Functions

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

All math problems require the same approach.  Read the question carefully and identify the bottom line that you must find.  Assess your options for working the problem, choose the most efficient strategy, and attack the problem.  Always make sure that your answer addresses the bottom line, especially in problems with multiple variables.

If the function f is defined by f(x) = 2x + 3, and if f(a) = 11, what is the value of a?

This question may look complicated because it uses functions, but it can be worked very quickly.  You are given a function using the variable x:
f(x) = 2x + 3

However, your bottom line requires you to solve for another variable: a. Think about the first information you are given in terms of a by substituting an a for every x:
f(a) = 2a + 3

Now plug in your last piece of information, f(a) = 11, and solve the problem using simple arithmetic.
11 = 2a + 3
8 = 2a
4 = a

Your bottom line was to solve for a so you are finished!  Take a look at the answer choices.

(A) 4
(B) 7
(C) 11
(D) 17
(E)25

The correct answer is (A).


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

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

Sentence Structure

Link of the Day

The SAT question today is about fossils and bugs.  Old stuff is interesting – really!   Some of you might not enjoy history, so you might not have put much thought into the historical examples you chose for your SAT essay.  This is a mistake!  Find something that interests you, something that you enjoy thinking about, so that you will immediately be able to connect that historical person or event to an essay prompt.  Maybe you cannot memorize military battles or names of rulers.   Maybe you wish you could have squished the first flying bug.  That is fine.  Identify your passion.  If your passion is art, or if you are even remotely interested in looking at art, take a look at this article describing new discoveries about the beginning of artistic endeavors.  Then do your own research.  When did your passion first become important to humanity?

8/30 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 this sentence carefully, using your knowledge of the Big 8 Grammar rules to decide whether there is an error in the underlined portion.  Remember that this kind of question might include no error or more than one error in the underlined portion.

New analyses of a fossil suggest winged insects having possibly emerged as early as 400 million years ago.

Is there a problem with this sentence?  Some sentences may just sound strange to you.  If you cannot immediately identify the error, try simplifying the sentence before looking at your answer choices.  In this sentence, you can remove a prepositional phrase (“of a fossil”) to see whether the subject and verb match.  “New analyses suggest,” correctly matches, so try simplifying the sentence even further.  You could end up with something like this:

New analyses suggest insects having possibly emerged a long time ago.

Without all the extra words it is easier to recognize the part of the sentence that is incorrect.  Idiomatically, the sentence should say that these analyses “suggest that” this fact is true.  The word “that” is necessary before the statement naming the precise suggestion.  Mark the error you found and read the sentence one more time.  Can you spot another error?  You would never say “insects having possibly emerged a long time ago” and expect others to understand this as a complete statement.  The verb tense is incorrect.  Instead, you would say “insects possibly emerged,” or “insects may have emerged.”  There can be more than one way to fix a sentence, but you are less likely to be distracted by wrong answer choices if you have identified all the problem areas.  Look down at your answer choices.

(A) suggest winged insects having possibly
(B) suggest that winged insects may have
(C) suggesting that winged insects, they may have
(D) that suggests winged insects as having possibly
(E) that suggest winged insects to have possibly

You know that (A) is incorrect.  (B) matches your prediction exactly. All the other answers only fix one of the errors in the sentence; they all include the word “that.” (C) adds an unnecessary pronoun that creates sentence structure problems.  (D) and (E) create sentence fragments that lack a main verb.


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

For more help with grammar 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. 

First, cover your answer choices.  You do not need to look at a lot of wrong words to know what belongs in the blank of any sentence completion question.  Read the sentence carefully, and make a prediction to fill the blank.  Then you can look at the answer choices to find out which answers can be eliminated and which answers match.  Make sure that you look at all of the answer choices so that you can be sure that you have the best answer.

Mr. Warmington considered himself a connoisseur of fine wines, claiming he could ------- variations in taste and quality among any range of vintages he was served.

Even if you do not know every single word in this sentence you can paraphrase it.  Mr. Warmington drinks fine wines, and he can do something to the taste and quality no matter which wine he is given.  This man sounds like an expert who has had many kids of wine.  To someone who never drinks, all wine may taste the same, but to someone familiar with wine, the subtle differences will be apparent.  He will be able to “recognize” the different tastes and different qualities of different wines.  Use the word “recognize” as your prediction.

(A) purvey
(B) discern
(C) efface
(D) mollify
(E) debate

(A) can be eliminated because someone who drinks wine does not produce the taste of the wine.  (B) matches perfectly. (C) and (D) are the opposite of your prediction. (E) does not match your prediction.  While anyone could debate the taste and quality of wine, you are specifically told that this man drinks fine wine.  There would be no need to mention this fact if the blank were to be filled with something that anyone could do.

Words used in this SC:
Connoisseur: a specialist, particularly in matters requiring taste
Purvey: to prepare for, to provide
Discern: to detect or perceive
Efface: to erase
Mollify: to soothe or reduce
Debate: to dispute or argue


On sat.collegeboard.org, 64% of the responses were correct.

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

Multiple Figures

Link of the Day

SAT geometry questions mention basic shapes such as squares and cubes or circles and spheres that are all around us in the natural world.  One sphere that people have always looked towards at night is the Moon.  Right now, people around the world are remembering the life of Neil Armstrong, the first man to set foot on the Moon.  Neil Armstrong is an excellent historical figure to mention in your SAT essay.  Review a few facts about the life of this famous man here.  See how Americans are responding to his death here.

8/28 Geometry: Multiple Figures

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

Geometry questions often require you to add labels to a diagram, so you must be especially careful to note exactly which information you are given when you read the question.  As always, make a note of the bottom line, assess your options for efficiently solving the problem, attack the problem, and loop back to make sure that you have answered the bottom line.  Writing what you know neatly will often help you see new ways to work with the shapes you are given.



In the figure above, O is the center of the circle and  is equilateral. If the sides of  are of length 6, what is the length of ?

Geometry problems can be difficult if you are not sure how to attack the problem.  Think of these kinds of problems as puzzles; use the pieces of information and the rules that come to your mind.  There are multiple ways of arriving at the correct answer, but this is one of the fastest ways to get there.

The first information that you are given is about an equilateral triangle (Triangle ABO).  Identify the equilateral triangle and label all of the interior angles 60̊°.  All equilateral triangles only have angles of 60°.  You are also given the information that the sides of this triangle have a length of 6.  Label all the sides of this triangle as well.

