Functions

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How to manage time and adapt to college life is a major concern for many students. A site full of College Study Tips could be a great help! This website has "college study tips, college study skills, study guides and tricks to help you manage your time, take better notes, study more effectively, improve memory, take tests, and handle the stresses of college life."

4/30 Functions

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

Always try to solve the problem as if the answer choices weren't there. This has two benefits: it makes you more efficient at multiple-choice questions, and it makes you more confident on grid-in questions. First, read carefully and look for important information. Identify the bottom line, then assess your options and select the most efficient way to solve the problem. Attack the problem, solve it quickly, and loop back to ensure that the answer you found matches the bottom line. Finally, check the answer choices and select the correct answer.

If the function f is defined by , where 0 < a < b < c, for which of the following values of x is f undefined?

I. a
II. b
III. c

Read carefully and focus on the bottom line.

f undefined when x = ?

The most important clue here is the word "undefined." What does "undefined" mean in a math problem? It means that you have attempted to do something impossible, such as dividing by zero. In order for this function to divide by zero, x - c must equal zero because it is the denominator. Given that, there is only one possible value for x. Any number minus itself equals zero, so if x = c, then x - c = 0. Any other answer choice would yield a positive or negative number for the denominator, and the function would not be undefined. Only choice III makes the function undefined.

Subject Verb Agreement

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The first Swiss chocolate factory was built in 1819. The man who founded it was in his early 20s and had been working as an "immigrant labourer" in Italy for four years because the chocolate he saw at a Swiss fair smelled so good! This short list of Swiss chocolate makers  Swiss chocolate makers can be used for Excellent Examples about entrepreneurship, determination, and dedication. 

4/29 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.

Remember to read through the sentence for anything that sounds strange, then focus on the part that must be changed to correct the error. If nothing sounds strange to you, check all the options against the rules of English grammar. After checking each option, if none of them are wrong, select choice E.

AAn abundant supply of milk Bfrom dairy farms nearby Cmake the Bern region of Switzerland Da leading producer of condensed milk and milk chocolate. ENo error

Sentence Completions

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After realizing how dangerous his explosives were, Alfred Nobel rewrote his will to establish the five Nobel Prizes. Many were shocked and contested the will, and the plan for the Nobel Prizes underwent several changes, but eventually the first Nobel Prizes were awarded in 1901. Any Nobel Prize winner would make a great Excellent Example, so look through this website to find an example to add to your list. 

4/28 Sentence Completions

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

Remember to read the sentence and look for clues before looking at the answer choices. Most of the answers are wrong, so any clues you find there will only lead you to the wrong answers. Instead, look for clues in the original sentence without looking at the answer choices at all. Make a prediction based on what the sentence says, then match that prediction to the answer choices.

When, in 1864, a factory established by Alfred Nobel to manufacture nitroglycerin blew up, the scientist discovered that the explosive was as ------ as it was powerful, ------ to detonate without warning.

Whenever you find yourself facing a two-blank sentence, don't automatically focus on the first blank first. Take a moment to determine which blank is easier. In this case, the second blank is easier to predict, so make a guess for that word first. Since one factory already blew up, it is easy to conclude that nitroglycerin is apt or likely to detonate without warning. Look in the answer choices for an option that matches.

A) dormant . . ready

B) fickle . . unlikely

C) volatile . . liable

D) unprecedented . . intended

E) inactive . . designed

Ratios

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Private consulting groups like College Funding Solutions, Inc, and GetCollegeFunding can help you find ways to pay for college. How do you get the best financial aid? Scholarships? Grants? Tuition discounts?Which forms do you fill out, and how? Where should you put your money to make the best impression on government funding groups? Their services may seem expensive, but they can save you enough money in college that you come out far ahead. 

