BoS Maths Trials 2019 (1 Viewer)

aa180 · Oct 11, 2019

For question 3, shouldn't $n$ and $2m-1$ be coprime?

Paradoxica · Oct 11, 2019

aa180 said:
For question 3, shouldn't $n$ and $2m-1$ be coprime?

Thanks for pointing this out. I have changed the files for both posts accordingly.

I pray this is the last mistake/technical gap we have *sighs heavily*

aa180 · Oct 11, 2019

Paradoxica said:
Thanks for pointing this out. I have changed the files for both posts accordingly.

I pray this is the last mistake/technical gap we have *sighs heavily*

You're welcs. Does that now mean that everyone who sat the paper gets a free mark for it or nah?

Paradoxica · Oct 11, 2019

aa180 said:
You're welcs. Does that now mean that everyone who sat the paper gets a free mark for it or nah?

eh; no, I doubt Trebla will go that way. Also nobody in the exam brought it up, so they must have made the implicit assumption as well

we're not that pedantic about the marking system so don't expect us to be like "oh this q was flawed free marks"

Carrotsticks · Oct 11, 2019

integral95 said:
Wow this is definitely harder than the previous years. I see that Carrotsticks having extra assistance from former BOS members (who are also math whizzes ) definitely revoluntionised the content.

However, with the new syllabus being implemented, I wonder what mathematical theorem do you plan to use that could be solved using strictly high-school math.

I had virtually no involvement in the papers this year. Too busy with other things. The other guys did a great job with filling in the gap that I've left!

Though, from next year with the new syllabus content, I will surely be back on board at full capacity.

TheOnePheeph · Oct 11, 2019

Just wanna say, that probability question after all the conic section stuff in q16 is super nice. Really cool paper overall.

Drdusk · Oct 11, 2019

Why is literally half of Bos a bunch of Math majors

blyatman · Oct 11, 2019

Drdusk said:
Why is literally half of Bos a bunch of Math majors

Gotta pay the bills right?

Paradoxica · Oct 11, 2019

Carrotsticks said:
The other guys did a great job with filling in the gap that I've left!

dubious

sharky564 · Oct 12, 2019

Anyone manage to solve Q11a?

integral95 · Oct 12, 2019

sharky564 said:
Anyone manage to solve Q11a?

$x = tan\theta$

Paradoxica · Oct 12, 2019

integral95 said:
$x = \tan\theta$

that is only worth one mark, you need to elaborate more

TheOnePheeph · Oct 12, 2019

sharky564 said:
Anyone manage to solve Q11a?

I didn't sit the paper, but here is my solution (spoilers for anyone who wants to solve)
$\text{Let I} = \int_0^{1}\frac{\arctan{\sqrt{x}} + \arctan{x^2}}{1+x^2} dx$
$\text{Consider:} J = \int_0^{1}\frac{\arctan{\sqrt{x}}}{1 + x^2} dx$
$\text{ Let u =} \sqrt{x}$
$du = \frac{1}{2\sqrt{x}}$
$J = \int_0^{1}\frac{2u\arctan{u}}{1 + u^4} du$
$\text{Using Integration By Parts:}$
$dv = \frac{2u}{1+u^4}$
$\therefore v = \arctan{u^2}$
$J = \arctan{u^2}\arctan{u}\Bigr|_0^1 - \int_0^{1}\frac{\arctan{u^2}}{1 + u^2}du$
$\text{Now} I = J + \int_0^{1}\frac{\arctan{u^2}}{1 + u^2}du$
$\therefore I = \arctan{u^2}\arctan{u}\Bigr|_0^1 - \int_0^{1}\frac{\arctan{u^2}}{1 + u^2}du$
$+ \int_0^{1}\frac{\arctan{u^2}}{1 + u^2}du$
$= \frac{\pi^2}{16}$

Trebla · Oct 12, 2019

Since some people asked at the seminars today, if you want to know the answer to a particular question please ask in this forum.

The full solutions will take some time to put together because we have to structure and check everything properly in LaTeX with diagrams and all - so please be patient. We’ll be more than happy to answer anything specific.

Paradoxica · Oct 12, 2019

meme post don't take seriously

>specifically says the base is less than 1

>mfw i see people drawing increasing exponentials instead of decreasing exponentials

DrEuler · Oct 12, 2019

Paradoxica said:
meme post don't take seriously

View attachment 27310

>specifically says the base is less than 1

>mfw i see people drawing increasing exponentials instead of decreasing exponentials

LOL

DrEuler · Oct 12, 2019

This is a great paper guys! Wow are the questions good

Paradoxica · Oct 12, 2019

apparently 90% of these students think that inverses that are tangent to each other are tangent to y=x. the syllabus teaches inverse functions so badly.

Paradoxica · Oct 12, 2019

basically what i am saying is that almost nobody was able to justify m²=1 in the only way that is correct. they claimed (falsely, as well) that the slope must be 1. given the base of the exponential is less than 1, this is literally impossible.

Drdusk · Oct 13, 2019

Paradoxica said:
apparently 90% of these students think that inverses that are tangent to each other are tangent to y=x. the syllabus teaches inverse functions so badly.

Math isn't my area but isn't this the case???????

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