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 the answers to sentence completion questions before you read the sentence.  Use the sentence to make a prediction about the word that will fill the blank, then match your prediction to the correct answer choice.  Eliminate any choice that does not match your prediction.  Check all the answers, even if you find one answer that seems right.

The ballet stage is a bright, seemingly weightless world where gravity is continually being------- by the dancers.

This sentence describes the stage as a “weightless world.”  In a weightless world, how would dancers respond to gravity?  They would not need it!   Try using the word “disregarded” or “ignored” as your prediction for the blank.  Then look down at your answer choices.

(A) prolonged

(B) reapportioned

(C) unbalanced

(D) reflected

(E) defied

There is only one answer that matches your prediction.  Ask yourself whether each word means “disregarded,” and eliminate any that do not have that meaning.  If you are not sure about an answer choice, think about what it would mean in context.  (A) means that the dancers would somehow continue the power of gravity, which does not match your prediction.  (B) indicates a change in the gravity, but the gravity is still in charge of this supposedly “weightless world.” (C) creates an odd picture: unbalanced gravity would be strong in some areas and not in others.  Dancers would careen crazily rather than move weightlessly.  (D) seems to increase the power of gravity rather than diminish it. (E) shows that the dancers are achieving weightlessness by ignoring or rejecting gravity.

The correct answer is (E).

Words used in this SC:

Prolonged: caused to continue longer

Reapportioned: to distribute anew

Unbalanced: unstable

Reflected: reproduced or cast back

Defied: resisted, challenged, or rejected

On sat.collegeboard.org, 73% of the responses were correct.

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

Algebra

Link of the Day

Many of you have been following the news about Hurricane Sandy, and our thoughts and prayers are with those affected by the storm.  For others, it may be easy to hear things like “school is out” and “the power is out” and wish you were in the same situation.  You may think of enjoyable times spent wrapped in blankets and telling stories as a candle or flashlight flickers.  Think for a moment about how important power is for a hospital.  Here is an article about how one hospital responded to the storm.  Think about broad themes such as courage, the fight for life, and the response to danger as you read about this current event.

10/30 Algebra

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

If you approach all math problems the same way, you are less likely to make a careless mistake.  Start by reading the problem carefully and identifying the bottom line.  Assess your options for solving the problem so that you do not do more work than you need to.  Then attack the problem and solve it.  Loop back after you have finished to make sure that you found the bottom line.

If  , for which of the following values of x is y NOT defined?

Bottom line:  Although the problem includes an equation for y, you need an x value.  Your answer will be an x value that does something specific to this equation to produce a y that is not defined.  So make a note: x = ?

Assess your options:  You could work backwards and plug in answer choices to find a value that produces a y that is not defined.  This might require you to work the problem numerous times.  Instead, think about your knowledge of number properties.

Attack the problem: Any time a number is divided by zero, it is not defined.  If y is not defined, then it must be equal to something over zero.   Take the bottom part of your fraction and set it equal to zero: (x + 3)(x – 4) = 0.  For which values is this true?  Well, anytime zero is multiplied by a number, the answer is zero.  If either of these binomials is equal to zero, then there will be a zero on the bottom.  So set each binomial equal to zero: x + 3 = 0 and x – 4 = 0.  When you solve both of these equations, you will get two answers: x = -3 and 4.  Both answers will create a zero in the bottom of your fraction.

Loop back:  You found two answers for x that will create a zero on the bottom of your fraction.  Look down at your answer choices to see which one is present.

(A) -4

(B) -3

(C) -1

(D) 2

(E) 3

The correct answer is (B).

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

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

Comparisons

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 original sentence to yourself, listening for errors.  Evaluate the underlined portion of the sentence using the Big 8 Grammar Rules.  Focus on the first problem that you find and check to see which answer choice fixes that problem.

Unlike her sister Heather, who would always put spiders safely outside if she found them in the house, Joanne’s fear kept her from going anywhere near the creatures.

This sentence may sound strange to you the first time that you read it.  If it did not sound strange, ignore the portion of the sentence between the commas and read it again.  The word “unlike” sets up a comparison.  What two things are being compared?  A person (Heather) is being compared to a feeling (Joanne’s fear).  This is not a logical comparison.  A person should be compared with a person.  Look down at your answer choices.

