## PSAT/SAT & ACT Math Attack – Two Problems Today

1) 2 times a certain number is 4 less than the number, what is the number?

1. -4
2. -2
3. 1
4. 2
5. 3

Explanation: The first step is to express what you see in words in a mathematical equation you can actually solve.

(2 x n) = n – 4

After expressing the problem, try to simplify it as much as possible:

2n = n ­– 4

From here, it is simply a matter of dividing by n:

2n/n = (n – 4)/n

n = -4

That question was easy, so today we’re going to give you two:

2) The average (arithmetic mean) of three numbers is equal to 50. If one of the numbers is 10, what is the sum of the other two numbers?

1. 40
2. 90
3. 100
4. 140
5. 150

Explanation: If the arithmetic mean of three numbers is 50, then the sum of those three numbers is 150:

x/3 = 50

x = 150

If the sum of three numbers is 150, and we know that one of those three numbers is 10, then we know the sum of the other two numbers must be 140:

10 + y +z = 150

y + z = 140

Interested in more PSAT and SAT Sample Questions? Check them out here! Learn more about the Test Masters PSAT/SAT course here!

## PSAT/SAT & ACT Math Attack – Percent of Integers

The PSAT & SAT are notorious for asking complicated questions about seemingly simple concepts; this is one reason the PSAT & SAT Math sections can be so difficult. Following College Compass’ SAT Math Attack series will help you understand the concepts behind the questions.

1. What percent of the integers from 3 to 12, inclusive, are neither primes nor multiples of 4?
1. 20%
2. 30%
3. 40%
4. 60%
5. 70%

Explanation: The use of the word inclusive is meant to alert test-takers to the fact we are to include the numbers 3 & 12 in this problem. Including the numbers 3 & 12 brings the total number of integers being considered to 10:

3, 4, 5, 6, 7, 8, 9, 10, 11, 12

The first step is to get rid of all integers that are multiples of 4:

3, 4, 5, 6, 7, 8, 9, 10, 11, 12

The next step would be to eliminate all prime integers:

3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Of our initial integers, we have 3 remaining:

6, 9, 10

To determine the percentage we would simply take the number of remaining integers (3) and divide them by the number of integers we started with (10):

3/10 = 30%

Interested in more PSAT and SAT Sample Questions? Check them out here! Learn more about the Test Masters PSAT/SAT course here!

## PSAT/SAT & ACT Math Attack – Ice Rink Party

To rent a room for a party at an ice-skating rink, the charge is \$50 per hour plus \$2 per person attending the party. Which of the following functions represents the charge, in dollars, to rent a room at the rink for a 2-hour party if n people attend the party?

A. f(n) = 102n

B. f(n) = 200n

C. f(n) = 100n + 2

D. f(n) = 100 + 2n

E. f(n) = 100 + 2n

Explanation: If the charge to rent a room is \$50/hour, and you are trying to rent a room for 2 hours, you know the cost of just renting the room is:

\$50/hour x 2 hours = \$100

Any additional cost for renting the room is associated with the number of people who attend the party. The charge is \$2 per person, or:

\$2n

Added together, these two values are the total amount to rent a room at the ice-skating rink for a party. The total amount of money it would cost, represented as an equation, looks like:

\$100 + \$2n

Because we are being asked to express this as a function in dollars, we must express it as such:

f(n) = 100 + 2n

Interested in more PSAT and SAT Sample Questions? Check them out here! Learn more about the Test Masters PSAT/SAT course here!

## Grammar Crammer: That vs. Which

Both the SAT and ACT test grammar; the SAT in the Multiple Choice Writing Section, and the ACT in the English Test. A thorough knowledge of English grammar is also necessary if you want a top score on the essay section of either exam. We now have a series of posts to help: Grammar Crammer! In this post we’ll discuss one grammar rule that is frequently tested on both exams: that vs. which. See our previous post here.

Both that and which are relative pronouns that introduce relative clauses. For an explanation of these clauses, see our previous post, Grammar Crammer: Clause vs. Phrase. For example:

The man stole the car that was unlocked.

