# How to screw up Australian Maths

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 22In the diagram, the shaded area is
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.

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