Grockit SAT ACT Prep

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Archive for May, 2010

Elementary Probability

Probability questions on the SAT basically test if you know one concept – the definition of probability.

Probability = Number of times a certain event might occur/Total number of events that might occur

So if a question tells you that there are 120 dorm rooms and 24 of them are painted yellow, the probability that a freshman is placed in a yellow dorm room is 24/120 = 1/5 because there are 24 yellow rooms that the freshman could be placed in, out of a total of 120 rooms.

Reverse probability

To make things difficult, the question might ask you a reverse probability question.  For example, if there are 120 dorm rooms and Amy has a  chance of 1/6 being placed in a blue room, then how many blue rooms are there?  Using the formula above, if there is a one in six chance of getting a blue room, that means that the number of blue rooms out of the total number of rooms is 1/6.  Since there are 120 rooms in total, then 1/6 = blue rooms / 120.  This works out to 20 blue rooms.

Probability of an event not happening

Another type of question is one like this.  Suppose there are only blue and red marbles in a bag.  Let the number of blue marbles be b and the number of red marbles be r. If the probability of drawing a blue marble is 5/7, what is the value of b/r?  The only number you have to work with is 5/7.  This number represents the odds of picking a blue marble, meaning that 5/7 = number of blue marbles / total number of marbles.  You can thus let there be 5 blue marbles and 7 marbles in total.  This means that there are 2 red marbles, so the value b/r is 5/2.

This type of question is essentially testing if you know how to find the probability of an event not happening.  If the probability of getting a blue marble is 5/7, that means that the probability of not getting a blue marble (i.e. getting a red marble) is 1 – 5/7 or 2/7.

Probability of multiple events

The most difficult type of probability question on the SAT generally involves 2 dice.  Remember the question tells you that Joe rolls a pair of dice and forms a fraction x/y where x represents the number rolled on the first die and y represents the number rolled on the second die?  It then asks for the probability that this fraction equals 1.  To work out this problem, you need to know the total number of dice rolls that could occur.  Each dice can roll 6 different numbers, which means that with 2 dice, there are 6 x 6 = 36 possible combinations.  Of those 36 combinations, there are 6 ways of forming a fraction that equals 1.  If a 1 and 1, or a 2 and 2, or a 3 and 3, or a 4 and 4, or a 5 and 5 or a 6 and 6 is rolled.  In each of these cases, the fraction will equal 1.

So since there are 6 cases that give us the value we need, out of a possible 36, the probability is 6/36 = 1/6

Don’t forget that the probability of an event can never exceed 1.  If the probability of an event is 1, that means that it is certain to happen.  If the probability of an event is 0, that means that there is no chance of it ever happening.  Probability values never go higher than 1 or lower than 0, so if you find yourself with such an answer, double check to see what went wrong.

Check out Grockit for more probability practice!

Whiteboard on Grockit!

Whiteboard is another new feature that helps make Grockit a great learning environment. Imagine a chalkboard in your web browser! Students can draw images and write out equations together in the same space. For math questions, there are pre-set geometric shapes, coordinate grids and coloring tools to easily map out graphical solutions. For English questions, students may edit sentences by copy-pasting text from the question into the whiteboard and applying any mark-up they like.

Grockit Instuctors will enjoy all the same tools for their lessons. Using Whiteboard in combination with our new Audio feature will allow students to visualize what the teacher is actually talking about. Additionally, instructors will have the ability to dictate which students can “come to the board” to work on a particular problem. Very cool!

Here is a screenshot using Whiteboard to draw a diagram to help solve an angles problem:

Summer Plans

The great thing about college in America is the breadth of classes available and the freedom to shop around before you decide what you want to major in.  The downside is that if you don’t know what you want to do, you spend more time shopping around, taking introductory courses rather than taking more classes than required in your chosen major.  While you might think that doing more than is necessary is a waste of time, specializing in your major indicates to your future employer that you are interested in what you are doing, that you do more than what is necessary and lets you get to know your professors better.

