it without reading it.

(B) The word “but” sets up a contrast; however, the original sentence sets up a comparison.  This answer changes the meaning of the original sentence.  In addition, if you read the whole sentence, you will notice that the portion after the comma is missing the verb “is.”  The verb “is” would be necessary for parallelism because you have “is produced” and then only “produced.”  When there is a comma before the word “but,” a complete sentence with subject and verb should follow.  Eliminate this choice for any of these reasons.

(C) This answer choice has the same parallelism and sentence structure problem as the previous choice.  Eliminate this choice.

(D) The word “although” sets up a contrast rather than a comparison.  It also has the same parallelism and sentence structure problem as the previous two choices.  Eliminate this choice.

(E) This choice eliminates both of the problems that you found in the original sentence and produces a sentence that is clear in meaning.  It does not have the parallelism or sentence structure problem that other choices had because those words, when preceded with a comma, are meant to link complete sentences, but “compared with” does not indicate that a complete sentence is coming.

The correct answer is (E).

On sat.collegeboard.org, 57% of the responses were correct.

For more help with SAT writing, visit www.myknowsys.com!

Sentence Completions

Link of the Day

The SAT question for today is about a literary figure who loathes public appearances.  Although she is now an established literary giant, no one asked Emily Dickinson to make public appearances because her talent was unknown until after her death.  Read this information about her life and consider using your knowledge of this poet and one of her poems as one of your five literary examples for the SAT essay.

Critical Reading: Sentence Completions

Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. 

Always cover up the answer choices so that they do not influence the way you think about the sentence.  Read the sentence carefully and use context clues to predict a word to fill the blank.  Then match your prediction to the correct answer, eliminating any choices that do not match.  Look at each answer choice, even if one of the first answers seems to be correct.

Because she has a great need for ------- , she loathes the public appearances demanded of her as a leading literary figure.

This question tests whether you know the meaning of the word “loathe.”  However, you can still answer this question correctly even if you do not know this word.  You can tell that this woman dislikes public appearances because she finds them demanding.  She would not feel that these appearances were demanding if she enjoyed them.   If she dislikes public appearances, then she appreciates the opposite – private moments.  Predict the word “privacy” and look down at your answer choices.

(A) luxury

(B) privacy

(C) reward

(D) devotion

(E) distraction

(A)  Luxury can be either private or public; it has nothing to do with your prediction.  Eliminate this answer choice.  (B)  This choice matches your prediction exactly.  Nevertheless, you should still quickly check the other answer choices before selecting it.  (C)  This answer is meant to distract you if you are only looking for something good.  Privacy could be a reward for an introvert, but “reward” does not mean “privacy.”  Eliminate this choice.  (D) Devotion requires something or someone outside oneself.  It does not mean “privacy.”  Eliminate it.  (E)  Distraction does not mean “privacy.”  Eliminate it.

The correct answer is (B)

Words used in this SC:

Loathes: hates, detests

Luxury: wealth and the comfort it brings

Privacy: seclusion from others, solitude

Reward: something given in return for an action

Devotion: attachment to a cause or person

Distraction: something that catches one’s attention and prevents concentration

On sat.collegeboard.org, 70% of the responses were correct.

For more help with SAT vocabulary, visit www.myknowsys.com!

Functions

Algebra: Functions

Read the following SAT test question and then select the correct answer. 

Always use the same process for math problems on the SAT.  Read carefully and make a note of the bottom line.  Then assess your options and choose the most efficient method to attack the problem.  When you have an answer, loop back to be sure it matches your bottom line.  

If the function f is defined by , where 0 < a < b < c, for which of the following values of x is f undefined?

I. a

II. b

III. c

Bottom Line: For which value(s) of x is f undefined?

Assess your Options: You could pick numbers, but that will get confusing with three variables.  You could just start plugging in the variables a, b, and c for x and then simplify the function, but you will end up wasting time.  Time is precious on the SAT!  Start with the information that you are given and think about it logically.

Attack the Problem:  Always think about the information that you are given before you jump into the problem.  The inequality that you are given simply tells you that all of your variables are positive numbers.  A function or a fraction is undefined whenever it is divided by zero because you cannot divide by zero. 

Think about it logically:  do you care what is on the top of the fraction?  No!  Focus on the bottom of the fraction.  How can you make x – c = 0?  The variable that you are changing in this problem is x.  If you set x = to c, then c – c = 0. 

