# SAT Math: Algebra

## Functions

Let the function be defined by f(x) = 5x - 10.  If 2f(m) = 20, then what is the value of f(3m)?

## Knowsys Method

Read the problem carefully.  This is a grid in question.  Instead of bubbling in a letter, you will bubble in your answer.  You should always guess on grid in questions because, unlike multiple choice questions, grid in questions do not have a wrong answer penalty.

Identify the bottom line.  f(3m) = ?

Assess your options.  This function problem is very straightforward.  All you have to do is plug in the information given to you and solve.

Attack the problem.

2f(m) = 20, so f(m) = 10

If f(x) = 5x - 10, then f(m) = 5m - 10.  Set that equal to the value you already know for f(m) and solve for m.

10 = 5m - 10
20 = 5m
4 = m

Now plug in the value of m to find f(3m).

f(3m) = f(12) = 5(12) - 10 = 50

Loop back.  Verify that you solved for the bottom line.

This is a medium level problem.

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.

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# SAT Writing: Identifying Sentence Errors

## Identifying Sentence Errors

Read the sentence and select the portion of the sentence that contains an error.  If there is no error, select E.

## Knowsys Method

Read the sentence carefully, listening for errors. If you do not find the error immediately, then check the underlined portion against the Big 8.

A. "Neither" must always be paired with "nor."  This choice is not an error, so eliminate it.

B. Anytime you see a verb underlined, check to make sure that it agrees with its subject.  Nouns used with either/or or neither/not are called "compound pairs."  In compound pairs, the subject always agrees with the second subject in the pair.  The verb "know" agrees with "I," so this is not an error.  Eliminate this choice.

C. When you see "which" underlined, you should ask yourself whether it should be "that" instead.  The word "which" must always be preceded by a comma, and since the comma in this sentence cannot be eliminated, "which" must be correct. Eliminate this choice.

D. This choice tests parallelism.  Both verbs ("making" and "giving") must match with each other.  They do match, so this choice is not an error.  Eliminate this choice.

E.  There is no error in the sentence, so E is correct.

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# Link of the Week: Purdue OWL

The Purdue OWL, or Online Writing Lab, has built up a solid reputation as a resource for writing MLA and APA citations, but it has so much more to offer than that.

If you have never done so before, check out the academic writing section, which includes a variety of in-depth articles that can help you to craft strong essays.  Need to review argumentative structure or thesis statements?  Looking for some help with sentence variety?  It's all there.

No matter what the writing assignment, be it a research paper for school or your SAT or ACT essay, this one-stop-shop for everything related to writing is sure to prove useful in high school, college, and beyond.

## Sentence Completions

Select the words that best fit the meaning of the sentence as a whole.

Given his ------- chocolate desserts, we were all a little surprised when my father vanilla cake and ice cream for his birthday this year.

A. predilection for
B. resurgence of
C. deference to
D. decorum around
E. aversion to

## Knowsys Method

Always start by covering up the answer choices so that they do not distract you.  Read the sentence carefully, then predict what you think the answer should be.  If the father's choice of vanilla cake and ice cream surprised his family, the father probably had an established preference for chocolate.  Using "established preference" as our prediction, let's go through the choices.

A. The word “predilection" comes from the Latin word "prediligere," meaning "to prefer before others."  A predilection is an established preference for something.  This matches our prediction perfectly, but we should still check the rest of the choices.

B.  “Resurgence" sounds a lot like what it means.  A resurgence is a revival.  Think: something is re- (again) surging (thriving, increasing, moving, etc.)  This choice does not match our prediction, so eliminate it.

C. "Deference" sounds like "preference," but don't be fooled!  It means something very different.  To show deference to someone is to show that person respect or esteem.  The father in the sentence probably likes chocolate, but it would make no sense for him to "respect" chocolate.  Eliminate this choice.

D. "Decorum" means "socially acceptable dignity or correctness of speech or behavior."  Here's an easy trick for remembering this definition.  If you are somewhere that is formally DECORated (like a ballroom, the White House, etc.), you should display a certain sense of DECORum.  This choice does not match our prediction, so eliminate it.

E. You can probably detect just from looking at this word that it has a negative connotation.  An "aversion" to something is a severe dislike of that thing.  This is the opposite of our prediction, so eliminate this choice.