(A) Joanne’s fear kept her from going anywhere near the creatures

(B) Joanne’s fear is what kept her from going anywhere near the creatures

(C) fear is why Joanne had not gone anywhere near them

(D) Joanne was too afraid to go anywhere near the creatures

(E) they scared Joanne too much to go anywhere near them

(A) is illogical.  You know that because it matches the original sentence.   (B) and (C) keep comparing a person with the feeling of fear.  (D) compares a person to a person.  (E) adds the pronoun “they.”  Now Heather is compared to “they,” which presumably refers to the spiders.  That does not make sense.

The correct answer is (D).

On sat.collegeboard.org, 56% of the responses were correct.

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

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 your answer choices before reading the sentence so that your mind will be clear and unbiased.  Read the sentence carefully, looking for clues to help you predict a word to fill the blank.  Match your prediction to the correct answer choice, and eliminate any words that do not match.  Be sure to check all 5 answer choices, even if you think choice A matches.

Many of today’s physicians and patients are ------- high technology, captivated by computer-designed drugs and laser surgery.

If you only read the first part of this sentence, anything could fit in the blank.  However, the second part of the sentence contains the key word “captivated.”  If you know the meaning of the word “captivated,” you know what belongs in the blank.  Use the words in the sentence for the most precise predictions.  You know that the physicians and patients are “captivated by” high technology, so use that as your prediction and look at the answer blank.  If you do not know what the word captivate means, try to think about whether it is positive or negative.  Make at least a vague prediction about the blank.

(A) nervous about

(B) defensive about

(C) tolerant of

(D) enamored of

(E) overwhelmed by

There is only one answer that matches your prediction and only one answer that is definitely positive.

The correct answer is (D).

Words used in this SC:

Captivate: to charm, to attract and hold interest

Nervous: anxious

Defensive: protective

Tolerant: accepting

Enamored: in love with or captivated by

Overwhelmed: overcome by something, unable to deal with it

On sat.collegeboard.org, 62% of the responses were correct.

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

Algebra Equations

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

Use the same method for all SAT math questions.  Read the question carefully, identify the bottom line, and assess your options for solving the problem.  Choose the most efficient way to solve the problem, and attack it!  Finally, loop back to make sure that you solved for the bottom line.

If  and , then t exceeds s by

Bottom line:  You need to know how much t exceeds s.  So the question you are asked is really, “How much bigger is t than s?”  Your bottom line is t – s.

Assess your options:  Normally you would simplify s before plugging the s value into the equation for t, then find the difference between t and s.  However, doing this will give you some ugly fractions and take a lot of time.  Instead, try starting with your bottom line and plugging in everything that you know.

Attack the problem:  Start with the t – s and plug in the equations for both of these:

Then plug in s one more time:

This looks terribly ugly, but keep calm and use the order of operations.  You always multiply or divide before you add or subtract, so your first job is to distribute the half within the brackets by multiplying it by every number within the first set of parentheses:

Look at the new equation that you have.  How many things cancel out when you start subtracting the second group of numbers from the first?  Almost everything!  You are left with a single fraction:



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

(A)
(B)
(C)
(D)
(E)

The correct answer is (E).

On sat.collegeboard.org, 41% of the responses were correct.

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

Idioms

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 original sentence to yourself, listening for errors.  Then quickly check the underlined portions of the sentence against the Big 8 Grammar Rules.  Identify and mark any error that you find and quickly check the other choices.

In the interior of the Arctic islands during the melting season, even small streams must be crossed Awith great care Bbecause near-zero water temperatures and the Ctypically rocky and unstable nature of Dstream beds. ENo error

(A)  Before the word “care,” it is idiomatically correct to use the word “with.”  Think of the phrase “handle with care.”  There is no error in this underlined portion.

(B)  The word “because” may seem right at first.  The word “because” indicates that there is a reason for the previous statement.  Why should you cross with care?  Cross with care because the waters are cold and the stream beds are unstable.  However, if you read until the end of the sentence, you will find that there is no verb after the word because.  That should sound odd to you; you should feel as if you need to add the phrase “are there” or “are dangerous” to the end of the sentence.  Think of other words that you could use to express reasons why you must cross with care.  The phrase “due to” may come to mind.  Replace “because” with “due to,” and you have found the correct idiom.

(C)  The word “typically” modifies the word “rocky.”  It lets you know that the streams in the Arctic are usually, but not always rocky, so it includes essential information.  The modifier is placed as close as possible to the word it modifies, so there is no error in this underlined portion.

