# Absolute Value

Happy St. Patrick’s Day!  If you like celebrating holidays, consider tracing the history of a holiday celebration as one of your historical events, or even tracing the history of a holiday up to the present for a current event.  There are many misconceptions about the origins of ideas and traditions, and the way that certain practices came about is fascinating.  Think about how this article about the history of St. Patrick’s day could be used to answer the following SAT essay questions:

(1)  Should people change their decisions when circumstances change, or is it best for them to stick with their original decisions?
(2)  Do you think that ease does not challenge us and that we need adversity to help us discover who we are?
(3)  What motivates people to change?

## Algebra: Absolute Value

Read the following SAT test question and then select the correct answer.
If , which of the following could be true?

Bottom Line: which of the following COULD be true?

Assess your Options:  You could come up with answers to solve this problem, but that will be a waste of time if they are not included in your answer choices.  Instead, look at the answer choices and methodically eliminate incorrect answers.

(A) a = 0
(B) b = 0
(C) a = b
(D) a = -b
(E) a = 1

For a “which of the following” question, Knowsys recommends that you begin with answer choice (E).

Hint:  Instead of thinking of the bars in your equation as absolute value, think of them as simply showing where a positive number will be.  If you do this, you will not have to plug in actual numbers and you can check each answer choice using logic. (This works because an absolute value simply tells you how far a number is from zero.  The double bars only affect negative numbers, making them positive.)

(E) a = 1    Plug a = 1 into your original equation.   Is there any way to start out with the number 1 and subtract a positive number to get the answer 5?  There is not.  Eliminate this answer.

(D) a = -b     This answer choice has a negative sign, but remember that any negative sign will go within the bars and come out a positive number.  So if you plug in b where the variable a is in this equation, you still end up with bb = 5.  Is that possible?  No!  Anything minus itself will be zero.  Eliminate this answer.

(C) a = b     This answer is essentially the same as the last one!  If you plug in b where you have an a, you wind up with bb = 5.  Again, anything minus itself will be zero.  Eliminate this answer.

(B) b = 0     Plug in 0 for the b in your equation.  You now have a positive number minus 0 equals 5.  Is that possible?  Yes!  5 – 0 = 5.  You are finished.  You don’t have to know that a can be either negative 5 or 5, and you don’t have to check the last answer choice.  Let’s check it just for practice.

(A) a = 0     Is there any way to start with 0 and subtract a positive number to get 5?  No!  Eliminate this choice.

On sat.collegeboard.org, 63% of the responses were correct.

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

# Sentence Completions

The SAT question of the day is about Gordon Parks.  If you have not yet chosen your five literary examples (or historical examples) to prepare for your SAT essay, consider using Gordon Parks.  This man is celebrated for his writing, photography, and film making.  Read more about Gordon Parks here and think about what a rich example he would make for any SAT essay question involving creativity.

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

Always cover up the answer choices so that they do not distract you as you read the sentence carefully.  Use the context clues in the sentence to predict an answer to fill the blank.  Then match your prediction to the correct answer choice, eliminating any word that does not match your prediction in meaning.  Be sure to look at all of the answer choices before selecting one.

With the 1969 film The Learning Tree, Gordon Parks proved what a truly ------- artist he was: he not only directed the film and composed its musical score, but also adapted its screenplay from his own novel.

This sentence tells you that Gordon Parks was extremely involved in doing a lot of different types of work for his movie.  Predict that he was an “accomplished” artist or an “all-around” artist and look down at your answer choices.

(A) complacent
(B) protean
(C) lauded
(D) clairvoyant
(E) harried

(A) Knowsys word!  The word “complacent” means “self-satisfied” or “unconcerned.”  While Gordon Parks may have good reason to be “self-satisfied” after so much work, doing a lot of work does not prove that one is self-satisfied.  This answer choice does not match your prediction.  Eliminate it.

(B) You may know that the Greek root “prot” means first.  You may also know that Proteus was a sea god who could change his form.  From these clues you can discern that protean means “like Proteus” in the ability to work with many forms, just as Gordon Parks works with many forms of art.  If you have no idea what this word means, keep it.  You can still find out the correct answer through the process of elimination.

