My solutions to the 2019 Mathematics Extension 2 Paper (1 Viewer)

[quickoats]

my solution for the probability question was a bit out there(I found an expression for PB and PA in terms of w and v which ended up with a quadratic inequality with the result as the solution).

I used that same method, and I've seen it a few times in other people's solutions, so it's probably not as uncommon as you think. Idk if there is any other method, since the ratio given had a surd in it.

 

[TheOnePheeph]

I used that same method, and I've seen it a few times in other people's solutions, so it's probably not as uncommon as you think. Idk if there is any other method, since the ratio given had a surd in it.

The surd is actually the golden ratio, so i thought there could be some weird super elegant solution, but I wasn't risking anything in the exam, just went straight for the first thing I saw that made sense lol.

 

[Arrowshaft]

I'm gonna guess about 73. I thought the alignment for 2017 was less crazy than that though.

I checked rawmarks.info, 77 aligned to a 90. But that might have been the extreme end for a 90, I have no idea of the exact e4 cut off though. Its weird, because I remember when Carrotsticks posted his solutions to the 2017 paper, he said it was hard and expected the e4 cut off to be around 68 (i believe).

 

[TheOnePheeph]

I checked rawmarks.info, 77 aligned to a 90. But that might have been the extreme end for a 90, I have no idea of the exact e4 cut off though. Its weird, because I remember when Carrotsticks posted his solutions to the 2017 paper, he said it was hard and expected the e4 cut off to be around 68 (i believe).

These raw marks are worrying me lol. In 2016 98 only rounded up to 99, which I assume means it wasn't a state rank, and 2016 was definitely harder than our paper, so maybe state rank for our year will be like 99 or 100 raw lol.

 

[quickoats]

The surd is actually the golden ratio, so i thought there could be some weird super elegant solution, but I wasn't risking anything in the exam, just went straight for the first thing I saw that made sense lol.

The limit F(n+1)/F(n) of the Fibonacci sequence comes to mind when thinking of the golden ratio, so maybe that has something to do with it? The probability involved layers so maybe its hidden in there? Even so, you'd need to prove its limit... idk I'm dumb so maybe that method leads nowhere.

 

[TheOnePheeph]

The limit F(n+1)/F(n) of the Fibonacci sequence comes to mind when thinking of the golden ratio, so maybe that has something to do with it? The probability involved layers so maybe its hidden in there? Even so, you'd need to prove its limit... idk I'm dumb so maybe that method leads nowhere.

Yeah oh well, the exams over now. If everyone else did our method in the solutions done hopefully we get full marks for it lol.

 

[quickoats]

These raw marks are worrying me lol. In 2016 98 only rounded up to 99, which I assume means it wasn't a state rank, and 2016 was definitely harder than our paper, so maybe state rank for our year will be like 99 or 100 raw lol.

I know of a girl who came 8th in 4u with a HSC mark of 99 in 2016, so it's definitely possible. Same with 3rd in 2018, he got a HSC mark of 99.

Our paper was a lot more doable than 2016 and 2018, but it was just kinda weird? so it may have thrown people off. Maybe state ranks will be roughly the same as previous years raw?

 

[Arrowshaft]

I used that same method, and I've seen it a few times in other people's solutions, so it's probably not as uncommon as you think. Idk if there is any other method, since the ratio given had a surd in it.

I think the most common solution to that was a GP infinite sum, which once you summed gave you a quadratic - seemed awfully 2u like in that sense, just with an inequality.

 

[TheOnePheeph]

I know of a girl who came 8th in 4u with a HSC mark of 99 in 2016, so it's definitely possible. Same with 3rd in 2018, he got a HSC mark of 99.

Our paper was a lot more doable than 2016 and 2018, but it was just kinda weird? so it may have thrown people off. Maybe state ranks will be roughly the same as previous years raw?

I thought the exact same thing about this years paper. Yes the questions were fairly easy, but it was honestly so unlike any other 4u paper, with a lot of bizarre computational questions that were easy to make dumb mistakes on. I don't like that they do it that way, it more tests accuracy than mathematical ability near the top lol. Supposedly in 2017 99 raw didn't get a state rank, but I'm not sure how reliable that is.

