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.]

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Tags: AHSME, AIME, distributive law

This entry was posted on December 3, 2007 at 6:24 pm and is filed under Competitions, Math Mistakes, Problems. You can follow any responses to this entry through the RSS 2.0 feed.
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December 5, 2007 at 12:22 pm |

This had me laughing the entire time. I can’t imagine how I would have done on something like that at your age, I am sure it would have been worse.

December 5, 2007 at 6:13 pm |

As I read this, I realized wow, I definally forgot a lot of stuff over the years but again, I thought wow, if I tried to take something like that at a much younger age, I would have looked at it like what? I understood the beads and coins problem, but I feel I would have made the exact same mistake as you did at that time.

I can’t remember exactly how to do the first problem that was posted with the sixes and raised to the sixth power. Is it supposed to be 6 raised to the 36? That is what I would have guessed.

For the circle problem, I forgot the little rules for the circles and the external points and angles outside the circle formed by cords. I could draw it which was good, but I forget how to solve it. Anyways, I wish I could find something like that from a long time ago that I could look over how I did it then compared to what I know now.

I remember I took a math exam, well it may have been a competition type thing I don’t remember exactly what it was because I was in elementary school, but I did very well on it and I just can’t remember what type of problems I had to solve, too bad I didn’t keep all my old exams.

But yes I feel like a nerd to! When people ask what you’re majoring in and you say math, people are like whoa! But I love math and if that makes me a nerd then I’m a happy nerd who knows what she is doing!

October 17, 2009 at 10:08 pm |

Problem 1 is 6*(6^6) or 6^7.

I might be taking the Putnam this year, any studying tips?

March 24, 2011 at 6:43 pm |

The solution for the circle problem is r^2=73. Let me know if you are interested in how to get it, I’ll post the procedure (too lazy now…)

Regards.

February 5, 2012 at 8:22 pm |

Hey Batman, would you care to share the full AHSME tests? I’m interested in trying them out of historical curiosity.

February 14, 2012 at 1:03 pm |

The AoPSWiki and this site have a lot of past exams, usually with solutions. There used to be more sites with archived exams, but several of my links are dead now.