Now look at the information a little differently.  The two triangles inscribed on the circle form a single larger triangle.  You labeled the length of one side as 6 (Side AB).  Look at Side AC.  Line AO forms the radius of the circle, as does Line OC, so both must be the same length.  Your total length of Side AC must be 12.

Here is a rule you should memorize: any triangle that has the diameter of a circle as one of its sides will be a right triangle.  The diameter forms the hypotenuse, so the opposite angle (in this case Angle B) must be 90°.  Once you know two sides of any right triangle, you can find the third.  Before you pull out the Pythagorean Theorem, notice that Triangle ABC is a special triangle.  Angle A is 60° and Angle B is 90°, so Angle C must be 30°.  For any 30-60-90 triangle, the corresponding sides will be x, x√3, and 2x.  In this case, your x = 6 and your 2x = 12, so what is the missing side?  Label the missing side 6√3 and look up at the question to see whether you have found your bottom line.  Then match your answer to the answer choices.

(A) 3√3
(B) 4√3
(C) 6√3
(D) 9
(E) 12

The correct answer is (C).

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

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

Parallelism

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. 

Your best method of attacking identifying sentence error questions is to read the original sentence to yourself, listening for anything that sounds odd.  If you do not immediately spot an error, check each underlined portion of the sentence against the Big 8 Grammar Rules.  Always remember that there might not be an error in the sentence.

AWhen people gave up the hunter-gatherer way of life and began to cultivate the soil and grow their food, they often Bbecame less mobile, built more substantial residences, and Cthey developed Dmore effective means of storage. ENo error

(A) underlines the word “when.”  If this word is at the beginning of a clause, it creates a dependent clause.  Your sentence structure rules inform you that a dependent clause must be supported by an independent clause.  If you take out the dependent clause (When…food), the rest of the sentence is able to stand alone.  There is no error.  (B) includes the word “became.”  The first thing that you should do when you see a verb is to check that it matches the subject as well as the tense of any previous verbs.  The phrase “people became” is fine, and the word “became” is consistent with the verb “gave up.” The word “less” is also the correct modifier for the word “mobile” because only two things are being compared (hunter-gathers and farmers).  (C) begins the last part of a list of three things.  Any list that you are given must be in parallel format, so check this rule first by examining the format of each listed thing.  The list says that the people “became..,” “built…” and “they…”  (verb, verb, pronoun).  This portion of the list is not in parallel format because it includes an unnecessary pronoun.  Delete the word “they,” and this portion of the list will also begin with a verb (developed).  Mark this error and quickly check (D).  (D) is correct because “more” is used to compare two things (hunter-gathers and farmers) rather than the word “most.” The word “means” is fine because it can be defined as a method (a means to an end), even though this word has many meanings.  (E) cannot be correct because you already identified an error.

The correct answer is (C).


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

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

Sentence Completions

Link of the Day

Today’s SAT question concerns polarizing issues.  Stem cell research has been the subject of polarizing debate in America for some time.  Take a look at this article and think about how the recent research of Johns Hopkins scientists might be able to change this debate.  Current events that are controversial make good examples for SAT essays – as long as you can stick to the facts and refrain from making broad pronouncements about which side is right and which side is wrong.

8/26 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. 

This sentence has two blanks, so focus on the easy blank first.  Just like single-blank questions, your method is to cover the answer choices, read the sentence carefully, and predict an answer to the blank you have selected.  Next, eliminate any answer choices that do not match your prediction.  When you go back to look at the other blank and predict that answer, you will not have to match your prediction for any of the answer choices that you already eliminated.

The meeting lasted more than five hours as participants ------- the presentation of the speaker, gradually polarized into factions, and, by the end, were further from ------- than at the start.

When your sentence has two blanks, it is especially important to paraphrase what you know about the sentence.  For this sentence, you know that there was a meeting that lasted a long time.  The participants broke up into factions.  At the end they were far from the start.

That is actually enough information to solve for both of the blanks.  The key information is hidden in the middle of the sentence; it is the part about the participants gradually polarizing into factions.  Look at the first blank that has to do with the presentation of the speaker.  Were the people listening to the speaker?  Can people break up into factions if they are sitting silent and passive?  No!  Perhaps the attendees at the meeting talked through the presentation or offered up their own arguments.  They most likely “hindered” the presentation of the speaker as they broke up into factions.  Look down at the options for your first blank:

(A) aided . . harmony
(B) interrupted . . a consensus
(C) denounced . . a scandal
(D) ended . . an argument
(E) encouraged . . disagreement

(A)  can be eliminated because factions fight, they do not aid the speaker.  This is the opposite of your prediction.  (B) is a perfect match. (C) and (D) are not perfect matches, but if you do not feel comfortable eliminating them yet, you can keep them as options as you look at the second blank in the original sentence. (E) is also the opposite of your prediction.

Look back at the second blank.  If the participants are in factions, they do not agree on anything.  People who do not agree need a solution that everyone involved can live with, so you might predict the word “agreement” or the word “compromise” for this blank.  Look down at the answer choices that you have not already eliminated.

(B) interrupted . . a consensus
(C) denounced . . a scandal
(D) ended . . an argument

(B) again matches perfectly.  (C) can be eliminated because we have no idea if anything scandalous was involved in the disagreement.  (D) can be eliminated because at the beginning no one was arguing.  The participants gradually started arguing, but that means that they could not be further from arguing at the end.

The correct answer is (B).

Words used in this SC:
Polarize: to divide into extremes
Factions: groups within a larger group that believe different things
Consensus: agreement among group members
Denounce: to criticize publicly


On sat.collegeboard.org, 75% of the responses were correct.

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

Logic

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

The Knowsys math method calls for you to read each question carefully, but you should be especially conscious of the possibility of misreading when your question involves a graph.  Be sure that you understand each label on the graph and take the time to read any additional information given in the question.  Identify the bottom line and asses your options for solving the problem in an efficient manner.  Select your method, attack the problem, and loop back to make sure that the answer you found fits the bottom line, that it answers the question that you were asked.

 

The bar graph above shows the number of people in attendance at each of the four meetings of the Maple Street Block Association that were held in 2011. Only members of the Block Association can attend the meetings, and no members joined or left the Block Association during 2011. Based on the bar graph, what is the least number of members the Maple Street Block Association could have had in 2011?

