Khan Academy

Sal Khan is crazy...about explaining things! His "Khan Academy" website has become pretty popular, especially since early 2011 when Bill Gates named Mr. Khan his "favorite teacher". Before that, Mr. Khan enjoyed a bit of fame for his videos back in 2008/09 on just what happened in the credit crunch. If he can make sense of CDOs and credit default swaps, then you can certainly trust him with GMAT math!

Mr. Khan's videos are pretty uniform, and his teaching style isn't for everyone (think "electronic whiteboard"). But if you like diagrams and narrated explanations, you can't go wrong here. He has EIGHTY algebra videos (and that's not including his "worked examples"), thirty on geometry, and about a million on pre-algebra and preparatory mathematics, if you're weak on your fundamentals. Oh, and while you're at the site, you can also learn about economics, finance, astronomy, chemistry, history, physics, and biology. Hey, why not? Check it out for yourself:

http://www.khanacademy.org

BONUS! Did I mention that he worked through every math problem in the 11th edition of "The Official Guide for GMAT Review"? If you have it (or the 12th edition; they changed only a small part of the math section), you can "check your work" here, and have the tough problems explained to you. One caveat, however: he doesn't always find the most efficient path to a solution, so sometimes he takes longer than you should on the test. Overall, though, a great resource!

http://www.khanacademy.org/gmat

Purplemath Algebra Review

Think fast!

If you just broke out in a cold sweat or had a flashback to your freshman year of high school, then I'm afraid I've got some bad news for you: algebra's back!

I've seen a lot of test prep guides say that "25% of the Quantitative section of the GMAT is Algebra". This is really kind of dishonest: maybe 25% is explicitly algebra, but all that geometry? A lot of that arithmetic? Stat? Rate problems? Algebra in disguise, all!

But if you're rusty when it comes to solving for x, don't panic! There's good news too. First of all, Veritas provides you with a good comprehensive Math Essentials textbook filled with practice drills. All Veritas students also have access to a prerecorded "Veritas On Demand" lesson to guide them through this book on their own schedule.

Some of you may feel that you need a more comprehensive approach to algebra than the refresher offered by a prep course! Here is another recommendation that Veritas instructors have been passing along for some time: Elizabeth Stapel's Purplemath.com.

Almost entirely the work of one math teacher (!), this website is essentially Algebra I and II for free, online. Tons of useful information, from pre-algebra rudiments all the way up through advanced subjects like matrices and logarithms (neither of which are on the GMAT). If you complete these lessons, you will know the algebra you need for this test.

Because so much algebra is useful for the GMAT, I will simply list below the sections of Purplemath that you don't need for the GMAT. Consider everything else required highly recommended reading:

Stuff to skip

• Preliminary Topics
• Metric Conversions
• Number Bases
• Significant Digits
• Beginning Algebra Topics
• Engineering Notation
• Okay to skim: all graphing topics
• Scatterplots & Regressions
• Scientific Notation
• Intermediate Algebra Topics
• Ellipses
• Even and Odd Functions
• Numerical Approximation of Zeroes
• Okay to skim: Variation
• Okay to skim: Advanced Algebra Topics. These topics are not covered at all by the exam:
• Logarithms
• Matrices
• Complex Numbers
• Okay to skip: all sections on trigonometry

http://www.purplemath.com/modules/index.htm

Grammar Girl Quick and Dirty Tips for Better Writing

For students looking for a quick grammar fix, I recommend Mignon Fogarty's weekly podcast "Grammar Girl". This podcast (with transcripts posted on the web, for those of you who prefer reading to listening) focuses on grammar and style issues, commonly confused words, and other tips to improve your writing.

Calling the show "Grammar Girl" is a bit misleading, though. This podcast is about "writing", not just grammar. That means that, while there are plenty of useful tips to be found, there are also a lot of subjective style judgments, and sometimes these opinions are mixed together with grammar rules without much thought.