(C) Knowsys word!  Remember that the word “lauded” is related to the word “applauded.”  The Latin root “laud” means “praise.”  If you check the logic of the sentence, you will see that finishing a movie, no matter how wonderful, will not prove that a person is praised.  This choice does not match your prediction.  Eliminate it.

(D)  This word comes from both Latin and French.  The Latin root “clar” means “clear” and the root “voyant” means “seeing, ”and is related to the French verb “voir.”  Making a movie does not prove that one sees clearly.  Eliminate this choice.

(E) This word comes from an Old English word that is related to an Old Norse word.  Does it sound negative to you?  Think about the word harassed.  You are not looking for a negative word.  Eliminate this choice.

Words used in this SC:
Complacent: self-satisfied or unconcerned
Protean: exceedingly variable, assuming different shapes or forms
Lauded: praised
Clairvoyant: able to see things not perceived by normal senses, such as the future
Harried: harassed, rushed, panicked or devastated

On sat.collegeboard.org, 45% of the responses were correct.

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

# Comparisons

Interested in technology?  On March 10, 1876, the first words were communicated by phone.  Check out this article to find out who said them and find more information about this famous inventor here.  The invention of the telephone would make an excellent historical example for an SAT essay.  Think about how telephones have changed over time and write down themes from the articles that will help you relate this historical event to an essay topic, as well as the details that will make you stand out as a prepared and informed writer.

## Writing: Identifying Sentence Errors

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

Read the entire sentence to get a sense of its structure and meaning before focusing in on the underlined portions.  Then valuate each underlined portion using the Big 8 Grammar Rules, being careful to look at all the answer choices before selecting one.

The introduction of elevators in hotels meant that previously undesirable rooms on the top floors, away from the bustle and noise of the street, became sought after and more expensive than the lower floorsNo error

(A)  The word “of” is idiomatically correct after the word “introduction.”  If you want to use a preposition after the word “introduction,” the most commonly used words are “of” or “to.”  There is no error here.

(B)  The word “previously” is an adverb modifying “undesirable.”  It is placed as close as possible to the word it describes, so there is no error here.

(C)  The words “away from” are idiomatically correct and clearly indicate that the location of the rooms on the top floor.  They are far from or distant from the noisy streets.

(D)  There is nothing wrong with the phrase “the lower floors.”  However, it comes right after the word “than.”  The word “than” sets up a comparison, so you should check to make sure that the two things that are being compared are logical.  You cannot compare “rooms on the top floors” with “the lower floors,” because there may be aspects of the lower floors that are not confined within the rooms.  You must compare “rooms on the top floors” with “rooms on the lower floors.”  Mark this error.

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

On sat.collegeboard.org, 34% of the responses were correct.

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

# Sentence Completions

If you are looking for a historical figure to use as an example for your SAT essay, you don’t have to pick your teacher’s favorite person.  Instead, pick someone who interests you.  Today’s SAT question is about Joe Louis.  This professional boxer would make an excellent historical example because he is not overused by students, and he has an interesting story involving a rise from poverty, an obsession with revenge, and a chance to challenge Hitler’s ideas about racial superiority.  Read more about Louis here, and be sure to write out relevant facts about his life if you chose to use him as one of your five prepared historical examples.

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

Joe Louis was ------- fighter: he inspired fear in many of his opponents.

This sentence defines the word that belongs in the blank; just look after the colon.  Colons indicate that an explanation or restatement of the first part of the sentence is coming next.  You could predict that Louis was “a fear-inspiring” fighter or simply that he was “a frightening” fighter.  Look down at your answer choices.

(A) a serene
(B) an impetuous
(C) an insipid
(D) a malleable
(E) a redoubtable

(A) If you have ever heard the word “serene” used to describe an idyllic and peaceful space, “a serene fighter” should sound contradictory.  It certainly does not match your prediction.  Eliminate this choice.