Source: Online Etymology Dictionary. Dan Harper. 2013. Web. 29 Jan. 2014.

Words used in this SC:

predilection: an established preference for something
resurgence: a revival
deference: respect or esteem due to a superior of an elder
decorum: socially acceptable dignity or correctness of speech or behavior
aversion: dislike and opposition

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## Sentence Completions

Select the word that best fits the meaning of the sentence as a whole.

After discovering a permanent marker in a kitchen drawer, my two-year-old nephew left ------- scribbles all over my sister's walls.

A. indelible
B. fallacious
C. altruistic
D. inept
E. ambivalent

## Knowsys Method

Always start by covering up the answer choices so that they do not distract you.  Read the sentence carefully, then predict what you think the answer should be.  A permanent marker would leave permanent marks on the walls, so use that as a prediction and check the answer choices.

A. The word “indelible” come from the Latin roots “in,” meaning “not or the opposite of,” and “delebilis,” meaning “able to be destroyed.”  Something indelible cannot be destroyed or removed.  This choice matches our prediction, so keep it.

B.  “Fallacious” means “deceptive or misleading.”  A useful trick for remembering the meaning of “fallacious” is to think about the word “false” which sounds similar and means something similar.   This does not match our prediction, so eliminate this choice.

C. "Debilitate" comes from the Latin "debilitare," meaning "to weaken."  To debilitate someone or something is to make that person or thing weak and potentially infirm.  This is the opposite of our prediction, so eliminate this choice.

D. An “altruistic” person is likely to donate money, do charity work, and share readily with others.  “Altruism” is “unselfish concern for others.”  This does not match our prediction, so eliminate this choice.

E. The word "ambivalent" was coined in 1910 by Swiss psychologist Eugen Bleuler.  As a psychological term, "ambivalent" means "having conflicting meanings," but it can also mean "having several possible meanings."  This does not match our prediction, so eliminate this choice.

Source: Online Etymology Dictionary. Dan Harper. 2013. Web. 23 Jan. 2014.

Words used in this SC:

indelible: permanent
altruistic: unselfishly concerned about the welfare of others
inept: awkward or unskilled
ambivalent: having several possible meanings

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# SAT Math: Data Analysis

## Median

The table above shows the number of students enrolled at Allenville Middle School from 2005 to 2011.  If the median enrollment over these seven years was 789, and no two years had the same number of students enrolled, what is the lowest possible value for y?

## Knowsys Method

Note: In the math section of the SAT, you will encounter questions that do not have answer choices.  Instead of bubbling in a letter, you will bubble in your answer.  These questions are called grid in questions, and you should always guess an answer for them because there is no penalty for getting the question wrong!

Read the problem carefully.   Review the definitions of important terms.  The median is the middle number in a set of numbers.

Identify the bottom line.  lowest possible y = ?

Assess your options.  There is only one possible method for solving this problem, and it is demonstrated below.

Attack the problem.  Whenever you are working with medians, you should start by putting the list of numbers in order.

737  755  776  789  804  811

Now you need to determine where y should fall in the list.  The problem tells you that 789 is the median,  and no two years had the same enrollment, so y must be greater than 789.  The smallest that y can be, therefore, is 790.

Loop back.  Check to verify that you have solved for the bottom line.

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.

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# Link of the Week: The Internet

This week's link is a testament the power of crowdsourcing on the Internet.  Nearly twenty years ago, an elderly woman who had been rendered non-communicative by a fast-moving cancer scribbled out patterns of letters onto dozens of note cards.  Her granddaughters believed that their grandmother had left them a code, and though they attempted to decode the seemingly random patterns of letters for months, the girls were unable to find a solution.  One of these granddaughters recently posted images of the cards on the website Ask Metafilter, and within a few minutes, site users had partially cracked the code.  Read more here.

Consider the application of this fascinating story to past SAT prompts such as:

•  Has today's abundance of information only made it more difficult to understand the world around us?
•  Is the most important purpose of technology different from what it was in the past?
•  Have modern advancements truly improved the quality of people's lives?

Good luck to those of you taking the SAT today!  Check back here next week for a new link.

# SAT Writing: Identifying Sentence Errors

## Identifying Sentence Errors

Read the sentence and select the portion of the sentence that contains an error.  If there is no error, select E.