One way to decide what you would like to major in before you get to college is to take a pre-college summer program in whatever interests you.  That way, you can determine if pre-med, or political science or anthropology is really how you want to spend the next four years of your life.  Furthermore, the courses offered often count for course credit, so you might be able to get some easy courses out of the way.

If you are interested in science, Stony Brook University offers a Biotechnology Summer Camp, MIT offers a Minority Introduction to Engineering, Entrepreneurship and Science program (MITE2S), and Boston University offers research internships in science and engineering.  Brown offers an online Exploring Engineering: Problem solving in Biotech, Nanotech & Renewable Energy course too.  There are many more science programs out there and while some are pricier than others, most offer some sort of financial aid.  Not only will you get a head start on your college career, you will also be able to add something interesting to your resume and meet many other like-minded college bound students.

If you are interested in math like I am, you could try the Ross Mathematics Program at the Ohio State University, the Michigan Math & Science Scholars Program at the University of Michigan, the Mathematics for Young Scientists program at Boston University, or the Pre College at Math Institute at Stanford.  I discovered too late in college that pure, theoretical math was not quite my cup of tea and wanted to switch to Statistics, so I hope you do not end up making the same mistake.

If writing and the arts interest you, you might want to look into the Iowa Young Writer’s Studio conducted by the University of Iowa’s prestigious creative writing program, or the Emerging Writer’s Institute at UC Berkeley or the Institute for Young Writers at the University of Massachussets Amherst, or the Center for Creative Youth at Wesleyan.  Several other universities, which do not offer specific writing programs, allow you to choose from over a hundred college level courses and feature several writing seminars.

Getting a head start on college is always a good thing.  It’ll be an opportunity for you to live independently for a few weeks and experience dorm life before you embark on the real thing.   It will also let you experience first hand, what it might be like as pursuing your chosen major for the next 3 to 4 years.  Hopefully, that will save you some shopping time when you are actually in college so that you can concentrate and become a pro in your chosen field!

College Spotlight: Sarah Lawrence

Have you ever dreamed of not having to worry about grades?  Do you hate the idea of huge, anonymous lecture halls?  If so, you might want to consider Sarah Lawrence College, which is located roughly fifteen miles north of Manhattan, New York, in a small town called Yonkers.

Founded in 1926 as an all-women’s college, Sarah Lawrence is known for its liberal arts education.  Rather than declaring majors, students are allowed to design their own curricula, or “concentrations.”   All students work closely with their academic advisors, called “dons,” to design their concentrations.

Students choose their courses from four major areas of study: history and the social sciences, humanities, natural sciences and mathematics, and creative and performing arts.  Students only take three courses per semester.  Most classes are run using a seminar-conference system; each class, usually consisting of no more than 10 students, meets twice a week with the professor to have in-depth discussions about projects and readings.  All courses focus heavily on developing students’ writing skills.

Sarah Lawrence has one of the lowest student-to-faculty ratios in the country: 9:1.  Since classes are rather intense – students are limited to only three per semester, and spend dozens of hours in discussion with the professor – students get to interview professors before deciding upon their classes.  At the end of each course, rather than receiving a grade, students receive detailed written evaluations from their professors.

Sarah Lawrence is no longer an all-women’s school; it began accepting males in 1968, and currently men comprise 26% of the 1,240 undergraduates at Sarah Lawrence.  Approximately 37% of applicants are admitted to Sarah Lawrence, and the average high school GPA is 3.6.

You might recall Sarah Lawrence from the movie 10 Things I Hate About You; angsty teen Julia Styles dreams of attending Sarah Lawrence.  There are many well-known, non-fictional Sarah Lawrence alumni, as well.  The school has been home to both individualistic women like Barbara Walters, Yoko Ono, Vera Wang, and Alice Walker, as well as male celebrities like J.J. Abrams (creator of the TV show “LOST”), and Cary Elwes, better known as the “Dread Pirate Roberts” from The Princess Bride.

