What raw marks in extension 2 generally correspond to state ranks? (3 Viewers)

[TheOnePheeph]

Well, our school has compulsory participation in the Australian Maths Comp for yr 7 and 8. I did it in yr 7 and got 131/135, which was equivalent to a medal (top 0.03% or smth), and was invited to the Australian School of Excellence. This is a maths camp designed specifically for ppl who are likely to go well in comp maths and train them for the IMO team. Have a look at the AMT website for more info about it.

Lol nice, I didn't know it went that deep. Highest I've ever gotten on it was high distinction in year 8 or something, and have only ever gotten credits/distinctions since then. I'm angry about the one this year though, the website kept crashing for us and there were like at least 3 of the last 5 questions that I could have done. I really hate the tests though, have never really been good at them. If there are kids like you out there doing the extension 2 paper though, I feel like its impossible for me to get a state rank haha.

 

[Carrotsticks]

Hopefully this year's last question doesn't prevent potential state-rankers from doing their best like last year's silly geometry question.

 

[TheOnePheeph]

Hopefully this year's last question doesn't prevent potential state-rankers from doing their best like last year's silly geometry question.

Yeah I hated that geometry question. It shows how bad some recent years have gotten in ext 2, either having easy Q16s (2014, 2017) or artificially difficult ones (2018). If you compare to like 2001 or even 2010, which had some really genuinely difficult questions, it is obvious how uninspired they have gotten. In fact the only post 2012 paper I thought was good was 2016, and even that wasn't great until Q16. Oh well, hopefully 2019 will be a bit better haha, since it is the last year.

 

[HeroWise]

Hopefully. But could be harder too. Especially for things like conics, probs that might be this years q16 which are getting remvd.

 

[UStoleMyBike]

There hasn't been a tricky integral in a couple of years, I feel like we are due for a hard integration question

 

[DrEuler]

There hasn't been a tricky integral in a couple of years, I feel like we are due for a hard integration question

We all know what happened the last time they tried that *2014 HSC*. All the top students/state ranks literally did it in two steps because it could be done by inspection.

So na after that disaster I don't think they will haha

 

[idkkdi]

Well, our school has compulsory participation in the Australian Maths Comp for yr 7 and 8. I did it in yr 7 and got 131/135, which was equivalent to a medal (top 0.03% or smth), and was invited to the Australian School of Excellence. This is a maths camp designed specifically for ppl who are likely to go well in comp maths and train them for the IMO team. Have a look at the AMT website for more info about it.

Did you end up making IMO?

 

[TheOnePheeph]

We all know what happened the last time they tried that *2014 HSC*. All the top students/state ranks literally did it in two steps because it could be done by inspection.

So na after that disaster I don't think they will haha

I think we could possibly have an integral similar to one of the ones we see in the integration marathons here, but that may be too hard for most 4u students. 2014 one was hilarious.

 

[TheOnePheeph]

Never really saw the point of doing those convoluted integral questions. 99% of it is spent doing algebraic manipulations rather than actual integrating, which is kinda pointless.

Yeah thats probably true. I personally enjoy the algebraic manipulations, I find the problem solving aspect quite interesting but yeah they aren't very good mathematically. When you have stupid stuff like the geometry question last year though it wouldn't be surprising for the last question to just be one of these convoluted algebraic manipulations.

 

[Drdusk]

I haven't seen it, but yeh the same logic applies, ridiculous convoluted geometry questions are also kinda pointless. In fact.... any ridiculous convoluted question is kinda pointless... which why I cheered when they scrapped conics.

Forget convoluted geometry questions

NESA when thinking of an actually good question 15 for the 2018 HSC:



This one was soo convoluted

 

[TheOnePheeph]

Forget convoluted geometry questions

NESA when thinking of an actually good question 15 for the 2018 HSC:



This one was soo convoluted

Lol completely forgot about that. What a ridiculous question. It wasn't even difficult, just a standard de moivrre's theorem identity, but god it took ages just because of all the algebra. 2018 in general had a lot of really stupid convoluted questions.

 

[TheOnePheeph]

I haven't seen it, but yeh the same logic applies, ridiculous convoluted geometry questions are also kinda pointless. In fact.... any ridiculous convoluted question is kinda pointless... which why I cheered when they scrapped conics.

Yeah conics is mostly garbage, although there have been a few decent questions, such as the 2000 one near the end of the paper (7b iirc), as well as the 2005 one, but even that was convoluted, it just required more mathematical reasoning than algebra. I honestly think the nicest topic in 4u is polynomials, even if 90% of the time those questions are dead easy.