## Knowsys Method

Read the sentence carefully, listening for errors. If you do not find the error immediately, then check the underlined portion against the Big 8.

A. The phrase "straining to reach" is idiomatically correct.  If this phrase looks strange to you, add it to your idioms list and read it over until it sounds right to you.  Eliminate this choice.

B. Whenever you see a reflexive pronoun (myself, yourself, herself, himself, themselves, ourselves) underlined, check to see whether that reflexive pronoun refers back to an antecedent that is already stated in the sentence.  In this case, "herself" clearly refers back to "the woman," so this usage is correct.  Eliminate this choice.

C. This choice may look right at first glance, but "was" should be "were."  If you are writing about something that you wish were true or that could be true but is not true, you should use "were."  For instance, you would say, "If I were a bird, I would fly away."  You are not a bird, have never been, and will never be, so the correct word is "were."  This choice is an error, but you should check choice D just to be sure.

D. "Taller" is the comparative form of the adjective "tall."  The comparative form is used when you are comparing two things ("Of the two dogs, this one is cuter").  The superlative form is used when you are comparing three things ("Out of all these dogs, this one is the cutest").  The sentence is comparing two things: the way the woman is and the way she wishes she could be.  This choice is not an error.

E.  We found an error in choice C, so E cannot be correct.

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## Sentence Completions

Select the words that best fit the meaning of the sentence as a whole.

The defendant's story seemed highly -------, especially since she had no witnesses to ------- her alibi.

A. innocuous . . vindicate
B. auspicious . . substantiate
C. inept . . debilitate
D. reticent . . scrutinize
E. implausible . . corroborate

## Knowsys Method

Always start by covering up the answer choices so that they do not distract you.  Read the sentence carefully, then predict what you think the answer should be.  In two-blank sentence completions like this one, start with the easier blank first, which, in this case, is the second one.  What would this defendant need a witness to do?  To confirm or support her alibi.  Using "confirm/support" as a prediction, let's look at the choices for the second blank.

A.  "Vindicate," like many SAT words, has a Latin origin.  It comes from "vindicare," which means "to set free, lay claim to, assert, or avenge."  Today, the word is no longer associated with laying claim or achieving revenge; it means "to clear of guilt or blame" or "to prove to be right."  The second meaning of vindicate matches somewhat with our prediction, so keep this choice for now.

B.  "Substantiate" is easy to remember because it sounds like "substance."  To substantiate something is to give substance to, to prove, or to establish that thing.  This matches fairly well with our prediction, so keep this choice for now.

C. "Debilitate" comes from the Latin "debilitare," meaning "to weaken."  To debilitate someone or something is to make that person or thing weak and potentially infirm.  This is the opposite of our prediction, so eliminate this choice.

D. "Scrutinize" means "to examine closely."  To help you remember this word, you could think of someone squinting their eyes to look at something very closely.  This choice does not match our prediction, so eliminate it.

E. "Corroborate" comes from the Latin "corroborare," meaning "to strengthen."  To corroborate something is to support it with evidence.  This matches fairly well with our prediction, so keep this choice for now.

Now look at the second blank.  If the defendant has no witnesses to confirm her alibi, then her story would be weak or difficult to believe.  Using this as a prediction, let's look at the remaining options for the second blank.

A. “Innocuous” comes from the Latin roots “in” (not) and “nocuus” (to harm) and means “harmless or inoffensive.”  This choice does not match our prediction, so eliminate it.

B. "Auspicious" sounds a little like "suspicious," but it means nearly the opposite.  Something auspicious is favorable or promising of success.  This choice does not match our prediction, so eliminate it.

E. The word "implausible" comes from the same Latin root (plaudere) as the word "applaud," though the two words have very different meanings today.  Something implausible is unlikely to be true or hard to believe.  (FYI, something plausible is reasonable or probable).  This choice matches our prediction, so E must be correct.

Source: Online Etymology Dictionary. Dan Harper. 2013. Web. 13 Jan. 2014.

Words used in this SC:

innocuous: harmless
vindicate: to clear of guilt or blame
auspicious: favorable or promising success
substantiate: to give substance to, to prove, or to establish
inept: awkward or unskilled
debilitate: to diminish strength
reticent: quiet and reserved
scrutinize: to examine closely
implausible: 1) unlikely to be true or 2) hard to believe
corroborate: to support with evidence or authority

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# SAT Math: Geometry

## Knowsys Method

Read the problem carefully.  This problem deals with sectors, which are sections of a circle.  If you think of a circle as a pie, then sectors are slices of that pie.