My recommendation? Listen to the podcast; it is a good one! But if you encounter any rule or advice that sounds particularly arbitrary, look into it: ask your GMAT instructor, or do some digging around on the web or in a good grammar book. The podcast is right far more often than it's wrong, but sometimes it's just a little too judgmental of nonstandard structures and styles for my tastes. I've noticed that the episodes written by Mignon herself tend to be a little more GMAT-relevant; Bonnie Trenga's guest episodes delve into subjective issues of style and problems with ambiguous solutions quite a bit more often.

I hope I haven't scared you off with all of these caveats! Honestly, you're not going to get bad advice from Ms. Fogarty, so don't be afraid to dive in and see if you like it. She's easygoing and keeps the issues simple, so if you've been bored with or lost by other grammar references, this is a great starting point. I've provided both a link to Grammar Girl's main page (and iTunes subscription link) and a link directly to her "grammar" archive (the episodes I find to be most useful for the GMAT student).

Main page: http://grammar.quickanddirtytips.com/Default.aspx [iTunes]
Grammar archive: http://grammar.quickanddirtytips.com/Tags/Grammar/page/1/sortbyalpha/

University of Ottawa's HyperGrammar

The Writing Center at the University of Ottawa has provided a terrific resource in their HyperGrammar electronic grammar course. Veritas has recommended this resource for years, and for good reason: it's comprehensive and well-organized, and it even provides interactive review sections to test everything you've learned!

This site starts with the basics--what is a noun, what is a verb, etc.--and quickly ascends through all the major building blocks of good sentence structure. Here are the sections I specifically recommend for GMAT prep:

• The Parts of the Sentence (complete lesson)
• Using Pronouns (Pronoun Reference)
• Using Verbs
• Compound Verbs
• Auxiliary Verbs
• Linking Verbs
• Verbals
• Forming and Using Verb Tenses
• Using Verb Tenses
• Using Verb Tenses in Sequence
• Using Verb Moods
• Modifiers (Misplaced and Dangling Modifiers)
• Building Phrases (complete lesson)
• Building Clauses (complete lesson)
• Building Sentences (complete lesson)
• Miscellaneous Topics
• Apposition
• Noun and Pronoun Characteristics

I know that's almost everything they have, but what can I say--grammar is a huge subject! This information is the perfect background to complement Veritas' VAMPIRES methodology for Sentence Correction questions, and can be an invaluable aid in your AWA and application essay writing as well.

One caveat that I should mention: HyperGrammar is Canadian, eh? That means that the Queen's English sneaks in from time to time. They use standard OED spelling (read: British), but don't let that throw you! The materials covered all look good and test-ready to me--even the discussion of the subjunctive mood, whose usage in British English differs slightly from formal American English (the dialect of the GMAT).

http://www.uottawa.ca/academic/arts/writcent/hypergrammar/

LSAT Logic in Everyday Life

When it was regularly updated, this podcast was one of my favorites. Hosted by Andrew Brody of the Princeton Review, this podcast examines media coverage of politics, health & entertainment news, and other current events. The focus here is on errors in reasoning that are frequently encountered on the LSAT. These errors, of course, also abound on the GMAT!

Sometimes classroom examples of flawed logic can seem sterile or oversimplified. Listening to real people making real decisions on the basis of flawed arguments can be eye-opening. Who knew how often correlation was confused with causation!

This podcast hasn't been updated in almost a year, and that's a shame. Fortunately, their full back catalog is still available. Each episode runs about ten minutes long, typically summarizing a single current event and critiquing common arguments in favor of or against certain decisions made by governments, organizations, celebrities,  opinion columnists, etc.

This podcast is run through the Princeton Review as a supplement to their LSAT prep classes. Technically they're a competitor, sure, but credit where credit is due: this is one offering that I think can be very useful...and it's free! Keep in mind that some of the topics covered may be a bit contentious; always remember when studying argument that it is the reasoning behind opinions and arguments that is being criticized, and not necessarily the conclusions themselves.


http://www.princetonreview.com/lsat-logic.aspx [iTunes]