What's the difference between mathematical reasoning and actual mathematics? Just curious (super late response I know), because the kids I knew who did well in this competition (and similar ones) were generally the ones who also did super well in VCE Maths.
Well, I tend to think mathematical reasoning is the ability to "think mathematically" - it's something that can be trained to some extent, but some people will have it to a greater degree than others, like I'm sure your logical/philosophical type reasoning skills would be stronger than most other people, for instance. The gist of these competitions is to apply mathematics into difficult scenarios where you actually have to interpret very complex ideas.
VCE maths is, like Thushan was hinting at, more computational. It relates to being able to hit the right buttons on the calculator and knowing learned facts. It requires a certain amount of reasoning, but less so. It requires other skills such as accuracy (not making errors) and consistency.
I can come up with several examples of those who did well on AMC competitions who didn't go on to do SUPER well on VCE maths (albeit they still did well). E.g. pi did better than me, as a whole, on these AMC competitions (he won several prizes, I think), whereas I never won a prize. However, I did better than him on VCE maths.
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