Identify the bottom line.  degrees in 1/6 of a circle - degrees in 1/9 of circle = ?

Assess your options.  If a sector makes up 1/6 a circle, then that sector must contain 1/6 of the 360 degrees in the circle.  The same idea applies to the other sector as well.  Use that logic to figure out how many degrees are contained in each sector mentioned in the problem, then subtract the smaller number of degrees from the larger number to find the difference.

Attack the problem.

Loop back.  Verify that you solved for the bottom line.

This is a medium level problem.

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.

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# SAT Writing: Improving Sentences

## Improving Sentences

Select the choice that results in the best sentence – the sentence that follows the requirements of standard written English and communicates effectively.

Elaine's decision to attend State College was influenced by the college's reasonable tuition rates and because of its convenient location.

A.  because of its convenient location
B.  because it is conveniently located
C.  it is conveniently located
D.  by its convenient location
E.  due to its convenient location

## Knowsys Method

Read the sentence carefully, listening for errors. If you do not find the error immediately, then check the underlined portion against the Big 8.

This sentence completion tests your understanding of parallelism.  Whenever two or more elements are listed in a sentence, they should be in the same format (parallel).

For instance, these two constructions are parallel:

Alisha likes to ski, to rock climb, and to swim.

Alisha likes to ski, rock climb, and swim.

These two constructions are incorrect because the elements in the list are not parallel:

Alisha likes to ski, rock climb, and to swim.

Alisha likes skiing, to rock climb, and swimming.

So, what is wrong with the parallel construction in the sentence above?  "Elaine's decision . . . was influenced BY the college's reasonable tuition rates, and BECAUSE OF its convenient location."  The phrase "because of" must be eliminated or replaced to make the parallel construction work.  You could rewrite the sentence as either:

1.  "Elaine's decision . . . was influenced BY the college's reasonable tuition rates, and BY its convenient location."  (both elements begin with "by")

OR

2.  "Elaine's decision . . . was influenced by THE COLLEGE'S reasonable tuition rates, and ITS convenient location." (both elements begin with a possessive noun/pronoun)

If you scan the answer choices, you will see that the only choice that works is D.

This is a medium level problem.

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## Sentence Completions

Select the word that best fits the meaning of the sentence as a whole.

Sarah wished she had a calculator to ------- her math homework because solving each problem by hand was taking her a long time.

A. mollify
B. expedite
C. circumvent
D. enumerate
E. bolster

## Knowsys Method

Always start by covering up your answer choices so that they do not distract you.  Read the sentence carefully, and then predict what you think the answer should be.  If Sarah's math homework is taking her a long time, why might she want to use a calculator?  To speed up her work, probably.  Using "speed up" as a prediction, let's look at the answers.

A. "Mollify" comes from the Latin word "mollificare," which means "to make soft."  To mollify someone is to calm or soothe that person.  This does not match our prediction, so eliminate this choice.

B. "Expedite" literally translates from Latin as "to free the feet from chains."  To expedite something is to make it faster or easier.  This matches our prediction, but we need to check the rest of the answer choices.

C. The word “circumvent" comes from the Latin term "circumventus," which is made up of two parts, "circum" (around), and "venire" (to come).  To circumvent something is to go around or avoid that thing.  Sarah wants to speed up her math homework, not avoid it, so eliminate this choice.

D. "Enumerate" means "to list out."  An easy way to remember the meaning of "enumerate" is to think about the fact that it looks a little like the word "number."  This does not match our prediction, so eliminate this choice.

E.  To bolster something it to encourage it or keep it raised.  For instance, an Academy Award nomination might bolster a film's ticket sales.  This does not match our prediction, so eliminate this choice.

Source: Online Etymology Dictionary. Dan Harper. 2013. Web. 13 Jan. 2014.

Words used in this SC:

mollify: to calm or soothe
expedite: to speed up or make easier
circumvent: to avoid or go around
enumerate: to list out
bolster: 1) to encourage or 2) to keep raised

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# Link of the Week: Released SAT Essay Prompts

Ever wonder how we know about so many past SAT prompts?  You, too can see past SAT prompts if you check out this page on College Board's educators site.  College Board releases essay prompts after each SAT, so you can check back after the January 25th test for the prompts used in that administration.