(B) This is a Knowsys vocabulary word and an attempt by the test makers to trick you.  Impetuous people may be likely to get in fights, so the two words may be easily linked in your mind.  However, the word “impetuous” does not mean “frightening.”  Eliminate it.

(C)  You might not be familiar with this word, but it is easy enough to remember.  The Latin root “in” can mean “not.”  Then comes “sip.”  If you don’t want to sip something, it is probably tasteless.  This has nothing to do with “frightening.”  Eliminate it.

(D)  The mind of a child is malleable.  If a word can be linked to a child, it is probably not too frightening.  Eliminate this choice.

(E)  This word is not an easy word to dissect.  It looks as if means “again” “distrust.”  However, there is an archaic use of the word “doubt” that also means “fear.”  The word comes from an Old French word, “redoubter,” which means “to dread.”  A person would dread or be afraid of an encounter with a redoubtable fighter, so this choice matches your prediction exactly.

Words used in this SC:
Serene: peaceful, calm
Impetuous: rash, hasty, or spontaneous - hotheaded
Insipid: flavorless, bland, or lacking character
Malleable: capable of being shaped
Redoubtable: eliciting respect or fear

On sat.collegeboard.org, 33% of the responses were correct.

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

# Sentence Completions

Happy birthday to Rosa Parks who would have been 100 today.  Was she someone who happened to be in the wrong place at the right time, or an activist dedicated to  changing the world?  Find out here.

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 the answer choices so that you will not be prejudiced by wrong answer choices as you read the sentence carefully.  Then make a prediction to fill the blank and compare it with the answer choices.  Eliminate any choices that do not match.  Be sure to look at all of the answer choices, even if you think that one answer matches perfectly.

Troy was ------- when he wasn’t elected class president: his spirits were so low that there was nothing we could say or do to cheer him up.

This sentence tells you exactly what belongs in the blank.  You know that Troy’s spirits were low and he could not be cheered up.  Predict the word that this information suggests to you; any word like “depressed” or “unhappy” will work.  Look down at your answer choices.

(A) unctuous
(B) disconsolate
(C) ebullient
(D) inscrutable
(E) tenacious

(A) You may not know the word “unctuous,” but you can probably see that it is a negative word.  Keep any word that you do not have a specific reason to eliminate.

(B) Break down this word.  The Latin root “dis” means “away.”  That leaves “consolate,” and you know that to console someone is to make them feel better.  If a person is away from or beyond feeling better, that person is definitely unhappy.  This matches your prediction; since you should generally pick what you know on the SAT rather than what you do not know, it might be the answer you pick.  However, before you select this choice, you should quickly check the other words.

(C) This is a Knowsys vocabulary word!  It comes from a Latin verb meaning to boil over: the “e” comes from “ex” and the “bullire” comes from the Latin “to bubble.”  If you are ebullient, you are so lively and enthusiastic that you cannot contain yourself.  This is the opposite of your prediction!  Eliminate it.

(D) The Latin root “in” can mean “not” while “scrut” is the same root that appears in your Knowsys vocabulary word “scrutinize.”  To scrutinize something is to examine it closely.  If you cannot scrutinize or understand something, it is mysterious, which has nothing to do with your prediction.  Eliminate it.

(E) The Latin root “ten” means “hold.”  If you are tenacious, you intentionally hold fast to something.  That sounds more like the word “determined” than the word “depressed.”  Eliminate it.

Words used in this SC:
Unctuous: having oily characteristics or excessively pious, even smug
Disconsolate: beyond consolation, downcast, cheerless
Ebullient: lively and enthusiastic
Inscrutable: difficult or impossible to comprehend
Tenacious: unyielding, stubborn, determined

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

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

# Modifiers

Is competition always a good thing?  Read this article, which explains why there is no such thing as a brontosaurus, before you answer.  What themes other than competition do you see in this historical example?  How could you use this story as an interesting addition to your SAT essay?

## Writing: Improving Sentences

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

Read the original sentence to yourself, listening for errors.  Evaluate the underlined portion using the Big 8 Grammar Rules.  Focus on the first error that you find to quickly eliminate wrong answer choices.

