itute stated cos@=cospi/10=0.951approx so cannot be sqrt((5-sqrt5)/8)Also, neither the Itute nor TL solns provided a satisfactory explanation for why the negativesolution was invalid in Q14c(ii).
Itute gave no reasoning for selection of the +ive inner surd, while TL reasoned that cos^2() must be positive (but clearly the [] solution is also positive).
My reasoning is that where we subst,
,
in order to get the polynomial, we could equally well have substituted
,
to get the same equation.
So the polynomial is equally valid for solving for,, as well as some other non acute angles (which clearly can be ignored).
So the two acute solutions,
correspond to solutions for cos(pi/10) and cos(3pi/10), and since cos() is a decreasing function on (0,pi), then the larger value must correspond to cos(pi/10).
Did anyone else use this reasoning?
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Maths Ext 2 Predictions/Thoughts (1 Viewer)
- Thread starter Anaya R
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Paradoxica
-insert title here-
Show that 117^(0.4)+pi^(5/3)-e^2.5 is positive.
is evaluating it and saying both are the same number not enough to prove it?
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It's a circular argument. Prove that this trig result holds. Oh look, they happen to equal on a calculator therefore it is proven!
just thought it was kinda like the roots thing, if this polynomial can be tan3theta solve for theta then find the roots, then by plugging in the numbers to see which ones are the distinct roots.
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But plugging in numbers to see what the exact trig value is lacks proper rigour, as you have effectively found the answer by direct computation rather than by proof. It is the same as claiming you have proven the exact value of something simply because the calculator says they're equal rather than by logical arguments.
It looks dirty
The point is that it's not about proving that it is the correct answer, it's about proving that the other surd is not the correct answer.
It would of course be invalid to try to use a calculator to prove that it was equal, because whatever decimal precision you use, it can never prove equity to the surd. But in terms of simply ruling out the other solution (the only other feasible solution), then it's dirty but it's valid (in my opinion).
Agreed that it looks dirty, but it's probably still valid.
The point is that it's not about proving that it is the correct answer, it's about proving that the other surd is not the correct answer.
It would of course be invalid to try to use a calculator to prove that it was equal, because whatever decimal precision you use, it can never prove equity to the surd. But in terms of simply ruling out the other solution (the only other feasible solution), then it's dirty but it's valid (in my opinion).
pi/10 < pi/6, cos(pi/10) > sqrt(3)/2, easily shown that sqrt((5 - sqrt5)/8) < sqrt(3)/2 and sqrt((5 + sqrt5)/8) > sqrt(3)/2
it seems last years 4u cohort was very weak (just look at how well my mark aligned). question 16b looking back was not very difficult for a 4u paper and i was very surprised to hear only 10 people got 5/5. the discriminant should be a go-to when you hear 'two values' of something. i might sound like a hypocrite cuz i only got 2/5 in that question, resulting from wrong algebraic expansion after dot product, so thats where my marks stopped, but I had the discriminant and justification included in my answer. the turly hard questions in this test imo were 15cii, 15d, 16aiii and 16c.
definitely not weak. more so that 2020 HSC 4u difficulty was a huge bait for what was to be expected.
maybe i was a bit harsh but ye i agree 2020 baited people. actually now that i think about it, i just think the marking centre was generous in the e4 cutoff. so maybe the cohort isnt weak per se but unprepared for the difficulty
synthesisFR
afterhscivemostlybeentrollingdonttakeitsrsly
wahs ECF???
synthesisFR
afterhscivemostlybeentrollingdonttakeitsrsly
this is funny reading everyone say how hard is was
but in the 2022 thread everyone was saying how easy this exam was
but in the 2022 thread everyone was saying how easy this exam was
synthesisFR
afterhscivemostlybeentrollingdonttakeitsrsly
help
ECF stands for Error Carried Forward. It is an approach to marking in subjects like maths, where you will only be penalised for errors in your working for the previous part of a question, rather than also penalising the error in subsequent parts of the question, which naturally makes your working and answers in subsequent parts of the question incorrect.
synthesisFR
afterhscivemostlybeentrollingdonttakeitsrsly
ah makes sense does this also apply for stuff like chemistry?
I believe it would. I have seen a few Chemistry trial papers where ECF was used in marking.