2010 April | Grockit SAT ACT Test Prep

Number Lines

By amanda chen posted April 29, 2010

There are typically two types of number line problems:

questions that show you an actual number line that require you to estimate and know properties of positive/negative numbers and decimals
and questions that require you to translate a word problem into a number line.

When a question gives you a drawing of a number line, always look out for which points are between -1 and 1. Numbers whose absolute values are less than 1 are points B, C, D, E, F, G in the picture below. An important property to note is that when these points are multiplied with another point that is greater than 1, it makes that number smaller. Try it! Suppose G is 0.5 and H is 1.5. GxH is 0.75 which is smaller than H.

Another important property to note is what happens when you multiply two negative points together or when you multiply a negative and a positive point. Two negatives make a positive, meaning BxC gives you a positive number – either E, F or G because those points are positive and less than 1. A negative and a positive makes a negative. So BxG would either be point C or D. If you estimate what the values of those points are, you would be able to say with greater certainty too that BxG has to be point D.

Here’s another number line question where the line is given.

If there are 8 equal intervals between 0 and 1. What is the value of x? I would start counting the number of points until I get to the one labeled √x and realize that it is the point 6/8 which is also 3/4 . Since √x – 3/4 that means that x – 9/16.

The other type of question requires you to translate a word problem into a number line. Let’s start off with an easy word problem.

The number m – 4 is how much less than the number m + 5?

I would draw a number line like the one above. And let m equal a number. Suppose m=0. That means that m-4 = -4 and m+5=5. If I circle -4 and 5 on the number line and count the spaces in between, I would realize that they are 9 units apart.

Here’s a longer question. An important thing to note about “number lines” is that it generally refers to the x-axis. So if points A and C are located on a number line such that AC=6 that means you can draw and x-y graph and put A and C as two points on the x-axis, 6 units apart. If I then tell you that point E is also on the x-y plane and located so that AE=3, where could you put E? You could put E on the x-axis between A and C or to the left of A.

That means that if A is at (1,0) and C at (7,0), then E could be at (-2, 0) or (4,0)

Or E could not be on the number line if you put E 3 units above A or 3 units below A.

The most difficult type of number line problem is the word problem. Try sketching a map of the buildings and stores in the following problem: Highland High School lies exactly halfway between the East and West bridges of town. Piggy’s Pizza lies halfway between the high school and the East bridge. Paul’s sub shop lies somewhere between the high school and the West bridge. All buildings form a straight line from the East bridge to the West Bridge. If Paul’s is 8 miles from the West Bridge and Piggy’s is 13 miles from the East bridge, how far is it from Paul’s to Piggy’s?

Did you manage to get the figure above? Since Highland HS is exactly halfway between the bridges that means that it must be 26 miles – 8 miles = 18 miles between the high school and Pual’s sub shop. So Piggy’s to Paul’s = 13 miles + 18 miles = 31 miles.

If you liked the examples on the page, try a custom number line math SAT game on Grockit!

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Interview Skills

By jordan schonig posted April 27, 2010

Let’s face it–you can’t stay in school forever. Sooner or later, you will have to get a job. Yikes. Just the sound of that three letter word makes me squirm. Whether you want to get a job in college to build your résumé or wait until you graduate, you will have to face the dreaded interview process.

Before we go over a few tips for acing the interview, there is one important thing you should know: interviewers can smell your fear. They secretly count every “um” you utter and every fidget you make on a tally sheet behind their desks. Their questions are impossible to answer correctly. They are malicious robots bent on world domination, fueled solely by your complete and utter failure. OK, enough of that. I’m only kidding of course.