Note:  You do not know whether a or b is equal to c, so you cannot assume that a – c or b – c would equal 0.  If you plug those variables in, you still have a lot of variables on the bottom!

Loop Back:  You found the only answer that will work out of the three that you were given.  Look down at your answer choices.

(A) None

(B) I only

(C) III only

(D) I and II only

(E) I, II, and III

The correct answer is (C).

On sat.collegeboard.org, 53% of the responses were correct.

For more help with SAT math, visit www.myknowsys.com!

Subject Verb Agreement

Writing: Identifying Sentence Errors

The following sentence contains either a single error or no error at all. If the sentence contains an error, select the one underlined part that must be changed to make the sentence correct. If the sentence contains no error, select choice E. 

Read the entire original sentence to yourself, listening for errors.  Quickly check the underlined portions of the sentence against the Big 8 Grammar Rules.  Identify and mark any error you find, but look at all of the choices before selecting your answer.

AAn abundant supply of milk Bfrom dairy farms nearby Cmake the Bern region of Switzerland Da leading producer of condensed milk and milk chocolate. ENo error

(A)  The word “an” is the correct article to use when the following word begins with a vowel.  There is no error here.

(B) The word “from” is the idiomatically correct preposition to explain the origin of something.  There is no error here.

(C) This is the first verb in the sentence.  Whenever a verb is underlined, check to make sure that it matches the subject.  Remember, the subject of the sentence cannot be part of a prepositional phrase such as “of milk” or “from dairy farms nearby.”  That leaves only one noun: “supply.”  Would you say “an abundant supply make?”  No!  “An abundant supply makes” is correct.  Mark this error and quickly check the remaining answer choices.

(D)  Check the article first.  “A” is correct because the sentence is talking about one specific place as a producer.  The word “leading” is a modifier that tells you that this place doesn’t just produce things, it produces them well and is among the best places to do so.  The modifier “leading” is as close as possible to the word it modifies, “producer,” so there is no error here.

(E) This choice cannot be correct because you already identified an error.

The correct answer is (C).

On sat.collegeboard.org, 57% of the responses were correct.

For more help with SAT writing, visit www.myknowsys.com!

Sentence Completions

Critical Reading: Sentence Completions

Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. 

Cover up your answer choices and carefully read the sentence.  Predict a word for the easier blank and eliminate any answer choices that do not match your prediction.  Then do the same with the other blank and the remaining answer choices.

When, in 1864, a factory established by Alfred Nobel to manufacture nitroglycerin blew up, the scientist discovered that the explosive was as ------- as it was powerful, ------- to detonate without warning.

Start with the blank that is easier for you, even if it is the second blank.  In this case the second blank is easy to predict if you take into account the information in the sentence.  If the explosive in the factory blows up the entire factory, it can detonate without warning.  Predict the word “able” and look down at your answer choices.

(A) dormant . . ready

(B) fickle . . unlikely

(C) volatile . . liable

(D) unprecedented . . intended

(E) inactive . . designed

(A)  Does “ready” mean “able?”  If someone is ready to something, that usually means that they are able to.  Hang onto this one if you are not sure that you can eliminate it.  (B)  “Unlikely” does not mean “able.”  You were just given an example of when something exploded, so it seems pretty likely that the explosive will blow up.  Eliminate this choice.  (C) The word “liable” has two meanings.  Most people know that it means “legally responsible.”  However, words can change meaning over centuries.  If you are liable for something, people can sue you if something bad happens connected with that liability.  It eventually became acceptable to use the word “liable” whenever something bad was likely to happen.  Ex: In an economic downturn people are liable to become stressed.  A factory blowing up is an unfavorable outcome, so keep this answer choice.  (D) The word “intended” has to do not with what actually happened, but what someone planned to happen.  Nobel did not plan for his own factory to blow up; he only discovered that it could.  Eliminate this choice.  (E)  “Designed” and “intended” can be used as synonyms.  No one designed this explosive to blow up the factory; Nobel just accidentally discovered that it could.  Eliminate this answer choice. 

Now turn your attention to the the first blank in the sentence.  Now that you have thought about the sentence while checking the other blank, you probably understand that Nobel was surprised by his discovery.  He did not know the explosive was so likely to blow up until his entire factory was gone.  It is okay to use a phrase as your prediction.  Predict that he discovered the explosive was “capable of exploding,” and look down at your remaining answer choices.