The man stole the car, which was parked under a tree.

So, what’s the difference? Well, the most obvious difference between the two sentences is that one has a comma while the other does not. Clauses that use which must be set off from the rest of the sentence with commas. If the above sentence continued after the clause “which was parked under a tree,” then you would need a comma after that phrase in addition to the one before it. Consider this example:

The car, which was under the tree, is long gone.

Relative clauses that begin with “that” should not be set off from the rest of the sentence:

The car that was stolen is long gone.

That’s really all you need to know for the test. But, why is there any difference at all? I’m so glad you asked!

This rule came about in the late nineteenth/early twentieth century, and was famously enshrined in Strunk & White’s The Elements of Style, one of the most influential books on grammar and usage in America. The justification for the rule is that “that” is used to introduce “restrictive clauses” while “which” is used to introduce “non-restrictive clauses.” What is the difference between a restrictive and a non-restrictive clause, you ask? A restrictive clause is a clause that contains information that is essential to the meaning of the sentence as a whole and cannot be left out without substantially altering the meaning of a sentence as a whole – it “restricts” the meaning of a sentence. Consider our previous example:

The man stole the car that was unlocked.

The fact that the car was unlocked was probably why the man decided to steal it and not another car, so the clause “that was unlocked” is considered to be restrictive. A non-restrictive clause on the other hand simply contains extra information that is just mentioned “by the way”; it could be left out without substantially changing the meaning of the sentence:

The man stole the car, which was parked under a tree.

The fact that the car was parked under a tree doesn’t have much to do with its being stolen, so this clause would be considered non-restrictive. Because restrictive clauses are integral parts of the entire sentence, they should not be separated from the rest of the sentence with commas; because non-restrictive clauses are not integral parts of the entire sentence, they should be separated from the rest of the sentence with commas.

If you’re not clear on the difference between restrictive and non-restrictive clauses, don’t worry. All you need to know for the SAT and ACT exams is that “which” needs commas and “that” doesn’t.

Interestingly, this rule didn’t actually exist before the twentieth century. For instance, consider the beginning of the Lord’s Prayer as translated in the King James version of the Bible:

“Our father which art in heaven, hallowed be thy name.”

Note that there is no comma before the word “which,” and the clause “which art in heaven” is restrictive, since it makes it clear that we’re talking about God, not your dad. According to Strunk and White, the bible would be wrong. However, because Strunk & White included this rule in their book, it became twentieth century English grammar law, and because the SAT and ACT were invented in the twentieth century, they test it, and because they test it, you have to know it.

Remember, if you want extra help studying for the SAT or ACT, you can always study with experts like me at Test Masters. Until next time, keep studying!

## Grammar Crammer: Clause vs. Phrase

Both the SAT and ACT test grammar; the SAT in the Multiple Choice Writing Section, and the ACT in the English Test. A thorough knowledge of English grammar is also necessary if you want a top score on the essay section of either exam. In this post we’ll discuss one grammar rule that, while not directly tested, is important to know in order to understand how many other grammar rules work: what is the difference between a clause and a phrase?

In a nutshell, a clause always has a subject and a verb; a phrase does not. All complete sentences must contain at least one independent clause. An independent clause is a clause that could potentially stand alone as a sentence. For example:

Pigs fly.

This is an independent clause: it has a subject (Pigs) and a verb (fly) and forms a complete thought that can stand on its own. There are also dependent clauses, which cannot stand alone for various reasons. Consider, for instance:

Who flies.

Unless this is a question, it would not make sense on its own, because we don’t know who is flying. “Who” is a relative pronoun: that means that it has to refer back to someone in order to make sense. Consider this version:

Superman is a superhero who flies.

Now, the dependent clause “who flies” makes sense because it is attached to an independent clause (Superman is a superhero) that tells us whom the word “who” refers to (Superman).