 

[fan96]

Forget convoluted geometry questions

NESA when thinking of an actually good question 15 for the 2018 HSC:



This one was soo convoluted

Honestly, that question was more annoying than all of Q16 put together.

 

[TheOnePheeph]

Yeh the entire conics chapter was useless. It was all just algebra and didn't contain anything new. The topic itself is also useless in the sense that it finds very little application in the real world. The only thing that I can think of is in trajectory calculations, and even then it doesn't really require all that much. My fav topic in 4u is mechanics since it's the only topic that actually applies the math to real world situations. Volumes is also nice too in that it's the only topic that demonstrates how an integral is used to build up a sum from its infinitesimal parts (a fact which they don't really teach), which is an important concept in physics/engineering. Complex numbers and integration are also pretty useful. Every other topic is more or less useless or nice-to-know.

Oh yeah I forgot about mechanics and volumes lol. Volumes is fun but my problem with it is that almost every question is the same. When there is a hard one though its really good. Mechanics is also fun but I generally only like the circular motion bit, the reaisted motion is literally the same thing every time: equation for acceleration, then integrate to get v in terms of t, sometimes incorporating terminal veloicty. There was a really good resisted motion problem in one of the BOS trials though where there was resisted SHM and you had to solve a second order linear differential equation (but it gave you the integrating factor and basically told you how to do it). Makes me wish differential equations were in the 4u syllabus, would make mechanics so much better. I reckon taylor series could also be in the syllabus instead of something like conics or graphs.

 

[Trebla]

Speaking of BoS trials....

BoS Maths Trials 2019

Sick of doing standard repetitive questions and want some good practice for the harder questions in the HSC maths exams? Want to be challenged and tested on how well you really know your stuff? Know someone at school who is a gun at HSC maths? It is that time of year again where Bored of...

community.boredofstudies.org

*cough* *cough*

 

[TheOnePheeph]

Speaking of BoS trials....

BoS Maths Trials 2019

Sick of doing standard repetitive questions and want some good practice for the harder questions in the HSC maths exams? Want to be challenged and tested on how well you really know your stuff? Know someone at school who is a gun at HSC maths? It is that time of year again where Bored of...

community.boredofstudies.org

*cough* *cough*

I do kind of want to do the BOS trial this year, but I am unfortunately outside of Sydney so it is a hassle to go up to do it. The past papers I have done from it have been quite a good challenge though (I think I've done 2018, 2017, 2015).

 

[sharky564]

Did you end up making IMO?

no, unfortunately, i simply didnt have consistent enough performance :/

 

[TheOnePheeph]

I think the main reason why Taylor series wouldn't be taught is because of the baggage that comes with it. Deriving the basic Taylor series is straightforward, but things like the remainder term, error bounds, radius of convergence (in the context of complex analysis) etc is more indepth that requires more than a surface understanding, and teaching that would feel somewhat out-of-place compared to the straightforwardness of all the other topics. Students don't even know the epsilon-delta definition of a limit, which is typically where you start with undergrad calculus. Likewise with ODE's: solving linear second-order ODE's is straightforward, but typically ODE's are paired with linear algebra, which students don't know.

Also, do you remember the SHM ODE? I'm curious, since I've never really seen integrating factors used to solve second-order ODE's, only in first-order ODE's.

Here is the question:
I remembered it slightly wrong, it basically involves making a substitution of y=v + nx to make it a first order seperable equation and then solving the remaining first order differential equation in x using an integrating factor, which it basically gives to you. I guess its basically like how you would solve a second order homogeneous linear equation without knowing how to use the characteristic equation. I still thought it was a pretty cool way to incorporate differential equations.

 

[TheOnePheeph]

Ah right, yeh so you break down the second-order ODE to a first-order ODE before using the integrating factor - that makes more sense. Is the integrating factor necessary though? The solution to y' + ny = 0 is simply just y = y0*exp(-nt).

The equation in y doesn't need an integrating factor, its just seperable, but when you subsitute v + nx back into it you get dx/dt + nx = y0exp(-nt), which does need an integrating factor.

 

[Trebla]

Here is the question:
I remembered it slightly wrong, it basically involves making a substitution of y=v + nx to make it a first order seperable equation and then solving the remaining first order differential equation in x using an integrating factor, which it basically gives to you. I guess its basically like how you would solve a second order homogeneous linear equation without knowing how to use the characteristic equation. I still thought it was a pretty cool way to incorporate differential equations.

The resisted SHM question given there was a special case where the roots of the characteristic polynomial were equal. This lends itself to a more 'first principles' approach to solving it in a nice way without calling upon any ODE specific theory.