Concerned that people will click to borrow an e-book from a library rather than click to buy it, library access to the e-book forms of most U.S. publishers' titles is blocked.

Think about the structure of this sentence.  The part of the sentence that is not underlined is an introductory phrase, modifying the part that comes next.  You know that because it does not name the subject of the sentence.  Who is concerned?  You don’t know.  When you have an introductory phrase followed by a comma, the very next independent noun must be the subject of the phrase.  However, in your original sentence, it sounds as if “library access” is what is concerned.  This does not make sense.  Look down in your answer choices for an answer that follows the rule.

(A) library access to the e-book forms of most major U.S. publishers' titles is blocked
(B) it is important to block library access to the e-book forms of most major U.S. publishers' titles
(C) the e-book forms of most major U.S. publishers' titles are blocked from library access
(D) most major U.S. publishers block library access to the e-book forms of their titles
(E) most major U.S. publishers blocking library access to the e-book forms of their titles

(A) You don’t need to read this option because you already found a modifier error in the original sentence.  Eliminate it.

(B) “It” is not who is concerned.  This does not fix the modifier error.  Eliminate it.

(C) “The e-book forms” are also not concerned.  Eliminate it.

(D) “Most major U.S. publishers” would definitely be concerned about sales of e-books.  This fixes the error that you found.  Keep it.

(E) This choice also fixes the original error that you have, but it changes “block” to “blocking.”  The Knowsys rule is to avoid words ending in “-ing” unless they are necessary in the sentence.  In this case, the extra “-ing” is not necessary but creates a sentence structure problem: you no longer have a complete sentence.  Eliminate it.

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

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

# Parallelism

Pina Bausch is the subject of today’s SAT question.  If you enjoy dance or other forms of performance, you may want to consider using Pina Bausch as one of your historical figures for your SAT essay.  She would relate to any questions about creativity, originality, planning, highly accomplished people, and reasons for change.  Check out some information about this choreographer here.

## Writing: Identifying Sentence Errors

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

Always read the entire sentence to yourself so that you can check the meaning and structure of the sentence as a whole.  Listen for errors as you read it.  Then, quickly check each of the underlined portions of the sentence against the Big 8 Grammar Rules.

The German choreographer Pina Bausch created dances that incorporated everyday human gestures and alternating between highly stylized, precise movements and more flowing, expressive ones. No error.

(A) When a verb is underlined, always check to make sure that it agrees with its subject.  This one does.  You could use “Pina Bausch created dances” as a complete sentence.  There is no error here.

(B) When do you use the word “that” and when do you use the word “which?”  Use the word “that” when the following words are vital to the meaning of the sentence.  The word “which” must have a comma before it, but there is no comma in this portion of the sentence, so the word “that” is correct.  Also, the word “incorporated” is past tense, matching the previous word, “created.”  There is no error here.

(C) This word follows a conjunction, “and,” so check the sentence for parallelism.  Pina Bausch’s dances incorporated one thing and alternating between two others.  Does that make sense?  No.  The word “alternating” must be changed to “alternated” in order to be parallel with the word “incorporated.”  Mark this error and quickly check the remaining choices.

(D) When you see a modifier that makes a comparison, such as the word “more,” make sure that the correct number of things are being compared.  In this case there are two things involved, precise movements and more flowing movements, so you need the word more rather than the word most.  The modifier more is also placed as close as possible to the word it modifies, “flowing,” just as it should be.  There is no error here.

(E) This cannot be the answer because you already marked an error.

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

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

# Idioms

It is now the month of November!  On the 1st of November in the year 1512, the Sistine Chapel ceiling was opened to the public.  Read an article about this amazing work of art here, and see the whole ceiling here.  This would make an excellent historical example for your SAT essay.  Think about the broad themes of creativity and planning in connection to this historical example.  What other themes connect to this work of art?