While an interview may be intimidating, it remains a necessary process for employers to become acquainted with their applicants. Think of the interview as a chance for you to show off your most marketable qualities, not as an inquisition that exposes your weaknesses. You want to show the interviewer that you possess not only the skills and experience for the position, but also a fitting personality for the company culture. Here’s how to show those interviewers that you have the right stuff:

Do Your Research: Before your interview, make sure you have thoroughly researched the company you are applying for. The best place to find this information is the company website, if they have one, of course. If you are a true overachiever, you’ll want to get your hands on materials that may be available at the company. If you know anybody who is or has been an employee with the company, or who uses their resources, ask him for advice. And if you want to make somebody else do all the work, call the company and try to gather some info from a receptionist or salesperson. The more you know about the company and the position, the better you can market yourself for the specific needs of the company.
Dress the Part: Make sure you dress appropriately for the interview, and err on the side of overdressing. In other words,leave your Che Guevara T-shirt, ripped jeans, and worn Chuck Taylors at home. If you are applying at an office, make sure you wear a professional business suit. If the environment is a bit more lax, then slacks, khakis, button-down shirts/blouses, skirts, and dresses will work. If you are not sure, then overdress! The interviewer will not fault you for looking better than him, so go for it.
Get There Early: Showing up late to an interview can be the kiss of death for some applicants. Some interviewers may be merciful–others may not. It is your job to plan for those not-so-merciful interviewers. Besides, if you are early, you’ll have time to relax and review your résumé. To avoid tardiness, make sure you know exactly how to get to the company, and leave early to avoid unexpected traffic delays. If you do happen to run late, call the company and let them know.
Attitude is Everything: Keep in mind that everybody judges by first impressions, especially interviewers. Your attire, your handshake, your smile, and most importantly, your demeanor give off a surprisingly detailed profile of your value as an employee. It is important to appear enthusiastic about the position for which you are interviewing, even if you aren’t.
Know Thy Enemy: Lucky for us applicants, interviewers are not very original. They may have a few unexpected questions, but, for the most part, they all want to get a good sense of your experience and your value to the company. It is pretty safe to assume that you will be asked the painfully vague cliché, “Tell me about yourself.” So, don’t be afraid to practice answering this question in front of a mirror or during the drive there. Also be sure to review your résumé and know how to best articulate your prior work experience. Try to tailor your experience to the position you’re applying for; don’t just rattle off a list of accomplishments.
Take Charge: After you have been in the hot seat for a while, the interviewer will often give you the chance to ask some questions. You might think it is polite to refrain from jumping at this chance, but that’s a mistake! The offer for you to ask questions is not just a courteous gesture; it is a chance to let you show your initiative. Go ahead–ask questions about the company or the position. Did the interviewer say something that stuck in your brain? Ask about it! Show some moxie!

Now, you can exhale. Doesn’t that feel good? All of this stuff makes test prep look relaxing.

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Idioms on the SAT

By amanda chen posted April 23, 2010

When you think of idioms, you might usually think of sayings such as “a pretty penny”, or “an arm and a leg” or “as the crow flies”. These idioms are expressions that have a figurative meaning in addition to what it literally means. For example, if a bottle of wine costs an arm and a leg, it doesn’t literally mean that you need to pay for it with an arm and a leg. It just means that it is expensive.

You generally do not need to know such idioms for the SAT. What you do need to know are prepositional phrases. For example, would you know which one is correct?

A: I can always count on you to come to my rescue.

B: I can always count for you to come to my rescue.

If you are familiar with English, you will automatically feel that something is ‘off’ with sentence B. If English is not your strong suit, here is a very, very limited list of prepositional phrases to learn. I would highly suggest adding to the list as you practice on Grockit .

An essay consists of an introduction, a body and a conclusion.
An essay comprises an introduction, a body and a conclusion. (Note that “comprise” does not require a preposition)
I ran into him at the basketball game.
I ran away from home when I was 10.
I showed up at school in a suit.
She applied to Cornell University.
She applied for a scholarship.
He showed up unannounced on my doorstep.
Compared to a desktop, laptops seem so much better.
What is your excuse for skipping school again?
What do you believe in?
Can I count on you?
I talked him into letting me stay.
I need you to work with me if we are to get this done on time.
I am looking forward to this vacation.
I’m not sure I can rely on anyone but myself.
She has fallen ill with a fever.
I need time to recover from this fever. Illogical structure

ILLOGICAL CONSTRUCTIONS

Illogical constructions have to do with figuring out what the subject of a clause is. Let’s look at the following examples from Grockit .

By attaching raw meat to canvases and leaving it out in the elements to rot and discolor, the attempt that David Lynch has been making is to find aesthetic value in the grotesque.

What is the first clause in this statement?