 Your bottom line is the least number of members belonging to the association.  You must use logic to determine which information in this graph is relevant.  The question is meant to mislead you, because as soon as you see the word “least,” you are likely to look for the smallest value on this bar graph.  Before you jump to any conclusions, think about what the bar graph represents.  At any of these four meetings, all of the members could have shown up, or only some of the members.  In other words, it is possible for people to be absent, but it is not possible for people to be at these meetings without being members.  All of the people present at any meeting must be members.  The greatest number of people who came to any meeting is 72.  Therefore, there cannot be fewer than 72 members in this club.  Look down at your answer choices.

(A) 61
(B) 65
(C) 67
(D) 72
(E) 268

The correct answer is (D).


On sat.collegeboard.org, 43% of the responses were correct.

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

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.  

As you read the sentence, listen for errors.  Evaluate the underlined portion using the Big 8 Grammar Rules.  Once you look down at the answer choices, focus on the first error to eliminate wrong answer choices quickly.

In Costa Rica, coffee, from the highlands, and bananas, produced mainly in the Caribbean lowlands, as the most important crops, they account for nearly half the total value of all exports.

This sentence may be hard to follow because it has a lot of commas, but identify the simple subject.  This sentence is about coffee and bananas.  Once you have the simple subject, look for the verb that matches that subject.  You will not find one.  There are verbs in this sentence, but they are in the wrong format to match the subject.  The verb “account” matches the pronoun “they” instead of matching “coffee and bananas.”  In order to fix this, you must add a plural verb as close to your subject as possible.  The sentence describes what coffee and bananas are (important crops), so change the word “as” to “are.”

You have improved the sentence now, but always remember that there might be more than one error in improving sentence questions.   Read the whole sentence with your change and you will see that you still have a problem with sentence structure.  You have two complete sentences with separate subjects and verbs that are only separated by a comma: a comma splice.  An easy way to fix this would be to make the second independent clause dependant.  All you would have to do is eliminate the unnecessary pronoun “they” and change the word “account” to “accounting.”

(A) as the most important crops, they account
(B) as the most important crops, which account
(C) are the most important crops, accounting
(D) are the most important of their crops by accounting
(E) have been the most important crops, which accounts

Even if you did not immediately spot the changes that should be made to this sentence, you can be strategic in how you eliminate answer choices.  You do not need to read choice (A) because you know it contains the original phrasing.  Furthermore, both choice (A) and (B) begin with “as.”  Instead of getting distracted or confused by the rest of their words that follow “as,” eliminate these choices right away.  You know that they will not fix the first problem that you found in the original sentence: the missing verb.  Look at (C). Remember that the Knowsys method tells you to lean towards answers that are concise.  This is the shortest answer, so check quickly to see whether it makes sense when you place it in the blank.  It does!  Quickly look at (D).  Coffee and bananas did not become important “by” accounting for a lot of the exports, so the logic in this choice is skewed.  (E) adds a lot of words and the word “which” does not make sense in context.

The correct answer is (C).


On sat.collegeboard.org, 71% of the responses were correct.

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

Sentence Completions

Link of the Day

Today’s SAT question references facts.  Facts are the details that are going to make your SAT essay stand out among a number of essays with unsupported opinions.  When used correctly, numbers and statistics are a wonderful tool that will make you sound informed.  You can quickly memorize a couple of numbers, which will hardly take a moment to write down, and impress your graders.  Which sounds more compelling:

(1) Americans should stop wasting so much food because other people do not have food.
(2) Americans currently throw away $165 billion dollars worth of food each day, a squandering of money and resources that is reprehensible in a world with starving children.

Read this article about the amount of food that Americans waste and realize that without concrete facts and numbers this article would have nothing to say.  This issue would make an excellent current event because it includes society, businesses and individuals, the environment and profit, and specific numbers.

8/23 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 the answer choices before reading the sentence so that you will not be distracted by wrong answer choices.  Read the sentence carefully and predict an answer.  Then match your prediction to the correct answer choice, making sure to look at all of the choices.  This process should be quick, not more than 40 seconds for most questions, and probably less for this particular question.

A judgment made before all the facts are known must be called -------.

This is a straightforward vocabulary-based question; the definition of the blank is “a judgment made before all the facts are known.”  Your keyword is “before.”  If someone makes a judgment before all the facts are known, it has been made too soon.  You might predict a word like “presumptuous” or “untimely.”  Look down at your answer choices to see which word matches your prediction.

(A) harsh
(B) deliberate
(C) sensible
(D) premature
(E) fair

(A) has nothing to do with the timing of the judgment, and you cannot know whether the decision was too harsh or too lenient.  Perhaps the facts that were unknown would have called for an even stricter punishment for a crime.  (B) is the opposite of your prediction.  (C) and (E) cannot be correct because a judgment made without considering the relevant facts will be neither sensible nor fair.  (D) is the only choice left.  Remember that your keyword in the original sentence was “before.”  The Latin prefix pre- actually means “before,” so the word “premature” means “before maturity” or simply, “too soon.”

Words used in this SC:
Harsh: rough, severe, or cruel
Deliberate: intentional, careful, having weighed facts and arguments
Premature: earlier than anticipated, before readiness or maturity


On sat.collegeboard.org, 85% of the responses were correct.

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

Number Properties

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

Read the question carefully so that you are sure you understand what you are being asked.  You must identify the bottom line that you will solve for; note it at the top of your scratch work.  Assess your options to find the most efficient way to solve the problem, and then attack the problem.  Be sure to write out your scratch work clearly so that you do not make careless mistakes.  Your last step is to loop back to make sure that your answer matches the bottom line.  You cannot get a question right if you solved for an answer that you were not asked to find.

For how many positive two-digit integers is the ones digit greater than twice the tens digit?

You must find out how many numbers fit the given requirements.  There is no formula to find numbers in which one digit is more than twice the other, so you must think about this question logically.  Your only option is to methodically check positive integers to see which numbers will work.

You know that you need a positive two digit integer, so your first digit, at the very least, must be a 1.  Your second digit must be more than twice the first.  The number 1 multiplied by 2 is 2, so the number 12 will not fit the requirement of having a ones digit greater than twice the tens digit.   However, any number that begins with a 1 and has a second digit larger than 2 will work.  List all the numbers that begin with 1 and fit the requirements of this problem:

13, 14, 15, 16, 17, 18, 19

After 19, you must start each number with a 2, so find out what the second digit must be.  Again, it must be bigger than twice the first digit, so it must be larger than 4.  24 will not work, so start with 25 and list all of the numbers that fit the requirements of this problem:

 25, 26, 27, 28, 29

Follow this procedure for numbers beginning with 3. 3 times 2 is 6, so only numbers larger than 36 will work.

