# “Bashing out” speaks too highly of it (calculus scholarship)

I *so* could have finished that calculus scholarship exam. I *so* should have. I wasn’t *that* far off. I mean, I spent like, eight minutes trying to figure out why my integral for question 1(b) was impossible, before giving up with that and 1(c) and moving on to question 2 and rest of the paper. When I got to the end of question 5, there were five minutes left. It then took me another minute to spot my error—the correction of which made Bob my uncle—and then three minutes to solve the now-much-easier integral. It is virtually impossible to make any mark-worthy progress on a part-question in one minute. I figure I would have needed about twelve minutes. Okay, so maybe I would still have been four minutes short. But still.

I would go ahead and start talking about how much easier it was than last year’s, but of course, having improved since the last time I did this, I *would* think that. To be frank, I was expecting an easier exam. Last year, they marked everyone up by ten marks because we were so useless. And the exam didn’t really surprise me, so either it was the same level as last year, or it was easier. To this note, though, the comment of a friend of mine deserves attention. He said that much of this year’s paper—an unusually high proportion—could be done on the calculator, without unknown constants or the like. Which, come to think of it, is a fair comment.

It was not, then, an exam to be “bashed out”. You bash out questions that require extensive algebraic manipulation, normally because of unknown constants or weird and wonderful functions. Some of this year’s questions required little—if any—real mathematical thinking at all. Question 2 is a perfect example of this. It involved the solving of a not-too-obscure trigonometric equation (I mean, I’ve seen worse), which was then used in the modelling of a “giant double Ferris wheel”. To call it something that can be bashed out would be to give it too much credit. You just tap it into the calculator, and give your answer as a decimal.

Question 3 had a similar calculator approach, though to be fair, it required an ounce or two of ingenuity. There seemed to be a theme among questions 2 through 4 where a result from part (a) would be incredibly useful in part (c). But I suppose I would have to concede that both questions 4 and 5 were in a more scholarship-like spirit. Question 5 would be nothing beyond the above-average the co-ordinate geometry-familiar candidate. Question 1—well it wasn’t hard, or it *wouldn’t* have been for me if I, having found d*y*/d*x*, then (d*y*/d*x*)², hadn’t substituted that into ∫ *y*√(1+(d*y*/d*x*)²) d*x* as if it were d*y*/d*x* (so that my (d*y*/d*x*)² was (d*y*/d*x*)^{4}), to give me an integral ∫ √[*x*(1+*a²*/*x²*)] d*x* that can’t be done with any technique I’m aware of.

Prior to the exam, I had asked our school’s head of calculus if he thought the exam, after last year, would be made easier again. He said it was likely, and they would probably put in one harder question to separate the top ten or so candidates. I think he was right. Question 4(b), I could see, which was about the Mandelbrot set, would have freaked out many candidates; indeed, it was the hardest question to understand. But once you knew what they were talking about, everything fell into place. Question 2 wasn’t the bash-out question. Question 4 was.

Having thought about it a bit more, I conclude that this year’s exam *was* easier than last year’s. By how much, I’m not sure, but easier to some extent. Last year’s marking involved a jaw-dropping loosening of the marking schedule once they realised no-one could do anything. If a similar fix is needed this year, it will only be whatever is required to pull the pass mark up to 20, which will be a lesser amount than last year. The top candidates are again likely to have finished or almost finished the paper, and be separated only in that question 4(b). However, because the remark won’t need to be as dramatic, their minor errors are likely to remain penalised; my prediction for the outstanding cut-off therefore goes slightly down on last year’s actual. To pass, 20; for outstanding, 32. I still think, though, that at least three people will gain all of the maximum possible 40 marks.

That was my second-to-last exam, and the last of the combined nine scholarship exams I’ve sat in my high school life (five this year, three last year, one the year before). This year, then, is my last chance to prove I’m worth something at this level. The ride with the scholarship exams—in particular the calculus one—has been interesting. It’s now just a three-month wait to see what it comes to.

##### Permalinks to earlier related posts

- Failure, sums it up (calculus) (10 December 2005)
- Calculus scholars should expect challenge (19 March 2006)
- NZ maths falls another notch (calculus: and some moments of stupidity) (24 November 2006)
- NZ Scholarship 2006 (and calculus: go easy on the useless mathematicians) (17 February 2007)