## 11/1 Identifying Sentence Errors:  Idioms

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

Read the entire sentence to yourself, listening for errors.  Then consider each underlined portion of the sentence, asking yourself whether it complies with the Big 8 Grammar Rules.  If you find an error, mark it.  Then quickly check the other choices.
Most ships move through the Suez Canal with their own power, but large ships must be assisted by a tugboat. No error

(A)  The word “move” is a verb.  Check to make sure that it agrees with the subject of the sentence.  It does.

(B)  Think about the word “with” in context.  “With” generally means “accompanied by,” or “in the same direction as.”  Is that the meaning that you need in this sentence?  No!  This is an improper idiom.  The power is actually moving the ship.  You need a word that will express that relationship.  Try inserting the word “under” or “by” into the sentence to make it idiomatically correct.

(C)  Check that the pronoun has one and only one antecedent and that it agrees in number with that antecedent.  “Their” refers to multiple “ships,” so it is correct.  Each ship also has its own level of power, so the addition of the word “own” makes sense.

(D)  The phrase “must be” adds important information to this sentence.  You could change it to another word such as “are,” but that would change the meaning of the sentence and is completely unnecessary because there is no error in this underlined portion.

On sat.collegeboard.org, 45% of the responses were correct.

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

# Sentence Structure

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.

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

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

# Algebra Equations: Translate

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

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

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

# Sentence Completions

Today’s question of the day is about Frank Lloyd Wright, one of the most famous American architects who ever lived.  Wright would make an excellent historical example for your SAT essay because he experienced a wide range of historical events and clearly articulated his aims in designing both public buildings and private residences.  To learn more about Wright, read some of his biographical information here and look up images of some of his most famous buildings such as Fallingwater, the Guggenheim Museum, and Taliesin.

## 10/16 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.

The visually captivating nature of Frank Lloyd Wright’s designs suggests that the architect is a true ------- , infusing his designs with beauty as well as functionality.

After you have read the sentence, think critically about the information it tells you.  The “visually captivating” work this architect did suggests what about him?  You know that he cares about making visuals pleasing.  The sentence goes onto say that his building designs have “beauty,” they are not just functional.  Make a prediction for the blank based on these context clues.  It does not have to be a specific word.  You could predict “lover of beauty” or “lover of art” if no word comes immediately to mind.  Look down at your answer choices.

(A) instigator
(B) nonconformist
(C) intellectual
(D) minimalist
(E) aesthete

(A) and (B) can be eliminated because they do not match your prediction.  Nothing is said about Wright’s originality in this sentence.  (C) also does not match your prediction.  Nothing is said about Wright’s intelligence.  (D) does not match your prediction.  It is far too specific and does not relate to the sentence.  Minimalism may be considered beautiful, but ornate spaces can also be beautiful.  That leaves you with (E).  Even if you do not know the precise definition of the word “aesthete,” this is your best answer because every other choice has been eliminated.  If you have been studying the Knowsys vocabulary, you should connect this word to the word “aestheticism” and quickly realize its meaning.

Words used in this SC:
Instigator: Someone who starts something (often trouble)
Nonconformist:  Someone who does not go along with established norms for behavior or beliefs
Intellectual: A highly intelligent person who has acquired knowledge
Minimalist: A person who seeks to reduce distractions into something simple
Aesthete: Someone who cultivates sensitivity to beauty in art or nature

On sat.collegeboard.org, 50% of the responses were correct.

For more help with SAT vocabulary, visit

# Exponents

On September 30, 1868, Louisa May Alcott published the first volume of Little Women.  The story was extremely successful and has been beloved by readers ever since.  Louisa May Alcott would make an excellent historical figure to use as an example on your SAT writing section.  You can read more about her life here, and if you have read Little Women, remember that it could make an excellent literary example too!

## 9/30 Exponents

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

Math questions need to be read just as carefully as reading questions. Avoid incomplete answers by making a note of the bottom line. Are you solving for x, or do you need the answer to 2x + 3? Assess your options for solving the problem, choose the most efficient method, and attack the problem! Once you have the answer, loop back to verify that it addresses the bottom line.

If , which of the following expresses a in terms of b?

Bottom line: This question asks you to solve for the variable a.