(D)  What kind of bed is unstable as the ice melts?  You are not concerned with the beds in your home, only stream beds.  There is no error in this underlined portion.

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

The correct answer is (B).

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

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

Sentence Completions

Link of the Day

Your SAT essay should include one current event as an example to show that you are well informed about the world.  Look for broad themes in current events, things like safety, science, accountability, justice, authority, and facing disaster.  One current event that connects to all of the things just listed is the reaction of an Italian court to an earthquake.  The court jailed scientists for not warning people of impending danger.  Read this article and think about all the ways that it could relate to previous SAT essay prompts.  Write down and memorize any facts you would need to use this as an excellent example for your SAT essay.

10/25 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 your answers before you read the sentence so that they do not prejudice your thought.  Read the sentence carefully.  If there are two blanks, predict an answer to the one that seems easier to you.  Eliminate any answers that do not match your prediction.  Then use the same process with the other blank.  Always consider all of your choices, even if your prediction matches one choice exactly.

Scientists are studying the birth and growth of thunderstorms to discover what causes the difference between showers that enable crops to ------- and ------- storms that cause floods and erosions.

Look at the first blank.  Rain showers “enable” crops to do something.  What do crops do when they get a sufficient amount of water?  They grow!  Use the word “grow” as your prediction and look down at your answer choices.

(A) flourish . . violent

(B) wither . . damaging

(C) grow . . harmless

(D) parch . . severe

(E) multiply . . essential

(A) matches your prediction.  Something that is flourishing is growing.  (B) is the opposite of your prediction.  Eliminate it.  (C) is exactly the word you predicted, but always check all of the answer choices.  Remember that many words have synonyms.  Your prediction is intended to eliminate words that do not match; it is not always the correct answer.  (D) does not match your prediction.  It does not make sense that showers would parch crops.  Eliminate this answer choice.  (E) is connected to the idea of growth, so do not eliminate it just yet.

Now look at your second blank.  You need a word to describe the storms that cause floods and erosions.  Both of the results of these storms are negative and even dangerous.  Do not spend too much time thinking of the perfect word; you can just predict the word “bad” when you know that the answer must be negative.  Look down at the choices that you have not yet eliminated.

(A) flourish . . violent

(C) grow . . harmless

(E) multiply . . essential

Only one of your answer choices is negative.  (A) is negative, (C) is neutral, and (E) is positive.

The correct answer is (A).

Words used in this SC:

Flourish: to thrive or grow well

Wither: to shrivel up

Parch: to dry out or scorch

Severe: very bad or intense

Essential: necessary

On sat.collegeboard.org, 74% of the responses were correct.

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

Number Line

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

Use the Knowsys Method for every question on the SAT.  The math method is always the same.  Read the question carefully, identify the bottom line, assess your options for solving the problem, select the most efficient method for solving the problem, and attack the problem.  Once you have finished your work, loop back to make sure that you solved for the bottom line.  Many problems have multiple steps, so you want to be sure that you are answering the question that was asked!

Which of the following statements must be true of the lengths of the segments on line m above?

I.  AB + CD = AD

II.  AB + BC = AD – CD

III.  AC – AB = AD – CD

Bottom Line:  You must find out which of the statements above must be true.  You will need to mark each one true or false in order to find the correct answer.

Assess your Options.  You could plug in numbers for these spaces, but you are given no numerical information about the line.  You run the risk of finding answers that can be true rather than answers that must be true if you use this method.  Instead, keep the information abstract and use the line to evaluate the equations that you are given in order to see which ones work.

Attack the Problem:

I.  You are given AB + CD = AD.  You can tell from the line what AD must be equal to if you add up all the parts within AD.  From the line you can see that AD = AB + BC + CD.  Now plug that information into the given equation for AD.  Your new equation is AB + CD = AB + BC + CD.  One side has no BC while the other side has a BC.  You know that BC cannot be equal to zero because it is allotted a certain measure of space on the line.  This equation is not true.

II.  You are given AB + BC = AD – CD.  Look up at the line and see which parts of the line are still included if you take AD and subtract CD.  You are left with AB and BC.  Your new equation is AB + BC = AB + BC.  If you cannot get that information from looking at the line, think about this problem a little differently.  Substitute what you know about AD into the problem.  AD = AB + BC + CD.  Plug that in and your given equation is AB + BC = AB + BC + CD – CD.  The CD will cancel when you subtract it from itself, and you are left with AB + BC = AB + BC.  Will that always be true?  Yes, this equation is true.

