Official BOS Trial 2016 Thread (1 Viewer)

InteGrand · Oct 6, 2016

InteGrand said:
$\noindent Oh, also realised, Q14 (a) of the Ext. 2 paper, it's saying let $x$ be a real number and show that $\left(1+x\right)^{n} \geq 1 + nx$ ($n\geq 2$ an integer). But it should say something like let $x \geq -1$, since that inequality doesn't hold in general if $x$ is allowed to be less than $-1$. (E.g. take $x = -5$, $n = 3$. Then $LHS = (-4)^{3} = -64$ and $RHS = 1 -15 > - 64 = LHS$.) The curious student can read more about this inequality (Bernoulli's inequality) here:$

https://en.wikipedia.org/wiki/Bernoulli's_inequality .

$\noindent Of course, for part (ii), we are having $x > \frac{n}{n-1}$ (which is greater than $1$), and we are going to use part (i) by saying $\left(1 + (x-1)\right)^n \geq 1 + n\left(x-1\right)$. So it suffices to just prove Bernoulli's inequality for $x > 0$ say for part (i) in order to use it for part (ii), since we are using it in (ii) with $x-1$ playing the role of part (i)'s $x$, and $x-1 > 0$, so we just need Bernoulli's inequality for positive numbers.$

(Of course, proving it for positive numbers is easy without induction – follows straight from the binomial theorem.)

PrelimTime · Oct 6, 2016

Are there fully worked solutions to this years trial?

Carrotsticks · Oct 6, 2016

InteGrand said:
$\noindent Oh, also realised, Q14 (a) of the Ext. 2 paper, it's saying let $x$ be a real number and show that $\left(1+x\right)^{n} \geq 1 + nx$ ($n\geq 2$ an integer). But it should say something like let $x \geq -1$, since that inequality doesn't hold in general if $x$ is allowed to be less than $-1$. (E.g. take $x = -5$, $n = 3$. Then $LHS = (-4)^{3} = -64$ and $RHS = 1 -15 > - 64 = LHS$.) The curious student can read more about this inequality (Bernoulli's inequality) here:$

https://en.wikipedia.org/wiki/Bernoulli's_inequality .

Thanks for pointing that out, I forgot to add in the condition.

PrelimTime said:
Are there fully worked solutions to this years trial?

Working on it right now.

PrelimTime · Oct 9, 2016

Sounds great, another question. Which year would you regard as most difficult for both 3u and 4u?

lilboat · Oct 14, 2016

hey just wondering when will the results be published?

Drsoccerball · Oct 14, 2016

lilboat said:
hey just wondering when will the results be published?

Trebla said they're nearly finished.

Prince_Svirby · Oct 15, 2016

When will the marks come out?

DatAtarLyfe · Oct 15, 2016

Prince_Svirby said:
When will the marks come out?

Drsoccerball said:
Trebla said they're nearly finished.

.

Carrotsticks · Oct 16, 2016

I am making the thread for the marks now. The solutions will be attached to the marks thread and will be available to download in 1 to 2 hours time.

Carrotsticks · Oct 16, 2016

Results can be found here.

http://community.boredofstudies.org...55310/2016-bos-trial-results.html#post7204460

Official BOS Trial 2016 Thread (1 Viewer)

InteGrand

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