Mathematics Extension 2 Predictions (4 Viewers)

tgone

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So kind for a student who just came here for two years, questions are abstract and see you E4.......
yeah it was like a really abstract test that’s a good way of putting it but for the most part just going through with calculations got to the required result so I think it’s ok- predicting a very low E4 cutoff this year though so don’t be too disappointed
 

sga2

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did anyone know how to do the final part of q.16?
 

tgone

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Bruh how, q16 b took too long I gave up on it
you can write “vector” CB = e^(ipi/3)CA since it’s equilateral
i’m just going to use zA=a, zB=b, zC=c
i.e.
b-c=(a-c) e^(ipi/3)
so b=c(1-e^(ipi/3))+ae^(ipi/3)

we know that:
b=xb+5i
c=xc-5i

subbing c and a into above the expression for b, you get an expression for b in terms of xc, and you can solve for xc by using Im(b)=5
 

tgone

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@tgone wtf they actually asked the same question as this in this year’s HSC (with minor variations)….
yeah literally i looked at it in reading time and did a double take … thought what the heck did he know about it… so glad i did it thank you so much 😆
 

tgone

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@tgone wtf they actually asked the same question as this in this year’s HSC (with minor variations)….
although to be fair when you sent I just skimmed over it and thought yeah I think I can do this after a bit of thinking so it just made it quicker in the test rather than letting me know how to do it
 

yanujw

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yeah literally i looked at it in reading time and did a double take … thought what the heck did he know about it… so glad i did it thank you so much 😆
Same lol it took me by surprise when I first saw it, thinking about how it looked really similar
 

synthesisFR

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To try find the substitutions the trick is often to try match up the powers. For example, if I was like prove that a^4+b^4+c^4>abc(a+b+c), you see the 4th power so instantly you're thinking along the lines of Am-Gm for four. Then, you see three terms on the LHS and you notice that on the RHS you've got a^2bc, so a is twice the power. Therefore a good guess would be Am-Gm for a^4+a^4+b^4+c^4≥4a^2bc. And you'll find that this works out if you to it for b and c and add them together. Like fr it's tricky but there are some hints in the question itself and it helps you narrow it down to like a couple guesses. Idk if this helps
Question
R u allowed to just use am hm of threes or fours without proving it first
 

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