A phrase, on the other hand, is any group of words that does not form a complete clause. Usually, phrases function as distinct grammatical units. Consider for example a very common type of phrase: the prepositional phrase. Prepositional phrases always consist of a preposition followed by a noun which functions as its object:

Prepositional phrase = preposition + noun (object)

For example:

through the clouds

Here, “through” is the preposition and “the clouds” is the object of that preposition. Note that the phrase “though the clouds” does not make sense as a sentence on its own. It needs to be part of an independent clause:

Superman flies through the clouds.

Why is this important? Consider the following sentence:

The man who flies in the air by planes with steel wings are very strong.

There is something wrong with this sentence. What is very strong? The wings? Or the man? The man, of course, because the man is the subject of the independent clause. Because “the man” is a singular noun, the plural verb “are” should be changed to the singular version “is.” Notice that the plural “are” does agree with the plural “wings”; however, the “wings” are the object of the preposition “with,” and the object of a preposition can never be the subject of a sentence. This is a common trick the test makers use to try to confuse students: they separate the subject of a clause from its verb with intervening wastes of prepositional phrases and hope that by the time you get to the verb you will have forgotten what the subject was.

One of the best things you can do on any grammar question is start by identifying the subject and verb of each clause in the sentence. Even if there aren’t any subject/verb agreement errors, you will have identified the essential structure of the sentence and will be well prepared to find other errors after that.

Remember, if you want extra help studying for the SAT or ACT, you can always study with experts like me at Test Masters. Until next time, keep studying!

## What does it really take to get into the Ivy League? Part IX: Checklist

Welcome back to College Compass’s series, What does it really take to get into the Ivy League? Now that we’ve covered all of the aspects of applying to an Ivy League school, I have taken the liberty of compiling the main points from the preceding posts into a convenient Ivy League admissions checklist:

• Straight As, with maybe 2-3 Bs max
• As many AP/IB courses as possible
• Summer before Junior year: know PSAT National Merit cutoff score for your state, practice and aim above that score (may include test prep sercives).
• Take SAT and/or ACT multiple times (perhaps once at the end of Junior year and once at the beginning of Senior year), aim above 2100 on SAT and above 31 on ACT (may include test prep services).
• Always take AP exams at the end of AP classes, try to get 5s on all of them.
• Take two SAT II subject tests, aim above 700 on each.
• One creative extracurricular for all four years of high school.
• One athletic extracurricular for all four years of high school.
• One volunteering extracurricular for all four years of high school.
• Hold an office/leadership position in a school club or other organization.
• Win an award/recognition for one of your extracurriculars.
• Ask two teachers from either your Junior or Senior year (who taught classes in which you got As) for recommendation letters at least one month before the application deadline.
• Write an essay about something you love, and mention how the specific school you are applying to will help you pursue your dreams.
• If possible, apply to your top choice early decision.
• Do not apply to all of the Ivies. Narrow down your choice as much as possible.

Next time, we’ll have a few concluding remarks about applying and getting into Ivy League undergraduate programs. Until then, best of luck, and keep studying!

This post is part of a series. Other posts in this series include:

What does it really take to get into the Ivy League? Part I: Grades

What does it really take to get into the Ivy League? Part II: PSAT, SAT, and ACT

What does it really take to get into the Ivy League? Part III: AP, IB, and SAT II Exams

What does it really take to get into the Ivy League? Part IV: Extracurriculars

What does it really take to get into the Ivy League? Part V: Essays

What does it really take to get into the Ivy League? Part VI: Recommendations

What does it really take to get into the Ivy League? Part VII: Application Strategy

What does it really take to get into the Ivy League? Part VIII: Interviews

What does it really take to get into the Ivy League? Part IX: Checklist

What does it really take to get into the Ivy League? Part X: Epilogue

## What does it really take to get into the Ivy League? Part II: PSAT, SAT, and ACT

Last time, we discussed the number one, most important part of your application: grades. In this post, we will turn to the next most important, and easy to measure, part of your application: standardized test scores.

Should I take the SAT or the ACT? Do I need a perfect score? Do I have to be a National Merit Finalist? All these questions and more will be addressed in this post.

