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BoS Maths Trials 2019 (1 Viewer)

aa180

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...and here is the latest version of Mathematics Extension 1 paper, solutions (now with colour in the graphs!) and results.

And that's wrap so thanks to everyone who helped and participated this year! :)

To the students, best of luck for the Mathematics Extension 1 HSC exam!
What software was used to draw the diagram for question 14?
 

Paradoxica

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either by ignoring the absolute values completely and fudging it, or only assuming one case (say p>q).

Students needed to carefully explain how to resolve the absolute values. Better responses showed that both cases p<r<q or q<r<p simplify the absolute values down to the same answer.
It is perfectly legal to only check one case. However, this is only acceptable if the student wrote "Without Loss of Generality", or WLOG, or similar.

This is just my opinion on the matter btw.
 

Paradoxica

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For 11 c), a much more obvious (at least to me) solution is to do the following:

α²(β + γ) = α(αβ + γα) = α(k - βγ) = -3α - αβγ

where -3 is the coefficient corresponding to αβ + βγ + γα

Repeating the same for the other terms results in

α²(β + γ) + β²(γ + α) + γ²(α + β) = -3(α + β + γ) - 3αβγ

And this is extremely easy to find the value of by looking at the cubic.
 

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