4/27 Ratios

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

Always remember to follow the Knowsys Math Method. This may take longer than simply solving the problem at first, as you learn the method, but it will save you time once you begin to use it consistently. Reading carefully will help you make sure you don't miss anything. Identifying the bottom line makes it clear exactly what you are looking for. Stopping to assess your options will help you select the most efficient way to solve every problem and keep you from losing time by spending too much time on a problem. Finally, looping back will ensure that the answer you found matches the question that was asked; if you found the value of m, but the question asked for m + 3, you might get that problem wrong even after doing all the math correctly.

A jar contains only red marbles and green marbles. If a marble is selected at random from the jar, the probability that a red marble will be selected is . If there are 36 green marbles in the jar, how many red marbles are in the jar?

When reading carefully, take note of facts that could help you solve the problem. For example, the fact that the jar only has red and green marbles means that this problem will involve only two variables, probably r and g. Later, the value of g is given, and the problem asks how many red marbles there are. The marbles are selected at random; that's good because it means you can rely on the probability given. If you reached into the jar looking for a red marble, the odds of finding one would be extremely high, no matter what the ratio of red marbles to green marbles is.

Next, identify the bottom line. The question asks "how many red marbles are in the jar?" That can be summarized as

r = ?

Now, assess your options. You could try plugging in the answers until you find one that works, but that could take a while. Or you could try setting up a proportion with the red and green marbles to calculate the number of red marbles in the jar. Conveniently, a ratio is already provided! You're halfway done already! So if there are two red marbles for every... Oh wait.

This is an example of why reading carefully is important. The ratio you need to find to solve the problem is r:g, but the ratio the problem gives you is r:a, or the ratio or red marbles to all the marbles in the jar. So, if 2 out of every 3 marbles are red, the remaining 1 must be green. Now you can set up a proportion.

Idioms

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Gabriel Garcia Marquez is one of the most famous and most well-loved authors in the Spanish-speaking world. His autobiography broke records in 2001 as the best-selling book ever. He is known for writing in the genre of magic realism, seamlessly blending the fantastical and the everyday. One of my favorite short stories of his is A Very Old Man with Enormous Wings, in which a decrepit old man with wings tumbles out of the sky after a storm and is put on display by the farmers who find him. Soon the farmers begin to charge for admittance and make a handsome profit off the strange old man. Villagers come to debate whether he is an angel or just a strange old sailor who smells like fish. Read and decide for yourself!

4/26 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 sounds better than any of the alternatives, select choice A.

First, read the sentence to see what sounds strange or wrong. Use that as your prediction and look among the answer choices for something that fixes the problem you found.

For both his shorter and longer works of fiction, Gabriel Garcia Marquez achieves the rare feat of being accessible to the common reader while satisfying the most demanding of sophisticated critics.

The biggest problem here is the word "both." Whenever you see the construction "both X and Y," remember that all the words between "both" and "and" need to be duplicated or paralleled after the word "and." The original sentence said "both his shorter and longer works," using "longer" as the parallel word for "shorter" but ignoring "his." Look for an answer choice that uses "both" correctly.

Sentence Completions

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Scientific hoaxes are not new. This top ten list includes frauds as early as 1726 and as recent as 2005! While there is not enough information on any of these examples to include them in an essay, a little bit more research could easily land you with a great selection of Excellent Examples. 

4/25 Sentence Completions

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

Always read the sentence and make a prediction before looking at the answer choices. Simply glancing at the sentence is not enough; you must think of a word or idea that would fill the blank. Then, matching that word with the answer choices is fast and easy.

Although the scientist claimed to have made a major breakthrough in his research, the evidence he offered as proof of his assertion was ------ at best.

Clearly, the scientist wants others to believe that he has discovered something new and amazing. In order for them to believe him, he must present solid proof of his breakthrough. Without evidence to support his claim, no intellectual would believe the scientist in this sentence. The clue to look for in the sentence is the word "Although" because it indicates an opposite. Since we've established that the scientist is making a claim that needs evidence to support it, the opposite would be a lack of support or weak evidence. Lacking, shoddy, or meager might work.

Fractions

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College can seem intimidating, and all the more so because it practically involves a different language. Learn the terms around college admission, and you will be able to navigate the process much more easily.