It is “By attaching raw meat to canvases and leaving it out… to rot and discolor”.

Now figure out what that clause is talking about. Who is attaching raw meat to canvases? Is it the attempt by David Lynch? Or is it David Lynch himself? Clearly it has to be David Lynch that is doing the attaching so, “David Lynch” should come immediately after the clause and the comma.

With this in mind, which would you pick out of these answers?

A. the attempt that David Lynch has been making is to find

B. David Lynch has been attempting to find

C. the purpose of this effort by David Lynch is to find

D. David Lynch has had the purpose in his effort to find

E. the attempt that David Lynch has made is finding

I hope all of you automatically eliminated choices A, C and E because “the attempt” and “the purpose” are not subjects of the clause. David Lynch is.

Let’s try another one.

Having not slept the night before, Ian’s errors while taking the test to get his license were careless.

The clause here is “having not slept the night before”. So you should ask yourself, who didn’t sleep the night before? Was it Ian’s errors? Errors can’t sleep! It was Ian. So Ian must come immediately after the first comma. Which of the following choices can you eliminate based on this knowledge?

A. Ian’s errors while taking the test to get his license were careless

B. Ian made careless errors while taking the test to get his license

C. there were careless errors in the test Ian took to get his license

D. Ian took the test to get his license while making careless errors.

E. the test Ian took to get his license had careless errors

Did you eliminate Choices A, C and E? The errors and the test cannot have not slept the night before!

Another strategy in dealing with clauses and illogical structures is to ignore the clause. Generally, this means that you can ignore the clause that lies between two commas. What do I mean?

Take this example:

John R. Peterson, a survivor of the attacks of 9/11, and later to work as a volunteer to help those who had lost loved ones on that fateful day.

“A survivor of the attacks of 9/11” is a clause that gives you further information about John R. Peterson. It does not have a verb in it. If you ignore this clause, whatever is said before and after the clause stand alone as a perfectly grammatical sentence.

In this case, does “John R. Peterson and later to work as a volunteer to help those who had lost loved one” sound grammatical to you?

Try putting “John R. Peterson” in front of the following choices:

A. and later to work as a volunteer to help those who had lost loved

B. later worked as a volunteer helping those who had lost loved

C. he later worked as a volunteer helping those who had lost loved

D. he later helped those who had lost loved ones, working as a volunteer

E. later working as a volunteer and helping those who had lost loved

“John and later worked…”, “John he later worked…” and “John later working…” all don’t make sense. The only grammatical one is “John later worked as a volunteer…nul, “

Try practicing these two strategies (especially the first one), they come in very handy in the SAT writing section!

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Making Grockit more adaptive

By ari bader-natal posted April 22, 2010

I’m happy to announce a recent improvement to a popular Grockit feature: In solo practice games, the questions that you see are selected based on your recent past performance. Grockit’s tailored Challenges — short assessment-oriented games that are unlocked over time — have a been popular way for students to benchmark their performance and get feedback on where they stand. We’ve now incorporated the core algorithm used to create Challenges into all solo practice games. Questions posed during these games are now selected in a way that takes into account both what you have seen in the past and how you’ve been doing on recent questions. We know that different students are stronger in different parts of a test, so you may notice that you’re seeing harder questions in one section than in another. You’ll find that the personalized question loader takes these variations into account.

As always, we’d love to hear your feedback. Please feel free to leave a send us a email or leave a comment below.

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College Spotlight: Carleton College

By jonathan peters posted April 20, 2010

Carleton College is a top-notch liberal arts college located in Northville, Minnesota, a small town some 44 miles south of Minneapolis. Carleton offers awesome academics and a strong community ensconced in one of the most bucolic corners of Minnesota. Some 1986 students call Carleton home; a small population that leads to a considerable amount of interaction; you will get to know your peers here. The average class size is eighteen and the student-faculty ratio is about 9:1, a good number that encourages a great deal of meaningful dialogue between student and professor.

Carleton offers 37 diverse majors, from Biology to Russian. The academics are excellent, and many of the professors are leaders in their fields. Like many liberal arts colleges, here all classes are taught by professors and not teaching assistants. During your four years here, you will be doing research, meeting with a professor about your paper, and finding the tools to become an independent learner. Some famous professors include Minnesota senator Paul Wellstone (now deceased) and philosophy of science writer Ian Barbour.

