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How to screw up Australian Maths

They were, perhaps, the easiest fifteen marks I have ever lost in a mathematics competition.

It was as if the paper was saying, "Here, have fifteen marks," in the most gracious, caring manner a paper ever could. And, due to a bout of stupidity that I’m still trying to get my head around, I said, "No, that’s okay, thanks. I don’t want them."

Question 22
In the diagram, the shaded area is

  1. between 1/4 and 5/16
  2. between 5/16 and 3/8
  3. between 3/8 and 7/16
  4. between 7/16 and 1/2
  5. more than 1/2

Question 25
The diagram shows a pentagon with one reflex angle. For a polygon with n sides, what is the maximum number of reflex angles?

  1. 1
  2. 2
  3. n − 2
  4. n − 3
  5. n

Question 27
A supermarket has seven checkouts, all of which can accept cash. The first four only can also accepty credit card payment. Kath, Kim and Sue are all at the supermarket. Kath wants to pay by credit card, while Kim and Sue want to pay by cash. In how many ways can the three queue at the checkouts? (Two people can queue at the same checkout.)

The above questions are © Australian Mathematics Trust 2005. Because I don’t have a copy of the paper, I’m not entirely sure of the wording.

They lay in three questions: gimme questions; ones where a method of finding a solution is immediately obvious. And I had them all sussed out. Until the last step.

   The first was in the twenty-second question. Having a general inability to solve geometry problems, a friend and I decided that should a question like this arise in the competition, the best method would be to construct a scale drawing and measure it to get an approximate answer. So that’s what I did.

I had brought with me some 7mm × 7mm grid paper, on which I drew a square 10 by 10 units — 70mm × 70mm. I constructed a scale diagram and measured my shaded area to get 59mm × 39mm = 2301 mm².

Then what did I do? I divided this by 100 × 100 = 10000 mm² to get my answer: 0.23. Less than one quarter: not an option. Thinking it was just an error in measurement, I selected option A, against instinct which told me that answer looked horribly wrong.

   The next stupid mistake was in question twenty-five: a very easy question indeed. So easy that I followed my gut instinct and immediately selected C: n − 2. Hmm. Two reflexes to a quadrilateral, and three to a pentagon. Not likely.

   And it gets worse. The twenty-seventh question I was certain I had. Kath can go to any of four checkouts, Kim and Sue to any of seven.

So then the answer is 4 × 7 × 7, which is clearly equal to 4 × 28 = 112. Easy? I wish I had got it right.

   I also lost the last two questions, but they, being the last two questions, weren’t nearly as simple as those ones. So even if my brain was working on that day, I would have lost them anyway. So they don’t bother me nearly as much.

But turning down such an offer of such easy fifteen marks. And, knowing me, I probably made some more mistakes like those in the first twenty too. That’ll cost me dearly, and I’ll be kicking myself for a while for that one, I will be.

The Australian Mathematics Competition comprises of thirty questions arranged in increasing order of difficulty. The first twenty-five are multiple choice; in the last five participants have to nominate a three-digit number. Participants are awarded certificates based on their ranking. A fuller explanation of scoring and awards criteria can be found on the AMT website.

For those that couldn’t figure out what I’d done wrong: in Q22 I should have divided by 70mm × 70mm = 4900mm²; in Q25 the answer is n − 3; in Q27 my arithmetic was incorrect, 4 × 7 × 7 = 4 × 49 = 196.

Related Links

  • Australian Mathematics Trust
  • Australian Mathematics Trust: Events including the competition
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    One Comment Post a comment
    1. Amena #

      You actually remember what questions you answered after giving the tests? O.o

      5 August 2005

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