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3U Maths HSC 2019 Solutions (1 Viewer)

avatarfahaad

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So I was bored and I decided to do the HSC 3U Maths for 2019. Please tell me if any of the answers are wrong. I am not a HSC student lol. In my opinion the exam was harder than last year so hopefully it scales better. Other than that have a look a through it
 

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Arrowshaft

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So I was bored and I decided to do the HSC 3U Maths for 2019. Please tell me if any of the answers are wrong. I am not a HSC student lol. In my opinion the exam was harder than last year so hopefully it scales better. Other than that have a look a through it
lol I made the exact same silly mistake, the integral isn’t tan inverse, it’s a natural log, as u=cos^2x, otherwise everything looks correct to me
 

integral95

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So I was bored and I decided to do the HSC 3U Maths for 2019. Please tell me if any of the answers are wrong. I am not a HSC student lol. In my opinion the exam was harder than last year so hopefully it scales better. Other than that have a look a through it
You can't justify your proof in 14bii) with just that

You made the assumption that


But that's only true if the function is strictly increasing (which is not true ripp)
 

integral95

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So I was bored and I decided to do the HSC 3U Maths for 2019. Please tell me if any of the answers are wrong. I am not a HSC student lol. In my opinion the exam was harder than last year so hopefully it scales better. Other than that have a look a through it
So you actually would also have to include the fact that

Which then you know the function is increasing for between the 3 values
 

avatarfahaad

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You can't justify your proof in 14bii) with just that

You made the assumption that


But that's only true if the function is strictly increasing (which is not true ripp)
but what if you proved that for a continuous function,

and
Therefore b , which is the only root, such that f(b)=0 has to lie between a and c for the curve to be both smooth and continuous

therefore
 

avatarfahaad

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lol I made the exact same silly mistake, the integral isn’t tan inverse, it’s a natural log, as u=cos^2x, otherwise everything looks correct to me
Yeah I realised that mistake, thanks for pointing it out
 

jathu123

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Does anyone have the pdf of the exam? Can't seem to find it on any thread (or im just blind haha)
 

integral95

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but what if you proved that for a continuous function,

and
Therefore b , which is the only root, such that f(b)=0 has to lie between a and c for the curve to be both smooth and continuous

therefore
This is why you shouldn't look at math at 1am lel..
Yeah you're right cause I was thinking of a counter example where you could have you roots



But your idea would negate that.
 

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