37, 38, 39

Move on to numbers that start with a 4.  4 times 2 is 8, so the second digit must be greater than 8.  This time there is only one number that fits the requirements:

49

Now you have reached numbers beginning with the digit of 5.  5 times 2 is 10.  You cannot have a value as your second digit that is more 10, so any number larger than 49 will not work.

Count up all of the numbers that you have found that fit the requirements of this problem.  That number will satisfy your bottom line.

(A) 16
(B) 20
(C) 28
(D) 32
(E) 36

The correct answer is (A).


On sat.collegeboard.org, 40% of the responses were correct.

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

Sentence Structure

Link of the Day

Hawaii has become one of the most popular vacation destinations in the United States, but do you know how this cluster of islands became a state?  President Eisenhower signed a proclamation welcoming Hawaii as the 50th state on August 21, 1959.  This action was not without controversy and intrigue.  Do you know the role that sugar played in the story?  What about the conflicting desires of Queen Liliuokalani and Prince Kuhio of Hawaii?  The difficulties that Hawaii faced on its road to statehood would make a great historical example for your SAT essay.  Read some of the facts here and look at some relevant documents here, but also search for some of the current opinions about this historical event.

8/21 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. 

As you read the original sentence to yourself, listen for errors.  Check the underlined portions of the sentence against the Big 8 Grammar Rules.  If you see an error, mark it, but be sure to quickly check the other choices.

The Sun has been shining for Anearly five billion years and is thought Bthat it has sufficient thermonuclear fuel in its core Cto shine Dfor about another five billion. ENo error

Look first at (A).  The word “nearly” modifies the “five billion years.” It is as close as possible to the words it modifies and it takes the –ly ending that most adverbs take, so there is no error in this underlined portion.  (B) should sound awkward to you.  Take out the words that are underlined and read the sentence.  “The Sun is thought __________ sufficient fuel.” You would not immediately place the word “it” in this blank because you already know that the subject is the Sun.  The word “it” is an unnecessary pronoun.  The correct phrasing is “to have.” Mark this error, but quickly check the other blanks. (C) is idiomatically correct because it uses the word “to;” you have enough fuel to do something.  (D) is idiomatically correct as well because you do something “for” a certain amount of time.   (E) cannot be correct because you already marked an error.

The correct answer is (B).


On sat.collegeboard.org, 59% of the responses were correct.

For more help 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 answer choices so that they will not prejudice your mind as you read the sentence carefully.  The Knowsys method requires you to predict an answer to fill in the blank, before matching that prediction to the correct answer choice.  Remember that you should always look at all the answer choices before moving on to the next question.

Professor Chen believes that the universal character of art refutes the prevailing notion that art is a ------- of civilization, a cultural frill, a social veneer.

This sentence uses difficult language, but you can make it less intimidating by putting it into your own words.  You might think, “This guy believes that because art is worldwide, it can’t be like everyone thinks, a blank, a cultural frill, a social veneer.”  Even if you do not understand every word in the first part of the sentence, you can now see that the important part of the sentence is the last two things listed.  “A cultural frill” and “a social veneer” must explain the phrase with the blank, they must have similar meanings.  Frills and veneers are things that are unnecessary, but a lot of people like them because they look fancy.  This will work as a general prediction, but try to think of a specific word with these meanings.  You might predict the word “indulgence,” or even “extravagance.”  Once your prediction is as specific as you can make it, look down at the answer choices.

(A) guarantee
(B) hallmark
(C) record
(D) luxury
(E) depiction

You might not be sure what all of these words mean, but in most cases you should go with what you know.  There is only one answer that matches your prediction.  Take a moment to note just how important it is to have a prediction before looking at these words.  Art could be considered a “guarantee of culture,” a “hallmark of culture,” or any of the other answer choices.  You will only be able to identify the correct answer when you have considered the sentence as a whole and have used the context clues to predict what belongs in the blank.

The correct answer is (D).

Words tested in this SC:

Refutes: proves something to be incorrect
Prevailing: current or common, predominant
Veneer: decorative covering
Hallmark: distinguishing characteristic
Luxury: something desirable but expensive
Depiction: an image of something


On sat.collegeboard.org, 43% of the responses were correct.

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

Writing Equations

Link of the Day

Today’s SAT question talks about apples, but many people are talking about a different kind of apple right now.  Your cell phone, sitting innocuously in your pocket, could be your link to an interesting current event example for your next essay.  The companies Apple and Samsung are currently arguing about patent infringement.  Think about the themes of technology, development, creativity, and competition.  What do you think about this case?  Are you curious about which company will win?

8/19 Writing Equations

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

Always take the time to read math questions carefully so that you will not make careless mistakes.  Identify the bottom line, which is the question you must answer, and assess your options for reaching the bottom line.  Choose the most efficient method to solve the problem and then attack it.  Do not forget to loop back and make sure that you solved for the bottom line, especially when you get a problem that requires multiple steps.

The price of 10 pounds of apples is d dollars. If the apples weigh an average of 1 pound for every 6 apples, which of the following is the average price, in cents, of a dozen such apples?

The bottom line that you are looking for is the cost of 12 apples in cents.  You can make a note of this by writing 12app = ¢?  Now ask yourself what you could do, and what you should do.  You could choose a number for the variable d and plug it into all of the answer choices, but then you would have to work several problems to find matching answers.  Instead, try working with the information you have, setting up the information in simple equations.

Your bottom line asks for the cost of 12 apples, but you were given information about 6 apples.  6 apples weigh 1 lb.  It is easy to change 6 to 12 by doubling it.

6 apples = 1 lb
12 apples = 2 lb

Now you have the dozen apples, so you must determine how many cents they cost.  You know that 10 lbs = d dollars.  Start by changing the dollars into cents, because you know you must end with cents.  To change dollars into cents, you must multiply the dollars by 100.

10 lb = d (solving for dollars)
10 lb = 100d (solving for cents)

Now you have the correct monetary unit, but you also still have an equation that solves for 10 lbs.  Your dozen apples is only 2 lbs.  To get from 10 to 2, divide both sides of your equation by 5.