4/24 Fractions

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

Remember to always follow the Knowsys Method when approaching math problems: First, read carefully. Then identify the bottom line and assess your options. Next, choose the most efficient method and attack the problem! Finally, loop back to make sure you have the correct answer.

If f(x) = x + ax, and , what is ?

First, as always, identify the bottom line.



Next, assess your options. You have variables in the question and numbers in the answer choices, so you could work backward from the answer choices. However, there are also numbers in the question, so you could plug in those numbers to see what that gives you. The second method will be far more efficient.

First, plug in the numbers. and , so plug each of those in where appropriate.



Next, following the Order of Operations (PEMDAS), multiply the last two numbers together. When multiplying fractions, simply multiply the numerators and then the denominators.

Subject-Verb Agreement

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It is easy to think of Shakespeare as a relic of the past, but his works are still being performed today. Groups like The Baron's Men perform Shakespearean plays in replica Globe theaters, even encouraging the audience to interact with the performers as they did in Shakespeare's day. Attending a performance could give your essay an exciting historical yet personalized touch. 

4/23 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. 

Remember to read the sentence and make a prediction, then check that prediction and the other answer choices against the requirements of standard written English. 

AAside from Shakespeare, Bperhaps no writer in English Chave engaged the public’s imagination Dmore thoroughly than Charles Dickens.  ENo error

Sentence Completions

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Have you ever wondered where mammals came from? This interactive page from the Smithsonian displays some fascinating information about how mammals evolved alongside dinosaurs and other prehistoric creatures. 

4/22 Sentence Completions

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

Whenever you see a sentence completions question, the first thing you should do is put your hand on top of the answer choices before you read them. Next, read the sentence and check for clues about the missing words. Make a prediction, then look at the answer choices to see which ones match your prediction.

Ms. Fergusson's main criticism of the artist's rendering of the ancient mammal's physical appearance is that, unsupported by even a ------ of fossil evidence, the image is bound to be ------. 

The clues here are the words "unsupported" and "even." Together, they convey that there was no evidence at all, so the first blank is a word that means "a tiny bit." For example, "fragment," "speck," or "iota" could be your prediction.

Digits

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http://www.collegeview.com/collegesearch/index.jsp is another college-finding search engine. Start by selecting the criterion most important to YOU--then look for colleges that fit what you want.

4/21 Digits

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

Remember to always follow the Knowsys Method to avoid selecting the wrong answer. Read carefully and identify the bottom line, assess your options, attack the problem, and loop back to ensure that what you found is actually what the problem asked for.

The sum of the digits of a three-digit number is 12. If the hundreds digit is 3 times the tens digit and the tens digit is the units digit, what is the tens digit of the number? 

First, as always, identify the bottom line.

tens = ?

Next, consider your options. What could you do to solve this problem? What should you do? The best strategy here is to assign a variable to the problem. Say the tens digit is x, and put the rest of the problem in terms of x. You know that the hundreds digit is 3 times the tens digit, so it becomes 3x. The tens digit is also half of the units (ones) digit, so the units digit can be translated 2x.

Participles

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Frida Kahlo is famous for her self-portraits and for her ability to blend surrealism with elements of her traditional Mexican culture. This site has a short biography and images of all her works. Look through them and consider how they make you feel. Some are sad, some simple, some downright creepy. Pick a few favorites and memorize the details around them--the date they were composed, the subject matter, the color scheme, and Kahlo's situation when she created the paintings--and you can use them as Excellent Examples that will really make your essay stand out. 

4/20 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.

Always take the time to read carefully and make a prediction before looking at the answer choices. You should also avoid looking at choice A since it is the same as the original sentence.

Mexican Painter Frida Kahlo drew inspiration from her Mexican heritage, where she incorporated native and religious symbols into her work.

The word "where" does not fit in this sentence because heritage is not a location. Obviously, Kahlo incorporated symbols of her heritage into her work, so some form of the word "incorporated" is still needed in the sentence. You might want to use "incorporated" as your prediction, but check the sentence:

Mexican Painter Frida Kahlo drew inspiration from her Mexican heritage, incorporated native and religious symbols into her work.