First of all, let’s discuss the two most common exams requested by almost all colleges: the SAT and the ACT. Elite, Ivy League-type colleges accept both the SAT and the ACT, and don’t have a preference between the two. It is thus common for aspiring students to take both exams and submit the scores from whichever one they did better on. Some students prefer one, others prefer the other. This blog has many resources dedicated to these tests, so I won’t dwell on comparing and contrasting them.

As to what score you need, consider the following: College Board currently states that at Harvard, the middle 50% of admitted students scored 690-790 on the Verbal section of the SAT, 700-800 on Math, and 690-790 on Writing; on the ACT, the middle 50% received a composite score of 31-35. So you don’t need a perfect score in order to get into Harvard (although that would help you to stand out). The ACT composite score is pretty self-explanatory, but for the SAT scores, remember that kids who scored 690 on Verbal probably got closer to 800 on Math, so a combined score of 2100 is probably a safe lower limit that you want to try to surpass, since that’s the score you would get if you got 700 on each section. For a really solid chance at getting in, I’d recommend aiming for a 2200-2250 combined score, and of course, the closer you get to that 2400, the better prepared you are.

The good thing about these standardized tests is that practice really does make perfect. I am firmly convinced that with enough practice, any college bound kid can make a perfect score on these exams. There are only so many things these exams test, and after doing practice, you begin to recognize the same old types of questions and vocab words coming up again and again. If you are willing to put in the time and effort, you can get your score as high as you want. A friend of mine at Columbia from Korea said that at her high school, they had an entire class just dedicated to the SAT, so they did SAT prep every school day for at least a year. If you did that you’d get a pretty amazing SAT score, too.

I also strongly recommend taking the exams multiple times. Most schools allow you to mix and match Verbal, Math, and Writing scores from different exams so that you can take your highest scores from each exam. In my case, I got an 800 on Verbal and a 790 on Writing one time I took the SAT, and a 760 on Math another time, but I still got to say I got a 2350 overall. The first time I took the SAT was in 7th grade, as part of Duke TIP’s 7th Grade Talent Search program (back before they added the writing section), and then, if I remember correctly, I took it two more times early in high school before taking it the two “real” times my Junior and Senior year. It is true that you can take it too many times your Junior and Senior year, but colleges don’t really care about exams you took before then.

For 1,300 years in Imperial China, entry into the elite civil service was determined by rigorous standardized exams that could last up to 72 hours.

As for the PSAT, preparing for the SAT will prepare you for the PSAT. The main differences between the two exams are that the PSAT is shorter and doesn’t have an essay section. The PSAT determines your national merit scholar status, which can be quite a feather in your cap, since the names of students who qualify as National Merit Semifinalists are released to colleges across the nation so they can start recruiting you and offering you scholarships. The PSAT score you need in order to qualify for national merit varies from state to state, since only the top 0.5% of scorers in each state qualify for consideration. Thus, if you live in a more populous state, or in a state with more money, or in a state with a better school system, it’s going to be harder to qualify because you’ll have more competition (if you want your state to have a better school system, register to vote when you turn 18 and start participating in state and local government!). You can find a list of score cutoffs here, and a more thorough explanation of the national merit process here.

Do you have to be a National Merit Finalist in order to get into the Ivy League? Well, in 2007 I was one of 56 National Merit Finalists at my high school (Bellaire Senior High School, in Houston, Texas – a public school, mind you!), and I think that included most of the people who got into elite colleges, so I would say try to make Semifinalist status at least. To prepare for the PSAT, you might consider doing some SAT prep the summer between Sophomore and Junior year, since the PSAT is normally taken your Junior year. Test Masters summer prep courses were like an annual rite of passage for most of my friends at Bellaire, so if it can work for them, it can work for you, too.

Next time on “What does it really take to get into the Ivy League?” we discuss AP, IB, and SAT II exams. In the mean time, keep studying!