10 lb = 100d
2 lb = 20d

Now put all the information that you have together to make sure that you solved for the bottom line:

12 apples = 2 lb = 20d

Look at your answer choices.

(A) 

(B) 

(C) 

(D) 

(E) 

The correct answer is (A).


On sat.collegeboard.org, 36% of responses were correct.

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

Idioms

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.  

As you read the following sentence to yourself, listen for errors.  Evaluate the underlined portion of the sentence using the Big 8 Grammar Rules.  Focus on the first error that you find to eliminate wrong answer choices, but do not forget that there may be more than one error in these types of questions.

Digital technology, like every marketer knows, it is synonymous with speed, precision, and the future.

One of the first things that you should notice when reading this sentence is that the underlined portion includes the word “like.”  The Knowsys material covers the word “like” because it is overused.  The word “like” should only be followed by nouns and pronouns, but in this sentence the word “like” is followed by the verb “knows.”  Instead of the word “like,” this sentence requires the word “as,” which can be followed by nouns and verbs together.  Make a note of that error.  You can now look down at your answer choices and begin eliminating incorrect choices.  However, there may be answer choices that do not use the words “like” or “as,” and there may be multiple answer choices that use the word “as.”  You have not yet finished examining the sentence just because you found one error.  When you read the sentence the first time, did any other part of the underlined portion sound strange to you?  Is the word “it” necessary?  Ignore the extra information between the two commas and the sentence reads “Digital technology it is synonymous with speed, precision, and the future.”  Make a note that the word “it” is an unnecessary pronoun that must be eliminated, and look down at your answer choices.

(A) technology, like every marketer knows, it is
(B) technology, similar to what every marketer knows as
(C) technology, as every marketer knows, is
(D) technology is what every marketer knows as
(E) technology that every marketer knows is

You know (A) is incorrect without reading it because you already identified errors in the sentence.  (B) sounds awkward and changes the sentence so that it is missing a verb.  “Digital technology” is the simple subject, but there is no simple verb to follow it.  (C) matches the changes you made perfectly.  You could probably have guessed this answer after only finding one error in the sentence, but accuracy is also important  to maximize your score.  (D) sounds awkward because of the word choices.  The word “as” is especially odd within the context of the sentence.  (E) subtly changes the meaning of the sentence because the subject is no longer all “digital technology,” but instead must be read as only the “digital technology that every marketer knows.”

The correct answer is (C).


On sat.collegeboard.org, 80% of responses were correct.

Want more help with the writing section?  Visit 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. 

Sentence completion questions will test your logic and vocabulary.  The best way to make sure that you are not prejudiced in how you think about the question is to avoid looking at the answer choices.  Most of them are wrong, so do not look at a single answer choice until you have read the sentence carefully and made a prediction to fill the blank.  When there are two blanks, focus on the easy blank first and eliminate any answer choices that do match your prediction.  Then move on to the second blank.

Dahntay’s ------- over winning the prestigious prize was ------- only by the fact that his father was unable to attend the ceremony.

When you have two blanks, it is best to focus on what you know.  You know that Dahntay won a prize, but his father was unable to attend the ceremony in which the prize was awarded.  Start with the first blank because it will help you with the second.  When someone wins a prize, what kind of reaction does that person have?  You probably thought of a word such as “happiness” or “joy.”  At the very least, you know that this blank must be positive.  Now that you have your prediction, look at your answer choices for the first blank.

(A) incredulity . . misconstrued
(B) ebullience . . tempered
(C) bashfulness . . extended
(D) satisfaction . . confirmed
(E) relief . . conveyed

The more specific your prediction, the more choices you can eliminate.  If you predicted “happiness,” you can eliminate (A) because it does not match.  Skip (B) if you are not sure what it means.  (C) does not match your prediction.  (D) matches.  (E) is positive, but relief is an emotion that occurs when a the threat of a negative occurrence is removed, not when something good happens, so it does not match “happiness.”  You have eliminated three answer choices and only two remain.

Look back at the second blank now.  Dahntay was happy about his prize, but then what happened to that happiness when he realized his father could not be at the ceremony?  “Lessened” or “reduced” would be good predictions for this blank.  Look at the second part of the answer choices that remain.

(B) ebullience…tempered
(D) satisfaction…confirmed

Skip (B) if you do not know what it means.  (D) is incorrect because you have two contrasting feelings.  Dahntay feels good that he won, but bad that his father cannot attend the ceremony.  It does not make sense to say that a positive feeling is “confirmed” only by something negative.  Even if you do not know the definition of the terms in choice (B), all of the other choices have been eliminated.  Normally you would want to pick what you know over what you do not know, but this case is an exception because you were able to confidently eliminate all of the other choices.

The correct answer is (B).

Words tested in this SC:

Prestigious: honored, important
Incredulity: unwillingness to believe, doubt
Ebullience: high spirits, exuberance
Bashfulness: shyness, easily embarrassed
Satisfaction:  contentment
Relief: emotion that comes with the removal of pain
Misconstrued: taken in the wrong sense, misinterpreted
Tempered: 1) having a temper of a certain character or 2) made less intense
Extended: stretched out, prolonged
Confirmed: made certain, settled
Conveyed: 1) communicated, 2) transported, 3) transmitted


On sat.collegeboard.org, 65% of the responses were correct.

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

Functions

Link of the Day

Many schools in the United States participate in campaigns to keep children from smoking.  However, there are countries that are taking even greater measures to make smoking unattractive.  Cigarette packaging in Australia will no longer display colorful logos, but instead will display images depicting the dangers of smoking.  As you read this article, think about whether or not you agree with these measures, and then think about the themes that might relate this current event to an SAT essay topic.

Also, if you are a senior who dreads the college application process, take a look at this checklist and remember to breathe in the next few months!

8/16 Functions

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

Read each math question carefully so that you can identify exactly what is being asked of you.  Once you have identified the bottom line, assess your options to find an efficient way to solve the problem.  Finally, attack the problem, solve it, and loop back to make sure that your answer addresses the bottom line that you were asked to find.

 
Which of the following could be the equation of the function graphed in the xy-plane above?

You have been given a graph, and you must find the equation that has been graphed.  You could plug all of the answer choices into your calculator, but that would take a long time and you risk making a typo.  Instead, break the graph down into its most basic components.  What shape that you have often seen does this graph most resemble?  It looks like a parabola opening upwards, so you know that f(x) = x² will be part of your equation.

