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Archive for December, 2009

Ratios, Proportions and Percentages

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If you knew your fractions and percentages, you probably won’t make the same mistake as the kid in the poem.  Two quarters is 50% of a dollar, three dimes is 30% of the dollar, 4 nickels is 20% of a dollar, 5 pennies is 5% of a dollar.  You would realize you’re getting less and less money even though you’re trading for more and more coins.  Ratios, proportions and percentages essentially deal with what fraction of a whole a certain piece constitutes.  SAT questions dealing with these concepts generally fall into very limited categories.  Here’s how to tackle them.

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Steps to Completing FAFSA

Filling out the Free Application for Federal Student Aid (FAFSA) is another necessary step these days as you apply for college. Unless your parents are Donald and Ivanka Trump, you will need financial help to cover college. Filling out the FAFSA is the first step to receiving this help, whether in the form of grants, loans, or work-study. This is the way colleges and universities determine how much aid you will receive; your final package will include elements of all three types of aid, whether grants, tuition you do not have to pay back, or loans, tuition you do, or work-study, work in exchange for tuition.

Don’t worry if you haven’t started the FAFSA, this year’s application is not available until January and the deadline is not until June, so you still have time, even after you apply for college. Just remember, after studying on Grockit for the SAT and ACT, make filling out the FAFSA a priority.

I would recommend that you apply online; this way you can cut down on paper and streamline the process. You must first request a four-digit PIN number. The address is here: http://www.pin.ed.gov/. This step is simple; all you need to know is your most basic personal information and your social security number. You can even predict the final aid package on their website thanks to the FAFSA4caster: http://www.fafsa4caster.ed.gov/F4CApp/index/index.jsf. This will give you an early indication of how much aid you may receive.

The next step is to fill out the application itself. For this you will need your parents’ income tax return forms from the past year (if you earned money you will need your tax returns too). You will also need a drivers license and social security number. For the final step, you will tell FAFSA which colleges you are applying to, so they can determine your aid. For this reason, you will need to know the school codes for your prospective colleges. You can find these through this website: http://www.fafsa.ed.gov/FOTWWebApp/FSLookupServlet. The schools’ aid award will depend on how much money your parents earn. The PIN will serve as your electronic signature.

The last step is perhaps the hardest: wait. You will receive your “Expected Family Contribution” in the Student Aid Report either in two to three weeks after filling out the paper form, or one business day after filing online. This will help the colleges make their final aid decisions. In April, you will hear back from your prospective schools about their admissions decisions and your financial aid package. It is up to you now to choose your college. Choose wisely and not simply on the aid package. Remember, you must reapply for FAFSA each year, and each year the amount you pay could change. Your dream school may seem unaffordable at first, but there are ways to make the price tag manageable. By working with your college’s financial aid office, you can negotiate your tuition into something reasonable. Your best education is a cause worth fighting for.

Semicolons, Colons, and Dashes on the ACT

While the comma is, hands down, the most important punctuation mark to know on the ACT, let’s not neglect the comma’s cousins: colons (which I just used), semicolons, and dashes. These three punctuation marks are probably the most confusing in English, and the function of one of them is often mistaken for the function of another. I’ll start with my personal favorite.

Semicolons: Semicolons are the most often tested punctuation mark of the three. Lucky for us, the rule with semicolon usage is simple: there must be an independent clause on either side of the semicolon. An independent clause, in layman’s terms, is a clause which can stand alone as a complete sentence. In uber-nerdy grammar terms, an independent clause is a group of words, with a subject and a verb, which expresses a complete thought. I don’t want to get too deep into a discussion of independent clauses versus dependent clauses, but here are a couple examples of what an independent clause looks like. In the following sentences, the independent clauses are italicized.

  1. Because it was raining, I brought my umbrella.
  2. Basketball games are fun to watch even if you aren’t a devoted fan of the sport.

The italicized clauses “I brought my umbrella” and “Basketball games are fun to watch” are independent clauses because they can stand on their own as complete sentences; they may be boring, but they are complete nonetheless.

Here’s an example of a sentence in need of a semicolon:

  • Students often don’t see the value of homework, they complete their assignments out of necessity rather than out of a desire to learn.