The campus is quite beautiful and features Cowling Arboretum that covers 880 acres next door to the main grounds. The environment is quite important here; Carleton students’ sustainable habits are well known and earned the campus an A- from the Sustainable Endowments Institute in 2008. Sports are important at Carleton; do not let their status as Division III fool you. Many students participate in sports, especially club sports like rugby.

As for student life, extra-curriculars abound, including an award-winning Model UN club. During the weekends, there are parties on campus, but the website reminds us that “since this is Carleton, there is probably someone playing Scrabble somewhere, or knitting, or juggling.” If you are looking for the perfect party school, Carleton is not it; of course, if you find knitting fun, then you are in luck.

Carleton is a highly selective college—about thirty percent of students are accepted each year. 74% of Carleton’s 2012 class came from the top tenth of their high school class. As for the ACT , the median score is between 29 and 33. The median scores on the SAT Writing, Verbal, and Math are 650-750, 660-740, and 650-730 respectively. Yet many in the class do not take the SAT. According to the admissions office, they strive to find a class “beyond grades,” one encompassing well-rounded students who care about learning whether inside or outside the classroom. They also strive to have a diverse class, not only in terms of gender, ethnicity, and socioeconomic status, but by interests as well. If you are the only left-handed piccolo player in their pile of applicants, you may have an in. It would be a good idea to spend a great deal of time on the essay. Remember, according to the website, “[Carleton students] are an intellectually insatiable group that approaches learning with enthusiasm, energy, and a uniquely Carleton brand of playfulness.” Demonstrate that you are equally unique.

The tuition is steep at about $50,000 per year, but many receive financial aid, in fact some $39.5 million was allocated for that purpose last year. The college promises to cover all demonstrated need. The price tag should not be a reason to dissuade you from applying, in fact, about two thirds of the loans students receive are scholarships or grants, the aid equivalent of a gift.

If you can handle the Minnesota weather, and love to learn, then apply today.

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A Perfect Collaboration: Grockit + Etherpad = Noteshare

By brian buser posted April 16, 2010

We’re really excited to introduce the first batch of Google related code and features we are rolling into Grockit’s collaborative learning communities. To start, we’ve incorporated Google’s collaborative document writing platform Etherpad into our lessons and courses. This adds a really useful component to Grockit’s collaborative study platform and let’s teachers dig into essays, writing assignments, personal essays for applications, and class notes. It’s awesome and we think you’re going to love it! We call it Noteshare in Grockit. Here is what our Academic Director Jake Becker has to say about it.

“Imagine the possibilities with Grockit’s new Noteshare feature…students can collaborate on writing samples, revise business school applications, practice timed essay prompts, and much more. The applications for students to perfect their writing with expert instructors are endless. Connecting instructors and students around the globe, our Noteshare feature enables people to work together in realtime to review and edit any writing sample. Combined with Grockit’s existing realtime audio capabilities, Noteshare’s integration into Grockit’s lessons has created one of the web’s most versatile tools in online writing instruction.

With Noteshare, students and instructors can type synchronously in the writing sample as they edit the document together. Each user’s text is highlighted in a different color. These color assignments are referenced next to the user’s avatar in the top right of the screen.

Noteshare is another feature that wonderfully leverages Grockit’s wide network of students and experts to collaborate in a creative and unique learning environment. Not only will students be able to refine their language skills in realtime, but they will be able to upload virtually any sample to work on live with a great instructor or their peers. Imagine the possibilities!”

Etherpad live in Grockit

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Inequalities

By amanda chen posted April 15, 2010

We can break SAT inequalities questions down into three types: those involving a word problem, those involving algebra and those involving absolute values. Let’s tackle the word problems first.

Word Problems

Do you remember this question on Grockit?

A pulley can handle no more than 800 lbs of weight. It is currently holding 4 steel frames that weigh 112 lbs each. Amanda wants to load as many bricks onto it as she can without it breaking. If x represents the total weight of bricks, in lbs, that she can add, which of the following inequalities could be used to determine possible values of x?

