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Archive for September, 2010

Balancing School Work and Social Life

By posted September 30, 2010

Think about college for a moment: a four year sleepaway camp with thousands of your peers, no parents, and unlimited pizza. OK, that last part was a bit of a stretch, but you get the idea. It seems unfitting that the purpose of college isn’t to socialize, but to learn. Yes, I know, it’s a bit of a paradox, but college is an institution of learning first and a funhouse second. As with all choices between extremes, the middle road is best. Balance. Yin and yang. You’ve heard it all before. To get the most out of your college experience, you must find a way to balance school and social work–no easy task.

Before you attempt such a feat, identify your goals. Every student’s priorities are different, and they will largely depend on the student’s individual ambition, personality, and particular school. If you are set on triple majoring in Engineering, Computer Science, and Ancient Greek, chances are you will not have much time for a social life–but that’s your choice to make. Similarly, your college may be a notorious party school on the one hand, or rigorously studious on the other. The social and academic atmosphere of your school will undoubtedly influence your behavior.

Most of you will lie somewhere in between these extremes, and, a result, you might seek some guidance on how to balance the two. For some, the challenge is resisting peer pressure to go out when you have an essay due the next morning. For others, the challenge is better scheduling your school work so you actually have time to hang out with friends. No matter what your priorities are, here are a few tips to make your college experience a well-rounded one.

  1. Choose Study Locations Carefully: Most of us know how and where we can study well. Some of us can block out the noise and activity of a dorm hall. Others thrive amidst the quiet buzz of intellectual activity in the library. And, in some extreme cases, one needs absolute silence and no distractions. Luckily, you will seldom have trouble finding the right location for you. The biggest challenge for most is getting out of that noisy dorm room and into a dorm study room or the library. Yes, it’s nice to be in the company of others, especially when you have to do something you really don’t want to do. For most of us, though, if you try to study and socialize at the same time, guess what–you’re not studying.
  2. Know the Law of Diminishing Returns: You know how the last agonizing bites of a 20 oz. steak dinner are not nearly as good as the first few? That’s the law of diminishing returns. If you continue an activity after a certain peak of performance, your effectiveness will decrease. The same goes for studying. Have you ever studied for hours on end? Did you notice that you started reading more slowly, and the words started to blur on the page? Chances are, if you reach this point, you’re not studying very effectively. Study breaks are our friends. They will not only make your studying more effective, but you can use the breaks to socialize. See? Balance.
  3. Choose Your Dorm Hall Carefully: Many dorm communities offer themed dorm halls, from academic, to international, to general. You can count on academic halls being a bit more peaceful–or “boring,” depending on your point of view. General halls, or those without a theme, tend to be a bit livelier (see “rambunctious”). Again, the choice in dorm hall comes down to personal preference. If you wish to make your dorm the ideal sanctuary for studying bliss, the academic hall might be a good choice. On the other hand, if you already plan to seek your study location elsewhere, you may not be so limited in your choice of hall theme.
  4. Get Involved: On the other side of the spectrum, your academics may be fine, but you may be seeking social stimulation. This kind of situation often arises after you move out of the dorm; no longer bombarded by attention-hungry peers, you may seek an outlet for social interaction outside of your living space. Check out the clubs and organizations to meet many students with similar interests. Clubs are not only fun, fulfilling, and filled with friends, but they make great additions to your resume.

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Ambiguous and Vague Pronouns

By posted September 27, 2010

Readers tend to hate vague writing. Why read something when it’s impossible to figure out what the author means? I’m not talking about the seemingly incoherent ramblings of modernist literature–those authors have earned the right to be eccentric. I’m talking about vague and ambiguous pronouns, a pesky error you’ll often find on SAT Writing questions. First, let’s look at a simple example of an ambiguous pronoun:

Jessica met with Susie after she had lunch.

You might read this sentence and automatically correct the pronoun ambiguity. For some reason, you might think that Jessica had the lunch. Some of you might think Susie had the lunch. The truth is, there is no way of knowing. The pronoun “she” is ambiguous because it has no clear antecedent: it can refer to either Jessica or Susie.

How do we fix this problem? Simple. Just replace the ambiguous pronoun with the noun it should refer to. Let’s say the author meant for “she” to refer to Jessica:

Jessica met with Susie after Jessica had lunch.

If you want to exercise your writing skills a bit, you might make it a bit more elegant by cutting back on these clunky nouns:

After having lunch, Jessica met with Susie.