There is one major downside to Sarah Lawrence; it is now the most expensive school in the country, with one year’s tuition costing roughly $55,000.  But don’t let that deter you – they provide financial aid, and offer many scholarships.

ACT vs. SAT

It’s the ultimate showdown between the frightening acronyms: SAT or ACT? Which test should you take? On which test will you score better? You may (and should) have a lot of questions like these as standardized testing seasons rolls around.

First, find out which tests are accepted at the schools you’re applying to. You will rarely find a school that only accepts the ACT; the SAT is still the more standard of the two, and nearly all colleges accept it. Most colleges on the East and West Coasts still require the SAT, though the acceptance of the ACT is steadily increasing. It is your job to review the application requirements for each prospective school; if the wording is unclear, call the school.

If you’ve discovered that you have your choice between the two tests, you’ll want to learn a bit about each test and your strengths and weaknesses as a test taker. According to the test-makers, the SAT is a “reasoning-based” test and the ACT is a “knowledge-based” test. The SAT strives to test your ability to reason your way through tricky–and sometimes deliberately confusing–questions. The ACT, on the other hand, tests your expected knowledge accumulated through high school courses. Experts say that adept test-takers excel at the SAT, while exceptionally studious and industrious students excel at the ACT.

To really figure out which test is for you, however, don’t waste time trying to place yourself in one of these rigid categories–most of you are somewhere in between. The best way to make your decision is to try practice tests; identify which test you are more comfortable with and which test you score better on.

Before you begin exploring, though, here are some key differences in academic content that may aid your decision:

  • The SAT tests vocabulary; the ACT doesn’t.
  • The ACT’s writing section is optional; the SAT’s is mandatory (though some colleges neglect your Writing score).
  • The ACT includes a Scientific Reasoning portion that tests your ability to analyze scientific data and research; the SAT doesn’t.
  • The ACT’s math section includes Trigonometry (about seven percent of the section); the SAT’s math does not exceed Algebra 2.
  • The SAT penalizes wrong answers; the ACT doesn’t–guess away.

Let these distinctions aid your decision-making, but be sure to experience each test before coming to a conclusion. Your high school should offer the PSAT and PLAN, the respective practice exams of the SAT and ACT.

If you happen to be a waffling overachiever who performs equally well on each test (thanks for making the rest of s look bad), taking both tests may be right for you. This way, the admissions office will accept the higher of the two scores. For most, though, one test is certainly enough.

Check out Grockit to find your strengths on the SAT and ACT today!

Finding Averages

SAT questions testing you on averages usually require you to realize that if the average of x numbers is n, then the sum of the x numbers is nx.  To illustrate with a numerical example: if the average age of 5 girls is 8, then the sum of their ages must be 5*8=40.

Knowing this principle is extremely important.  Let’s try and do a few questions together so that you can see how it works.

If the average grade of k students is 51 and the average grade of m students is 64 and the average of all the students is 54.  Then find k/m

  1. if the average of k students is 51, the total score of the k students = 51k
  2. if the average of m students is 64, the total score of the m students = 64m
  3. if the average score of all the students is 54, the total score of (k + m) students = 54(k + m)
  4. since the total score of k students + total score of m students = total score of all the students, then

51k + 64m = 54(k + m)

Most of you might get here and worry about getting k/m.  It’s actually not that difficult.  If you expand out the equation you get 51k + 64m = 54k + 54m.  Putting the k’s on one side and the m’s on the other, you get 10m = 3k.  Dividing both sides by m, then dividing by 3, you get k/m = 10/3

If a question tells you that in finding the average of a group of things, some values were measured wrongly, then here are the steps you should take.

  1. Given the average, find the total by multiplying the average by the number of things in the group.
  2. Subtract or add the incorrect amount from this total
  3. Divide by the number of things to find the actual average.