Picture the f(x) = x² parabola in your mind.  It passes through the origin at (0,0).  However, the graph in this problem would extend past the point (0,0) into the negative numbers if you continued the basic curve of the parabola.  To translate the function down on the graph, you would need to subtract a number from the original function.  Now you have f(x) = x² - n, where n = any number.

There is one more step.  The basic curve of the normal parabola has been reflected across the x-axis in this problem so that all the values of the parabola are now positive.  What can you do to make sure that all of the numbers in a function are positive?  Take the absolute value of the function.  Now you have f(x) = |x² - n|.  Look down at your answer choices.

(A) y =  (-x)² + 1
(B) y = -x² + 1
(C) y = |x² + 1|
(D) y = |x² - 1|
(E) y = |(x – 1)²|

(A), (B), and (C) cannot be the answers because they all add to the equation and would result in a parabola that has been shifted above the x-axis.  (E) will not be symmetric to the y-axis, and the graph that you have remains symmetric to the y-axis; it has not been shifted to the right or the left. The (x – 1)² part of the equation in (E) shifts the entire parabola away from its original position on the y-axis.  (D) is the only answer that matches the equation you wrote for this graph.

The correct answer is (D).


On sat.collegeboard.org, 39% of the answers were correct.

For more help, visit www.myknowsys.com!

Subject Verb Agreement

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 sentence to yourself, listening for errors.  The best way to identify errors is to check each underlined portion against the Big 8 Grammar Rules.  Identify and mark the error that you find in the sentence, and then quickly check the other choices.

Audio recordings, and the equipment (A) used to make and play them, (B) comes in (C) many forms, (D) including records, CDs, and analog and digital tape recorders. (E) No error

(A) contains more than one word, so you need to think about the role each word plays in the sentence.  “Used” is correct because it follows “equipment,” which can be used.  It is also idiomatically correct to use a “to” and a verb after “used.”  (B) underlines  a verb separated from the subject.  Look back to find the simple subject of the sentence and you will find that it is plural.   You cannot say “audio recordings comes” because the verb does not match the subject in number.  Instead you must say “audio recordings come.”  Mark this error, but quickly check the rest of the sentence. (C) includes the word “many,” so you should immediately think of the difference between “many” and “much.”  “Much” is used with things that you cannot count while “many” is used for thing that you can count.  You can count the different forms available (6 records or 23 CDs), so the word “many” is correct. (D) uses a word that ends in –ing, so you should check to make sure that the –ing is correct. No other form of the word “including” makes sense in this sentence.  (E) is wrong because you already identified one error.

The correct answer is (B).

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

For more help, visit www.myknowsys.com!

Sentence Completions

Link of the Day

August 14, 1945 marked the end of World War II, the deadliest conflict in human history.  Although Japan’s formal surrender to the Allied Nations would occur later in September, soldiers and civilians took to the street as soon as they heard the announcement of Japan’s surrender.  Do you recognize this iconic image from New York?  It was taken on the 14th, a day that has been termed V-J Day (Victory over Japan Day).  World War II is a vast topic, probably much too general for an essay example.  However, any of the events of World War II, including V-J Day, would make excellent examples.  Think of the joy that people felt as they realized that years of sacrifice had come to an end, but think also of the great cost of finishing the war.  Why did Japan finally surrender?  Learn the facts about V-J Day here.

8/14 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. 

Sentence completion questions are very quick, but you should still approach them using the Knowsys method to make sure that you answer accurately.  Cover the answers so that they do not distract you, and read the entire sentence carefully.  You will be tested on logic as well as vocabulary.  Predict an answer to fill the blank and then match your prediction to the correct answer choice.  Eliminate any answers that do match your prediction, but be sure to examine all of the answer choices even if you find an answer that matches before reaching the last choice.

Their conversation was unsettling, for the gravity of their topic contrasted so oddly with the ------- of their tone.

Paraphrase this sentence in your mind so that you are sure that you understand it: Their conversation was strange because the gravity of the topic did not match their tone.  The word “gravity” is not meant to be understood as a scientific term; the word has another meaning.  Think of a grave topic as similar to a weighty issue.  These are serious matters.  Looking back at the context of the sentence, you need a word that contrasts with gravity – something that means the opposite of serious.  If you are not taking something seriously and treating it with importance, you are taking it lightly.  "Levity" or "lightheartedness" would fit in the blank.  Look down at the answer choices now.

(A) uniqueness
(B) rapidity
(C) lightness
(D) precision
(E) reverence

As you read the answer choices, be sure to stick to your prediction because your first thought is usually correct.  (A) is distracting because things that are odd are often unique, but it does not match your prediction.  (B) may seem like a good answer because it can be unsettling to hear rapid speech, but rapidity has nothing to do with importance.  (C) matches your prediction. “Lightness” is like the word “gravity” in that it has more than one meaning.  This word is not meant to imply the opposite of darkness, instead it takes the meaning of frivolity or silliness.  (D) looks like a good choice if you missed the word “contrasted,” because things that are taken seriously are often spoken of with precision, but it does not match your prediction. (E) is the opposite of what you predicted because if you treat something with reverence it is important to you.

The correct answer is (C).

Words tested in this SC:
Gravity: seriousness
Uniqueness: the quality of being one-of-a-kind
Rapidity: quickness
Lightness: frivolity or silliness
Precision: exactness
Reverence: showing awe and respect


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

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

Solids

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

The Knowsys method requires you to read each math question carefully and identify the bottom line.  You must also assess your options to find the best way to attack the problem, solve it, and loop back to make sure that you solved for the bottom line.

A right circular cylinder has height 6 and volume 54π. What is the circumference of its base?

Make a note of the fact that you are solving for the circumference of the base by writing C  = ? under the problem.  You should know that C = 2πr, and based on that you should realize that this problem will require more than one step.  You cannot solve for the circumference of the base without knowing the radius of the base circle.  You do know the volume of the cylinder, so you can use that information to find out more about the base circle.  You should have the formula for the volume of a cylinder memorized: Volume = πr²h. Plug in the values you already know to solve for the radius.

V = πr²h
54π = πr²6   (divide each side by 6π)
9 = r²    (take the square root of both sides)
3 = r

You now have the information that you need for the circumference formula.  Be careful not to look down at your answers yet, because even though you solved part of the problem, you have not yet found the bottom line.