That was a simple example. There was no reason why “she” would refer to either Jessica or Susie. What if the pronoun isn’t so obviously ambiguous? What if there seems to be a logical antecedent even though the pronoun is grammatically ambiguous? Check out this example:

John gave his little brother a toy for Christmas that he played with constantly.

Wouldn’t it make sense that “he” refers to the little brother? The toy is his gift, after all. So, “he” must refer to the little brother, right? Well, not exactly. Though it makes sense that the little brother played with the gift he received, it is possible that John is just a selfish older brother. Perhaps, after having given the gift, John realizes just how awesome the toy really is, so he hogs it. Notice that, by trying to figure out the correct antecedent of “he,” I’ve wasted a lot of time and energy. We should not have to speculate on the correct antecedent of a pronoun, nor should e have to make up ridiculous stories to justify our choice. In this sentence, “he” is ambiguous. Period. Here’s a possible fix:

John’s little brother constantly played with the toy that John gave him for Christmas.

Now that we’ve looked at ambiguous pronouns, let’s check out vague pronouns. Unlike ambiguous pronouns, which refer to one of two or more pronouns in a sentence, vague pronouns do not have identifiable antecedents in the sentence. Rather, the antecedent of a vague pronoun is implied, but not stated:

They say that a bad cough, if left untreated, can have a detrimental effect on lung function.

While you won’t raise any eyebrows for using this vague pronoun in everyday speech, the SAT will deem it a grammatical error. When we use the construction “they say,” we don’t really have an antecedent in mind for “they.” We mean to imply that the thing “they say” is common knowledge, or that we’ve heard it somewhere but cannot identify who said it. For the SAT, though, this construction is wrong. To improve it, find a logical antecedent for “they” and replace the pronoun:

Doctors say that a bad cough, if left untreated, can have a detrimental effect on lung function.

or

Experts say that a bad cough, if left untreated, can have a detrimental effect on lung function.

The strategy for catching ambiguous and vague pronouns is simple: every time you see a pronoun, identify its antecedent. If you are stuck between two pronouns, or if you cannot find the logical antecedent in the sentence, then you must fix or identify the problem.

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Independent and Dependent Clauses

By posted September 25, 2010

When it comes down to identifying grammar errors in a sentence, you really cannot afford to overlook the dynamic duo of the grammar world: independent and dependent clauses. A clause is an expression (group of words) that includes both a subject and a verb. The difference between the independent and the dependent clause is simple: an independent clause is a complete thought that can stand alone as a sentence; a dependent clause is an incomplete thought that cannot stand alone as a sentence.

Independent Clause

When trying to identify independent clauses, use your instincts. If the clause can stand on its own as a complete sentence, it is independent. Below are examples of simple and complex sentences; the independent clauses are italicized:

  1. I brought my umbrella.
  2. Because it was raining, I brought my umbrella.
  3. I brought my umbrella, but John insisted that it wasn’t necessary.
  4. I brought my umbrella, only to find out that it wasn’t raining at all.

Notice that only the italicized parts of the sentence can stand alone as sentences. While the expression “because it was raining” contains both a subject and a verb, it cannot stand alone as a sentence, so it constitutes a dependent clause.

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Vocabulary in Context

By posted September 23, 2010

When I was studying for the SAT years ago, I made the mistake of looking up one of those immensely long word lists online and trying to memorize all the words.  It was agony.  SAT prep has improved a lot since then and there are much better word lists out there that actually pick out good words for you rather than try to make you memorize the dictionary.  Studying for the GRE a few months ago, I chose not to rely on any wordlists.  Rather, I practiced guessing the meaning of words from context clues.

When you see a question along the lines of “what does vocabulary word (line 17) mean in context”, I would immediately look to line 17 and read the sentence once carefully then read the sentences before and after.  If possible, try to find a synonym for the word without looking at the answer choices! When you think you have a synonym, look at the answers and see if there’s one that is close in meaning.

When looking at the passage, try and determine if the word has a positive, negative or neutral meaning.  Some words simply sound negative and you’ll get better at recognizing them as you go along.  For example, repudiate, anguish, and abhor all have a very negative sound to it if you read it out loud.  Whereas words such as mirth and exalt have a positive ring to it.

By reading around the word, you can usually gain some idea as to the definition of the word.  Let’s practice on a few sentences.

