Absolute Value

Link of the Day

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.

Attack the Problem:  Look at your answer choices:

(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 b – b = 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 b – b = 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.

The correct answer is (B).

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

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

Verb Form

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 whole sentence to yourself, listening for errors.  Then quickly check each underlined portion of the sentence against the Big 8 Grammar Rules, identifying and marking any error.

In order to Aprepare for the speech he Bwas given to all of the parents and teachers at the school, George practiced speaking Cin front of a group of Dhis friends. ENo error

(A)  When you use the word “prepare,” you prepare to do something (verb) or you prepare for something (noun).  The words following the preposition “for” are “the speech,” a noun, so this portion of the sentence is idiomatically correct.  There is no error here.

(B)  If you did not read the whole sentence, this portion of the sentence may look fine.  However, you don’t usually need to prepare for something that is given to you.  If you are preparing something, you will probably be the one giving something.  Instead of “was given,” you need the words “was to give” or “will give.”  Mark this verb form error and quickly check the remaining choices.

(C)  The words “in front of” constitute an idiomatically correct phrase to explain the location of something or, in this case, someone.  There is no error here.

(D)  When you see a pronoun, check to make sure it has one antecedent and that it matches the antecedent.  The antecedent for “his” is “George,” and the possessive pronoun is correct because the people are his friends rather than our friends.  The word “friends” must be plural because you cannot have a group without more than one friend.  There is no error here.

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

The correct answer is (B).

On sat.collegeboard.org, 82% of the responses were correct.

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

Sentence Completions

Critical Reading: Sentence Completions

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

Always cover up your answers as you read the sentence.  Choose the easier blank and predict an answer to fill that blank.  Eliminate any choice that does not match your prediction.  Then use the same process with the other blank.

Although the conference speakers disliked one another and might have been expected to -------, it turned out that on several substantive issues they were in complete ------- and were able to avoid petty squabbling.

This sentence give you many context clues.  Paraphrase it as you read it:  even though many people did not like each other, they avoided squabbling.  If people do not get along, especially speakers at an event, you can expect them to argue.  Predict the word “argue” and look down at your answer choices.

(A) argue . . disagreement

(B) bristle . . apathy

(C) debate . . dissonance

(D) concur . . denial

(E) bicker . . accord

(A)  This choice matches your prediction exactly.  However, you should always check all of the choices for synonyms of your prediction.  (B)  Bristle sounds like a negative word, and argue is also a negative word.  Keep this word if you are not sure you can eliminate it.  (C) Debate and argue sound similar, even though debate has a more positive connotation than argue.  If you are not sure you can eliminate a word, keep it.  (D)  The Latin root “con” means “with” or “together.”  The root “cur” means “run.”  If people are running together, they are in agreement instead of working against each other.  Eliminate this choice.  (E)  This word sounds negative, and your prediction was negative, so keep it.

Now turn your attention to the second blank.  Something kept these people from arguing.  These people must have found areas of agreement.  Predict the word “agreement” and look down at your remaining choices.

(A) argue . . disagreement

(B) bristle . . apathy

(C) debate . . dissonance

(E) bicker . . accord

(A)   “Disagreement” is the opposite of your prediction.  Eliminate this choice.  (B)  Knowsys word!   If you are apathetic, it means that you do not care, not that you agree.  Eliminate this choice.  (C)  This word starts with the same Latin root as the word “disagreement.”  The root “dis” means “away” and the root “son” means “sound.”  You may recognize this word if you are a musician, but even if you are not, you can eliminate this word because it does not match your prediction.  (E)  At first glance, the word “accord” may not seem to match “agreement,” but think of the phrase “of one accord” or “in accordance with.”  These phrases are used when people come together and agree on something or with one another. 

The correct answer is (E).

Words used in this SC:

Substantive: essential or considerable

Petty: trifling, little, or inconsiderable

Squabbling: quarreling

Bristle: to react with fear or suspicion

Apathy: lack of interest

Dissonance: inharmonious, harsh sounds or disagreement

Concur: to agree

Bicker: to quarrel about petty things

Accord: agreement

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

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

Circles

Link of the Day

Anytime something new happens to something very old, the result is a rich current event that could be interpreted in many different ways.  The Catholic Church has chosen a new pope, and for the first time ever, the pope is from the Americas.  Look for broad themes in this article that would make it easy to relate this current event to an SAT essay topic.

Geometry: Circles

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

Read the question carefully and identify the bottom line.  Then assess your options and choose the most efficient method to attack the problem.  When you have an answer, loop back to make sure that your answer matches the bottom line.

In the figure above, a shaded circle with diameter  is tangent to a large semicircle with diameter  at points C and D. Point C is the center of the semicircle, and  is perpendicular to . If the area of the large semicircle is 24, what is the area of the shaded circle?

Bottom Line: A sm =? (What is the area of the small, shaded circle?)

