Actually read the question.

I'll be honest: I hate that I'm actually devoting space on this site to reminding you to read each question very carefully, but I am because I've worked with enough kids to know that errors due to misreading (and misbubbling -- ARGH!) are unspeakably common.

Rest assured that, if there's a way a question could possibly be misinterpreted by a test taker, the SAT writers have anticipated that error and made it an incorrect answer choice. So if you don't read the question carefully the first time, you'll feel warm and fuzzy about your incorrect answer. You might catch your mistake if you finish early and have time to review your answers, but there's also a pretty good chance your warm-and-fuzzy will carry all the way through until you get your score report back and see than you missed #6 and you're all like WTFFFFFF.

The SAT has been known to:

• Give all the question information in feet, and ask for an answer in inches. Of course, make the same answer in feet an incorrect choice.
• Ask testers to solve for x², which is 49 (a perfect square – those monsters). Make 7 an incorrect answer choice to give the warm-and-fuzzy to everyone who automatically solved for x like they do every other day of the year.
• Write a question about John and Susie buying iguana treats or some crap. Ask how many Susie bought. Make the number John bought a choice too.

So yeah. This isn't really a “strategy” so much as it is me imploring you to actually put your eyes on the paper and read the question carefully, because the SAT has a long history of humbling those who don't.

You may be laughing now. You won't be when you lose precious points because of careless errors. Read the question carefully. Always.

Weekend Challenge - With an ACTUAL PRIZE

I lifted a box that was too heavy this week and I screwed up my back so bad that every time I put weight on my right foot, searing pain shoots up my entire right side. Getting older is awesome!

The prize this week for the first correct response: FREE Beta Access to my book. A $5 value! Read up on the deets, if this is the first you're hearing of it.

How many positive integers less than 1,000 contain exactly one odd digit?

Put your answers in the comments, and I'll post the solution and contact the winner (if there is one) on Monday. Good luck!

UPDATE: Congratulations to Chong Lee, who nailed it first. Welcome to the Beta, Chong Lee. I hope you enjoy the book.

Solution below the cut.

A bit of practical advice about maximizing your SAT math score

I've covered this before at length, but it's important to remember that, in general, you'll increase your score more by making fewer silly mistakes than you will by getting more of the hardest questions right.  I've always left the actual calculations and decision making in your court, though.

Well, the decision making is still in your court, but I've made the calculations a little easier for you. I went ahead and aggregated the scoring tables of a bunch of old tests, averaged the scaled scores, rounded them down to the nearest 10, and made a nifty little spreadsheet that you might find useful:

Based on multiple scoring tables...your particular scoring table obviously might vary a bit.

The bold rows are the rows that represent skipping the same number of questions per section. (For example, for a score of about 690, you can skip 6 questions, or two per section. If you just want to break 600, you can skip FIVE QUESTIONS PER SECTION if you get all the rest of the questions right. Seriously.)

This is not about limiting your scores; it's about maximizing them. Questions on the SAT are arranged in order of difficulty, so you can predict very easily where the toughest ones will be. Take your time on the simple ones, make sure you collect all the easy points, and only then worry about the tough ones. If you run out of time and have to leave a few blank at the end, don't worry about it. If you're perfect (or almost perfect) on the ones you answer, leaving a few blank won't hurt you much.

Beta Access

So...I guess it's about time I let you know that I've been working on a book. It's going to be called the PWN the SAT Math Guide, and I'm hoping that you'll think it's really good.

I'm going to be running a small experiment with early versions of the book, which I'm calling a "Beta" because this is the Internet and that's what we call crazy experiments here. Basically, 200 people will be allowed to see early versions of the manuscript as I polish it. I'm hoping to get some valuable feedback from these folks, so that when it's finally time to send this book to the printers, it'll be the best it can possibly be.

I'm asking for $5 for access to the Beta, which I will refund to you if you spot a typo, grammar error, or math error. Clever, no? All the details and ordering information are here.

Weekend Challenge - OMFG IT IS SO HOT.

Guys. It's apparently going to break 100° today in New York. Seriously.

The prize this week for the first correct answer: You will awake in a bathtub of ice, and have no idea how you got there. Your first concern will be a suspicious scar on your abdomen, but that will quickly be replaced by relief that you are in a bathtub of ice, and not in New York City, where it is frikkin' 100°.

A wheel is rolling in a straight line, without slipping, on a flat surface. Two points on the wheel have paint on them, and they are leaving spots on the surface as the wheel rolls (wheel is rolling from left to right in the figure). What is x?

Put your answers in the comments. I'll post a solution Monday.

UPDATE: You guys rock. Special congratulations to the anonymously sweltering newcomer, for getting it first. Great job.

Solution below the cut.

Do you have a process?

Click the flowchart to enlarge and see what a dork I am.

I had an interesting conversation with a colleague last night about the importance of having a process. The gist of his argument was this: it's all well and good to understand what a run-on sentence is (for example), but there are lots of kids who know, objectively, what one is, and still miss run-on questions all the time. Top scorers don't let any of those slip by because they have a process, and they stick to it.