The board of directors lauded the chairman for his skillful negotiation of the takeover of the failing company.

Even if you don’t know what lauded means, reading that the chairman “skillfully negotiated the takeover” suggests that lauding is a positive thing.  In fact, I would replace laud with praise, which is exactly what it means.

Dr Smith is at the zenith of her career.  She recently completed several successful brain surgeries and is about to publish the results of her cutting edge research on the effects of a drug on brain tumors.

Now what could zenith possibly mean?  Is Dr. Smith at a low point or crossroads in her career?  The fact that she is a successful surgeon and researcher suggests otherwise.  I would replace zenith with “peak” or “high point”.

It gets a little difficult if you don’t know what the words in the answer choices mean as well, especially since there are no contextual clues to help you figure that out.  But the positive/negative/neutral method also applies here or you could try breaking the word down into its latin roots to guess at its meaning.

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Prime Numbers

By posted September 20, 2010

A prime number is any number that has as factors itself and the number 1.  For example, the numbers 5, 7, 11 are all prime numbers while the numbers 6, 12, 15 are not.  (6 has factors 1, 2, 3, 6; 12 has factors, 1, 2, 3, 4, 6, 12 and so on).  Questions involving prime numbers in the SAT usually require you to know

1)      that a prime number only has two factors: 1 and itself

2)      how to find the prime factors of a non-prime number

Let’s briefly discuss point 1 before we move onto the more complicated point 2.  For example, I could tell you that the set A is the set of all two digit even numbers while set B is the set of all prime numbers.  What numbers do set A and set B have in common?  If you think about it, all two digit even numbers cannot be prime: 10, 12, 14 and so on have 2 as a factor by virtue of being an even number.

Moving onto prime factorization.  To find the prime factors of any number, start by dividing by 2 (the first prime number).  Keep dividing by 2 until you can’t divide by 2 any longer, then try dividing by the next prime – 3, then the next prime and so on.  For example, let’s find the prime factors of 525.  525 is not divisible by 2 since it’s an odd number.  So we try the next prime number – 3.  525 divide by 3 = 175.  Let’s try dividing 175 by 3 again.  But that’s not possible!  So we try the next prime number 5.  Keep dividing by primes until the quotient is a prime, then stop.  The prime factorization for 525 is demonstrated more concisely below:

525
3 175
5 35
5 7

So 525 = 3 x 5 x 5 x 7

This technique can be applied to solve the following two questions

Question 1

A number a is the greatest prime factor of 68, while a different number b is the greatest prime factor of 80. What is the value of a – b?

68 = 2 x 2 x 17

80 = 2 x 2 x 2 x 2 x 5

That means a is 17 and b is 5.  So a-b = 17-5 = 12

Question 2

[(x1/3 )(y1/5 )]15=1944.  Find xy

To solve questions like the one above, simplify and try to find the prime factors.  There’s no way that you can solve such a question easily if it didn’t have to do with prime factorization because there would be too many combinations for you to figure out within too short a span of time.

simplifying the exponents, you get:

[(x1/3 )(y1/5 )]15 = x5y3 = 1944

Most likely 1944 can be factored out into two primes, one to the fifth power and one to the third power.    Let’s try it: start by dividing by 2 and so on.

1944 = 2 x 972

972 = 2 x 486

486 = 2 x 243

243 = 3 x 81

81 = 3 x 27

27 = 3 x 9

9 = 3 x 3

So 1944 =  3523 meaning x = 3 and y = 2.  Thus xy = 6.

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One Short Passage for the SAT Reading

By posted September 17, 2010

One of the least daunting types of questions on the SAT Reading section is the short passage. The advantage of passage-based questions is that all of the answers are directly in front of you, no grasping for complicated vocabulary words required.  The challenge of passage-based questions is usually skimming through the passage quickly enough to answer all of the questions, while still locating all of the pertinent information.  Short passages provide a unique opportunity to gain a firm grasp on the entire passage – all of the benefits of passage-based questions without the major challenge.  You should read the whole passage carefully, ascertaining the author’s main thesis and conclusion, and noting the placement of important ideas within the passage.  Then, when answering questions, you can quickly and easily refer back to the passage.

Of course, basic passage-based strategies still apply.  Correct answers will always correspond with information directly stated in the text.  Ensuring that an answer choice is correct is easier with short passages, because you can quickly check to make sure that your answer is referenced in the passage.  Answer choices may be factually correct, or may sound like something that the author would agree with; however, if the answer is not based on something actually stated in the passage, it is not correct.