(A) dormant . . ready

(C) volatile . . liable

(A)  The Latin root “dorm” means “sleep.”  An explosive is active, not “sleepy” or “inactive.”  Eliminate this choice.  (C)  The Latin root “vol” means “fly.”  An explosion definitely sends things flying.  Think of a volcano that sends fire up into the air very suddenly.  Keep this choice.

The correct answer is (C).

Words used in this SC:

Detonate: to explode suddenly and violently

Dormant: inactive, as if asleep

Fickle: quick to change, not loyal

Volatile: explosive

Liable: likely to do something or susceptible to something, prone to

Unprecedented: never before seen or done

Intended: planned

Inactive: not functioning or passive

Designed: intended or planned

On sat.collegeboard.org, 60% of the responses were correct.

For more help with SAT vocabulary, visit www.myknowsys.com!

Probability

Data Analysis: Probability

Read the following SAT test question and then select the correct answer. 

Always read each question carefully and make a note of the bottom line (what you are trying to find).  Assess your options to find the best strategic method and use that method to attack the problem.  When you have an answer, loop back to verify that the answer matches the bottom line.

A jar contains only red marbles and green marbles. If a marble is selected at random from the jar, the probability that a red marble will be selected is . If there are 36  green marbles in the jar, how many red marbles are there in the jar?

Bottom Line:  You want to know how many red marbles there are, so use r to represent red and just write r = ?

Assess your Options:  You could try to work backwards from the answer choices to find a number that, when combined with 36, makes the right fraction.  That won’t be any faster than just solving the problem.  Use the probability formula.

Attack the Problem:  The probability formula is:

In this problem, you know the red marbles are the relevant outcome, while the red and green marbles together are the total (all that is in the jar).  Use g for the green marbles.  There are 36 green marbles.

You have already been given the probability that a red marble will be selected.  Set the formula that you created equal to the probability that you were given.  Then solve for r with cross-multiplication.

3r = 2(36 + r)

3r = 72 + 2r

r = 72

Loop Back:  You solved for your bottom line, so you are ready to look at the answer choices.

(A) 18

(B) 24

(C) 54

(D) 72

(E) 108

The correct answer is (D).

On sat.collegeboard.org, 47% of the responses were correct.

For more help with SAT math, visit www.myknowsys.com!

Parallelism

Link of the Day

One of the most interesting aspects of living in today’s world is having an abundance of information at the tip of your fingertips.  A released SAT essay prompt asks, “Has today’s abundance of information only made it more difficult to understand the world around us?”  Before answering, read this current event about information storage.  You could use this article to answer yes – we have difficulty storing all the information and accessing it, or no – we are getting better and better at storing information.  There is no right answer.  However, using specific details from this article will make you sound a lot more intellectual than if you just answer with an “I think” statement.  Using facts to back up your opinion is crucial.  Identify other themes in this article that you could relate to other SAT prompts if you want to use this as one of your five prepared current events.

Writing: Improving Sentences

Part or all of the following sentence is underlined; beneath the sentence are five ways of phrasing the underlined material. Select the option that produces the best sentence. If you think the original phrasing produces a better sentence than any of the alternatives, select choice A.  

Read the entire original sentence to yourself, listening for errors.  Then focus on the underlined portion and evaluate it using the Big 8 Grammar Rules.  Use the first error that you find to quickly eliminate any choices that do not fix that error.

For both his shorter and longer works of fiction, Gabriel García Márquez achieves the rare feat of being accessible to the common reader while satisfying the most demanding of sophisticated critics.

As soon as you see the word “both,” you should think of your idiom chart.  The word “both” is used in the structure “both x and y.”  This sentence has an “and,” but are the x and y parallel?  Remember that when two things are linked they must have the same grammatical form.  In this case you have “his shorter” followed by “longer.”  If you have a possessive for one element, you must have a possessive for the second.  Focus on this error and look down at your answer choices.

(A) For both his shorter and longer

(B) For both his shorter, and in his longer,

(C) In both his shorter and his longer

(D) Both in his shorter and his longer

(E) Both his shorter and longer

(A) You already found a problem with the original sentence.  The first choice always matches the original sentence, so you can eliminate it without reading it.

(B) This choice adds a possessive to both elements, but it also adds the preposition “in,” which means that the structure is still not parallel.  The extra comma that has been added is unnecessary and introduces an error rather than making the sentence more clear.