C = 2πr
C = 2π3
C = 6π

Now that you have an answer, match your answer to the answer choices.

(A) 2π
(B) 3π
(C) 6π
(D) 9π
(E) 18π

The correct answer is (C).


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

For more help, visit www.myknowsys.com!

Sentence Structure

Link of the Day

This SAT question mentions the writer Toni Morrison.  Toni Morrison is an African American novelist whose novels have received numerous awards.  She would make an excellent historical figure to write about in your SAT essay, and any of her works of literature would also make excellent examples.  Take a moment to read about Toni Morrison’s life here or here.  You just might be inspired to pick up one of her celebrated novels.

8/12 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 and evaluate the underlined portion by checking it against the Big 8 Grammar Rules. Your goal is to create clear and precise sentences.

With the 1977 publication of Song of Solomon, Toni Morrison both received popular and critical acclaim.

Did the original sentence sound odd to you?  Your first task is to identify the problem.  This sentence is hard to understand because the word “both” is misplaced.  The formula for linking two things by conjunctions is “Both X and Y.”  With the word “both” before the verb “received,” it sounds as if there are two people receiving things rather than two kinds of things being received.  You know that the person who wrote this sentence wants to emphasize the idea that there are two kinds of acclaim, but that the sentence is not as clear as it could be.  Look down at the answer choices.

(A) both received popular and
(B) both received popular and also
(C) received popular, along with
(D) received popular as well as
(E) received both popular and also

(A) and (B) can be eliminated right away because they maintain the incorrect structure of the original sentence with the word “both” before the word “received.”  (C) adds an unnecessary comma that complicates the sentence rather than making it more clear.  (D) correctly uses the idiomatic phrase “as well as,” which maintains the emphasis on two different types of acclaim while making the meaning of the sentence clearer.  Remember to check (E) even if (D) seems like a good answer.  (E) may look correct at first glance because the word “both” is moved to a position after the word “received.”  However, this choice adds to the word “both” an “also.”  The function of both of these words is to draw attention to the fact that there are two different types of acclaim, so choosing either “both” or  “also”  would be more concise.  Remember that you want to avoid redundancy.

The correct answer is (D).

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

For more help, 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. 

When you look at a sentence completion question, the first thing you should do is cover the answers. The test makers come up with four wrong answers just to distract you from the right one, so ignore them all. Instead, focus on the question itself. Read the sentence and look for clues about the correct answer, make a prediction, and then compare your prediction to the answer choices. Eliminate any answers that do not match and, hopefully, you'll be left with only the correct answer.

Always ready to ------ achievement, Miller was as eager to praise a new production as the more mean-spirited critics were to ------ it.

First, decide which blank you want to predict. The first blank in this sentence is rather vague; there are lots of things one could do with "achievement" that would not be "mean-spirited." The second blank, however, clearly refers to something that mean-spirited critics do to new productions. "Criticize," "denounce," or "castigate" are all good predictions for this blank. Look at the answer choices to see which options do not match, eliminate those, and then go back to evaluate the first blank.

Number Properties

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

In the SAT math section, you must read every problem carefully and identify the bottom line.  Assess your options before solving the problem so that you are able to choose the most efficient method of solving the problem.  Then attack the problem to find your answer, and loop back to make sure that your answer addresses the bottom line.

The sum, product, and average (arithmetic mean) of three integers are equal. If two of the integers are 0 and -5, the third integer is…

This problem asks you to find one unknown integer.  You could try to write equations or plug in the answer choices to solve this problem.  However, these methods will take you longer than thinking logically about the properties of the numbers involved.

You know that the sum, product, and average of three integers must be equal.  One of the numbers that you are given is a zero.  Zero multiplied by any other number will always be zero, so the product must be zero.  That means that the sum and the average of these three numbers must also be zero. What do you have to add to 0 and -5 in order to get zero? The only possible answer is a positive 5.  Additionally, if you add 0, -5, and 5 together and then average them, your sum already equals zero, so zero divided by 3 will still be zero.  The product, sum, and average are all 0 when the missing third integer is 5.

0 + -5 + x = 0
x = 5

(0 + -5 + x) / 3 = 0
x = 5

Before looking at the answer choices, check to make sure that your answer fits the bottom line that you were asked to find.

(A) -5
(B) 0
(C) 2
(D) 5
(E) 10

The correct answer is (D).


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

For more help, visit www.myknowsys.com!

Sentence Structure

Link of the Day

The 2012 Olympic Games have proven to be historic in more than one regard. One landmark is the fact that these Games are the first in which every country has sent both male and female athletes. Most notable is the nation of Saudi Arabia, which was nearly barred from sending male competitors if it did not also send female athletes and finally agreed only two weeks before the start of the Olympics. Because participation in sports (among many other things) is severely restricted for Saudi women, the two athletes who were accepted into the Olympics did not actually have high enough scores to qualify--not that it mattered, as screaming crowds cheered them on. Instead, the International Olympic Committee admitted them under the Olympics' universality clause, which "allows athletes who didn't meet qualifying times to compete when their participation is deemed important for reasons of equality." This clause has been used in the past to promote participation from underrepresented nations. Read more here and here.

8/9 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.

The Knowsys method for identifying sentence errors requires you to read the original sentence to yourself, listening for errors.  Quickly check each underlined portion of the sentence against The Big 8 Grammar Rules.  Identify and mark any error, being sure to check all of the underlined portions of the sentence for errors before moving on to the next question.

AOne of the northernmost countries Bof Europe, CFinland's borders are Russia on the east, Sweden on the west, Dand the tip of Norway on the north. ENo error

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.

Sentence completion questions provide you with answer choices, but four out of the five they give you are incorrect.  Do not look at the answer choices until you have read the entire sentence carefully and predicted a word to fill the blank.  Using this method, you will match your prediction to one of the answer choices and eliminate all of the answers that do not match.  Make sure that you check your prediction against all of the answer choices.

The senator chose to incur dislike rather than ------- her principles to win favor with the public.

This sentence uses the word “incur,” but you need not be intimidated by this word.  Paraphrase the sentence: “The senator chose dislike instead of doing something to her principles to win favor with the public.  When people want others to like them, they often feel pressured to give up their principles.  Use “give up,” “relinquish,” “abandon,” or any words meaning the same thing as your prediction.