The word "incorporated" alone does not work. It is a verb, but the sentence does not provide a subject. What you need is something that looks like a verb, but doesn't act like one. For example, the participle "incorporating." Now that you have a prediction, look at the answer choices.

Sentence Completions

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What's the point of a clean room? They are used to keep sensitive materials or chemicals from being contaminated. Everyone who enters usually needs special garments to keep flakes of skin or strands of hair from mixing with the materials. When those special garments are worn out, labs send them to Kimberly-Clark to be recycled.In fact, the company is currently expanding their cleanroom and laboratory garment recycling initiative to include gloves. This program takes used materials from clean-room laboratories and clinics to make new plastic materials such as plastic lumber and picnic tables. Cool!

4/19 Sentence Completions

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

Remember to read the sentence and make a prediction before looking at the answer choices. Looking at the choices before predicting the correct answer will cost you time and is very likely to change how you think about the question. The sentence will have clues built in to lead you to the correct answer, so rely on them instead of looking at the answer choices.

Mrs. Williams found it ironic that her twelve-year-old son, who made all A's on his report card, was so ------ at home, apparently unable to follow her most basic instructions concerning such commonsense matters as tidiness.

First, look for clues. This sentence has plenty. The boy is clearly smart, since he regularly earns good grades in school. However, when he gets home, his mother finds that he cannot (or will not) follow her instructions regarding tidiness... basically, he didn't want to clean his room. His mother found this apparent dip in intelligence ironic. The blank, then, would have a word that means the opposite of "smart," so "dense," "dull," or "slow" would work.

Mrs. Williams found it ironic that her twelve-year-old son, who made all A's on his report card, was so dense and slow at home, apparently unable to follow her most basic instructions concerning such commonsense matters as tidiness.

Graphs

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Scholarships and college funding are a major concern for many families. No matter what your background, there is something for you among the myriad scholarships, grants, and funds available. Scholarships.com provides a free scholarship-hunting service to help you find your share of the money. The site also sends your information out to colleges so they can recruit you while you find money to pay for their services.

4/18 Graphs

This question involves graphs, which mean you must take a slightly different approach to reading carefully. Skimming over the images to get to the words is extremely tempting, but the labels and trends easily visible on graphs can be instrumental in solving the problem.




Look at the graph before you read the instructions in the question. First, the title is "PURCHASES AT A GROCERY STORE," so you know what the dots represent. Next, look at the axes. The X-axis displays the number of items by multiples of 5, and the Y-axis displays the total cost of each purchase. Finally, look at the content of the graph. This scatterplot shows that, in general, the more items people buy, the greater the cost of their purchase. Some people are able to get more groceries for their money, but not many people spend huge amounts of money on few items.

Now that you know what the graph shows, look at the question.

The scatterplot above shows the number of items purchased at a grocery store by 28 customers and the total cost of each purchase. How many of these 28 customers bought more than 10 items and spent less than $20?

The bottom line in this question has two parts: more than 10 and less than $20. Look at the scatterplot to find an answer that fills both requirements.

Subject Verb Agreement

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Chinua Achebe's novel Things Fall Apart is one of the first and one of the most famous English works written by an African author. Achebe skillfully portrays his native Ibo culture as one full of rich history and traditions, though the main character is eventually destroyed by his stubborn determination to hold onto the culture he knew as a boy. This book could be used in an essay about culture clashes, colonialism, masculinity, or a host of other topics. 

4/17 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. 

First, read the sentence to see whether anything sounds wrong. If something sounds "off" or strange, check it against the rules of standard written English. If the answer choice you predicted is breaking the rules, it is the correct answer.

Although the number of books Awritten in African languages Bare growing, many African writers Cfind a larger audience Dfor works written in Portuguese or English. ENo error

Sentence Completions

Link of the Day

The Layman's Guide to Psychology provides interesting psychological explanations for all kinds of human and animal behaviors. If you choose one for your essay, be sure to include the source!