(C) This sentence is parallel: “his shorter” and “his longer.”  Notice that the preposition “for” has been changed to the preposition “in.”  Does this clarify the meaning of the sentence?  Yes!  In the original sentence, it seems that Márquez is doing something “for” his books (is he concerned about their understanding?), when the focus is supposed to be on what he is doing for readers and critics “in” his books.  Keep this choice and quickly look at the remaining choices.

(D)  This sentence links “in his shorter” and “his longer.”  These two elements are not parallel because only one has the preposition “in.”

(E) This answer choice is again not parallel; however, notice that there is a bigger problem.  Read the entire sentence, and it should be clear to you that without any preposition in the underlined portion this sentence has a major structure error. 

The correct answer is (C).

On sat.collegeboard.org, 66% of the responses were correct.

For more help with SAT writing, visit www.myknowsys.com!

Sentence Completions

Critical Reading: Sentence Completions

Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. 

Start by covering up the answer choices and reading the sentence carefully.  Use context clues to predict a word to fill the blank.  Once you have a prediction, uncover the answer choice and find the word that matches your prediction in meaning.  Eliminate any word that does not match.  Make sure to check all of the possibilities even if one of the first choices seems to match exactly.

Although the scientist claimed to have made a major breakthrough in his research, the evidence he offered as proof of his assertion was ------- at best.

This question tests your ability to think logically as well as your vocabulary.  The word “although” tells you that there must be a contrast between the first portion of the sentence and the second.  That means you need something that contrasts with the claim that a scientist made a major breakthrough.  The next portion of the sentence has to do with evidence.  What kind of evidence would not support the claim of a major breakthrough?  We know the scientist offered some evidence, but it was not enough or not sufficient.  Predict the words “very little” or the word “scanty.”  Any prediction along these lines will work as you examine your answer choices.

(A) conclusive

(B) indubitable

(C) paltry

(D) copious

(E) extensive

(A) Does “conclusive” mean “very little?”  No. If the evidence was conclusive, it would support the scientist’s claim.  You are looking for something that does not support it. Eliminate this choice. 

(B) This word is here to trick even those of you who know your Latin roots.  The Latin root “in” can either mean “in” or “not.”  The Latin root “dub” means “doubtful.”  So this word could mean “in doubt” or “not doubtful,” which is either what you are looking for or not what you are looking for in order to create a contrast with a definite claim.  Before you get caught up in an internal debate, ask yourself does either of these words mean “very little?”  No.  Eliminate this choice.

(C) You may not know this word, but it should sound negative to you.  Etymologists haven’t quite determined where this word came from first, but it relates to nouns in German and other languages that mean “trash” or “rag.”  After the 1550s, the word has shifted slightly in meaning to “worthless” or “insignificant.”  Keep this word if you aren’t sure whether it means “very little.”

(D) The word “copious” is the opposite of what you need.  It comes from the Latin root “copia,” which means “abundant.”  Think of the related word “cornucopia” that you should associate with the harvest.  Eliminate this choice.

(E) Think of the related word “extend.”  When you extend your arms, you reach out as far as you can.  The word “extensive” means “far-reaching.”  This is the opposite of what you need, so eliminate this choice. 

The correct answer is (C).

Words used in this SC:

Conclusive: decisive

Indubitable: clearly true, having no possibility of doubt

Paltry: meager, of little value

Copious: great in quantity or number

Extensive: widespread

On sat.collegeboard.org, 52% of the responses were correct.

For more help with SAT vocabulary, visit www.myknowsys.com!

Functions

Link of the Day

As you look for current events to use in an SAT essay, pick news that you can relate to so that it will be easier for you to remember.  For example, take a look at this article about high school graduation rates.  Education and the economy will definitely affect your lifestyle.  Identify other themes that are present in this article.  What does it have to say about change, progress, motivation, rewards, and other words that have shown up in previous SAT essay topics?  There are also a lot of numbers in this article.  Numbers and statistics are fantastic because you can insert them into an essay quickly and seem knowledgeable without taking time away from your argument to explain a whole situation.  Don’t try to memorize all the numbers – focus on a few eye-catching statistics! 

Algebra: Functions

Read the following SAT test question and then select the correct answer. 

Read each question carefully and identify the bottom line to avoid making careless mistakes.  Then assess your options and choose the most efficient method to attack the problem.  When you have an answer, loop back to verify that it matches the bottom line.

If f(x) = x + ax, and ,  what is ?

