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What if I mis-bubble the whole test?It’s every student’s nightmare: you’ve got a few minutes left in your test section, and you go to bubble in the answer to question 25, only to find that your answer to 24 is on the line for #25. Trying to squelch the rising feelings of panic, you scan your answer sheet only to find a blank line at question 11 — but you know you answered number 11. You’ve just mis-bubbled more than half your section.
So, what do you do? Start hysterically crying? Fake a fainting spell? Scream and throw a tantrum?
How many questions should I skip?Every year, we take on plenty of students who are about to take a particular standardized test for the first time. In our first lesson with a new Testing student, the “guessing question” usually comes up within the first 20 minutes. Most people have talked through the issue with their friends and/or teachers, but they still want to hear it from us.
So, for all our honorary students who just don’t happen to be in the same zip code as we are, we will try to answer the general question with a few tips: Read the rest of this entry »
Getting The Right Answer RightWhat does it mean to get the right answer on a math question?
Some may give the quick answer and say that a right answer is one that earns you full credit. But that answer, while necessary, is not sufficient. For any given problem, there’s usually more than one way to get to the right answer, even if you’re not taking a multiple-choice test, where you know the right answer is staring back at you before you even start the question. There are textbook right answers, there are clever right answers, there are inefficient right answers, and there are lucky right answers. Of course you always want to get the answer right, but you want to do it in the best way possible.
It’s worth examining some of the different paths to the right answer:
The Unit CircleConsider the equation:
x2 + y2 = 1
Math geeks can appreciate its elegance and simplicity: the unit circle, a circle with a radius of 1.
For anyone who has taken pre-calculus or above, you also (hopefully) know it as it relates to trigonometry. You probably griped about having to memorize it. But if you got to the point where pure memorization gave way to real understanding and internalization, you probably now also appreciate just how useful it is.
For anyone who is about to take pre-calculus, examining this circle in a bit more depth will give you a preview of what’s to come:
These links are just a few of many sites that extol the virtues of the unit circle. For my part, I will just say that your life (or at least calculus) will be considerably easier if you take the time to memorize (and then really understand) this “simple” little function.
Sample Question: Perimeter and RatiosHere’s today’s medium-level SAT Question of the Day (note that if you saw it on the SSAT/ISEE, it would be a Hard question):
In the figure above, the large rectangle is divided into six identical small squares. If the perimeter of the large rectangle is 30, what is the perimeter of one of the small squares?
A) 5
B) 8
C) 9
D) 10
E) 12
How do you solve this problem in the quickest way possible?
Here’s how the College Board thinks you should solve it. That’s the “right” way to do it: use the ratio of length to width to set up an equation using the overall perimeter. And assuming you don’t make a careless algebra error, that will get you to the right answer. For some students, it may even be the fastest way to get to the right answer.
But not every student is going to see this way immediately. If you’re one of them, consider another way: working backwards, sometimes called guess-and-check. Start with the middle answer choice and assume it’s the perimeter of a square. Figure out what each side of the rectangle then has to be, and see if that matches the given perimeter of the whole rectangle. If it does, you have your answer. If not, you should be able to tell whether you need the perimeter to be bigger or smaller, so you can figure out which answer choice to try next.
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