Here, we have two independent clauses (both clauses can stand alone as sentences) so closely related that they belong in the same sentence. The problem with this sentence is the comma; as it stands, this sentence is a comma splice. Just replace the comma with a semicolon to fix it:

  • Students often don’t see the value of homework; they complete their assignments out of necessity rather than out of a desire to learn.

Looking for extra ACT practice? Try this ACT English practice question and test your skills.
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How To Deal with One Long Passage on the SAT

I’ll admit it- even I don’t love long SAT passages. These passages are no one’s favorite since it can be easy to get bored and confused by them, so let’s focus on some important strategies that will help you better understand the passages and get more questions correct!

When faced with one long SAT reading comp passage, it is especially important to take notes as you read. Make sure you underline the main idea of the paragraph and circle any important details. When you finish reading one paragraph, make sure you write down what the function of that paragraph was before moving on. The function should answer the question: why did the author write this paragraph? How does it fit into the whole passage? What’s its purpose?

Some common functions include: to introduce the topic, to support the topic, to introduce a new viewpoint, to bring in a counterargument, to provide an example, to describe a hypothesis, to offer an explanation, etc. A passage is simply the sum of its parts (in this case, its paragraphs). If you understand the parts, you’ll understand the whole. Think of each paragraph in terms of a verb and you’ll be on your way to answering those tough “The third paragraph serves primarily to…” questions. The key rule here: Don’t keep reading if you don’t understand why the author wrote the paragraph.

Looking for more tips on rocking the SAT? Check out this post on the best tips for acing SAT writing.

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Making the most of your calculator on the ACT

2Only certain calculators are permitted while you are working on the Math section.  Be sure you check the ACT website for the most updated list of calculators because it is not worth it to get dismissed from the test for bringing in the an unauthorized calculator, such as the common TI-89 graphing calculator.  Certain other models of graphing calculators are allowed but note that you can only turn it on during the math section, and that if you finish early, you are not allowed to start playing the games on your calculator.  (I know Brick is addictive!)

The ACT math test is 60 minutes long and has 60 multiple choice questions.  Of those 60 questions, 24 questions will test you on basic algebra, linear equations and functions.  You shouldn’t need to use a calculator for this unless you need to evaluate a complicated function or to find the value of a number raised to an exponent.  Make sure you know where the “square” button is on your calculator or where the “to the power” button is.  The systems of linear equations on the ACT are generally fairly simple and with enough practice, you should be able to evaluate them quickly in your head.  Try not to waste time using your calculator to solve equations like 8x = 40.

Another 18 questions will test intermediate algebra and coordinate geometry.  It helps to know how to sketch quadratic and linear graphs without the aid of a graphing calculator.  To be honest, I only ever used my graphing calculator to construct lists for complicated or long statistics questions with a lot of data points.  If a question asks for the intersection point of two graphs, you can actually solve it quite quickly without plotting the graphs at all.  If you have time and you know how to plot graphs quickly on your calculator, you can do that and hover over the intersection points to see if you got the right coordinates.

Find out how Grockit can provide personal study plans and allows you to review your work with full explanations!

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Subject/Complement Agreement

So, you’ve conquered subject/verb agreement, pronoun case, and idiom usage. Bravo. Are you ready to move on to something a bit more challenging? This next topic in SAT Writing, if pondered long enough, can make even the pickiest English teachers scratch their heads. Lucky for us, though, the SAT isn’t malicious (I think). Once you nail the fundamentals of subject/complement agreement, leave the tough stuff for the grammarians.

First of all, what’s a complement? Look at the sentence “He is my friend.” In this simple example, “He” is the subject and “my friend” is the complement. Obviously, there is no agreement problem there. But how about this sentence: “Lions and tigers are the most ferocious beast of the animal kingdom.” Certainly, there is an issue with the complement “ferocious beast;” it should be plural since the subject is plural. Here’s a not-so-easy example:

1. The host asked his guests to bring a dish to the party.

This probably sounds fine to most of you. In fact, there may be some grammar authorities out there who insist that it is fine, but it is certainly ambiguous. The ambiguity in this sentence comes from the complement “a dish.” According to the SAT school of grammar, this sentence implies that the guests will collectively bring one giant dish. Imagine, if you will, a cluster of formally-dressed dinner guests huddling under a giant Tupperware container of potato salad, each guest doing his part to hold up the mass of mayonnaisey deliciousness. This is what the subject/complement problem does to us: it makes us imagine crazy things. To fix the problem, make the complement plural:

1. The host asked his guests to bring dishes to the party.

The tragedy is, of course, that we no longer know that each guest was required to bring just one dish. It’s a small price to pay to avoid that ridiculous image we thought of earlier. Can you think of a better way to write this sentence? If you did, you deserve a gold star. Here’s the best correction:

1. The host asked that each guest bring a dish to the party.

By changing the plural “guests” to the singular “each guest,” we eliminated the need to change the number of our complement. Don’t worry–you don’t have to be that clever on the SAT. That last correction was a tip for your own writing.

On the SAT Writing, you will most likely see singular complements that need to be plural, since we have a tendency to make that error in English. Here are a few more examples of sentences which violate subject/complement agreement:

2. After having to sit in the front row of the movie theater, the brothers complained that their neck was sore.

Though we know that each brother only has one neck, this sentence implies that the brothers share a neck.

Correction: After having to sit in the front row of the movie theater, the brothers complained that their necks were sore.

3. All children love their first grade teacher.

While we want to convey the idea that each child has only one first grade teacher, this sentence implies that there is one first grade teacher who teaches all children. If such a person existed, he or she would deserve an award–and a vacation.

Correction: All children love their first grade teachers.

4. All the women waited for their husband to arrive.

While we want to make it clear that each woman has only one husband, this sentence suggests that these women share a husband.

Correction: All the women waited for their husbands to arrive.

There is one more case we have to cover. When the complement is an abstract or uncountable noun, it remains singular. For example:

5. Despite the tempting offer to throw the game, the basketball players rejected the offer and retained their integrity.

Because “integrity” is an abstract noun and cannot be counted (we can’t have three integrities), we keep it singular: integrity.

6. After an intense game of four square, the kids drank water from the drinking fountain.

Notice that the only time you can “drink waters” is when you are drinking bottles of water. As the sentence indicates, such is not the case. “Water,” in its unbottled form, is an uncountable noun. No matter how many gallons of water there are in the ocean, water remains singular.

Just remember: if you can count it, make it plural. If you can’t, leave it alone. But be careful–these days you can bottle anything and make it countable (I wouldn’t be surprised if they sold bottles of integrity for three bucks a pop). I still like my uncountable nouns to be singular–the way nature intended.
Meet me in a Grockit game for more SAT ID sentence errors practice!

Picking the Right College

Often when you study for the ACT, you feel you must do well because, well, the schools are picking you and you need to do your best. Actually, the process is quite the opposite:you pick the school. Remember, you are spending the next four years there and you have the last word on where you go. When you take the reins of your college admission process, then you will choose wiser, feel better, and could even have some fun in the process.5

What are the dimensions of this choice? There are many categories for choosing a school, foremost academics. What are you planning on focusing on? If it is liberal arts, then try looking for schools that have a strong program, for example Washington and Lee in Virginia, Reed in Oregon, or Swarthmore in Pennsylvania (my school). If you are interested in nursing, why not check out the University of California in Los Angeles? Do you do better with large lecture type learning (Indiana University) or smaller classrooms (Hope College in Michigan)? Let’s be honest, though, most prospective freshmen do not know what they want to study, and you may not either. What then?

Choose another rubric to make your choice. For example, you may feel more comfortable at a school that is ethnically and racially diverse. Let’s face it, some schools are more diverse than others. According to the U.S. News and World Report, CUNY Baruch College (New York) is one of the most diverse colleges in the nation. Is this important to you? If so, then consider applying there or schools like Rutgers (New Jersey) or La Sierra College (California) which are also very diverse.

Up there with academics is college life. Some schools have no extra-curriculars, such as say, sports, others are completely focused on athletics to the extent of obsession. If you go to, say, The University of Michigan or The University of Southern California you will have to attend a football game at some point. If you are interested in being a journalist, check out the University of Missouri, which has an excellent program and a thriving student paper. Other schools, like Harvard University in Massachusetts are known for other extra-curricular pursuits, like their nationally recognized Harvard Lampoon humor magazine.

