Suggested Answers to the HSC 2016 Maths Extension 1 Exam (+Discussion!)

[jakesilove]

Do you guys know if there can be a penalty if you didn't draw the circle geo diagram?

Look, I actually don't think there would be! It just might piss the markers off a bit, which could have generally detrimental results. But, like, there aren't actually marks allocated to it, despite what the questions indicates.

[huwsername]

I can't see why Question 8 isn't D :/

the answer you've given makes sense, but I thought that 3C1 (1 required left handed) * 17C10 (everyone else) = 58344 would also work. it's about 50-50 among my friends, too. can anyone help put me on the right track?

[Blissfulmelodii]

Just out of curiosity, does scaling work differently depending on whether extension 1 is worth 1 unit or 2?? Or does the amount of units the course is worth not matter in this case?

[RuiAce]

I can't see why Question 8 isn't D :/

the answer you've given makes sense, but I thought that 3C1 (1 required left handed) * 17C10 (everyone else) = 58344 would also work. it's about 50-50 among my friends, too. can anyone help put me on the right track?

You choose 1 out of the three to be left-handed, and then there's double counting.

Let's say persons A, B and C are left handed.

Choose any one out of person, say A, to be left handed.
One possible scenario for the remainder 17 people are B, D, E, F, ...

BUT, instead, choose B to be left handed
"Another" possible scenario for the remainder 17 people are A, D, E, F, ...

But the above two are clearly the same outcome. Hence you have double counted when TWO (or even all THREE) people that are left handed, have been chosen.

Hence the mistake.

Because the question is asking for 'at least one' which also means that two left handed people can be chosen etc. The solution you've provided only accounts for one left handed person, not more than one.

Nah the number is too large, not too small. There is no undercounting here. Especially since he claimed to use ¹⁷C₁₀

[RuiAce]

Just out of curiosity, does scaling work differently depending on whether extension 1 is worth 1 unit or 2?? Or does the amount of units the course is worth not matter in this case?

No that impacts on nothing at all.

[jakesilove]

Just out of curiosity, does scaling work differently depending on whether extension 1 is worth 1 unit or 2?? Or does the amount of units the course is worth not matter in this case?

Scaling will work exactly the same! In the end, if 3U is worth one unit, your mark out of 100 (or 200?) will just be cut in half; your unit count doesn't effect scaling.

[Blissfulmelodii]

Scaling will work exactly the same! In the end, if 3U is worth one unit, your mark out of 100 (or 200?) will just be cut in half; your unit count doesn't effect scaling.

Ahhh okay that makes total sense. Thanks!!

[ladyofathena]

You choose 1 out of the three to be left-handed, and then there's double counting.

Let's say persons A, B and C are left handed.

Choose any one out of person, say A, to be left handed.
One possible scenario for the remainder 17 people are B, D, E, F, ...

BUT, instead, choose B to be left handed
"Another" possible scenario for the remainder 17 people are A, D, E, F, ...

But the above two are clearly the same outcome. Hence you have double counted when TWO (or even all THREE) people that are left handed, have been chosen.

Hence the mistake.
Nah the number is too large, not too small. There is no undercounting here. Especially since he claimed to use ¹⁷C₁₀

Oops, realised my mistake haha

[RuiAce]

Oops, realised my mistake haha

Nah all sweet. I think you could sort of tell what was going on because you were able to consider two or three being left handed, just that you thought in the wrong direction afterwards.

[Nech]

hey for q12c) the very last part, how does the cos() in the denominator turn into a tan()? i got stuck there but i knew it somehow had to = -1 for the lines to be perpendicular at that point

[RuiAce]

hey for q12c) the very last part, how does the cos() in the denominator turn into a tan()? i got stuck there but i knew it somehow had to = -1 for the lines to be perpendicular at that point

[jakesilove]

hey for q12c) the very last part, how does the cos() in the denominator turn into a tan()? i got stuck there but i knew it somehow had to = -1 for the lines to be perpendicular at that point

Because we know, from the question/graph, that cos(a)=tan(a). That's the whole point of the question! It took me a while to get that too

[RuiAce]

Because we know, from the question/graph, that cos(a)=tan(a). That's the whole point of the question! It took me a while to get that too

Seems like last part of Q12 for both 3 and 4U were trippy. I stared at that for 2 minutes before I realised wait there must be a trick. And that's when I started thinking trig identities...

[Nech]

Because we know, from the question/graph, that cos(a)=tan(a). That's the whole point of the question! It took me a while to get that too

OMG lmao i spent a bit of time playing around with trig identities AHAHA, thanks

[queueq]

Hey for the last question, finding values of t, I just used distance formula, then differentiated to find stationary points and confirmed with 2nd derivative that it was a min. I still got t= sqrt2 and -sqrt2
Do I get full marks??