Official BOS Trial 2015 Thread (4 Viewers)

Ekman · Oct 2, 2015

InteGrand said:
$What do you mean ``justify''? Justify its convergence to the value of an integral as the number of trapezoids used goes to $\infty$?$

(Well we'll find out soon enough anyway, if the paper is uploaded.)

It wasnt about proving the trapezoidal rule, it was about justifying its geometrical significance

Sy123 · Oct 2, 2015

ヽ༼ຈل͜ຈ༽ﾉ UPLOAD THE PAPER OR RIOT ヽ༼ຈل͜ຈ༽ﾉc

InteGrand · Oct 2, 2015

Ekman said:
Actually it was different, it was about proving the inequality by using function derivatives, and substituting a suitable function that gives the AM-GM inequality

Pólya's proof?

Ekman · Oct 2, 2015

Sy123 said:
ヽ༼ຈل͜ຈ༽ﾉ UPLOAD THE PAPER OR RIOT ヽ༼ຈل͜ຈ༽ﾉc

Why weren't you there lol?

FlyingKanga · Oct 2, 2015

I kept looking at the front of my exam to see if I was actually doing the 2U exam. Oh God I've got a long way to go.

Drsoccerball · Oct 2, 2015

LOL i was doing question 15 and i look over and ekmans up to questions 11 i nudge him "DUDE HURRY UP" nek minute ekman gets 70+

Sy123 · Oct 2, 2015

Ekman said:
Why weren't you there lol?

it's a Friday, I went last year but it started late and I had to leave halfway through

Trebla · Oct 2, 2015

Hope you guys enjoyed that paper!

leehuan · Oct 2, 2015

I cried. Maybe out of enjoyment. Anyway, this was Q16 (a)

(Q16b was the overestimation of trap rule for concave up)

$\\ $A continuous function $f(x)$ has the property that for any ${ x }_{ i }>{ x }_{ j },\quad f^{ { \prime } }\left( { x }_{ i } \right) \le f^{ { \prime } }\left( { x }_{ j } \right) \\ $(i) Explain, with the use of a graph, why$ \\ f^{ { \prime } }\left( { x }_{ i } \right) \le \frac { f\left( { x }_{ i } \right) -f\left( { x }_{ j } \right) }{ { x }_{ i }-{ x }_{ j } } \le f^{ { \prime } }\left( { x }_{ j } \right) $ 1 mark$$

$\\ $(ii) Let $\alpha $ be a constant such that $0<\alpha <1$. \\ Show that for any ${ x }_{ 1 }$ and ${ x }_{ 2 }, \\ f\left( \alpha { x }_{ 1 }+\left( 1-\alpha \right) { x }_{ 2 } \right) \ge \alpha f\left( { x }_{ 1 } \right) +\left( 1-\alpha \right) f\left( { x }_{ 2 } \right) \\ 2 marks$

$\\ $(iii) Let ${ a }_{ 1 },{ a }_{ 2 },{ a }_{ 3 },\dots ,{ a }_{ n } $ be ANY set of positive numbers such that ${ a }_{ 1 }+{ a }_{ 2 }+{ a }_{ 3 }+\dots +{ a }_{ n }=1 \\ $Use mathematical induction to prove that for $n\ge 2 \\ f\left( { a }_{ 1 }{ x }_{ 1 }+{ a }_{ 2 }{ x }_{ 2 }+\dots +{ a }_{ n }{ x }_{ n } \right) \ge { a }_{ 1 }f\left( { x }_{ 1 } \right) +{ a }_{ 2 }+f\left( { x }_{ 2 } \right) +\dots +{ a }_{ n }f\left( { x }_{ n } \right) \\ 3 marks$

$\\ $(iv) By choosing an appropriate function for $f\left( x \right) $ show that $ \\ \frac { { x }_{ 1 }+{ x }_{ 2 }+\dots +{ x }_{ n } }{ n } \ge \sqrt [ n ]{ { x }_{ 1 }{ x }_{ 2 }\dots { x }_{ n } } \\ $for all positive values of $ { x }_{ 1 },{ x }_{ 2 },\dots ,{ x }_{ n } \\ 1 mark$

Q16(a) up!

Ekman · Oct 2, 2015

If people really want to see question 16, ill take a pic and post it

seanieg89 · Oct 2, 2015

Ekman said:
If people really want to see question 16, ill take a pic and post it

Yeah do it. Might be a while before full paper is uploaded.

Ekman · Oct 2, 2015

Drsoccerball said:
LOL i was doing question 15 and i look over and ekmans up to questions 11 i nudge him "DUDE HURRY UP" nek minute ekman gets 70+

You were so annoying in the exam, distracted me so much

Plus the way I did the exam was different. I didnt do it in chronological order

Mr_Kap · Oct 2, 2015

FlyingKanga said:
I kept looking at the front of my exam to see if I was actually doing the 2U exam. Oh God I've got a long way to go.

How hard was the 2u compared to other years BOS trials. Because in last year's BOS 2u paper that I did a few weeks ago I just gave up at Q13 and want to know if this years was around the same or harder.

Trebla · Oct 2, 2015

What did you guys think was the hardest question in the paper? (both 2U and 4U)

leehuan · Oct 2, 2015

Trebla said:
What did you guys think was the hardest question in the paper? (both 2U and 4U)

Every single mark that I did not get out

Ekman · Oct 2, 2015

Here is Question 16 for 4u. Sorry for any blurriness, couldn't get proper lighting

DatAtarLyfe · Oct 2, 2015

anyone think they got 60+ for 4u?

glittergal96 · Oct 2, 2015

It's a shame Q16b didn't go on to prove an error estimate for the trapezoidal rule (with n points of division). Most of the work was done for it.

(This kind of analysis is what I was looking for in my open-ended post in the MX2 integration marathon about comparing the accuracy of the trapezoidal rule and the Simpson's rule.)

Drsoccerball · Oct 2, 2015

Carrot trolling with the crap volume diagram in question 11... Im getting better in ex 2 then 1 lol left the whole question 14 blank

Drsoccerball · Oct 2, 2015

Also when i heard the fire alarm i was so happy thinking that the exam was cancelled...

Official BOS Trial 2015 Thread (4 Viewers)

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