For practice, you could write an entire essay on one of the prompts, or you could identify one historical, one literary, and one current event example that could be useful for each prompt.  If you have taken a Knowsys course, you will remember that you should research and memorize 5 literary, 5 historical, and 5 current event examples on a variety of topics before you walk into the test.  This strategy saves you valuable time and ensures your examples are detailed, accurate, and original.

ACT does not release its most recent essay prompts, but its site does contain a page explaining the ACT essay and how it is scored.  Check that out here.

Thanks for reading!  Check back here next week for a new link.

# SAT Math: Algebra

A. -16
B. -4
C. -2
D. -1
E. -3/4

## Knowsys Method

Read the problem carefully.  If you have never seen this problem type before, it might look strange to you.  Don't worry, though.  We will show you just how simple these problems are!

Identify the bottom line. c = ?

Assess your options.  At Knowsys, we call these problems "symbol problems" because they use non-mathematical symbols like stars, hearts, smiley faces, etc.  To solve a symbol problem, all you have to do is plug in the information given to you.  Use the following steps to ace these problems on the SAT.

1. Write out the symbol problem defined in the question.  For instance,

&a = a + 2

2. Directly below that, write out the new version of the symbol problem, aligning the symbol in the original with the symbol in the new version.

&a = a + 2

&b =

&7 =

3. Substitute the variable(s) or number(s) in the new version for the variables in the original.

&a = a + 2

&b = b + 2

&7 = 7 + 2 = 9

Attack the problem.  Let's apply those steps to the symbol problem above.  First, write out the original symbol problem defined in the question.

You will have to deal with the right and left sides of the new version of the symbol problem separately.  Start with the right side.  Write that part out below the original, and substitute the variables into the original.

Now, repeat the same step with the left side.

Use FOIL, distribute the -2, and then combine like terms.

Now, set the solutions you have found for each side equal to each other and solve for c.

Loop back.  Check to make sure that you have solved for the bottom line.

This is a hard level problem.

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.

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# SAT Writing: Identifying Sentence Errors

## Identifying Sentence Errors

Read the sentence and select the portion of the sentence that contains an error.  If there is no error, select E.

## Knowsys Method

Read the sentence carefully, listening for errors. If you do not find the error immediately, then check the underlined portion against the Big 8.

A. Chances are, the phrase "almost all of the board members" does not strike you as incorrect.  "Almost" is an adverb, and it modifies "all," which in this case is functioning as an adjective.  This is not the error, so eliminate this choice.

B. Whenever you see a verb underlined, check to make sure that it agrees with its subject and with the tense of the sentence.  The verb "agreed" agrees with the subject "board members," and it is in past tense like the rest of the sentence.  This is not an error, so eliminate this choice.

C. Here's another verb, so check to make sure that it agrees with its subject and with the tense of the sentence. The verb "was" agrees with the noun "John Smith," and it is in past tense like the rest of the sentence.  This is not an error, so you can eliminate this choice.

D.  The clause "John Smith was the more qualified" probably sounds strange to you, but it is grammatically correct!  When you are comparing two items, people, etc., the correct word is "more."  When you are comparing three items, people, etc., the correct word is "most."  If you rearrange the sentence, the use of "more" might sound a little more natural.  "Almost all of the board members agreed that John Smith was the more qualified of the two job candidates they had interviewed."  This is not an error, so eliminate this choice.

E.  We did not find an error, so the answer must be E, no error.

This is a hard level problem

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## Sentence Completions

Select the words that best fit the meaning of the sentence as a whole.

Seeing the ------- bicycle, which was over 80 years old now, made the elderly man feel ------- for the carefree days of his youth.

A. recalcitrant . . abstemious
B. precursory . . cynical
C. arcane . . somber
D. hackneyed . . tenacious
E. antiquated . . nostalgic

## Knowsys Method

Always start by covering up your answer choices so that they do not distract you.  Read the sentence carefully, and then predict what you think the answer should be.  In two-blank sentence completions like this one, predict the easier blank first.  The first blank in this sentence is easier because there are more direct context clues, so we will start there.  If a bicycle is over 80 years old, what word would you use to describe that bicycle?  Probably "old," "rusted," "disused," something along those lines.  With those predictions in mind, let's look at the answer choices for the first blank.