Assess your options: You could try to plug in the answer choices for a and choose a number for b to try to find the answer. However, that method requires you to work several problems and includes multiple steps. Instead, use algebra to rearrange the equation.

Attack the problem: You see two numbers with exponents. When two bases are the same, then the exponents can be set equal to each other. Your two bases are 2 and 4. How can you make both bases the same? Use the fact that 2² = 4 by plugging that into your equation.

$2^{a} = 4^{b}$

$2^{a} = 2^{2b}$

Now you can ignore the bases and set the exponents equal to each other. You now have:

a = 2b

Loop back: The question asked you to find a in terms of b, and that is just what you did. Look down at your answer choices

(A)

(B) b

(C) 2b

(D) 4b
(E)

On sat.collegeboard.org, 54% of the responses were correct.

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

# Sentence Completions

Technology makes an interesting current event for your SAT example, but have you thought about how technology can influence the way that history is understood? A new iPad app allows users to scrutinize slices of Einstein's brain. Read this article and think about the numerous themes that could relate this current event to an SAT essay prompt.

## 9/25 Sentence Completions

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

Barbara McClintock’s systematic examination of corn demonstrated the transposition of genes, a finding that overturned entrenched beliefs and proved that ------- study may produce brilliant insights and ------- change.

This sentence is full of clues about the words that should fill the blanks. Look at the first blank, and ask yourself what kind of study Barbara used to find out about corn and genes. The sentence has already described Barbara’s study as a “systematic examination.” Rather than spending time thinking of a synonym for “systematic,” use the word you are given as a prediction for the first blank. Then look down at your answer choices, and eliminate any answers that do not match the word “systematic.”

(B) inherent . . controversial
(C) improvised . . startling
(D) methodical . . revolutionary

(A) Does haphazard mean systematic? No. It means the opposite. Eliminate it. (B) Does inherent mean systematic. No. Eliminate it. (C) Does improvised mean systematic? No. It means the opposite. Eliminate it. (D) Does methodical mean systematic. Yes. This choice matches your prediction. (E) Does derivative mean systematic? No. Eliminate it.

Note that it is possible to eliminate all but the correct answer choice just by looking at one blank. However, if you did not know the meaning of any of the above words, you would still have multiple answer choices remaining. In that case, continue to eliminate choices by looking at the other blank.

What kind of change did Barbara’s finding bring? A finding that “overturned entrenched beliefs” must produce some “surprising” and “completely new” changes. Look now at any answer choices that you have remaining.

(D) methodical . .revolutionary

The word “revolutionary” matches your prediction.

Words used in this SC:

Haphazard: random, chaotic
Inherent: due to a permanent or natural attribute
Controversial: causing debate
Improvised: unrehearsed
Methodical: organized, systematic
Revolutionary: radically new, sudden complete change
Derivative: imitative

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

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

# Modifiers

Today’s question mentions Enrico Caruso, an opera singer who became an international celebrity without the use of radio or television.  He relied on newspapers, silent films, and phonographic records to reach his audiences when he was not traveling.  Click here to learn more about Enrico Caruso’s career and hear his voice.  He would be an excellent historical figure to mention in an example for your SAT essay.

## 9/23 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 Grammar Rules.  Your goal is to create a clear and precise sentence.

Enrico Caruso sang opera in Italy before traveling to the United States, then he gave his first performance at the Metropolitan Opera in November 1903.

Paraphrase this sentence.  Enrico sang opera in Italy before going to the US, then gave his first performance at the Metropolitan Opera.  Does that make sense?  The timing in the original sentence is illogical.  The man cannot give his first performance after going to the United States because he sang opera in Italy before that.  An opera is a performance!  If the underlined word is misleading, how can you change it?  The second part of the sentence describes where Enrico performed (at the Metropolitan Opera).  Replace the word “then” with “where” and see whether that improves the sentence.  Now the first performance at the Metropolitan is Enrico’s first performance in the United States, rather than his first performance ever.  That makes sense. Look down at your answer choices.

(A) then
(B) when
(C) and which
(D) in that
(E) where

On sat.collegeboard.org, 77% of the responses were correct.