(A) gratify

(B) endorse

(C) accuse

(D) compromise

(E) advertise

(A), (B) and (E) are all positive words that describe what the senator would like to do in relation to her principles, but they do not fit in the original sentence because “rather than” tells you that she will not be doing the thing that fits in the blank.  (C) does not make sense because “accusing her principles” will not win the senator favor.  The only word that matches your prediction is (D) “compromise.”  When you compromise, you must give up some of your desires to satisfy the desires of others.

The correct answer is (D).

Words tested in this SC:

Incur: to bring upon oneself

Gratify: to please

Endorse: to support

Accuse: to blame

Compromise: to settle differences or to make a shameful concession

Advertise: to announce publicly

Percents

Link of the Day

College loans may seem like the only way to get through your education, but they can be risky. Ben Bernanke, chairman of the Federal Reserve, warns that over-investing in college loans can lead to economic ruin. Instead of loans that you will have to pay back, look for scholarships, grants, and federal aid money that other agencies are willing to pay because they see it as an investment in their future. Scholarships and awards are given out for a dizzying variety of reasons, so make your search thorough! Do you have good grades? Do you have a hobby or sport that you're good at? Is there a cause you've volunteered for? Do you or does someone in your family have a rare disease? Some scholarships are restricted to members of certain racial or ethnic minorities; others are based on religious affiliation. Check if your parents' employers have any kind of scholarship fund. Sites like fastweb.com, educationconnection.com, and findtherightscholarship.com can help in your scholarship search. 

8/7 Percents

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

When you work a percent problem, it is especially important to read the problem carefully because small words like “of” make all the difference in describing a percentage.  Once you have understood the question and identified the bottom line, assess your options and choose a method to attack the problem.  After you have finished the problem, loop back to verify that the answer addresses the bottom line.

The population of Norson, the largest city in Transitania, is 50 percent of the rest of the population of Transitania. The population of Norson is what percent of the entire population of Transitania?

Your bottom line is a percentage: the number of people in Norson as a percent of the entire population of the country of Transitania.  At the top of your scratch work, write N = ?%  Next, assess your options.  You don’t know how many people are in the country of Transitania, so solving the problem algebraically would be challenging. Instead, pick a number so that the problem will be more concrete.  When picking numbers on a percent problem, you should always pick 100 because 100 is the easiest number to use; the answer you find is already out of 100 so you will never need an extra step to find the correct percentage. Now you're ready to attack the problem. 

If you assume that there are 100 people total in all of Transitania, you still do not know how many people are in the city of Norson.  Use the variable “N” to represent the people in the city.  The problem tells you that the population of this city “is 50% of the rest of the population of Transitania.”  You know that Norson has half as many people as the rest of the population.  Think about it this way: for every person in Norson, there must be 2 people outside of the city.  Write an equation representing this knowledge and solve it.

Idioms

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. 

You must read the following sentence and evaluate the underlined portion using the Big 8 Grammar Rules.  Remember that re-reading choice A is a waste of time because it is the same as the original sentence.  Make sure that the sentence is as clear and precise as possible.

Like machinery was integral to the development of industrial capitalism, so the rapid transfer of information is the force driving modern business. 

Sentence Completions

Link of the Day

We once thought that sending a man to the moon was impossible. Well, NASA has done the impossible again. The Curiosity space rover, a mobile lab the size of a small car and weighing around a ton, landed safely on the surface of Mars last night after a completely autonomous seven-minute landing sequence. Because of the size and weight of the rover, NASA had to invent an entirely new process to get Curiosity to the planet's surface. The sequence involved an "automated flight-entry system," a supersonic parachute, and a giant jetpack NASA calls a "sky crane." Most impressive of all, the entire landing was accomplished without the help or input of any humans. There is a 14-minute communications delay between Earth and Mars, so it would be impossible to respond to any problems in time, and on top of that the Earth disappeared below the Martian horizon two minutes before Curiosity touched down. Read more about the landing here and about the mission here. 

8/5 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.

Sentence completion questions test your vocabulary and your ability to think logically.  Never look at the vocabulary in the answer choices until you have read the entire sentence carefully and predicted an answer choice for a blank.  If there are two blanks, focus on the easy blank and eliminate any choices that do not match your prediction for that blank.  Then return to the other blank, make a prediction for that blank and eliminate any remaining choices that do not fit with your prediction.

It was difficult to believe that the sophisticated piece of technology had ------- through the centuries from such ------- and rudimentary apparatus.

It is easy to fill in the blanks for this sentence if you understand all of the vocabulary.  However, even if you are unsure of a definition (or several), you can still use the Knowsys method to come up with a prediction.  Look at the first blank.  Paraphrase the sentence using the terms you know: “I can’t believe that technology like this came from something like that.”  The key to predicting the first blank is to find out what happened to technology over time.  It clearly changed from one description to another, but try to make your prediction a little more specific.  “Sophisticated” is a positive word, so it is safe to assume that technology improved over time.  Use the word “improved” as your prediction and look down at the first part of your answer choices. 

(A) developed . . an intricate

(B) resulted . . a complicated

(C) evolved . . a quaint

(D) degenerated . . an obsolescent

(E) differed . . an exotic

(A) matches.  (B) is a little awkward, but you can keep it in mind. (C) matches – “evolved” and “developed” can be synonyms. (D) can be eliminated because “degeneration” is a negative word; technology did not get worse over time.  (E) can be eliminated because “differed” is a neutral word for change and you are looking for a positive one.  Three answer choices remain, so look at the second blank. 

You know that something new came from something older and simpler.  The “simpler” part of this prediction is clearer if you know the definition of “rudimentary,” but you can eliminate all the wrong answer choices just by predicting the word “old.”  Look at the second answer choices now for the letters you have not yet eliminated.

(A) developed . . an intricate

(B) resulted . . a complicated

(C) evolved . . a quaint

(A) And (B) can be eliminated because “intricate” and “complicated” do not mean “old” and they are the opposite of “simple.”

The correct answer choice is (C).

Words tested in this SC:

Sophisticated: refined

Rudimentary: basic

Apparatus: a machine or tool

Intricate: complex

Quaint: having old-fashioned charm

Degenerated: degraded, having deteriorated

Obsolescent: becoming obsolete or antiquated

Exotic: foreign, non-native (*this is the second time in three days that this word appears in a question!)

On sat.collegeboard.org, 71% of responses were correct.

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