On a recent visit to my mom’s house (also the house in which I grew up), I was going through some of my old things (that is, I was asked to take them with me or throw them out) and I came across some math competitions I had taken in high school. (See, here’s the part where you say, “Wow, you’re a nerd,” and I reply, “See the title of this post.”) Specifically, I found two years of the American High School Mathematics Examination (AHSME, pronounced ahz-mee), and one of the American Invitational Mathematics Examination (AIME, pronounced ay-mee). My initial reaction was to recycle them, but something made me peek at the questions, and I ended up bringing them home, mostly to find out if I had any idea what I was doing back then.
As I started to read through the questions, I was pleased to discover that I could do most of the 1994 AHSME questions in my head (the ’94 AHSME is generally considered the easiest AHSME ever), which I’m certain was not the case in 1994. I did, however, show considerable improvement from the 1992 exam, in which I blew the first three questions:
- (I said .)
- If , then (I said . At this point I have to believe that in 1992 I didn’t quite understand the distributive law.)
- An urn is filled with coins and beads, all of which are either silver or gold. Twenty percent of the objects in the urns are beads. Forty percent of the coins in the urn are silver. What percent of the objects in the urn are gold coins? (I said 40%, a standard mistake.)
and several more after that. The ’92 test was harder, too — at least, I couldn’t do as many of the questions in my head yesterday. For example:
27. A circle of radius has chords of length 10 and of length 7. When and are extended through and , respectively, they intersect at which is outside the circle. If and then ?
(It was multiple choice, but it’s more fun without the choices.) Feel free to discuss these problems in the comments.
I’m glad I kept the exams, both after I took them and just last week. It serves as confirmation that I have indeed learned something after all these years. For anyone starting out in mathematics, I assure you that some things do get easier.
[Of course, there is one other benefit to keeping the exams: I now have an excellent source of problems for our newsletter, and I’m sure the Problem Solving class will be seeing many of these in the spring.]