For more help with SAT writing questions, visit

# Sentence Structure

It is common to hear that women’s sports do not get the attention that they deserve.  However, it also seems that most Americans are at least comfortable with the notion that women play sports.  Billie Jean King is one woman whose athletic prowess helped to bring respect to female athletic competitors.  Although she has a long list of achievements, she is best known for accepting the challenge of Bobby Riggs, an older tennis player who boasted that he could beat her because she was only a weak woman.  The two played a highly publicized match on September 20, 1973 and King won the “Battle of the Sexes.”  Read more about this event here and here.  Think about how you could use this historical event as an excellent example for an SAT essay.  Think about how easily this story relates to the themes of expectation, adversity, perseverance, lasting change, success, motivation, courage, responsibility, respect for elders and tradition, how individuals are defined… the list continues.  If you choose to use this as one of your excellent historical examples, be sure to write down and memorize details that will show that you are well informed.

## 9/20 Identifying Sentence Errors

Top of Form
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 whole sentence to yourself, listening for errors.  If there is an error, you will be able to fix it by changing only one underlined portion, but most of the time you cannot spot the error by only reading the underlined portions.  You need the context of the whole sentence to choose the correct answer.  Once you have read the sentence, quickly check the underlined portions of the sentence against The Big 8 Grammar Rules.  Mark any error you see and check the rest of the choices.

It weaves across a strip of tropical land where the Isthmus of Panama narrows in the shape of a long flattened letter S, the Panama Canal links the Atlantic and Pacific Oceans. No error

After reading the sentence, do you feel as if you have too much information?  You should.  This sentence is actually two sentences connected with a comma; it contains a comma-splice.  Normally you could change the comma to a semicolon or add a conjunction to the sentence, but that portion of the sentence containing the comma is not underlined.  That means that you must change one of those complete sentences into a dependent clause that modifies the other.

Another way to think about this sentence is to realize that a comma splice is basically a problem involving too many subjects or verbs.  Ignore some of the “extra” information in the sentence so that you can more easily see the basic structure of the sentence.  Then the sentence will look like this:

It weaves across a strip of tropical land where the Isthmus of Panama narrows in the shape of a long flattened letter S, the Panama Canal links the Atlantic and Pacific Oceans.

The comma splice is more apparent now, and it is also obvious that changes to two of the underlined portions will not fix the comma splice.  Look quickly at each underlined portion.

(A) “It weaves” contains both a subject and a verb that match, so you might be tempted to move on to the next blank.  However, you know that you are looking for a way to make a dependent clause.  If this portion of the sentence were changed to “As it weaves” or “Weaving” you could create a dependent clause and fix the sentence structure problem.

(B)  “Where” is the correct word to describe a location.

(C) “Narrows” is a verb, so check to make sure that it agrees with the subject.   Ignore the prepositional phrase “of Panama” that separates the noun from the verb, and you will see that “the Isthmus narrows” is correct.

(D) First check subject and verb agreement because “links” is a verb.  “The Panama Canal links” correctly matches subject and verb.  There is also a conjunction between the two different oceans.  (You cannot create a dependent clause by changing this portion of the sentence because the subject is not underlined and the verb is necessary because the information that follows requires it.)

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

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

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

# Sentence Structure

Woody Guthrie is the subject of today’s SAT question, and he is also a fascinating folk musician who would make an excellent historical example for your SAT essay.  Singers and songwriters influence culture in profound ways.  Guthrie's message was about love.  He wrote, "I hate... songs that run you down or songs that poke fun of you on account of your bad luck or your hard traveling.  I am out to fight those kinds of songs to my very last breath of air and my last drop of blood."  You can find out more about Guthrie and the songs he wrote here.

Today also marks the 11th anniversary of the September 11th attacks.  Take a moment out of your busy day to remember the victims and their families.  You can read more about the 11th anniversary here.

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

Woody Guthrie wrote and adapted more than a thousand songs, many of them are about the struggles of workers and the poor in the United States.