III.  You are given AC – AB = AD – CD.  Look up at the line.  If you consider all of AC and then subtract out AB, what are you left with?  BC.  If you consider all of AD and then take out CD, what remains?  AB + BC.  Will BC = AB + BC?  Again, a space on a line cannot be equal to zero, so this equation is false. 

Loop Back:  You broke down each of these equations and determined whether they were true or false, so look down at your answer choices.

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) I, II, and III

 The correct answer is (B).

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

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

Sentence Structure

Link of the Day

Today's question involves Jean Piaget, a man who changed the way that we think about thought.  He would make an excellent example for your SAT essay, particularly because most students do not know about his contributions to psychology. Most students will use the same historical figures: George Washington, Martin Luther King Jr., or Hitler.  Take a moment to read about Jean Piaget's life here, and consider using him to make your essay stand out.

10/23 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 original sentence to yourself, listening for errors.  Evaluate the underlined portion using The Big 8.  Focus on the first error you find to eliminate wrong answer choices.

Jean Piaget, a Swiss psychologist, and the first scientist that made systematic studies of how children learn.

As you read this sentence, you should be confused when you reach the “and.”  There is no information before the “and” that would necessitate a conjunction.  You are told that Jean Piaget is a Swiss psychologist, but that information is not given as part of a list that would require an “and.”  Once you notice this, you can be sure that your task will be to decide how to deliver the information about Jean Piaget.  Remember that your goal is always to create clear and precise sentences.  Continue reading the sentence and think about its structure.  You will need a verb to fix this sentence fragment: a verb that relates to Jean Piaget.  Notice that the original sentence includes “made” in the past tense.  It is also logical to look for a sentence that is in the past tense because you know that this man was the first to do something.  Look down at your answer choices.

(A) Jean Piaget, a Swiss psychologist, and the first scientist that made

(B) Jean Piaget was a Swiss psychologist, also the first scientist making

(C) As a Swiss psychologist, it was Jean Piaget who was the first scientist making

(D) Swiss psychologist Jean Piaget, the first scientist in having made

(E) The Swiss psychologist Jean Piaget was the first scientist to make

(A)  You already know the original sentence is incorrect, so do not take the time to reread this answer choice.  (B) The verb “was” does not agree with “making." (C)  This answer is not concise.  Try to avoid “it was” constructions.  (D) This answer choice does not fix the sentence fragment, and it uses the awkward phrase “in having made.”  (E) This answer choice presents all the information in the original sentence clearly, without even using a single comma.

The correct answer is (E).

On sat.collegeboard.org, 74% of the responses were correct.

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

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 your answer choices before you read the sentence so that they do not distract you.  Then read the sentence carefully, and predict an answer to fill the blank.  Match that prediction to the correct answer choice, eliminating any answers that do not match.  Be sure to look at all 5 answer choices before selecting an answer.

Everyone who saw the play agreed that the lead actor’s performance was especially
------- : it was so deeply affecting that it moved many audience members to tears.

There are two types of sentence completion questions: vocab-based and logic-based.  Vocab-based questions include the definition of the word that belongs in the blank, usually after a comma or semi-colon.  This sentence uses a colon, but you should be able to realize that the word in the blank must show how the performance “was so deeply affecting that it moved many audience members to tears.”  You could predict the word “affecting” or the word “moving” for the blank.  Look down at your answer choices.

(A) negligible

(B) insipid

(C) poignant

(D) amiable

(E) receptive

Even if you do not know all of the words in your answer choices, eliminate those that are too negative or too positive.  (A) If “negligible” sounds negative to you, eliminate it. The performance was a success if it was moving.  (B) You may realize that “insipid” is also a negative word and can be eliminated.  (C) If this word is unfamiliar, keep it.  (D) Have you ever heard of someone’s smile being described as “amiable?”  If so, eliminate this choice because this performance induces tears.  (E) This word describes the audience, not the performance, so it can be eliminated.  Remember not to guess on an SAT question unless you can eliminate at least two choices.

The correct answer is (C).

Words used in this SC:

Negligible: too small or unimportant to be of concern

Insipid: boring or bland

Poignant: affecting or moving

Amiable: friendly

Receptive: taking in knowledge or ideas

On sat.collegeboard.org, 58% of the responses were correct.