 

[TheOnePheeph]

I think the most common solution to that was a GP infinite sum, which once you summed gave you a quadratic - seemed awfully 2u like in that sense, just with an inequality.

I did it by getting the probability of A winning on either side of an equation, i.e A= x + Ay, which could be done because the pribability of A winning after both A and B had their first turn was exactly the same, and then equating the probability from that. I did the same thing for the probability of B, then said B>A which ended up with a quadratic. Really worried they are not gonna mark this right now lol.

 

[Arrowshaft]

I did it by getting the probability of A winning and B winning on either side of an equation, i.e A= x + Ay, and then equating the probability from that, then saying B>A which ended up with a quadratic. Really worried they are not gonna mark this right now lol.

Exactly what I did, which is why I think I lost marks for prob. for not showing an infinite sum, but I don’t know, they might think its a different way of thinking. By the way, did you get and then , then express the quad. in terms of ?

 

[TheOnePheeph]

Exactly what I did, which is why I think I lost marks for prob. for not showing an infinite sum, but I don’t know, they might think its a different way of thinking. By the way, did you get (y/w)>(y/w)^2+1 and then (y/w)^2-(y/w)-1>0, then express the quad. in terms of y/w?

Yep. It would be absolutely ridiculous if they didn't mark us right for this, but I'm scared they are gonna do it lol. Like you don't need an infinite sum to express the probability, and in fact our way probably shows a greater understanding of probability.

 

[quickoats]

Exactly what I did, which is why I think I lost marks for prob. for not showing an infinite sum, but I don’t know, they might think its a different way of thinking. By the way, did you get (y/w)>(y/w)^2+1 and then (y/w)^2-(y/w)-1>0, then express the quad. in terms of y/w?

I got the exact same quadratic expression by using an infinite sum for the probability of A winning, then setting it to <0.5 since P(A winning) and P(B winning) are complementary, rather than doing P(B winning)>P(A winning), so I'm not sure if they'll give me the marks either.

 

[TheOnePheeph]

I got the exact same quadratic expression by using an infinite sum for the probability of A winning, then setting it to <0.5 since P(A winning) and P(B winning) are complementary, rather than doing P(B winning)>P(A winning), so I'm not sure if they'll give me the marks either.

Lets just hope the markers have enough mathematical sense to see the logic in each different way, which I would hope they would. We ended up with the exact same expressions for probability, just using different mathematical tools to limiting sums.

 

[Arrowshaft]

I got the exact same quadratic expression by using an infinite sum for the probability of A winning, then setting it to <0.5 since P(A winning) and P(B winning) are complementary, rather than doing P(B winning)>P(A winning), so I'm not sure if they'll give me the marks either.

That's fine, you're essentially showing the same thing, but addressing its complement. you're in the clear, its justTheOnePheeph and I who have to be worried about the markers deducting marks lol

 

[Arrowshaft]

I thought the exact same thing about this years paper. Yes the questions were fairly easy, but it was honestly so unlike any other 4u paper, with a lot of bizarre computational questions that were easy to make dumb mistakes on. I don't like that they do it that way, it more tests accuracy than mathematical ability near the top lol. Supposedly in 2017 99 raw didn't get a state rank, but I'm not sure how reliable that is.

AND WHAT WAS WITH ALL THE 4 MARKERS??

 

[akkjen]

Can they really not give you marks for having an alt solution to theirs?

 

[TheOnePheeph]

Can they really not give you marks for having an alt solution to theirs?

We don't really know, but we are worried they can.

 

[akkjen]

We don't really know, but we are worried they can.

surely if you show your approach and it is logical it will be fine. otherwise we would have to also guess what approach they want us to take for some questions

 

[Arrowshaft]

surely if you show your approach and it is logical it will be fine. otherwise we would have to also guess what approach they want us to take for some questions

Fair point, but our main concern is in the marker’s haste to finish marking our exam within the allocated time slot, they may not understand our reasoning and simply assume we fudged the result.