Greek life is another factor to consider. Do you want to join a fraternity or sorority? Some have very active chapters like Duke in North Carolina, others like Princeton University in New Jersey, do not encourage them. Some schools have very little social life going on. A commuter school will have fewer parties than one where students dorm. This is something to keep in mind. Do you want parties or do you want to hit the books and then go home?

Location is particularly important to most students. Eighty percent of college students will not travel out of state to attend college, according to USA Today. It is normal to want to stay near family and friends. Do you like the suburbs or do you want to experience the city life? Where do you want to live in five years? Perhaps you want to find the peaceful country life at a rural institution like Grinnell College in Iowa. Now is the time to explore, for college is the best time to acclimate to a new place—trust me, it is much easier to do this during school than after.

Maybe you want a school with a religious focus. Perhaps you plan to become a member of the clergy after college or you are just interested in your college life matching your beliefs. I will not recommend specific colleges, because there are just too many, but just know that they are out there. Whatever your religious persuasion, there are colleges and universities that can fit your profile.

There are reasons not to pick a school, foremost rankings, like those published in the U.S. News and World Report. This is of little value to anyone, including the schools, and should be ignored. Instead, choose the school that represents your interests and your personality best. There are many dimensions to picking a good college. Be very persistent on this one. This is four years of your life, and hopefully many of your best memories. It is of no sense to choose based on something like the percent of alumni who donate (a real factor in the U.S. News ranking). But don’t worry too much, thirty percent of college students transfer (according to the U.S. News and World Report), so you always have a second or third chance to get it right.

Functions

Functions look complicated but are in fact very easy once you understand how they work.  A function maps or sends a number to another number.

Take for example the function g.  Let g be defined as g(x) = x + 4.5  This means that when you apply the function “g” to any number “x”, it adds 4.5 to x.

So g(20) = 20 + 4.5  = 24.5

and g(0) = 0 + 4.5 = 4.5

The  key is to replace “x” with whatever you see in the brackets.  For example, if the function f was defined as f(x) = x2 – 2x +4, you can find f(2) by replacing “x” with “2” everywhere.

So f(2) = (2)2 -2(2) + 4 = 4 – 4 + 4 = 4

Suppose I want to find f(2n).  Then I would replace x with 2n and get

f(2n) = (2n)2 -2(2n) + 4 = 4n2 -4n +4

In the SAT, function questions usually involve several more steps, but now that you understand what the notation means, it shouldn’t be too hard.  The key thing to remember is to use the definition.  This means that whenever you see something like f(4) or g(n) or f(2n+1), look at what the function is defined as and replace x by whatever is in the brackets.

Suppose h(x) = x2 + 4

The question then tells you

h(2k) = h(k) + 12 and asks you what k is?

Look at the left hand side, you know from the definition that h(2k) = (2k)2 + 4 = 4k2 + 4

Now look at the right hand side of the equation. h(k) + 12 = (k2 + 4) + 12 = k2 + 16

Equating the two sides (since h(2k) = h(k) + 9) you get

4k2 + 4 = k2 + 16

This becomes an equation that you know how to solve!

3k2 = 12

k2 = 4

k = 2 or -2

Sometimes, the question might take it a step further and ask you for the value of h(k+1).  In which case, all you do is add 1 to k such that it becomes 3 or -1 and plug that into the definition.  You would get h(3) and h(-1) which you can double check to see if it comes out to 13 and 5.

Remember, doing the right practice will help!

ACT English: Pacing

The ACT English exam is one of the most difficult tests the ACT has to offer. This exam focuses on identifying and fixing grammar mistakes within passages, much like the SAT Writing’s “Improving Paragraphs” section. Each question will focus on one part of the passage and how to improve it. The test makers expect you to answer seventy-five questions in the span of 45 minutes, meaning you have less than a minute for each one, not enough time to be truly thorough. With Grockit practice, this test can become less daunting.

Just as a marathoner takes a couple of long runs before the race, you need to sit down with the ACT English and practice taking the test, in order to gauge your readiness. During the practice test you need to simulate the conditions of the test, meaning you must eliminate all distractions, and you need to time yourself. This way you will begin to pace correctly. Since on average you are given thirty-six seconds per question, give yourself about three minutes for each five questions. The exam is split up into five passages and each passage has fifteen questions, so if you are moving on to new essays every nine minutes, you are in good shape.

