# BoS Maths Trials 2019 (1 Viewer)

#### aa180

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

##### -insert title here-
For question 3, shouldn't $\bg_white n$ and $\bg_white 2m-1$ 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

##### Member
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?

##### -insert title here-
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

##### Retired
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

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

#### Drdusk

##### π
Moderator
Why is literally half of Bos a bunch of Math majors

#### blyatman

##### Well-Known Member
Why is literally half of Bos a bunch of Math majors
Gotta pay the bills right?

##### -insert title here-
The other guys did a great job with filling in the gap that I've left!
dubious

#### sharky564

##### Member
Anyone manage to solve Q11a?

#### integral95

##### Well-Known Member
Anyone manage to solve Q11a?
$\bg_white x = tan\theta$

##### -insert title here-
$\bg_white x = \tan\theta$
that is only worth one mark, you need to elaborate more

#### TheOnePheeph

##### Active Member
Anyone manage to solve Q11a?
I didn't sit the paper, but here is my solution (spoilers for anyone who wants to solve)
$\bg_white \text{Let I} = \int_0^{1}\frac{\arctan{\sqrt{x}} + \arctan{x^2}}{1+x^2} dx$
$\bg_white \text{Consider:} J = \int_0^{1}\frac{\arctan{\sqrt{x}}}{1 + x^2} dx$
$\bg_white \text{ Let u =} \sqrt{x}$
$\bg_white du = \frac{1}{2\sqrt{x}}$
$\bg_white J = \int_0^{1}\frac{2u\arctan{u}}{1 + u^4} du$
$\bg_white \text{Using Integration By Parts:}$
$\bg_white dv = \frac{2u}{1+u^4}$
$\bg_white \therefore v = \arctan{u^2}$
$\bg_white J = \arctan{u^2}\arctan{u}\Bigr|_0^1 - \int_0^{1}\frac{\arctan{u^2}}{1 + u^2}du$
$\bg_white \text{Now} I = J + \int_0^{1}\frac{\arctan{u^2}}{1 + u^2}du$
$\bg_white \therefore I = \arctan{u^2}\arctan{u}\Bigr|_0^1 - \int_0^{1}\frac{\arctan{u^2}}{1 + u^2}du$
$\bg_white + \int_0^{1}\frac{\arctan{u^2}}{1 + u^2}du$
$\bg_white = \frac{\pi^2}{16}$

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#### Trebla

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.

##### -insert title here-
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

##### Member
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

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

##### -insert title here-
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.

##### -insert title here-
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

##### π
Moderator
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???????