This post is part of a series. Other posts in this series include:

What does it really take to get into the Ivy League? Part I: Grades

What does it really take to get into the Ivy League? Part II: PSAT, SAT, and ACT

What does it really take to get into the Ivy League? Part III: AP, IB, and SAT II Exams

What does it really take to get into the Ivy League? Part IV: Extracurriculars

What does it really take to get into the Ivy League? Part V: Essays

What does it really take to get into the Ivy League? Part VI: Recommendations

What does it really take to get into the Ivy League? Part VII: Application Strategy

What does it really take to get into the Ivy League? Part VIII: Interviews

What does it really take to get into the Ivy League? Part IX: Checklist

What does it really take to get into the Ivy League? Part X: Epilogue

## SAT or ACT? Which Exam Do You Take?

Having trouble deciding over taking the SAT or the ACT? Not even sure what the difference is? We’re here to point you in the right direction by providing facts about both exams.

GENERAL INFO

The SAT is divided into ten sections which include: 3 Critical Reading, 3 Math, 3 Writing, and 1 experimental section which is not scored.

Each section is scored from 200-800 points.

There is one required essay which is scored on a 0-12 scale.

Actual testing time without any breaks is 3 hours and 45 minutes. A perfect score on the SAT is a 2400.

The ACT is divided into four sections which include English, Math, Reading, and Science. Each section is scored on a scale, from lowest to highest, 1-36. Your composite score is the average from each of the four sections.

There is an optional essay that is scored on a 0-12 scale.

Actual testing time without any breaks is 3 hours and 25 minutes, not including the essay. A perfect score on the ACT is a 36.

GUESSING PENATLY

The SAT has a guessing penalty. For every answer that is marked wrong, ¼ point is subtracted from your raw score. The SAT made it this way so that all you lucky guessers out there cannot be awarded.

However, the ACT does not penalize for wrong answers. So rather than leaving your answers blank during the SAT, on the ACT you can bubble in every single answer without any added penalty.

ESSAY

The essay for the SAT is required, and you are allowed 25 minutes. It is scored on a scale of 0-12, and is factored into your overall score. The essay presents a broad issue in which you are to pick a side and support your argument using examples from history, literature, and/or current events.

A big difference here is that the essay on the ACT is optional, although more and more colleges are starting to require it. It is also scored on a 0-12 scale, but it is not included in your composite score. This essay will give you two different perspectives on a particularly controversial issue. You may choose to support one of these perspectives, or you can develop a response based on your own perspective.

VOCABULARY & SCIENCE

The SAT verbal section places much more emphasis on vocabulary as opposed to the ACT english section. So if you are good at memorizing vocabulary words, the SAT may be better for you.

The ACT does not place as much emphasis on memorizing a list of vocaublary words. But it does have a section that the SAT does not have, and that is the science section. This covers areas such as chemistry, biology, physics, and also earth science. The good thing about the ACT science section is that it does not necessarily require previous knowledge from your science classes. It simply tests your ability to read and understand graphs, scientific hypotheses, and research summaries. Statistically, those who do well with critical reading often do well on the ACT science reasoning test.

Most of the time, either exam is acceptable for college. But some colleges have their own specific preferences as to which exam they favor. When doing your college research, find out which schools prefer which exam. You can also check to find out the SAT and ACT scores that are required for admissions so that you have an idea as to which score you need to be shooting for.

## 4 Winter Break Tips 4 the Juniors

Final exams are almost finished and winter break is just around the corner! We understand that a vegged-out winter hibernation is much needed. You’ve worked extremely hard and you should be proud. Treat yourself to a little break and recharge those batteries. But don’t overdo it. There is a fine line between taking a break and going into full-on lazy mode. Do not cross that line Juniors, you still have work to do. Before you ring in the New Year, make it a goal to complete the following tasks:

2. Start Applying for Scholarships

While you have some down time, start searching for scholarship opportunities. Aside from using the internet as a resource, asking about scholarship opportunities is another great question that your counselor can help you with. When applying for scholarships, the key is to apply to as many as possible. Do not get discouraged if you get turned down. Just keep at it. There are plenty of scholarship opportunities out there for you. You just have to search around and find them.