Notice that the underlined portion of the sentence comes directly after a comma.  This is a good indication that you should check sentence structure.  When you read the sentence, does it seem as if it includes two separate thoughts?  This sentence is a comma splice; the comma should be a period.  Which underlined word could you replace in the original sentence to create a grammatically correct sentence?  If you immediately see a way to fix the problem, make a note of it.  You are now ready to look down at the answer choices.

(A) many of them are
(B) many of which are
(C) many are
(D) which are, many of them,
(E) and many of them that are

You do not need to read (A) because it matches the original sentence and you found an error in the original.  (B) fixes the comma splice by changing the second independent clause into a relative clause that modifies “songs.” (C) fails to remedy the comma splice.  (D) and (E) are needlessly complex and introduce new errors into the sentence.

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

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

# Sentence Structure

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 Structure

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 nearly five billion years and is thought that it has sufficient thermonuclear fuel in its core to shine for about another five billion. No 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.

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

For more help visit www.myknowsys.com!

# Sentence Completions

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.

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!

# Triangles

Yesterday's Question of the Day about Red Cloud piqued my interest, so I decided to look him up for today's Link of the Day. Red Cloud was an amazingly successful war leader of the Lakota Indians, assaulting several United States Army forts along the Bozeman Trail in the 1860's. By the end of the decade, the US agreed not only to abandon its forts in Lakota territory, but also to guarantee Lakota control over a vast land area, including the western half of modern South Dakota and parts of Montana and Wyoming. Unfortunately, Red Cloud's victories did not last, and eventually the white settlers reclaimed and broke apart the Lakota holdings. Red Cloud's tireless efforts to protect his people and his culture would make an outstanding Excellent Example for your essay.

Let's take this a step further: What kind of essay prompt could you answer with the story of Red Cloud? Please respond in the comments!

## 7/26 > Triangles

Whenever you approach a math problem, remember to follow the Knowsys method. Rather than charging in, take a moment to read the problem carefully and identify the bottom line. Consider the best way to approach the problem--what could I do? What should I do? Then attack the problem and, finally, loop back to the top and make sure you answered what the question was actually asking. The last and easiest step is to match your answer to the provided answer choices.

In triangle ABC, the length of side $\overline{BC}$ is 2 and the length of side $\overline{AC}$ is 12. Which of the following could be the length of side $\overline{AB}$?

First, note the bottom line at the top of your scratch work.

$\overline{AB}$ = ?

Next, consider your options. What does the problem tell you? What strategies, formulas, or theorems do you know that could help you solve it? In this case, the problem tells you that you are dealing with a triangle and supplies two side lengths. With so little information, you really only have one tool that can help you: the Triangle Side Lengths Inequality.

The Side Lengths Inequality states that any side of a triangle must be less than the sum and greater than the difference of the other two sides. When you think through it, this actually becomes fairly obvious. If one side were longer than the other two sides put together, the shape could no longer be a triangle. It would fold flat into a line. If one side were too short, it would not be able to "reach" the other sides and the triangle would just be three line segments rather than a closed shape. The Side Lengths Inequality is usually expressed this way:

$\left | y-x \right |

For simplicity's sake, you can rename the sides of the triangle in the problem x, y, and z rather than shuffling As, Bs, and Cs around. (Be sure to note this in your bottom line!) Now that you've chosen the most efficient way to solve the problem, attack it ruthlessly!

First, take the side lengths you are given and plug them into y and z.

$\left | 2-12 \right |

Next, perform some simple arithmetic to solve for x.

$\left | -10 \right |

$10

Now you've narrowed down the range of possible values of x. Loop back to double-check the bottom line. If you remembered to update it earlier, it should look something like this:

x = $\overline{AB}$ = ?

Since you've found the possible values of x, you've also found the possible lengths of side $\overline{AB}$. The last step is to find an answer choice that matches what you found.

(A) 6

(B) 8

(C) 10

(D) 12

(E) 14

Note that the inequality uses "less than" signs, not "less than or equal to" signs. That means that side $\overline{AB}$ cannot equal 10 or 14; it must be 12. The answer is D.

On sat.collegeboard.org, 45% of responses were correct.

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