Standardized test math doesn't behave like normal math. On a normal math test, your knowledge of the concepts and material is being tested, using (hopefully) fair test questions. On a standardized test, though, they're looking for you to think outside the box, to apply math concepts and algorithms to unusual situations, and to really understand what they're looking for and find the quickest way to go about it. Let's take a question from a recent GRE student's lesson:
If 4x – 5y = 10 and 6y – 3x = 22, then what is x + y?
Now, this is a set of two equations with two variables each, so it looks to me like a perfect candidate for solving as a system. If I were solving this one on a regular math test, I'd start off trying the substitution method, since I'm more comfortable with that one. So let's explore that one first:
I'll start by solving the first equation for y:
4x – 5y = 10
- 5y = 10 – 4x
y = (-10/5) – (4/-5)x
y = -2 + (4/5)x
The “silly mistake” is quite possibly the most mischievous and irksome of the math demons. It is a sly beast that lurks in the deepest recesses of your mind, emerging only periodically to sully your scores in a most disturbing way. Because of its crafty nature, it is able to lull you into the false belief that your thorough understanding of mathematic concepts will keep you safe from its clutches. But, as I’m sure you know, “silly mistakes” afflict even the most soundly prepared students.
What exactly constitutes a “silly mistake?” Here are some common examples for standardized tests:
Misreading the question (or failing to read the entire instructions)
Filling in the wrong bubble on your answer sheet
Making a slight arithmetic error
Incorrectly copying down the original problem
Turning a negative number into a positive number (or vice versa)
I don’t care who you are, what your educational background is, or where you go to school… you have been...