A. "Recalcitrant" literally translates from French as "kicking back."  The word is typically used today to mean "stubbornly defiant or resistant of authority."  Think of a stubborn mule that does not want to go anywhere and kicks you when you try to make it move.  This word does not match our prediction, so eliminate this choice.

B. "Precursory" comes from the Latin "praecursor," which means "forerunner."  The word still means the same thing today; something "precursory" is something that comes before or leads to something else.  For instance, like land line telephones were the precursors to cell phones.  This word somewhat matches our prediction, though not exactly.  We should keep this choice for now and check the second blank later.

C. The word “arcane” shares a common root with the word “ark” (perhaps best known from Biblical story of Noah’s Ark).  Both come from the Latin word “arca,” meaning “chest, box, or place for safekeeping.”  Something “arcane” is mysterious, secret, or known only to a few.  This choice does not match with our prediction, so eliminate it.

D. The word "hackneyed" has a complicated origin.  It comes from the Old English "Hacan ieg," or "Hook Island," an area of land that is a part of contemporary London.  Horses were once kept on Hook Island, so the term "hackney" came to refer to a horse that could be rented out for hire.  "Hackneyed" meant "kept for hire," but it eventually developed a new meaning, "unoriginal or trite."  This makes sense, since if something is rented out over and over again, it will become overused.

E.  Have you ever heard the word “antique?”  If so, you can probably guess what “antiquated” means.  Both terms come from the Latin word “antiquus,” meaning “ancient, former, or aged.”  Something antiquated is old and outdated.  This matches our prediction, so keep this choice.

Now, focus on the second blank.  This man is feeling (something) for the carefree days of his youth.  He is probably feeling a sense of longing for his youth.  Using that as our prediction, let's look at the remaining choices.

B. The word "cynical," which means "distrustful of human nature," refers back to a school of Greek philosophy, the Cynics, who believed that people must reject indulgent pleasures and luxury and live a simple life.  This choice does not match our prediction, so eliminate it.

E. "Nostalgia" means "homesickness or a wistful yearning for the past."  The term comes from the Greek words "nostos," or "homecoming," and "algia," or "distress."  This choice matches our prediction, so E must be the correct answer.

Source: Online Etymology Dictionary. Dan Harper. 2013. Web. 13 Jan. 2014.

Words used in this SC:

recalcitrant: stubbornly defiant and resistant of authority
abstemious: not eating or drinking too much
precursory: preliminary, coming before something else
cynical: distrustful, especially of human nature
arcane: mysterious or understood by only a few
somber: gloomy and melancholy
hackneyed: unoriginal or trite
tenacious: persistent
antiquated: outdated or related to the past
nostalgic: 1) homesick or 2) feeling a wistful yearning for the past

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# SAT Math: Percents

## Picking Numbers with Percents

A local electronics store marks up its items 30% from their wholesale cost.  At its annual Spring sale, the store discounts the prices of all items by 20%.  The sale price is what percent of the wholesale cost?

A. 90%
B. 100%
C. 104%
D. 110%
E. 117%

## Knowsys Method

Read the problem carefully.  Make careful note that the price is originally INCREASED by 30%, then it is DECREASED by 20%.  Also, notice that the problem asks, "the sales price is what percent OF the wholesale cost," not what percent OFF the wholesale cost.  That is an important distinction.  For instance, if a shirt is discounted by 30%, then the price is 30% OFF, but 70% OF the original price.

Identify the bottom line.  sale price = what % of wholesale cost?

Assess your options.  You can solve the problem by working solely with percents, or you can pick numbers.  We recommend the latter method because it is more concrete.

Attack the problem.  Whenever you are picking a number to use in a percent problem, it is easiest to use 100.  So, let's say that the wholesale cost of an item is \$100.  That cost is marked up 30% to create the regular price at which the item is sold to customers.  There are two ways to find that price.

100 + (.3)(100) = 130

100 x 1.3 = 130

The regular price of the item (before the sale) is \$130.  At the sale, this price of \$130 is marked down by 20%.  There are two ways to find the sale price.

130 - (.2) (130) = 104

130 x .8 = 104

The sale price is \$104, and the wholesale cost was \$100.  104 is 104% of 100, so the answer is C.