For example, if the average of John, Bob and Sally’s backpacks is 60lbs and the person weighing the bags forgot to set it to zero and added 10lbs to each of the measurements, what is the real average of the three bags?

  1. Find the total: 60lbs x 3 = 180 lbs
  2. Subtract the false weight that was added, which was 10lbs per bag, so 180lbs – 30lbs = 150lbs
  3. Divide 150lbs by 3 to find the actual average: 150 lbs / 3 = 50 lbs

The last type of averages question usually wants you to find a new average when the number of items has changed.  In this case, you have to find the total of all the items given, subtract the value of the items they don’t want, and divide by the remaining number of items to get the new average.

For example, if Adam, Bob and Chris has an average age of 12 and Chris is 8 years old, what’s the average age of Adam and Bob.  You would take 12*3 = 36 to find the total age of Adam, Bob and Chris.  Subtract Chris’ age 8 to get 28 and divide that by 2 (because its only Adam and Bob now) to get the new average of 14.

Conversely, the question could also look like this: Adam and Bob’s average age is 14.  When Chris’ age is added, the average is now 12.  How old is Chris?

  • Adam + Bob + Chris’ age = 12*3 = 36
  • Adam + Bob’s age = 14*2 = 28
  • So Chris’ age is 36 – 28 = 8

Remember, when dealing with averages, unless it’s a straightforward question that applies the definition of average, you usually need to find the total first, adjust it to what the question needs and then find the new average.

ACT English: Word Connotations

Though the English language abounds with synonyms, very few exact synonyms exist. Words with similar meanings often carry different connotations, i.e. the culturally subjective meanings or emotional associations suggested by certain words. A word’s connotation is different from its denotation, or standard dictionary meaning. Though the ACT English will not test you on difficult vocabulary with obscure meanings or denotations, it may test your ability to recognize the connotations of familiar words, especially those with similar denotations.

You may not have realized it, but word connotation is one of the few linguistic topics we often discuss in casual discourse. Friends or couples may fight over one’s unwitting misuse of a certain word (e.g. when intending to compliment a friend’s thin physique, the word “scrawny” may slip out). Schoolmates may playfully argue over the subtle but important differences between slang terms: that which is not particularly “cool” may be “rad,” and something that “sucks” may also, paradoxically, “blow” (pardon the anachronisms). Studying word connotations, then, can be as fun as it is edifying; it will improve your ability to converse effectively (and diplomatically) as much as your ability to write formally.

To really grasp the importance of word connotations, let’s look at some familiar examples. Remember the “scrawny” scenario I just gave you? The adjective “thin” has many synonyms with vastly different connotations: skinny, slim, slender, bony, scrawny, lean, emaciated, skeletal, svelte, gaunt, etc. Looking at the list, you may notice that some of the words have positive connotations while others have negative or pejorative connotations. “Slim,” “lean,” and “slender,” for example, often connote a healthy physique; you might compliment a successful dieter with the words “slim,” “lean,” or “slender.” Words like “bony” and “scrawny,” however, aren’t so positive. A “bony” person looks so thin that he or she is unattractive or unhealthy looking. A “scrawny” person is a thin person who appears feeble. Words like “emaciated” and “gaunt” both connote an extreme thinness, but there are even clear differences between their connotations: “emaciated” connotes a severe wasting away of the body characteristic of medical illness, and “gaunt,” a far less formal word, emphasizes the physiognomic characteristics of a weary and hungry person.

On the ACT English, some questions may ask you to critically examine the author’s word choice, paying strict attention to word connotation. In these circumstances, it is imperative that you accurately identify the author’s tone, or his attitude toward his subject. If the author clearly has bitter feelings about his subject, you may want to choose words with negative connotations. For example, if the author bitterly describes a business’s frustratingly thrifty financial behavior, you may opt for the words “cheap” and “stingy.” Conversely, if the author tries to promote that same business, you should opt for words like “frugal” and “prudent.” Most often, authors of sample texts are formal and neutral in tone, and the word choice should reflect that. If you detect a formal tone, avoid words that carry extreme connotations. Sometimes, an accurate phrase may suffice; if your author strives for neutrality in the above example, the phrase “careful with money” will be a better choice than “cheap” or “stingy.”