On your first “long run” your goal should be to finish under the time limit. For each time trial after, make sure you are more thorough and more polished as you make your way to the finish line. Awareness of time is important, but do not let this be a distraction. If you are practiced enough, the time should come as second nature, you will know how fast you are working. Remember, unlike the SAT Reading Comprehension, the hard questions are never the last ones. This is more reason to be steady.

Test your pacing skills with this ACT English practice question.

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Misplaced Modifiers

Remember what your mother always told you: don’t misplace your modifiers. …What? Your mother never told you that? I guess it was just me.

Misplaced modifiers are common errors in English often made by writers who have no idea what they want to say. Even worse, these people think they can cover up their ambiguity with a sentence structure that sounds nice; in reality, though, the structure only sounds nice when it’s used correctly. As a result, those who misplace modifiers end up sounding a little silly, which I think is hilarious.

Don’t be discouraged if you suspect you might be one of them. We’ve all been there. But, have no fear; I’m going to clear it up for you. Modifiers are words or phrases that, well, modify a noun or verb. They qualify the noun or verb, describe it, or change its meaning. A misplaced modifier happens to modify something that you did not intend to modify, often–or hopefully–with humorous consequences.

The most common type of misplaced modifier question on the ACT involves a modifying phrase. Here is a classic example from Grockit of a sentence on the ACT with a misplaced modifier:

1. Watching television in the evenings, the chair is where Dad relaxes before it is time to eat dinner.

I hope that everybody sees something seriously wrong with this sentence. As it stands, the sentence implies that the chair watches television in the evenings, which I find a little disturbing (nothing freaks me out more than the idea of animate furniture). When we begin the sentence with a modifying phrase like “Watching television in the evenings,” the first word after the comma must be the noun that the phrase describes. We must ask ourselves, “Who or what is watching television in the evenings?” The answer, of course, is “Dad,” not “the chair.”

To improve this wretched sentence, you would place the true subject of the sentence, Dad, right after the first comma:

1. Watching television in the evenings, Dad relaxes in the chair before it is time to eat dinner.

To improve it even further, you could rearrange the clauses to figure out what the author is really trying to say:

1. In the evenings, Dad relaxes in the chair and watches a bit of television before he eats dinner.

With this correction, we got rid of the original modifying phrase altogether. Sometimes, you just have to let go. Here are a few more examples of misplaced modifier sentences you might find on the ACT:

2. Known for his public-speaking ability, Barack Obama’s powerful speech received a standing ovation.

Use the same strategy for this sentence that you used for the last one. Ask yourself: Who is known for his public-speaking ability? Why, Barack Obama, of course! And what is the first thing you see after the comma? It’s Barack Obama, right? So, does that mean “Barack Obama” is the modified noun? Not quite. Notice that, in this sentence, Barack Obama is not the subject, but “speech” is. “Barack Obama’s” is a possessive noun (functioning as an adjective) that describes “speech.” Here’s how to fix it:

2. Known for his public-speaking ability, Barack Obama received a standing ovation for his powerful speech.

Now, Barack functions as the proper noun he is; “Barack Obama” is now the subject of the sentence.

Here’s another example, just to make sure all this makes sense:

3. After winning the Tour de France once again, the success of Lance Armstrong was easily attributed to his unmatched perseverance.

Correction:

3. After winning the Tour de France once again, Lance Armstrong easily attributed his success to his unmatched perseverance.

In the case that you cannot locate the noun modified by the modifying phrase, we call that a “dangling modifier.” For example:

4. Admiring the beautiful cloud formation, the sky seemed different that day.

Of course, we know that the sky cannot admire its own clouds. That’d be a little narcissistic (not to mention impossible). In fact, there is no noun in the sentence that could logically work as the correct subject. The writer probably meant something like this:

4. Admiring the beautiful cloud formation, I noticed that the sky seemed different that day.

To avoid dangling and misplaced modifiers, try to say what you mean. To spot them on the ACT, make sure the noun following a modifying phrase actually fits its description. Now, go impress your friends with what you’ve learned.