Bottom Line: 

Assess your Options:  You could use your graphing calculator to solve this problem, but it would probably take you more time to type in the fractions than to just solve the problem.  You are given a value for each variable in the problem so all you need to do is plug them in.

Attack the Problem:  Start by plugging in the value of a to the function that you were given.




Simplify the problem by adding.  Remember that the first x is a whole 1x, but that you must have like terms before you can add fractions.




Now solve your function by plugging in the value for x that you were given.

Loop Back:  You found your bottom line, so you are ready to look down at the answer choices.

(A) 
(B) 
(C) 
(D)
(E) 

The correct answer is (E).

On sat.collegeboard.org, 61% of the responses were correct.

For more help with SAT math, visit www.myknowsys.com!

Subject Verb Agreement

Writing: Identifying Sentence Errors

The following sentence contains either a single error or no error at all. If the sentence contains an error, select the one underlined part that must be changed to make the sentence correct. If the sentence contains no error, select choice E. 

Always read the entire sentence to yourself so that you understand its structure and meaning.  Listen for errors as you read the sentence, and then evaluate each underlined portion using the Big 8 Grammar Rules.  Identify any error that you find and mark it, but be sure to quickly check all of your choices.

Aside from Shakespeare, Bperhaps no writer in English Chave engaged the public’s imagination Dmore thoroughly than Charles Dickens.  ENo error

(A)  This is an idiomatic phrase that means the same thing as “apart from” or “except for.”  The word “from” is the correct preposition to follow “aside.”  There is no error here.

(B)  The word “perhaps” adds a degree of uncertainty to the sentence.  Of course you could eliminate it, but that would change the meaning of the sentence.  There is no error here.

(C)  When you have a verb underlined, always check that it matches the subject.  Here the subject is separated from the verb by the prepositional phrase “in English.”  Ignore that phrase.  Would you say “no writer have engaged?”  No!  You must use the singular verb “has” instead of the plural verb “have” because “writer” is singular.  Mark this error and move on.

(D)  The word “more” is used when only two things or people are being compared.  Here a nonexistent, hypothetical writer (singular) is compared to Charles Dickens, so “more” is correct.  The word “thoroughly” is a modifier.  It ends in “-ly,” as adverbs should, and is placed as close as possible to the word it modifies.  The word “than” is used for comparisons; the word “then” is related to time and used for sequences.  There is no error here.

(E)  This cannot be the correct answer because you have already identified an error.

The correct answer is (C).

On sat.collegeboard.org, 81% of the responses were correct.

For more help with SAT writing, visit www.myknowsys.com!

Sentence Completions

Link of the Day:

Current events can be part of tradition or even mandated by the U.S. Constitution.  Read this article about President Obama’s inauguration, and think about how the present interacts with the past.  How and why do things change or stay the same?  Look for themes that are likely to show up in an SAT essay, and make note of interesting details and facts that could be used to support your opinions about these themes.

Critical Reading: Sentence Completions

Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. 

Cover up your answer choices and devote all of your attention to reading the sentence carefully.  Choose the easier of the two blanks to examine first.  Predict a word to fill the blank, and then eliminate answer choices that do not match your prediction for that blank.  Repeat the same process with the second blank.

Ms. Fergusson’s main criticism of the artist’s rendering of the ancient mammal’s physical appearance is that, unsupported by even a ------- of fossil evidence, the image is bound to be -------.

If a sentence seems complicated, paraphrase it.   Ms. Fergusson is critical of a drawing because it is unsupported by even some kind of evidence so the image is something.  Focus on the second blank.  If the appearance of the rendering is unsupported, what kind of drawing will it be?  Unsupported!  Using a word from the sentence as your prediction can help you be more precise and save time.  Look down at your answer choices.

(A) modicum . . speculative

(B) particle . . supplemented

(C) perusal . . substantiated

(D) fabrication . . obsolete

(E) recapitulation . . exhausted

(A) The word “speculative” has to do with “conjecture” or “abstract reasoning,” so it could mean “unsupported.”  Keep it.  (B)  A “supplement” is something additional.  The problem is that the artist may have just made up the image or added more than is backed by evidence.  If you are not sure about this word, keep it.  (C) The word “substantiated” is the opposite of “unsupported.”  Eliminate this answer choice.  (D)  The word “obsolete” should be connected to the word “old” in your mind.  That does not match your prediction.  Eliminate this choice.  (E)  The word “exhausted” should be connected to the word “tired” in your mind.  That does not match your prediction.  Eliminate this choice.