From the question, I have deduced the following information:
• I can have a MAXIMUM of 800 lbs
• I have 4 frames, each weighing 112 lbs. That means, all 4 frames weight 4*112 = 448 lbs
• In addition to the 4 frames, I want to load x lbs in bricks.
I can thus conclude that x + 448 lbs must not exceed 800 lbs or my pulley will break.
In mathematical notation, x + 4(112) < 800 Don’t get tricked if the answer is written as 800 > x + 4(112). This statement is exactly the same as the statement above. 800 is greater than x + 4(112) is the same as x + 4(112) is less than 800.

Algebraic Inequalities

Another type of inequality involves algebra. Suppose y = 2x + 4 and x < 3 and you need to find an inequality involving y.

Start with the inequality you have x < 3
Look at the equation involving y. There is a 2x in it. Since x < 3, that means 2x < 6
If 2x < 6, that means 2x + 4 < 6 + 4 = 10. Thus 2x + 4 < 10
But 2x + 4 is simply y, so we can conclude that y < 10

The trick is to make your inequality look like the equation. Can you work the next two examples out on your own?

If 2y = 2x + 4 and x < 3, find an inequality involving y

Answer: Like before, we have 2x < 6 and 2x + 4 < 10. But now we have 2y < 10, meaning y < 5

If y = -2x + 4 and x < 3, find an inequality involving y

Hint: Don’t forget, that when multiplying an inequality by a negative number, you have to switch the signs.

Answer: If x < 3 , then -2x > -6. That means that -2x + 4 > -2 so we get y > -2

Absolute Value Problems

The last type of question tests your knowledge of absolute values. Absolute values are denoted by two straight lines | |. Absolute values make negative numbers positive.

So |10| = 10 and |-10| = 10 too.

Now that we’ve established what absolute values do, we can solve absolute value inequalities. Here’s a Grockit question:

A theater company is auditioning for actors to portray the leading character in a new play. The company is looking for actors between the ages of 20 and 40 (inclusive). Which of the following inequalities can be used to determine whether an actor of age a is eligible to audition for the part?

| a-10 | ≤ 40
| a-20 | ≤ 40
| a-30 | ≤ 20
| a-30 | ≤ 10
| a-35 | ≤ 5

The answer is 20 ≤ a ≤ 40. But how do we make that look like one of the inequalities above?

Take the average of 20 and 40. That’s 30.
Subtract 30 from everything to get 20 – 10 ≤ a – 30 ≤ 40 – 30
You get -10 ≤ a – 30 ≤ 10 Note that the left and right side of the inequality is the same number, except that the one of the left is negative
Now we can say, | a – 30 | ≤ 10

So the answer is clearly choice D.

Can you work out the lower and upper bounds of the other choices? I’ll do Choice A for you.

Choice A says | a – 10 | ≤ 40.

=> -40 ≤ a – 10 ≤ 40

=> -40 + 10 £ a – 10 + 10 £ 40 + 10

Thus Choice A is effectively saying -30 ≤ a ≤ 50, which is not the answer at all.

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Profile Pages That Rock

By brian buser posted April 13, 2010

We’re excited to show off our new profile pages. Check out the screenshot below. You’ll notice styling changes were made to bring the look and feel of profiles in line with other recent updates to Grockit. We love the new look. In addition, the performance analytics stand out more. Said Grockit CEO Farbood Nivi, “…these new profile pages really blow up your analytics and make them more prominent.” We hope your test scores blow up equally!

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Movies Filmed on College Campuses

By amanda chen posted April 8, 2010

Five years ago, when I was applying to colleges, I had a difficult time deciding which Ivy League college I wanted to apply to. I had good grades and my parents were insistent that I at least try, but because I didn’t visit any of the colleges, none of them really stood out to me. But then I saw “A Beautiful Mind” and thought, “Princeton! That’s where I want to go!” (I wanted to be a math major and my favorite economist/journalist Paul Krugman teaches there as well). So Princeton it was. I didn’t get in and I later found out that the movie was mostly filmed at Fordham University.

