(Finalised) Official BOS Mathematics Trial Examinations. (1 Viewer)

kingkong123 · Sep 1, 2012

Re: Official BOS Mathematics Trial Examinations: Spring Edition.

Carrotsticks said:
Please excuse the fact that it looks wonky and everything. it's because I took screenshots of different parts, so naturally they are not going to align properly when posted up here as images.

This question unfortunately had to be left out not because of the difficulty (was one of the rather easy ones), but because it was more tedious than difficult.

Hence, despite the pretty end-result, it had to be let go ='(

nice question. dat der squeeze theorem

Sanjeet · Sep 1, 2012

Re: Official BOS Mathematics Trial Examinations: Spring Edition.

Anyone got a solution for b) (iii) ? I can't seem to get it..

seanieg89 · Sep 1, 2012

Re: Official BOS Mathematics Trial Examinations: Spring Edition.

The limit at the end is just an expression for the derivative of ln(x) at x=1, and the derivative of ln(x) is 1/x...which is 1 at x=1.

Kieran95 · Sep 1, 2012

Re: Official BOS Mathematics Trial Examinations: Spring Edition.

If people have done it, can somebody please post up a solution of aii for me (i'm an idiot lol)

Sanjeet · Sep 1, 2012

Re: Official BOS Mathematics Trial Examinations: Spring Edition.

Kieran95 said:
If people have done it, can somebody please post up a solution of aii for me (i'm an idiot lol)

$$The definite integral from a to b is greater than the area of the trapezium (from the graph)$\\ $Length of base is the y value of the tangent when x = a$\\ y = \frac{4}{a+b}(1-\frac{a}{a+b})\\ $Similarly the length at x = b, $ y = \frac{4}{a+b}\left(1-\frac{b}{a+b}\right) \\ \\ \int_{a}^{b}\frac{1}{x}dx > \frac{1}{2}(b-a)\left ( \frac{4}{a+b}-\frac{4b}{a+b}+\frac{4}{a+b}-\frac{4a}{a+b}\right ) \\ lnb - lna > \frac{1}{2}(b-a)\left(\frac{8}{a+b}-\frac{4b-4a}{(a+b)^2}\right) \\ lnb - lna > \frac{1}{2}(b-a)\left(\frac{8}{a+b}-\frac{4(a+b)}{(a+b)^2}\right) \\ lnb - lna > \frac{1}{2}(b-a)\left(\frac{4}{a+b}\right) \\ \therefore lnb - lna > \frac{2(b-a)}{a+b}$

Sanjeet · Sep 1, 2012

Re: Official BOS Mathematics Trial Examinations: Spring Edition.

asianese said:
Go to page 3 I have the solution.

Oh sry - that was part 4.

You need to use the inequalities from both a) and b). The root ab should be on the top but that was just a typo/error.

Oh wow. lol that's what I got but it was driving me crazy because I didn't know it was a typo

Kieran95 · Sep 1, 2012

Re: Official BOS Mathematics Trial Examinations: Spring Edition.

Props to you Sanjeet, thankyou very much!

Carrotsticks · Sep 2, 2012

Re: Official BOS Mathematics Trial Examinations: Spring Edition.

Here is another question, which I decided to scrap.

Reason: The concept of continuous compounding might be too ambiguous for some students.

TYPO: Second limit should read n -> infinity, not n -> 0.

Carrotsticks · Sep 2, 2012

Re: Official BOS Mathematics Trial Examinations: Spring Edition.

Also, I will be including an 'attendance list' on the beginning post.

Please PM me if you're not on the list, and you'd like to be.

Carrotsticks · Sep 2, 2012

Re: Official BOS Mathematics Trial Examinations: Spring Edition.

And a small typo, the second limit should be as n -> infinity, not n -> 0.

Sanjeet · Sep 2, 2012

Re: Official BOS Mathematics Trial Examinations: Spring Edition.

Carrotsticks said:
And a small typo, the second limit should be as n -> infinity, not n -> 0.

These questions are awesome. How difficult is this one compared to the ones in the paper?

I just realised that it's first principles lol

Carrotsticks · Sep 2, 2012

Re: Official BOS Mathematics Trial Examinations: Spring Edition.

=)

Carrotsticks · Sep 2, 2012

Re: Official BOS Mathematics Trial Examinations: Spring Edition.

Another scrapped question.

Reason: Too easy. More suitable to 2U.

But it'll at least let you guys see what kinds of questions are in the paper. They're not the usual boring 'Find the volume of X' etc etc.

Sindivyn · Sep 2, 2012

Re: Official BOS Mathematics Trial Examinations: Spring Edition.

Judging by the questions that were scrapped for being 'too easy', I'll slowly build up confidence until the 9th/10th/11th of Octboer, then all of it will be gone

Sanjeet · Sep 2, 2012

Re: Official BOS Mathematics Trial Examinations: Spring Edition.

anyone done a) (i) and (ii)?

mraznboy · Sep 2, 2012

Re: Official BOS Mathematics Trial Examinations: Spring Edition.

i'll come

jeffwu95 · Sep 2, 2012

Re: Official BOS Mathematics Trial Examinations: Spring Edition.

Imma come! but ill probably fail

Sy123 · Sep 5, 2012

Re: Official BOS Mathematics Trial Examinations: Spring Edition.

A solution to the question on page 5:

$\pi=\pi \int_{\frac{k}{2}} ^k e^{2x} \ dx \\ \\ 1=\frac{e^{2k}}{2}-\frac{e^k}{2} \\ 2=e^{2k}-e^{k} \\ \\ u=e^k \\ u^2-u-2=0 \\ \\ k=\ln 2$

Carrotsticks · Sep 6, 2012

Re: Official BOS Mathematics Trial Examinations: Spring Edition.

This was actually intended to be the last question in the paper, but I figured it was fairly straightforward (if you saw what had to be done) so probably not worthy of being in it.

This was the intended Projectile Motion Question, which again was scrapped because it wasn't exactly 'last Q of the paper' kind of difficulty.

deswa1 · Sep 6, 2012

Re: Official BOS Mathematics Trial Examinations: Spring Edition.

Wow- these look like very solid questions. I'm going to print off all the ones from the thread and try and do them tomorrow. But seriously nice- the projectile looks fairly straightforward at a first glance but that first one looks very nice

(Finalised) Official BOS Mathematics Trial Examinations. (1 Viewer)

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