Thread: BoS Maths Trials 2017

1. Re: BoS Maths Trials 2017

When it says use relevant projectile motion equations from the formula sheet but there are none

3. Re: BoS Maths Trials 2017

Thank you for all those attended . It was great to see so many people keen on doing the BoS trial papers this year. Hopefully the papers were challenging and interesting for you.

Hopefully the rather unfortunate disruptions we had in the afternoon sessions weren't too much of an issue (if anything, maybe they bought some more thinking time?). We hope you can appreciate the difficult decisions we had to make given the already complex logistical arrangements.

Massive thanks to Carrotsticks, Paradoxica, jjlim7, strawberrye, ml125 and the UNSW Mining Engineering staff for helping to supervise the exams.

The papers are attached below. Please note that they have incorporated some mostly minor feedback (e.g. on wording) so they may differ slightly to the hard copy you have.

4. Re: BoS Maths Trials 2017

Also keen to hear your thoughts on both the papers. Were there any questions you particularly liked? How was the difficulty in general and in comparison to previous years (if you attempted those)?

5. Re: BoS Maths Trials 2017

Haha good choice of Q16 .

6. Re: BoS Maths Trials 2017

Originally Posted by Paradoxica
You mean half the paper left in 5 mins

Originally Posted by Trebla
Also keen to hear your thoughts on both the papers. Were there any questions you particularly liked? How was the difficulty in general and in comparison to previous years (if you attempted those)?
What language was question 16 written in

One person behind me said they only missed 11 marks meanwhile I probably barely got over 11 haha

7. Re: BoS Maths Trials 2017

Lol wow that's new. Proving e is transcendental.

8. Re: BoS Maths Trials 2017

Originally Posted by Trebla
Also keen to hear your thoughts on both the papers. Were there any questions you particularly liked? How was the difficulty in general and in comparison to previous years (if you attempted those)?
Just a couple of minor comments on Q16 to the examiners:

1. You introduce the notion of a prime, but none of its properties besides its definition. In several steps of the proof, we prove that integers are indivisible by p essentially because they are the product of integers indivisible by p. Whilst this is a pretty basic number theoretic fact (p|xy => p|x or p|y), it isn't a trivial consequence of the provided definition of the prime number. (It is more work to establish than several steps of the proof that were worth marks). Did you expect students to know this already or prove it? Or did you have something else in mind? Given that NT is not strictly syllabus, it is my feeling that this should have been provided as a black-box fact like you did for the mean value theorem.

2. (V. minor) The lack of a visible k-dependence in the notation of \alpha could have been confusing to students. Of course, since you are led through the proof step by step, this does not lead to any illegal math so no biggie.

3. Good work as always giving up your time to organise this for the students, I hope everyone got something out of it!

9. Re: BoS Maths Trials 2017

Originally Posted by Trebla
Also keen to hear your thoughts on both the papers. Were there any questions you particularly liked? How was the difficulty in general and in comparison to previous years (if you attempted those)?
Did 4U only - it was challenging as expected (duh!) but I still enjoyed it. q16 looked quite interesting, and while I didn't get to do more than one mark of it, I'm looking forward to trying it at some future point, without time pressure. The rest were, to me, a good mix of doable to borderline impossible, which is fine with me for a paper intended like this.

Cauchy-Schwarz inequality was a nice touch :P

10. Re: BoS Maths Trials 2017

To me, the paper was more difficult than the past papers, but then again it could just be the time pressure under exam conditions that I might not have at home. Overall great paper and very engaging questions!

11. Re: BoS Maths Trials 2017

Originally Posted by Paradoxica
But my heart will go on

12. Re: BoS Maths Trials 2017

tf I couldn't even do the 1st integration question in 4u...guess i'm fked for the hsc

13. Re: BoS Maths Trials 2017

Originally Posted by aycaramba
tf I couldn't even do the 1st integration question in 4u...guess i'm fked for the hsc
This guy behind me (calamebe) said he only missed 11 marks the whole exam and he couldn't do it either, and so couldn't many others (including me) so all good.

14. Re: BoS Maths Trials 2017

I feel like that integral has been on the marathon somewhere before...

\text{A bit of experimenting later... and u=sin or u=cos looks problematic} \\ \begin{align*}I&=\int \frac{1}{\sin x \sqrt{\sin 2x}}dx \\&= \int \frac{\sqrt{2\sin x \cos x}}{2 \sin^2x \cos x}dx\\ &= \frac{1}{\sqrt2} \int \frac{\sqrt{\frac{\sin x}{\cos x}}}{\sin^2 x} dx\end{align*}

\text{Let }u=\cot x\\ \begin{align*}I&=-\frac{1}{\sqrt2}\int \sqrt{u^{-1}}\,du\\ &= -\sqrt{2u}+C\\ &= C-\sqrt{2\cot x}\end{align*}

...feel like I might've messed up though

15. Re: BoS Maths Trials 2017

Originally Posted by leehuan
I feel like that integral has been on the marathon somewhere before...

\text{A bit of experimenting later... and u=sin or u=cos looks problematic} \\ \begin{align*}I&=\int \frac{1}{\sin x \sqrt{\sin 2x}}dx \\&= \int \frac{\sqrt{2\sin x \cos x}}{2 \sin^2x \cos x}dx\\ &= \frac{1}{\sqrt2} \int \frac{\sqrt{\frac{\sin x}{\cos x}}}{\sin^2 x} dx\end{align*}

\text{Let }u=\cot x\\ \begin{align*}I&=-\frac{1}{\sqrt2}\int \sqrt{u^{-1}}\,du\\ &= -\sqrt{2u}+C\\ &= C-\sqrt{2\cot x}\end{align*}

...feel like I might've messed up though
For me, I divided top and bottom by cos^2 and it just becomes integral with secx and tanx

16. Re: BoS Maths Trials 2017

Originally Posted by apinix
For me, I divided top and bottom by cos^2 and it just becomes integral with secx and tanx
I used t-formula

17. Re: BoS Maths Trials 2017

If you use t-results while letting t=tanx, it's a trivial question. Can't believe I missed it in the exam ...

18. Re: BoS Maths Trials 2017

Last question was pretty well-written in my opinion. It felt like I was really doing real analysis.

19. Re: BoS Maths Trials 2017

Outside of Q16, what questions did you find the most challenging?

20. Re: BoS Maths Trials 2017

Originally Posted by Trebla
Outside of Q16, what questions did you find the most challenging?
All of multiple choice

21. Re: BoS Maths Trials 2017

legit only one person got the spiky volumes question correct

I feel attacked

22. Re: BoS Maths Trials 2017

Originally Posted by Trebla
Outside of Q16, what questions did you find the most challenging?
Multiple choice, Q11, Q12, Q13, Q14, Q15

Originally Posted by Paradoxica
legit only one person got the spiky volumes question correct

I feel attacked
calamebe confirmed

23. Re: BoS Maths Trials 2017

Originally Posted by pikachu975
calamebe confirmed
can confirm that it isn't

24. Re: BoS Maths Trials 2017

Originally Posted by Paradoxica
can confirm that it isn't
RIP

I just skipped it because I didn't know how to find the area of the cross section and I didn't think of integrating for area because it was 2 marks haha

25. Re: BoS Maths Trials 2017

Originally Posted by Paradoxica
can confirm that it isn't
I got the same answer as Calamebe so I must've gotten it wrong too

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