I know I've spelled out processes for my students verbally a thousand times, but last night it occurred to me that I'd never tried to put one down on paper. After sitting down this morning and trying to create a flowchart for Error ID questions, I think I know why. Still, maybe this spaghetti mess is helpful?

I'm thinking of trying to do these for other question types, too. If I do, I'll also try to tidy this one up a bit more, too. Thoughts?

Weekend Challenge - R.A. Dickey edition

I found this awesome graphic at Amazin' Avenue, and it inspired me to write a baseball-themed challenge question this week. I'm a huge Mets fan, and my favorite player on the team right now is R.A. Dickey. He faces the hated Phillies tonight. I am so pumped to watch.

The prize this week: A free (imaginary) R.A. Dickey bobblehead doll! Best prize ever!

In the 2011 season, R.A. Dickey has thrown 1758 pitches and batters have completed 494 plate appearances against him as of July 15. What is the least number of batters he would need to face to have a pitch per plate appearance average under 3.50?

Put your answers in the comments. I'll post the solution Monday.

Let's go Mets!

UPDATE: solution below the cut.

Moving is the worst.

I'm moving this week, which is one of the purest forms of torture. My internet access has been spotty and will probably continue to be so, so there probably won't be any new content on here until the Weekend Challenge on Friday. I will do my darndest to get one of those up this week, even if I have to type it on my phone. Fair warning: it will likely involve average weights of packages, or sweat as a function of temperature, or a pictograph of pics like our friend to the left there representing my rage level at various hours of the day. Seriously. I. Hate. Moving. So. Much.

If you're starved for content, why not have a look at some of my oldies but goodies?

• Not every math fact is an SAT math fact
• Want an 800 in math?
• Run-ons and fragments (featuring The YUNiversity!)
• Dangling modifiers
• A strong vocabulary is necessary but not sufficient
• Practice reading for the main idea

Weekend Challenge - more fun with 3-D edition

I'm having a lot of fun playing around with some geometry drawing software this week (nyeeerd!), so I figured I'd use it again to make another "fun" 3-D problem for the weekend challenge. This is a bit tougher than you'd find on the SAT, but the underlying concepts, as always, are important for the SAT.

The prize this week inspired by my current situation: If there should ever come a time in your life where you're trying to move from Brooklyn to the Bronx, you'll be smart enough not to bother trying to move yourself in your Toyota Yaris and instead just hire movers. And when you do, they won't break your stuff.

Point B is in the center of the top face of the cube in the figure above, and point A is one of the cube's vertices. If the distance between points A and B is d, then what is the cube's volume in terms of d?

Put your answers in the comments, and I'll post the solution Monday. Good luck!

UPDATE: Nice work, JD. You were wrong at first, but you corrected yourself before I did. Solution below the cut.

Working in 3-D on the SAT

It's not uncommon for a question or two involving three-dimensional shapes to appear on the SAT. Luckily, most of the time these questions either deal directly with the simple properties of three-dimensional shapes (like surface area and volume), or are just 2-D questions in disguise. It's pretty rare to come across a truly difficult 3-D question -- but you know I'm gonna give you some in this post because I care about you so.

Volume

Generally speaking, the SAT will give you every volume formula that you need, either in the beginning of the section (rectangular solid -- V = lwh; right circular cylinder -- V = πr²h) or in the question itself in the (exceedingly) rare case where you'll have to deal with the volume of a different kind of solid. It's worth mentioning, though, that the volume of any right prism* can be calculated by finding the area of its base, and multiplying that by its height.

For example, if you needed to calculate the volume of a prism with an equilateral triangle base, you'd find the area of an equilateral triangle:

And multiply that by the height of the prism:

You almost definitely won't need this particular formula on the SAT, but it's nice to know how to find the volume of a right prism in general: just find the area of the base, and multiply it by the height.

Most volume questions you'll see on the SAT will require you to deftly maneuver between the volume of a solid and its dimensions. Let's see an example (and showcase my fresh new drawing software):

15. If the volume of the cube in the figure above is 27, what is the length of AF?
    
    (A) 3
    (B) 3√2
    (C) 3√3
    (D) 3√5
    (E) 6

Weekend Challenge - Fireworks edition

It is my hope that, as soon as you're done figuring this problem out, you'll be on your way to a wonderful (and professionally arranged and totally safe) fireworks display. What follows is not an SAT question, but if you enjoy math enough to visit my blog regularly and try these challenge questions, my hope is that you'll think it's fun anyway.

The prize this week: you'll be close enough to the fireworks to feel the explosions in your gut. I love that. If you don't love that, your prize can be different. I'm easy!

The height, in feet, of a pyrotechnic rocket t seconds after the fuse is lit is given by the function above, where r is a constant. If the rocket explodes 6.5 seconds after the fuse is lit at a height of 324 feet, for how many seconds does the fuse burn before the rocket takes off?

Put your answers in the comments. I'll post the solution on Tuesday. Happy 4th of July, if you're in the States. :)

UPDATE: Solution below the cut.