Quite a few other movies do the same thing. When I think of university related movies, my mind immediately jumps to Legally Blonde. Reese Witherspoon is a “Malibu Barbie” who decides she has to get into Harvard in order to get the man of her dreams back. Harvard is supposed to feature a lot in the movie, but it was mostly filmed at the University of Southern California (USC) and the University of California Los Angeles (UCLA).

campus#1

Reese Witherspon as Elle Woods, introducing herself to her classmates at Harvard.

Because of their close proximity to Hollywood, USC and UCLA actually feature a lot in movies. Another scene in Legally Blonde in which Reese Witherspoon arrives at her new dormitory was shot in front of the Bovard Auditorium at USC. Other movies featuring the Bovard Auditorium are Forrest Gump, Princess Diaries 2, What Women Want and Road Trip. If you’re from LA, the scenes from Old School and The Nutty Professor might look a little familiar.

Students check out the new arrival – Elle Woods

The actual Bovard Auditorium at USC

Moving up to Northern California, I know of two movies that take place at my alma mater – UC Berkeley. Patch Adams, which features classroom scenes in Wheeler Hall and Le Conte, and Boys and Girls, which has quite a few scenes from all around campus. The immediate scene below is at Sather Gate, the main thoroughfare on the Berkeley campus where various student groups can be found tabling and handing out flyers. The a cappella group also performs right beside the gate around 1pm several days a week. The scene below that is right in front of the Valley Life Sciences Building, where most of the biology classes are held. It also has an awesome dinosaur skeleton inside.

Sather Gate at UC Berkeley, in the film “Boys and Girls”

Outside the Valley Life Sciences Building at UC Berkeley

On the East Coast, Columbia University can be seen in movies such as Spiderman and Ghostbusters. In the opening scenes of Spiderman, Peter Parker visits Columbia University on a field trip. The scene below is shot on the steps leading to the Low Library. In the background, you might be able to spot a bronze statue of Alma Mater. On a side note, the library sits in front a big open plaza and nearby, in front of the School of Journalism, is a statue of Thomas Jefferson. A friend at Columbia told me that one year, on Valentine’s Day, some students dripped red paint across the plaza from the Jefferson statue to the Alma Mater statue, leaving red handprints on her chest.

Having seen those pictures, I’m sure this scene from Ghostbusters will look familiar too you. After they are fired from Columbia University, Peter Venkman (Bill Murray) and Ray Stantz (Dan Akroyd) sit on the east side of the plaza with the Low Library in the background.

So while I’m sure many of you are cramming for the January SAT or busy writing your application essays, maybe you want to google the colleges you’re interested in applying to see what movies they were featured in.

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ACT English: Organization of Ideas

By jordan schonig posted April 7, 2010

You’ve probably read this comment from your English teacher at least once in your educational career: “Interesting ideas, but lacks organization.” Well-executed prose, flowery descriptions, and complex, original theses will only get you so far. You have to help your reader along your argument by organizing your writing. On the ACT English , you’ll be asked to identify and fix the organization errors in a sample composition–that’s right, it’s your turn to play teacher.

Organization questions are divided into three types: sentence organization, paragraph organization, and passage organization. Just as expected, the larger the section of text you have to reorganize, the more information you have to understand. Sentence organization problems are essentially syntax questions disguised as rhetorical skills while passage organization problems require a thorough knowledge of the author’s argument and each paragraph’s function.

1. Sentence Organization: Sentence organization questions ask you to reorder a sentence to improve clarity. These questions will often test you on grammar rules like “misplaced modifiers.”

Example: “John was still able to lead his team to victory, a feat he would forever be proud of, hindered by a sprained ankle.”

The underlined phrase would be placed most logically
Where it is now
After the word “feat”
After the word “John”
After the word “lead”

This is how a typical sentence organization question will look. Again, the question seems to ask about organization, but really tests us on fundamental principles of sentence structure. The problem with the sentence as it stands is that the modifier “hindered by a sprained ankle” does not modify John as it should. In its current placement, it seems that John will only be proud of his feat while he is hindered by a sprained ankle, which doesn’t make any sense. I want to place the underlined portion so that it modifies John. I can either place it before or after John; C gives me the choice to place it after John, so C is the best answer.

Need the full ACT test prep experience? Add an ACT video course to your Grockit membership.

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