You may think that I’m here to offer study techniques around memorizing equations and graphing, but I’d like to offer you something different. It’s hopefully a technique that you have been told before, but I am here to re-iterate it to you. In fact, the entire strategy is around one simple idea.
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
First off, we are proud to announce that Newor Media has acquired Calculus-Help.com. Newor Media is owned and operated by teachers, so you can continue to expect some great Calculus content in the future. If you have any suggestions for us, we would love to hear them, and we may include some fun puzzles as well.
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:
If the second derivative f” is positive , then the function f is concave up (looks like a U shape) .
If the second derivative f” is negative , then the function f is concave down (looks like an upside down U shape)
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 derivative turns 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:
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
Up for sale is a TI-n spire calculator owned and signed by by W. Michael Kelley, the author of The Complete Idiot’s Guide to Calculus and The Humongous Book of Calculus Problems. Is Kelley famous? No. Does the signature actually add any monetary value to the auction? No. In fact, like graffiti, it may actually devalue the sale. That’s a chance we’re willing to take in a fund raiser to reboot Calculus-Help.com for the new school year: http://www.ebay.com/itm/140846256145.
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.)
Unless you live in Chicago, the new Problem of the Week may be unsettling because it is rife with bears. Not the cute kind of bears that get stuck in a rabbit’s tree house because they may or may not be morbidly obese. (“Oh, bother.”) No. These are the “I’d rather eat you, bones and all, than pretend that I am a cloud to hustle some bees out of their honey” kind of bears. The dangerous kind.
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.
Are you pro-derivatives? If so, well, our politics may clash in the new Problem of the Week, as it is firmly anti-derivative. Only one tool is allowed to solve this pair of problems–the power rule for integration. No u-substitution allowed!
The last Problem of the Week for 2011 is now posted, and it’s feeling all festive. Take a journey deep into the cold, barren wastelands of the Northern ice cap and search among the iceburgs to find a certain toymaker’s workshop. (In case you need help calculating the derivative of a polar equation.)
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.