Assess your Options:  There are two good ways to approach this problem.  Both ways require you to know the formula for the area of a circle. On collegeboard.org you will find a method that is especially efficient for students who are good at writing equations.  The method used here will focus on geometry skills and estimation in order to avoid the mistakes that often come with working more abstract formulas.

Attack the Problem:  You know the most about the large circle, so start there.  A semicircle is just half of a whole circle.  Therefore, to find the area of the whole circle, you would simply double the 24. 

24 × 2 = 48

If you know the area of the large circle, you can use the area formula to find out more information.  The area of a circle is   Plug in the area you just found to find the radius. 

Note: working backwards using the area formula for a circle is difficult, because using pi will always result in icky decimals.  If you glance at your answer choices, all of them are whole numbers.  You can estimate pi as 3 instead of 3.14 in order to keep this problem as easy as possible.

48 = 3r²

16 = r²

4 = r

You now have the radius for the big circle.  Now look back up at the diagram.  The radius for the big circle is also the diameter for the little circle!  If the diameter of the little circle is 4, the radius will be half of that.  Once you know that the radius of the little circle is 2, you are ready to find the area!

A = 3 × 2²

A = 3 × 4

A = 12

Loop Back:  You found the area of the small circle, so you are ready to look at your answer choices.

(A) 8

(B) 10

(C) 12

(D) 14

(E) It cannot be determined from the information given.

The correct answer is (C).

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

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

Style

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.  Then evaluate the underlined portion of the sentence using the Big 8 Grammar Rules.  Focus on the first error that you find to quickly eliminate wrong answer choices.

The advent of innovative computer and communications technology toward the end of the twentieth century ushered in a new era, not dominated by industry anymore, rather it was information.

This sentence has a style problem: it uses very complicated language to say something very simple.  You want to convey the meaning that the era was dominated by information instead of industry.  Look for a concise way to say this that is grammatically correct.

(A) era, not dominated by industry anymore, rather it was information

(B) era, it was dominated by information over industry

(C) era, which was not dominated anymore by industry but rather information

(D) era dominated by information rather than industry

(E) era dominated not by industry, but it was information

(A)  This answer matches the original wordy sentence.  Eliminate it.

(B)  This answer is a comma splice (two sentences incorrectly joined by only a comma.)  Eliminate it.

(C)  This sentence is better than the original, but you do not need both “but” and “rather.”  Both words show contrast, so they are redundant.

(D)  This answer is clear and concise.  Keep it.

(E)  This answer has a random and unassociated “it.”  Avoid answers that include pronouns without an antecedent.  Eliminate it.

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

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

Sentence Completions

Link of the Day

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.

Critical Reading: Sentence Completions

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

Always cover up the answer choices so that they do not 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.

The correct answer is (B).

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!

Sequence Problems

Arithmetic: Sequence Problems

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

Always read the question carefully and identify the bottom line.  Then assess your options and use the most efficient method to attack the problem.  When you have an answer, loop back to make sure that you solved for the bottom line.

8, a, 14, b, 20, …

The first term of the sequence above is 8. Which of the following could be the formula for finding the nth term of this sequence for any positive integer n?

Bottom Line: You want a formula to describe this number sequence.

Assess your Options:  You could try to write a formula, but you will have a hard time doing that because you do not know the second and fourth terms in your pattern.  You also do not need to find numbers for the variables a and b in order to solve this problem.  Instead, use the answer choices to help you find an answer.

Attack the Problem: The first thing to do is realize that n is not a variable that you have to find algebraically; the nth term just describes the number of that term in the sequence, like the first, second, third, fourth, or fifth.  Therefore:

8,   a,  14,  b,   20, …

1,   2,   3,   4,     5

That means that when you plug in 1 to the formula, you should always get 8, when you plug in 3, you should always get 14, and when you plug in 5, you should always get 20.

Take a look at your answer choices:

(A) 2n + 6

(B) 3n + 5

(C) 5n + 3

(D) 6n + 2

(E) 6n + 5

You could start by plugging in 1 and finding out which of these equals 8, eliminate any that do not, and then try plugging in 3 and then 5 (this method is used on collegeboard.org).  However, just by looking at the numbers (a lot of 2s and 6s and a lot of 3s and 5s) you should be able to tell that a lot of these will equal 8.  To save time, start by plugging in the biggest term you know, the fifth, and see which answer choices equal 20.

(A) 2(5) + 6 = 16

(B) 3(5) + 5 = 20

(C) 5(5) + 3 = 28

(D) 6(5) + 2 = 32

(E) 6(5) + 5 = 35

Note: if you use logic, you do not even have to work out (C), (D), and (E) because the product of the first two numbers is larger than 20 before you even add to them.

Only one answer choice results in the correct 5^th term of 20.  You don’t need to check any other numbers!

Loop back:  You found the only formula that will work for every number in the sequence, so select that answer.

(A) 2n + 6

(B) 3n + 5

(C) 5n + 3

(D) 6n + 2

(E) 6n + 5

The correct answer is (B).

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

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