Just remember, when you are unsure of a word’s connotation, think of a situation when you would use it. It may be difficult to articulate a word’s connotation, but we can often imagine a circumstance that calls for a certain word. Let your imagination do most of the work here. Connotations are not to be memorized like obscure vocabulary words. You probably know most of them already; the more detailed your imagined context for a word, the more accurate you’ll be.

Verb Tense

Verb tense is often a simple error to spot on Writing multiple choice problems, but when it comes to harder problems, you really should know the ins and outs of verb tense.

It’s easy to spot errors like “I will play basketball yesterday.” We know that such a sentence is logically impossible, and to fix it, we simply change the future tense to the past tense: I played basketball yesterday.

Many problems, however, aren’t so simple. To master these, it’s best to learn the different tenses in English–the ones most often tested on the SAT–and their function.

First, let’s take a look at the simple tenses:
Simple Present: The man runs. (He’s running right now)
Simple Past: The man ran yesterday. (He ran in the past)
Simple Future: The man will run tomorrow. (He will run in the future)

You may be thinking “duh,” but it helps to organize your knowledge of tenses–even the easy ones.

Here are the perfect tenses. The perfect tenses are a bit more complicated.

Present Perfect: I have practiced, so I am ready for the recital.

The present perfect often indicates something that you have just done, or something that you did in the past and may continue to do so or are doing so at the moment). Think of this example where we use present perfect vs. past: John (worked / has worked) at the coffee shop for three years. Notice that “worked” would tell us that John no longer works at the coffee shop; he’s talking about three years of his life that have already passed. If we use “has worked,” though, it suggests that John has worked at the shop for three years and continues to work there.

Past Perfect: I had practiced, so I played well at the recital.

The past perfect is used to indicate an action that occurred before another action in the past. Notice that both the practicing and the recital took place in the past, but we want to communicate the order of events: practicing took place before the recital. Thus, we use the past perfect for the practicing, and the simple past for the “playing well.”

Future Perfect: I will have practiced, so I will play well in the recital.

The future perfect is used to indicate an action that took place before another action in the future. We know that the practicing and the recital will both take place in the future, but I will certainly practice before the recital (but haven’t done so yet. This example sentence suggests that I have made a prediction about events in the future. It’s like saying: Don’t worry about me. By the time the recital comes around, I will have practiced, and I will be great.

Now that we know the tenses, let’s explore what some tense problems might look like.

Here’s an example from Grockit to get us started:

Without a doubt, one of the most interesting things about our trip to Paris next May was the change from speaking in English to speaking in French.

Here, we have to figure out the true tense of the sentence from a tense cue, “Our trip to Paris next May.” If the trip happens next May, then it will take place in the future. Thus, we cannot speak of the trip in past tense with the verb “was.” Change that “was” to “will be.”

Here’s another example that tests something different while still testing knowledge of tenses:

When he claimed that he had spoke to the dignitary, Ken neglected to mention that the correspondence had been conducted chiefly through her secretary.

The problem here is not with the kind of tense used, but the improper application of that tense. The author wants to use the past perfect of “speak,” but says “had spoke” instead of “had spoken.” In all the perfect tenses, we must use the past participle of the word, which does not always look like the past tense of a word. The past participle of speak is “spoken.” The past participle of drink is “drunk.” The past participle of swim is “swum.” If any of these surprise you, review a list of irregular English verbs to fortify yourself against these nitpicky tense questions.

Making College Affordable

According to College Board, average2009-10 tuition fees at private four-year colleges are $26,273 (up 4.4% from the previous year) and $7,020 at public four-year colleges (up 6.5%).   And this doesn’t even other costs such as food, rent, and textbooks!  So how are you going to keep college affordable?