Use your valuable break time to create your own resume. This will be particularly useful once you decide to attend a summer program or internship, or even a job opportunity. Now is a wonderful time for you to brainstorm information about yourself and your accomplishments so you can put it together on paper. There are many resume templates online to help guide you. Once again, this is another piece of information that your counselor can more than help you with.

4. Register for the SAT and/or ACT

Congratulations for those of you who are signed up for the January SAT! Way to be ahead of the curve! For the rest of you, we understand that you just took the PSAT and that you absolutely want nothing to do with another standardized test. Take a deep breath and count to ten. Now, go ahead and schedule yourself to take these exams sometime during the spring. By taking these exams during your junior year, it will help familiarize yourself and it will also make you a more comfortable test taker. Plus, your score will let you know whether or not you need to work on improvements over the summer.
For those of you who are not signed up for the January SAT, you can still register up to December 30. Late registration deadline is January 13. After that, the next available dates are:

March 10, 2012
May 5, 2012
June 2, 2012

Reach these winter break goals and you will truly enjoy your holiday break. See you next year!

## Exam Day = Game Day

Throughout your high school career, one of your biggest, yet most important worries may come from the SAT, ACT, SAT II, and even the AP exams. Here are some things to think about when preparing for these dreadful tests.

Treat These Exams The Way You Treat Your Hobbies.

Some of you might enjoy playing sports, or a musical instrument, or maybe you enjoy playing video games for hours on end. Whatever your hobby may be, in order to be really good at it, you must work at it every single day. So why should these exams be any different?

The Beginning Is Always The Hardest.

The first time you ever set foot on a soccer field, played the guitar, or picked up your Xbox controller, chances are you were probably terrible at it. You might have even embarrassed yourself. But it was okay because after working at it for a while, you finally got good at it. The same concept applies to your exams.

Nobody gets a perfect score on their exam the first time around. Just like your hobbies, your first practice exam will probably be quite an embarrasing performance. But after putting in the work and improving on your mistakes, you will eventually become a really good test taker.

Nothing Good Comes Easily. You Must Put In The Practice.

Why do you think your athletic coaches and music directors make you guys practice every single day? Because these are skills that must be drilled into you on a daily basis. Improvement and progress can only be made just a little bit each day.

Being in such after school activities you are required to do daily stretches and warm ups, followed by numerous drills, and then you may end with a scrimmage.

You must prepare for your exams in the same way. Set aside a reasonable amount of time each day for exam preparation. Maybe just 30 minutes, or even an hour. Pick just one subject to work on for that day. Do one set of practice problems as a daily warm up. Find out which problems you missed, and why you missed them. For your drills, work on ways to improve in these areas of weakness. Your scrimmages will be your full length practice tests.

You Must Be Ready Not Just Mentally, But Physically.

When you take these exams, you will most likely take them very early in the morning on a Saturday. Most of you guys have devoted Saturday as “Sleep-In Day”. This is unacceptable. This is when you must take your full length practice tests. So from now on, turn your Saturday into “Game Day”.

Not only do you have to train your body to be able to wake up abnormally early on Saturday, but once you’re up, you have to train your body to be able to endure a good 4-5 hours of solid test taking. There is no easy way around this, so get in the habit now.

You Cannot Cram The Week Before, And Especially Not The Night Before.

You absolutely cannot procrastinate when it comes to taking such important exams. Cramming will only prove to be harmful to you and your desired score.

Does Tom Brady cram the night before a big game by lifting every single weight in the gym? Does Michael Phelps cram the night before an olympic race by swimming hundreds of miles nonstop? Absolutely not. They would probably severely hurt themselves, and so would you if you tried the same method on your exams. You must commit yourself to practicing just a little bit each day the same way the professionals do.

Just Because You Got Did Well On A Practice Test Doesn’t Mean You Get To Quit Practicing!

You have to stay sharp when taking these exams, which means you have to continuously put in the work no matter what. Only after you take the real exam and achieve your dream score can you stop practicing. If the undefeated Green Bay Packers still have to go to practice, then so do you.