Recently, I have just been talking about love, love, and love. And I am boy gettin tired of it. So for today, I will switch my view to mathematics. Mostly because yesterday, I took the AMC 10 B, which I’d like to say I did poor on it. The beginning half I felt good, but the later half, there were some I left blank and some I just assumed it should be right. Man, the AMC is harder than it seems!
Here’s one question (no. 14) from that test I took:
Define . Which of the following describes the set of points (x,y) for which .
Here was my thought process, which eventually turned out to be wrong:
, so this also equals ab (a-b). Similarly, for , it would be xy(x-y) = yx (y-x) thus x-y = y-x thus 2x = 2y and thus x=y. That would satisfy answer B.
The actual way to solve it, unfortunately to my dismay:
and . Therefore, we have the equation Factoring out a gives Factoring both sides further, . It follows that if , , or , both sides of the equation equal 0. By this, there are 3 lines (, , or ) so the answer is (E) three lines.
Well, look’s like this question I missed. There were also a few other problems in which I missed due to miscalculations. For instance, one question I saw 5-3 as 5+3 and put my answer as 8, when it was supposed to be 2. Next time I take the AMC, I better be careful of these silly mistakes.
Updated 9:40 pm: By the way, refer to my previous mathematics posts to know more about the AMC.