4/16 Sentence Completions

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

Always remember the power of prediction: making an educated guess to fill in the blank before looking at the answer choices will save you time. Even when you cannot come up with a word, just a general idea or the connotation of the word will help you narrow down your answer choices that much more quickly. 

Since the explanations offered are ------ to the exposition, it would be unfair to treat them as ------ parts of the studies under consideration. 

This sentence is a little tricky to predict. Few clues are given, and some of those are confusing. What is "exposition?" How does it relate to considering studies? One work, however, might be all you need: "unfair." Since it would be unfair to treat something as something unlike it, the blanks are probably opposites. Look at the answer choices for two words that have opposite meanings.

Rates

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College.gov has your starting place for financial aid. One of the major concerns for prospective college students is money; college is expensive, and rising tuition costs combined with less government funding show no end in sight. However, there is money available to help students who need it, and the FAFSA is the best place to start. 

4/15 Rates

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

Always remember to follow the Knowsys Method--even in your math classes. Thinking strategically and logically will help you be more efficient far beyond the SAT. First, read carefully to see what the question is actually asking. Then assess your options and select the best one. Attack the problem efficiently, then loop back to make sure that the answer you found matches the question that was originally asked.

A train traveling 60 miles per hour for 1 hour covers the same distance as a train traveling 30 miles per hour for how many hours?

First, note the bottom line.

train 2 hours= ?

Next, look back at the question to determine how you could solve it. You could determine the total distance traveled by train 1 and then calculate the time it would take train 2 to travel the same distance. You could also calculate the times relative to one another. That might sounds odd, but it is actually more efficient than the first method.

The first step is to set up a ratio of  the two rates given. Put the "new" rate, that of train 2, on top because it is the variable you are trying to find. Always reduce ratios to lowest terms.



You now have a ratio of the two rates. Here's the cool part: simply flip it over to find a ratio of the two times.

If a car or train travels at twice the planned speed, the trip will take half as long as projected. If it travels at half the planned speed, the trip will take twice as long. This rule applies when traveling 2/3, 5/4, or any fraction of the original rate; the ratio of the times will be the reciprocal of that fraction.

Verbs

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The search for evidence of the earliest Americans is still ongoing. National Geographic published this article a few years ago, documenting revisions to the theory of the Bering land bridge.  

4/14 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.

Remember to read carefully and make a prediction before you look at the answer choices. This is more efficient than simply comparing the answer choices. Also, avoid looking at choice A. Since it is the same as the original sentence, reading it is a waste of your time.

The North American continent, first colonized by people from Siberia, crossing the now sunken land bridge between Siberia and Alaska about 15,000 years ago.

First, read the sentence to see whether anything sounds wrong. This sentence should sound strange because it is lacking a main verb. "Colonized," "crossing," and "sunken" are all participles and are not used as verbs. Look at the answer choices to find an option that includes a main verb.

Sentence Completions

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The Congressional Medal of Honor is America's highest military decoration. The US Army Center for Military History maintains a record of every Medal of Honor recipient and what he did to earn the award. For example, in 2003 Sergeant First Class Paul R. Smith gave his life to protect around 100 fellow soldiers from a surprise attack at Baghdad International Airport. He killed around 50 enemy soldiers using a machine gun mounted on a damaged personnel carrier and helped to defeat the attack. Similar details are available on the astonishingly brave actions of Soldiers, Sailors, Airmen, Marines, and Coast Guardsmen since 1861. 

4/13 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 take time to read the sentence carefully before you look at the answer choices. The sentence will have clues about the omitted word or words, so use them to find the word instead of using the answer choices to reinterpret the sentence.

Because he was ------ in the face of danger, the explorer won the government's highest award for conspicuous bravery.

The explorer was obviously very courageous, since he received an award for bravery. "resolute," "fearless," or "indomitable" would work as predictions. Next, look at the answer choices.