Although short passages afford an opportunity to be very thorough, you should still try to answer as quickly as possible in order to leave more time for other, more difficult, questions.  One of the best ways to minimize time is to keep the author’s main point in mind, and use that in conjunction with process of elimination.  If you already know that the author is, say, arguing for more funding for science classes, you can quickly eliminate answer choices that do not support, or contradict, that main point.

Additionally, taking note of the layout of the passage during your initial reading will allow you to quickly refer back to relevant portions.  Some questions may ask about the use or meaning of a particular sentence, rather than the passage as a whole.  It is important to read these sentences in context, which is where being able to locate sentences quickly comes into play.  It is also important to divorce the sentence’s main idea from the passage’s main idea.  While the central idea of the passage may inform the main idea of the sentence, often a particular sentence or example will have a meaning of its own or serve a different purpose than the general thesis.

This may seem like a lot of strategy to keep in mind for a few dozen sentences.  However, short passages should be viewed as a valuable opportunity, as well as a welcome break from the tediousness of long passages.  Short passages are also a great place to start practicing passage-based skills.  You can get all of the strategy down with less stress, so that when you finally tackle long passages, you’ll only have to worry about finding the relevant information.

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Sequences

By posted September 15, 2010

A sequence is an ordered list of numbers that follow some pattern that’s related to its position in the list.  For example, let’s look at the sequence: 5, 8, 11, 14, 17, …  Clearly the second term is 3 more than the 1st term.  And the 3rd term is 4 more than the 2nd term.  And so on.  In fact, you could probably tell me that the terms after 17 are 20, 23, 26, 29 and so on.  If you can’t see what pattern the sequence follows and the question doesn’t tell you, chances are, the question is going to ask you what pattern it is and the right answer will be amongst one of the 5 choices.  So just plug in the numbers in the sequence into the choices one by one.  The right choice will be the one that fits all the numbers in the sequence.

Usually students can handle the questions that have explicit numbers.  But suppose the question doesn’t tell you what the first number is.  Rather, it assigns it a letter, for example, let n be the first term.  The question should give you enough information relating the 1st and 2nd term to let you create a sequence in terms of n.

For example, in a sequence, the second term is 5 more than twice of the first term and so on.  “5 more than twice of the first term” is the same as saying “5 more than 2n”, which is the same as saying “5+2n”.  So if the first term is n, the second term is 5+2n. What would the third term be?  5 more than twice of the second term?  That’s right!  (Algebraically, that would be 5+2(5+2n) which is the same as 15+4n.

So far, we have the

1st term: n

2nd term: 5+2n

3rd term: 15 + 4n

The question would usually ask you, what is the ratio of the first to the second term.  Or perhaps, what is the ratio of the third to the second term.  Ratios can sound terrifying, but they’re simply fractions.  So the ratio of the first term to the second term is the 1st term divided by 2nd term. In the example above, it would be n/(5+2n).  The ratio of the third to the second term is 3rd term / 2nd term, or (15+4n)/(5+2n).  Once you get past the wording for sequences, its actually pretty simple.  (If at this point you want to review translating words into equations, you should review Grockit’s helpful article about this).

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ACT English: Subject – Verb Agreement

By posted September 9, 2010

It’s extremely likely that you’ll face some questions in the ACT English section that test your knowledge of subject-verb agreement. With just a little practice this can be one of the easiest areas to rack up points in the English section.

Let’s look at some basic rules governing Subject-Verb construction.

1. Verbs agree with their subjects in person.

First-person:

I am a good student.

We are good students.

Second-person:

You are going to get a great ACT score!

Third-person:

He was very good at writing essays.

She is excellent at trigonometry.

Sharon is going to study abroad next year.

The movie was a romantic comedy.

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All About Circles

By posted September 7, 2010

There are four main things you need to know about circles to tackle any ACT Math question.

  1. The definition of Diameter and Radius.  For a pictorial illustration, see the diagram below.
  2. The formula for Circumference given by (diameter)(p)
  3. The formula for Area given by (p)(radius2)
  4. Knowing what fraction of the circle the sector is.  Note that a sector is what the ‘slice’ in the circle, an example sector is the yellow wedge show in the green circle.  The white part of the circle is also known as a sector, even though it doesn’t look like your typical ‘slice’.