Note: Look at answer choice D.  NEVER fall for this trap: 100 + 30 - 20 = 110.  Remember that the price goes up by 30%, then decreases by 20% off the NEW price.

Loop back.  Verify that you solved for the bottom line.

This is a medium level problem.

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# SAT Writing: Improving Sentences

## Improving Sentences

Select the choice that results in the best sentence – the sentence that follows the requirements of standard written English and communicates effectively.

Of all the plays in which I have performed, my experience in Shakespeare's King Lear was the most challenging because the lines were so complex.

A.  my experience in Shakespeare's King Lear was the most challenging because the lines were so complex.
B.  my experience in Shakespeare's King Lear challenged me the most because of the complexity of the lines.
C.  the challenge presented by the complex lines of Shakespeare's King Lear was the worst for me.
D.  Shakespeare's King Lear, because of the complexity of the lines, challenged me mostly.
E.  Shakespeare's King Lear was the most challenging for me because the lines were so complex.

## Knowsys Method

Read the sentence carefully, listening for errors. If you do not find the error immediately, then check the underlined portion against the Big 8.

What do you notice about the original sentence?  It sounds a little like "my experience" is a play.  The modifier at the beginning of the sentence describes plays, so the name of a play should directly follow that modifier.  That eliminates answer choices A, B, and C right off the bat.

D.  Choice D begins with the name of a play, so it fixes the modifier error, but it introduces new problems.  Placing the phrase "because of the complexity of the lines" in commas interrupts the sentence unnecessarily and reads awkwardly.  The use of "mostly" is also incorrect because it changes the meaning of the sentence.  Eliminate choice D.

E.  Choice E fixes the modifier error, it does not change the meaning of the sentence, and it follows a logical sentence structure.  Choice E is correct.

This is a medium level problem

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# Link of the Week: Top 10 News Stories of 2013

Taking the SAT in the Spring of 2014?  What better way to get some current events ideas and relive some of the most climactic moments of the past year than to check out the Top 10 U.S. News Stories of 2013?  This list, compiled by Time Magazine, overviews the ten most news-worthy events that rocked the nation this past year.  If you would like to see stories about pop culture, best and worst Tweets, or international news, head over to Time's complete listing of all 2013 Top 10 lists. There, you can navigate through 54 lists on a wide range of topics, one of which is sure to spark your interest.

Then, try a practice essay on one of these topics using your newly-generated Excellent Examples

• Do we need other people in order to understand ourselves?
• Is it important to question the ideas and decisions of people in positions of authority?
• Is the world changing for the better?
• Is it more important to remain consistent than to change our minds when circumstances change?

Good luck, and check back here next week for a new link!

## Sentence Completions

Select the word that best fits the meaning of the sentence as a whole.

Jared is ------- around strangers, but when he is alone with family and friends, he becomes lively and loquacious.

A. disingenuous
B. erudite
C. verbose
D. dispassionate
E. reticent

## Knowsys Method

Always start by covering up your answer choices so that they do not distract you.  Read the sentence carefully, and then predict what you think the answer should be.  Jared is lively and loquacious (excessively talkative) around his friends and family, but he acts differently around strangers.  Our prediction should be the opposite of lively and loquacious, something like "shy and quiet."  Using that as our prediction, let's look at each of the answer choices.

A. "Disingenuous" means "insincere or calculating."  To help yourself remember the meaning of this word, think that "disingenuous" means "not genuine."  This does not match our prediction, so eliminate this choice.

B.  If you read the Divergent books, you may already recognize the word "erudite," which means "intellectual or learned." In the book series, "Erudite" is the name of a faction of people who believe that intelligence is the most important trait one can have.  This choice does not match our prediction, so eliminate it.

C.  "Verbose," "verb," and "verbal" all come from the Latin word "verbum," which means "word."  "Verbose" means "wordy" and can be used to describe a piece of writing, spoken words, or a person.  This is the opposite of our prediction, so eliminate this choice.

D.  "Dispassionate" means "neutral or not affected by emotions."  Think, "dispassionate = not passionate/not emotional."

E.  "Reticent" comes from the Latin verb "reticiere," which means "to be silent."  Someone who is "reticent" is quiet and reserved.  This matches our prediction, so E is the correct answer.