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

Algebra Equations: Translate

Link of the Day

A recent SAT Question of the Day involved the architect Frank Lloyd Wright.  On this date in history, one of Wright’s most famous buildings opened to the public.  The Guggenheim Museum opened its doors in 1959 and is now one of the wealthiest museums devoted to Modern art in the world.  If you are at all interested in art or architecture, consider using the Guggenheim opening as one of your excellent historical examples for the SAT essay.  You can find more information about the museum opening here and see photos from the event here.

10/21 Algebra

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

Use the same method for every math question on the SAT.  Read the question carefully, identify the bottom line, and assess your options for solving the problem.  Once you have identified an efficient method to solve the problem, attack it!  Before you choose an answer, loop back to verify that the answer addresses the bottom line.

If x + 2x is 5 more than y + 2y, then x – y =  

Bottom Line: x – y = ?

Assess your Options:  It would not be easy to work backwards and plug in answer choices for this problem.  Instead, translate the written words into a mathematical equation and solve for the bottom line.

Attack the problem:  Identify the terms in the original sentence that easily translate from English into math terms.  The word “is” translates to “equals,” and you know that if you need “more than” the original, you will be adding the specific number.  You can now write the information that you are given as a single equation: x + 2x = y + 2y + 5.  You can simplify this equation by combining like terms: 3x = 3y + 5.  With many other problems, you would want to solve the problem by isolating a variable.  However, you are only working with one equation, so you will need to solve for the bottom line and not a single variable.  Notice that your bottom line includes a positive x and a negative y on the same side of the equation.  You can rearrange your equation to create this: 3x – 3y = 5.  Now notice that the x and the y both have a three in front of the variable.  Factor out that three so that you have 3(x – y) = 5.  If you divide both sides by 3, you will find that x – y = .

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

(A) -5

(B)

(C)

(D)

(E) 5

The correct answer is (D).

On sat.collegeboard.org, 44% of the responses were correct.

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

Parallelism

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 original sentence to yourself, listening for errors.  After you have read the whole sentence, quickly check the underlined portions of the sentence against the Big 8 Grammar Rules.  When you think you have found an error, mark it.  Quickly check to see whether there is an error in any of the remaining answer choices before moving to the next question.

AAs a Supreme Court justice, Thurgood Marshall Bwas known for his quest to end racial discrimination, his Copposition to the death penalty, and Dhe supported free speech and civil liberties. ENo error

(A) Think about the function of the word “as” in this sentence.  It is part of an introductory phrase and lets you know the context of the sentence.   You are not concerned with Thurgood Marshall as a private citizen; you are only interested in Thurgood Marshall “as” a Supreme Court justice.  The “as” represents an essential part of the information that you are given in this sentence, and it does not need to be changed in any way.

(B)  You have probably heard from your English teachers that you should avoid the passive voice.  Although “was known for” is in passive voice, it is not an error.  If you changed “was known for” to an active verb, you would change the meaning of the sentence from emphasizing Thurgood Marshall’s reputation to emphasizing his actions.  The “was” is singular and matches “Thurgood Marshall,” while “for” is the idiomatically correct preposition to use after “known,” so there is no error in this portion of the sentence.

(C) When you reach a series of things that are listed, check the parts of the list that are not underlined so that you know how each part of the list must be presented to be parallel.  The first element in this list is “his quest,” and the second element is “his opposition.”  These two things are listed in the same format.  You also know that the correct preposition to follow “opposition” is the word “to.” Expressing that someone is opposed “to” something is idiomatically correct.  There is no error here.

(D) After the “and,” you know that you have the final element in the list.  However, this time you have a problem when you check parallelism.  The first item is “his quest,” the second item is “his opposition,” and the third item is “he supported.”  In order for this list to be parallel, the third item should be “his support of free speech and civil liberties.”

(E) This answer cannot be correct because you found an error involving parallelism.

The correct answer is (D).

On sat.collegeboard.org, 69% of the responses were correct.

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

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 answers and carefully read the sentence.  When a sentence completion question has two blanks, you will choose the blank that seems easier, predict a word to fill that blank, and then match that prediction to the answer choices.  Eliminate any choices that do not match.  Then go back to the other blank and follow the same process.  The only difference is that you do not need to look at any of the answer choices that have already been eliminated.  Remember to look at all the answer choices that have not been eliminated, even if you make a prediction that perfectly matches one choice.

A dictatorship ------- its citizens to be docile and finds it expedient to make outcasts of those who do not ------- .