Let’s try and apply the concepts to see if you understand.

Suppose I told you that the diameter of a circle is 12 cm.  What would be its circumference?  And what would be its area?  Simply apply the formulas to get:

circumference – (diameter)(π)-(12)(π)-12π

area-(π)(radius)²-(π)(6)²-36π

Don’t forget that radius is half of the diameter, so if the diameter is 12 cm, the radius is 6 cm.

The question might add another step by telling you that there is another circle with diameter 6 cm and ask how many times bigger, in terms of area, is the circle with diameter 12 cm than this circle?  Just because one has diameter 12 cm and the other has diameter 6 cm does not mean that the bigger circle is twice as big.

Use the formulas to figure out that the area of the new circle is 9π cm² while the area of the big circle is 36π cm², as we found out earlier.  This means that the bigger circle is 4 times as large as the smaller circle.

The last concept involves applying your knowledge of circumference and area to sectors.  Sectors are basically a fraction of the entire circle.  If I told you that the yellow sector in the circle above had an arc of 45° that means that it is 1/9 of the entire circle, because a circle has 360°.  The implications of this are two fold:

The arc length of the yellow wedge is also 1/9th of the circumference

The area of the yellow wedge is also 1/9th of the area of the circle

Thus, if I told you that the radius of that circle was 10 cm.  Then its circumference would be 10π cm and its area would be 25π cm².  Correspondingly, the arc length of the sector would be 10π/9 cm and the area of the sector would be 25π/9 cm².

If the question wants you to find the perimeter of the yellow wedge, all you have to do is add the radius twice to the arc length you found to get (10 + 10π) cm.

Remember these four concepts in mind and you’ll have the tools to solve any circle problem!  For practice, you could try solving these practice problems.

  • A circle has area 50π cm2.  A second circle has half the area of the first circle.  What is the diameter of the second circle?  (Ans: 10 cm)
  • A circle has a shaded sector.  The sector is 1/6 of the whole circle.  What is the area of the circle if the sector has area 6π cm2 ?  What is the diameter of the circle?  (Ans: 36π cm2; 12 cm)

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Sets: Tables or Venn Diagrams?

By posted September 5, 2010

It’s really a matter of preference; some students like to use Venn diagrams, and others make tables.  Personally, I prefer tables, but there is no “better” way.

On the SAT, you will encounter a few questions that contain overlapping groups with specific characteristics.  These are “set” questions, where one set had a certain characteristic (e.g. students in track & field), another set has another (e.g. students in band).  You will almost never see more than two characteristics (since you can’t draw 3D on your paper).  To illustrate, let’s take a look at the following example.

70 Children visited a doctor last week.  40 of them had a cold but not a cough.  20 of them had both a cold and a cough.  How many children do not have colds?

There are two characteristics (cough and cold) and two categories for each (yes or no), so there are four total combinations: with cough, without cough, with cold, without cold.

This table summarizes the information we have.

I’ve filled in the information from the question and the numbers in parenthesis is inferred.  If we sum vertically, we can infer that there are 60 total children with colds.  Because there are 70 total children, this also means that 10 do NOT have colds.  So the answer is 10.

We may also visualize the question as a Venn diagram, in which there are still two characteristics, represented by overlapping circles.

Note that the entire area OUTSIDE the “Cold” circle represents “Not Cold”. Therefore, if there are 60 children in the “Cold” circle, and 70 total, then there are 10 children without colds.

Let’s try another question.

Each of the dogs in a certain kennel is a single color.  Each of the dogs in the kennel either has long fur or does not.  Of the 45 dogs in the kennel, 26 have long fur, 17 are brown, and 8 are neither long-furred nor brown. How many long-furred dogs are brown?

A. 26

B. 19

C. 6

D. 8

Again, we are provided with a small amount of overlapping information and our table can simplify our visualization.  First, I filled in everything that was GIVEN in the question. That is the 17, 8, 26 and 45. The numbers in parentheses can be INFERRED. These are (19) and (28). Because all tables may sum both vertically and horizontally, you can use a combination of GIVEN and INFERRED information to find the correct answer (6) in the top-left quadrant.

Of all the types of math questions on the SAT, overlapping sets are some of the most like puzzles.  This should make you very, very excited.  Because who doesn’t like puzzles.  Got a tough set question?  Post below!

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