Sleep. That's right, good 'ole fashion sleep. One of the biggest mistakes that you can make going into your exam is just getting out of a late night cram session. A sleep-deprived person cannot focus and therefore cannot learn or apply anything efficiently. Secondarily, being chronically tired to the point of exhaustion means that you are less likely to perform well. Which means that in the weeks leading up to your exam, you should be training your body to sleep better.

So here is my suggestion for you. If you are often too tired to stay awake for an early morning class, then **take at least 10 days to re-adjust your sleep pattern** so you can fall asleep earlier in the night. Don't try to change your pattern in just one night... it won't work.

Slowly change your routine so that on the night before the exam, you can fall asleep easier and be well rested. My second piece of advice? Wake up a little bit early and do some exercise. Running, jumping jacks, sit-ups, anything to get the blood pumping. About 20 minutes of exercise can help increase your mental energy and get you pumped. Just make sure you shower after so you don't distract your fellow test takers.

Remember, sometimes you can do all the studying in the world but you leave out the essentials. Don't be like these students:

Craming for AP calc because it's totally going to help me.... #striveforafive

— Colin Geray (@GerayColin) May 6, 2014

]]>Craming for ap Calc with @theOGgarbear like... pic.twitter.com/7PC0WavqmG

— Spencer Scamman (@j_scamman) October 5, 2015

Now on the question at hand. First, some quick references for you. The first derivative of the function f(x), is the slope of the tangent line to the function at the point x:**If the first derivative f' is positive, then the function f is increasing (pointing upwards)If the first derivative f' is negative, then the function f is decreasing (pointing downwards)**

As for the second derivate, the second derivative of a function is the derivative of the derivative of that function:

The second derivative is like the movie Inception. The first derivative tells us whether or not the function is increasing or decreasing. The second derivative shows us whether or not the first derivative is increasing or decreasing. So the second derivative plays directly off of the first.

If the second derivativeturns out to be positive, then the first derivative will be increasing. The slope of the tangent line to the function is increasing as x increases. If the second derivative turns out to be negative, then the first derivative is decreasing. The slope of the tangent line to the function is then decreasing as x increases

Here is some more in-depth information, but this should be a good start. If you would like to see it in action, take a look:

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Are you getting ready to take the SAT? Have I got the book for you! Presenting *The Humongous Book of SAT Math Problems*, your one-stop show to a metric ton (give or take) of math practice for the SAT Test. The book contains all of the following, except for one. Try to figure out which is not included:

- Test-taking tips, including specific advice for multiple-choice and grid-in questions
- In-depth mathematical tutoring on all of the major topics included on the SAT
- Practice problems for all four categories of mathematical SAT questions
- The math sections of three full-length practice SAT tests
- A bronze bust of former president William Howard Taft

Set your math phasers to "excited"! Click here for ordering info.

]]>Click here to download and print the chart. Alternately, you can right-click and select "Save Image" to save it to your computer.

Note that the chart opens in a new window. If you can't see it, you may need to temporarily disable pop-up blockers.

]]>Every day Mike gets a ton of email from people practically begging to buy advertisements on his site. Actual begging. We feel sorry for these people, because what they don't know is that Mike made a (probably very short-sighted) pledge to never sell ads on the site for any reason. "But can't we just throw money at you?" they ask, usually in the form of impersonal spam. "No," Mike says. "I must hold to a promise, a sacred covenant, that I sometimes really regret making." For those of you thinking, "Sure, there's no advertising, but practically every page is an ad for Mike's books. Doesn't that count as advertising?" understand that I am staring at you with a squinty stare, telepathically asking you to kindly put a sock in it, because you're embarrassing me in front of my new friends--friends that could potentially buy the calculator I ruined by signing it with a silver Sharpie.

To help keep the site free, Mike is auctioning off this calculator, which is lightly used, but it contains all the important pieces (like connection cables, the manuals, an alternate TI-84 face plate (let your dork flag fly) and is in incredible shape. It works like a charm, as you can see by the mundane and meaningless calculations I took a picture of. In case you were wondering if this complicated piece of machinery can add, the answer is a resounding YES! (I may or may not have utilized the full power of this guy.)

]]>Are you thinking, "This must be an optimization problem, where you are asked to calculate the *bear* minimum"? If you did think that, please know that I am, as you read this sentence, smiling approvingly and giving you polite golf applause for your clever pun. However, this problem is all about definite integrals, so there is no time for joking around.

Steel yourself for the battle of your life! Attack this problem with your *bear* hands! But please, before you do, I would like the polite golf applause reciprocated.

With a nod of his head and a wink of his eye, he will promptly ask you to stop trespassing, and for Christmas this year? A restraining order from Santa.

No, this is not how you planned things at all...

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