Functions

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

Remember that your goal is to get as many questions right as possible, not to answer as many as you can. In some cases, leaving a question blank can be better for your score than guessing, but best of all is to solve the problems efficiently and confidently enough that you can answer every question right. Solve each problem as if it did not have answer choices by reading carefully, noting the bottom line, assessing your options, attacking the problem, and looping back to double-check your answer.

In the xy - plane, line l is perpendicular to the graph of the function f(x) = 5x - 2. Line l could be the graph of which of the following functions?

Your bottom line in this case is "Which of the following?" In WOTF questions, always check E first and work your way back up to A. WOTF questions are much more likely than normal questions to have D or E coded as the correct answer. (The exception to this is Roman Numeral questions, in which the actual answer choices will say things like A) I and II, B) II only, etc. These are random.)

Next, assess your options. You could guess, and since this is a "which of the following" question, you would be relatively safe in guessing D or E. Or you could work from what you know to make a prediction about the correct answer.

You should know that the slope of any line is the negative reciprocal of the line perpendicular to it. That is, if the first line has a slope of m, the second line has a slope of . You should also know that slop-intercept the formula for a line is y = mx + b. Since the equation in the problem is f(x) = 5x - 2, the slope of the given line is 5. Therefore, the slope of the perpendicular line is .

Verb Phrases

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Tibet, the highest nation in the world, has a rich history spanning well over a thousand years. If you have in interest in Chinese or Tibetan history and culture, excellent examples could be found in the Dalai Lama, the Potala Palace, or the Jokhang Temple.

4/11 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. 

First, read the sentence to see if anything "sounds wrong," and use that as your prediction. Check that section of the sentence against the English grammar rules you know, and if necessary continue to check the other options as well. Finally, select the section of the sentence that contains the error.

ALong been isolated Bfrom the outside world and perched Chigh in the Tibetan Himalayas, Lhasa is the capital of Tibet, Dan autonomous region of the People’s Republic of China. ENo error

Sentence Completions

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West Side Story is one of the most famous retellings of Shakespeare's classic Romeo and Juliet that has been written. It maintains the original "gang" mentality and love story central to Shakespeare's original, but the costumes, characters, and even languages are changed to match the time and place of the new version of the story. The lasting fame of both versions of the tale prove that true love can transcend all boundaries. 

4/10 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 the answer choices, read the sentence, and make a prediction. After that, match your prediction to the answer choices and select the one that has the closest meaning. For two-blank sentences, select the easier blank first, and remember that the easy blank is not always the first blank.

Understandably, it is the ------ among theater critics who become most incensed when producers insist on ------ classic plays.

The first clue here is the word "incensed." If you didn't know that it means "angry," you could infer from the word "insist" that the producers are doing something with classic plays that these particular critics do not like. Ask yourself what tends to upset theater critics--obviously, they are upset when producers seek to change the original play. Now you have a prediction:

Understandably, it is the ------ among theater critics who become most incensed when producers insist on changing classic plays.

Inequalities

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This page lists some of the great mathematicians of the ages, including Newton, Archimedes, Euclid, and others. Using any of them in an essay will help you stand out and earn a higher score. 

4/9 Inequalities

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

Be sure to read carefully--reading carelessly will cost you points. Mark the bottom line and assess your options, then choose the fastest route to the answer. Remember: The long way is the wrong way! After you find an answer, check it against your bottom line before looking among the answer choices for the number you found.

If a number is chosen at random from the set {-10, -5, 0, 5, 10}, what is the probability that it is a member of the solution set of both 3x - 2 < 10 and x + 2 > -8?

First, look for your bottom line. It is in two parts here, so one thing you could do is try to combine them to simplify the problem. You could also find the numbers that satisfy each half of the bottom line and then combine them. The long way is the wrong way, so you will need to combine the inequalities. First, isolate x.

p (both inequalities) = ?

3x - 2 < 10                                                               x + 2 > -8

3x < 12                                                                    x > -10

x < 4

Next, you can combine the two inequalities into one compound inequality.