Now look at that first blank.  You know that there is not enough evidence about the appearance of this mammal.  Logically, you can deduce that there is only a little bit of evidence, if any.  Use “little bit” as your prediction, and look down at your remaining answer choices.

(A) modicum . . speculative

(B) particle . . supplemented

(A) Maybe you know the Latin root “modus” can mean “measure” or “size,” so you can discern that this word relates to the amount of something, whether it is a lot or a little.  Maybe you have heard someone say that a person needs “at least a modicum of common sense.”  If you aren’t sure about the meaning of the word, keep this answer choice.  (B)  This answer is meant to distract you because a particle is very small.  Read the sentence with this word in the blank.  How would anyone ever know that this mammal existed if there was not a particle of fossil evidence?  The word “supplement” means in addition to something else, but if there is not a particle of evidence, you cannot add to it.  This choice is illogical, so you must eliminate it.

The correct answer is (A).

Words used in this SC:

Modicum: a small or minimal amount

Speculative: based on guess or unfounded opinions

Particle: a tiny piece of matter

Supplemented: added to something

Perusal: reading or study

Substantiated: supported, proved, or established

Fabrication: something made up or a lie

Obsolete: no longer in use, outdated

Recapitulation: a review or summary

Exhausted: without energy or used up

Did you spot the two Knowsys vocabulary words in this question?

On sat.collegeboard.org, 55% of the responses were correct.

For more help with SAT vocabulary, visit www.myknowsys.com!

Functions

Algebra: Functions

Read the following SAT test question and then select the correct answer.

Use the same method for every math question on the SAT.  Start by reading the question carefully and identifying the bottom line; what do you need to find?  Then assess your options and choose the most efficient method to attack the problem.  When you have an answer, loop back to make sure that it matches the bottom line.

In the xy-plane, the graph of the line with equation y = a intersects the graph of the quadratic function f(x) = x² - 6x + 8 in exactly one point. What is the value of a?

Bottom Line: a = ?

Assess your Options:  You could just try plugging this into your calculator, but if you do not think carefully about what you are doing, you are likely to answer a question that was not asked.  Instead, think through every piece of information that you were given in this problem.

Attack the Problem:  What kind of graph is the function that you are given?  A parabola!  You know this because it has an x².  Picture a parabola in your mind (you know that this is a normal, upward-facing parabola because there is no negative before the x²).  Draw a u-shaped parabola on the xy-axis as part of your scratch work.

Now think about the fact that when y equals a certain number, it creates a vertical line. No matter what y equals, that vertical line will only ever intercept the graph at one point. That's not very useful! However, try flipping the given equation on its head: consider a = y. Remember that a =  is just like x =  and will create a horizontal line. Depending on what x equals, the horizontal line might cross the graph at two points, at no point at all, or at exactly one point--the vertex. You know that you must find the vertex of the parabola, so solve your function for x by setting your polynomial equal to zero and finding the roots of the equation:

x² - 6x + 8 = 0

(x – 2)(x – 4) = 0

(x – 2) = 0 and (x – 4) = 0

x = 2 and x = 4

You just found the two places where the parabola crosses the x-axis: 2 and 4.  All parabolas are symmetrical.  That means that the vertex must be halfway between these two numbers at x = 3.  You found the x value of the vertex, but you need the y value. 

Plug in 3 for the x in your original equation:

f(x) = x² - 6x + 8

f(3) = (3)² - 6(3) +8

f(3) = 9 – 18 + 8

f(3) = -1

Loop Back:  When you solve a function for the f(x), you solve for y.  In this problem, you are told that y = a.  You have solved for a, so you are ready to look down at your answer choices.

(A) -3

(B) -1

(C) 1

(D) 3

(E) 4

The correct answer is (B).

On sat.collegeboard.org, 31% of the responses were correct.

For more help with SAT math, visit www.myknowsys.com!

Sentence Structure

Writing: Improving Sentences

Part or all of the following sentence is underlined; beneath the sentence are five ways of phrasing the underlined material. Select the option that produces the best sentence. If you think the original phrasing produces a better sentence than any of the alternatives, select choice A.  

Read the entire sentence to yourself, listening for errors.  Then evaluate the underlined portion of the sentence using the Big 8 Grammar Rules.

Mexican painter Frida Kahlo drew inspiration from her Mexican heritage, where she incorporated native and religious symbols into her work.