The most important thing that you can do is to complete the FAFSA form when you are applying to colleges.  FAFSA stands for free application for federal student aid and most colleges generally require that you submit this form.  FAFSA is responsible for most offers of financial aid and the application would put you in the running for federal and state need-based grants, loans, work-student programs, institutional grants and scholarships.

Aid typically comes in three forms.  Grants vs. loans vs. work-study.  Grants generally do not need to be repaid, loans have to be repaid but the interest is very low and work-study opportunities guarantees you a job, on campus typically.  Some colleges, particularly private schools, will also have a separate financial aid form to determine how much the school themselves can offer you.  This is separate from federal aid, which makes it open to international students who do not qualify for federal aid.

You should expect that whatever aid you receive would not cover 100% of the cost of attendance.  Schools determine your financial need by subtracting the expected family contribution from the estimated cost of attendance.

Cost of attendance – expected family contribution = financial need

Most people I know receive different types of financial aid to help alleviate the cost.  In college, you should keep an eye out for departmental awards and writing competitions.  Internships are another good way of getting college credit or a stipend and networking with an eye to a future job offer.  If volunteer service or teaching speaks to you, you should also consider Americorps or Teach for America.  These two-year service programs help pay for future educational expenses (in grad school) or to repay qualified student loans.  They also award an education award at the end of each year of service.

There are also some things you could do in high school to up your chances of getting a bigger aid package.  Start practicing on Grockit early to improve your SAT score so that you can sign up to take the Preliminary SAT/National Merit Scholarship Qualifying Test.  Not only will this test give you feedback on your future performance on the SAT, it lets you enter the National Merit Scholarship Corporation’s programs.

Must Have iPhone Apps for College

Taking your iPhone to college? Upgrading or purchasing a new phone to keep in touch with family and friends? Here are the Top 18 must-have iPhone apps that will make your college transition that much easier! (And because you’re going to be on a budget, they’re all free!)

Wikipanion Let’s you access Wikipedia from your phone. No idea what your professor is talking about? Look it up before anyone else!

Associated Press News Feed – Keep up on the latest news from all over the world.

Craigsphone – Looking for a new roommate? Check the craigslistings from your phone!

Amazon Mobile – Book store prices too expensive? See if you can find a cheap used edition on Amazon!

Wordbook English Dictionary and Thesaurus – Lookup definitions and synonyms to and improve the syntax of your term papers.

Mobile calculators – Do simple calculations on your phone. A fully-functional graphing calculator app is available for less than $5!

iHomework – Manage your homework schedule with this awesome organization app. Use it as a planner to keep track of your assignments and obligations!

MyWisdom – This great app includes a searchable database of quotes organized by category. Find a great quote to introduce your essay topic!

Sparky – A fast and easy way to browse SparkNotes online.

Word of the Day Lite – Learn a new word every day – the quickest way to improving your vocabulary!

Pizza! – Dining hall closed? Find the closest (and cheapest) pizza near your dorm room!

Free Wi-Fi finder – Wanna know which coffee houses near campus have wi-fi? Use this app and you’ll soon be sipping your chai latte and blogging away.

iTranslator – Studying a foreign language? Thinking of studying abroad? This app will help you connect to Google Translator, Babel Fish or Free Translation.

Take Me Home, I’m Lost! – Lost in a new city? This app will help you find your way back to your dorm!

Stress Reducer – Let’s face it – college can get stressful! This app can play soothing ocean noises through a virtual shell.

Blackboard LearnA great way to access Blackboard on the go! Find out about next week’s homework and look-up your test grades!

MyGPA Calculator – Use this app to calculate your GPA for each quarter or semester.

College Football Live! – Sports fanatic? Keep up with all the latest college football statistics.

And, of course, Grockit’s SAT FlashCard app if you haven’t taken the SAT yet!