-10 < x < 4

Idioms

Link of the Day

Maria Luisa Bombal wrote "highly poetic works about women trapped within the constraints of a patriarchal society" and blurs the lines between realism and fantasy. 

4/8 Improving Sentences

Part or all of the following sentence is underlined; beneath 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. 

Always read the sentence before looking at the answer choice so that you can make a prediction. Remember not to look at choice A until last; since it is the same as the original sentence, it is a waste of your time. 

Chilean novelist and short-story writer Maria Luisa Bombal wrote innovative and influential stories about heroines which create fantasy worlds in order to escape from unfulfilling love relationships and restricted social roles. 

Sentence Completions

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You may not have heard of Mary Wollstonecraft Shelley, but her inventive mind spawned one of the most well-known creatures in all of literature--Dr. Frankenstein's monster! Frankenstein's monster is a corpse that he reanimates using the power of electricity, and in 1816 electricity was a new and, to some, frightening idea. Frankenstein's monster could be an excellent example to illustrate humanity's innate fear of change and of the unknown. 

4/7 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 follow the Knowsys Method for sentence completions: Cover the answers, read the sentence carefully, and make a prediction based on the clues given in the sentence. Match your answers to the prediction and then select the answer that is the most similar to the word you selected.

The impoverished city lacked the financial means to update its ------ electrical infrastructure.

What clues are embedded in the sentence to lead you to the right answer? Something in need of an update is archaic, outdated, or simply old. Moreover, a city that is impoverished would logically have a difficult time paying for the much-needed improvements to keep its equipment and facilities up to date. Look for an answer choice that is a synonym of "old," "outdated," and "archaic."

Rates

Link of the Day

The Industrial Revolution is well-known as a time of explosive economic growth and invention. Here are five top inventions--and why they're important! Any of them would make a noteworthy Excellent Example in your SAT essay. 

4/6 Rates

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

Always stop and read carefully before you do anything else. Make sure that you mark the bottom line and carefully label each step of your scratch work. It's easy to let confidence trick you into thinking it's safe to skip steps, but on a high-stakes test like the SAT, writing down each step and making sure that every answer is right can be the difference between acceptance and rejection at the school of your dreams. Once you find an answer, loop back to make sure that you have answered what the question asked. Then, and only then, should you select your answer from among the answer choices.

A machine can insert letters in envelopes at the rate of 120 per minute. Another machine can stamp the envelopes at the rate of 3 per second. How many stamping machines are needed to keep up with 18 inserting machines of this kind?

When you read this question carefully, one thing that should jump out at you is the fact that you have two different units of measurement. Immediately think, "I could convert both of these to seconds." Look for the bottom line: How many stamping machines do you need?

s = ?

Next, focus on your options. What could I do? What should I do? You could, as previously mentioned, convert one rate so that they use the same unit of measurement. But what could you do after that? You could guess, if you feel that this problem is too hard and that your time is better spent elsewhere, but guessing is only allowed on the test. No guessing during practice! The next option is to write an equation to describe what is happening in this problem, and then solve for s.

Let's start by converting the inserting machine's rate into seconds.

i: 120/60 = 2

Each inserting machine can stuff 2 envelopes per second.

Next, set up a formula to compare the number of envelopes that the machines can prepare. Each inserter can stuff 2 envelopes each second, and each stamper can stamp 3 envelopes per second. Plug the 18 inserting machines n for i.

Prepositions

Link of the Day

Thomas Edison is best known for inventing the light bulb, but he also invented several other devices that are common (in updated forms) today. He invented an early type of camera for recording motion pictures, and he also developed the phonograph, a device for recording and replaying sound that was the 1880 version of the iPod. 

4/5 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 sentence first to see if anything sounds wrong. Make a prediction, and check that prediction against the requirements of standard written English. Check the other answers to be sure you have the right answer, then select the correct answer choice.
Except for the phonograph, the performances Bof great musicians and the voices of famous people Cwould have been lost Dto history. ENo error