This sentence completion question is about a dictatorship.  The second blank may be a little easier to think about:  What kind of people would be outcasts in a dictatorship?  Anyone who does not obey the dictatorship!  Use “obey” as your prediction and look down at the second part of all of your answer choices.

(A) forces . . rebel

(B) expects . . disobey

(C) requires . . conform

(D) allows . . withdraw

(E) forbids . . agree

(A) and (B) are the opposite of your prediction.  Eliminate them.  (C) matches your prediction.  (D) does not directly concern obedience, so you can eliminate it.  (E) is not a perfect match, but you can hang onto any choices that you are not sure about.

Now look at the first blank.  In a dictatorship, do citizens have any kind of choice?  No.  Even if you are not sure about the meaning of the word “docile,” you can eliminate anything that is not a forceful word for this blank.  Think about how the word “docile” relates to your second blank.  If the dictatorship is making outcasts of those who do not obey, it makes sense to say that they are forcing people to obey.  It is logical to predict that the word “docile” has something to do with obeying authority.  A good prediction for the blank would be “makes” or “forces.”

Note: Your prediction exactly matches (A), but you already eliminated (A)!  Look for synonyms in the remaining answer choices that have not yet been eliminated.

(C) requires . . conform

(E) forbids . . agree

(C) matches your prediction.  (E) is the opposite of your prediction.

The correct answer choice is (C).

Words used in this SC:

Dictatorship: a government that holds absolute power and control

Docile: obedient or easily taught (Knowsys vocabulary word!)

Expedient: easy, quick, or convenient

Rebel: resist authority

Conform: act according to set rules or act like others

Withdraw: pull back or take back

Forbids: does not allow, prohibits

On sat.collegeboard.org, 67% of the responses were correct.

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

Functions

Link of the Day

Current events that make excellent examples for SAT essays often hold two ideas in tension.  Read this article about a Turkish pianist who is being prosecuted for irreverent tweets.  Think about the conflicting themes in this article.  One side argues for respect while the other side argues for freedom of expression.  These are broad themes that apply to people around the world, so they are likely to show up on the SAT.  Two previous SAT essay prompts are "Should heroes be defined as those who say what they think when we ourselves lack the courage to say it?" and "Is it important to question the ideas and decisions of people in positions of authority?"  Think also about the modern use of technology.  Which facts from this article would you need to memorize if you wanted to relate this current event to an SAT essay prompt?

10/18 Functions

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

For every SAT math problem, read the problem carefully so that you know exactly what information you are given.  Then identify the bottom line, the information that you must find.  Assess your options for solving the problem, and choose the most efficient method to get to the answer.  Attack the problem to find the answer, and loop back to your bottom line to make sure that your answer matches what you were supposed to find.

A manager estimates that if the company charges p dollars for their new product, where 0 ≤ p ≤ 200, then the revenue from the product will be r(p) = 2,000p – 10p² dollars each week. According to this model, for which of the following values of p would the company’s weekly revenue for the product be the greatest?

Bottom Line:  Which of the following values of p will result in the greatest revenue?

Assess your options:  You could work backwards by plugging in all of the answer choices to r(p) = 2,000p – 10p², but that will take time.  Instead, use what you know about functions to determine the answer.

Attack the problem:  You know what the graph of x² looks like: a parabola that makes a “u.”  What happens to that graph when it is -x²?  That “u” turns upside-down and the parabola looks like a hill.  That is what you have for your function r(p) = 2,000p – 10p².  Now simplify your function by pulling out the numbers and variables that your two terms have in common so that r(p) = 10p(200 – p).  If you set each part of this equation equal to zero, you will find where the parabola crosses the x-axis.  If 10p = 0 and 200 – p = 0, then p = 0 and 200.  The parabola crosses the x-axis at 0 and 200.  That makes sense because you were told in the problem that 0 ≤ p ≤ 200.  Think about the characteristics of parabolas once more.  All parabolas are symmetrical.  Where will your greatest value for the revenue be?  It will be at the top of that “hill” exactly between 0 and 200.  What is the midpoint between 0 and 200?  100.

Loop back: Your bottom line was the value of p that would have the greatest revenue.  Although your function used r(p) rather than f(x),  that p value had to be on the x-axis.  You solved for the bottom line, so you are ready to look down at the answer choices. 

(A)  10

(B)  20

(C)  50

(D)  100

(E)  200

The correct answer is (D).

On sat.collegeboard.org, 37% of the responses were correct.

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