The underlined portion contains the word “where.”  “Where” refers to a place; however, there are no places in the sentence.  “Mexican heritage” is not a place!  Mexico would be a place.  Eliminate the “where” and you have created a comma splice.  A comma splice is two complete sentences with separate subjects and verbs that are incorrectly joined with a comma.  The easiest way to fix this new problem is to eliminate the underlined subject “she” and change the verb “incorporated” to make this sentence flow better.  Look down at your answer choices.

(A) where she incorporated

(B) in which she incorporated

(C) incorporated

(D) incorporating

(E) therefore, she incorporated

(A) This answer choice always matches the original.  Eliminate it without reading it.

(B) This answer changes the meaning of the sentence and makes it unclear.  It sounds as if Frida is incorporating symbols into her heritage and somehow creating her own heritage.  Eliminate it. 

(C) You cannot just put the word “incorporated” into this blank.  You would need “and incorporated” to avoid sentence structure problems.  Eliminate it.

(D) Changing “incorporated” to “incorporating,” creates a dependant clause that cannot stand alone.  You no longer have the incorrect relative pronoun “where” and you have fixed the sentence structure problem that resulted from its removal.  This is a clear and concise sentence.  Keep it.

(E) This answer choice is wordy.  It is also incorrectly punctuated.  There should be a semicolon before the transitional word “therefore.”  An entire sentence still comes after the comma, and you must avoid a comma splice.  Eliminate it.

The correct answer is (D).

On sat.collegeboard.org, 57% of the responses were correct.

For more help with SAT writing, visit www.myknowsys.com!

Sentence Completions

Link of the Day

Have you caught the flu?  Have you had a flu shot?  Even something as mundane as the flu virus can make a great current event for your SAT essay.  Instead of focusing on your own experiences, take a broader look at the debate about flu vaccinations.  Read this article, looking for themes that are likely to show up on the SAT.  Be sure to scrutinize how the people in this article make the choices that they make.  If you choose to use this as one of your current event examples, memorize some specific details and facts so that your essay includes more than vague generalizations.  For those of you about to take the January SAT:  Take care of your health!  The SAT will seem much longer if you are sick! 

Critical Reading: Sentence Completions

Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. 

Cover up your answer choices and read carefully so that you can predict a word to fill one of the blanks.  Make a prediction for the easier blank and eliminate the answer choices that do not match your prediction.  Do the same for the other blank.

Alvin is an exceedingly ------- person: he unselfishly ------- his friends without ever expecting anything in return.

Start with the blank that seems easier.  What would an unselfish person do for his friends?  Help them!  Use the word “helps” as your prediction, and look down at your answer choices.

(A) opportunistic . . supports

(B) noble . . undermines

(C) bemused . . aids

(D) caustic . . neglects

(E) altruistic . . assists

(A) "Supports" can mean "helps".  Keep this choice.  (B) Undermining someone is the opposite of helping them.  Eliminate this choice.  (C) "Aids" and "helps" are synonyms.  Keep this choice.  (D) Neglecting someone is not helping!  Eliminate this choice.  (E) "Assists" and "helps" are synonyms.  Keep this choice.

Now look back at the first blank.  Right after the blank, you read that Alvin is unselfish.  Predict that Alvin is an “unselfish” person, and look down at your remaining answer choices.

(A) opportunistic . . supports

(C) bemused . . aids

(E) altruistic . . assists

(A) Does "opportunistic" mean "unselfish?"  No.  People who are always looking for opportunities may just be looking for opportunities for themselves.  Eliminate this choice.  (C)  Don’t confuse the word “bemused” with the word “amused,” but they both refer to the way that one person feels.  You aren’t looking for a feeling word; you are looking for a word that means unselfish.  Eliminate this choice.  (E) This word comes from French: “autrui” means “to others.”  Altruistic people are concerned with others; they are unselfish.

The correct answer is (E).

Words used in this SC:

Opportunistic: taking advantage of situations (often selfishly)

Supports: helps or keeps from falling

Noble: honorable or aristocratic

Undermines: hinders or sabotages

Bemused: confused or preoccupied

Aids: helps

Caustic: burning, sharp or bitter (often refers to language)

Neglects: disregards, fails to care for

Altruistic: Unselfishly concerned for others (Knowsys word!)

Assists: helps

On sat.collegeboard.org, 72% of the responses were correct.

For more help with SAT vocabulary, visit www.myknowsys.com!