Comments on: Inglourious *BEEP* Chapter Two: The Insane Bugis Junction Carpark Ah Lian http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian Sassy O Level Maths Tuition, Questions & Tips from Singapore's Favourite Private Tutor Sun, 05 Feb 2012 17:08:39 +0000 hourly 1 By: Travel is Fatal: Water Sports | Sports Leisure Knowledge http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comment-32382 Travel is Fatal: Water Sports | Sports Leisure Knowledge Sat, 14 Nov 2009 23:19:13 +0000 http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comment-32382 [...] Inglourious *BEEP* Chapter Two: The Insane Bugis Junction Carpark … [...] [...] Inglourious *BEEP* Chapter Two: The Insane Bugis Junction Carpark … [...]

]]> By: Nash http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comment-30723 Nash Sat, 10 Oct 2009 10:50:42 +0000 http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comment-30723 Ok part (2) noted... The story-sum questions you post are more refreshing than the traditional questions in papers and made me intrested in maths again. Thanks alot! Lesson learnt: 1) Don't irritate mathematically edgy teachers with half-baked maths statements 2) Value your car before dignity 3) Carry a pepper-spray (in case of ah lians with claws instead of hands) 4) Go to the toilet BEFORE driving 5) The phrase "-BOOMZ-" has changed from mockery to a cool statement? Ridiculous =_=... Ok part (2) noted...

The story-sum questions you post are more refreshing than the traditional questions in papers and made me intrested in maths again. Thanks alot!

Lesson learnt:
1) Don't irritate mathematically edgy teachers with half-baked maths statements
2) Value your car before dignity
3) Carry a pepper-spray (in case of ah lians with claws instead of hands)
4) Go to the toilet BEFORE driving
5) The phrase "-BOOMZ-" has changed from mockery to a cool statement? Ridiculous =_=...

]]> By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comment-30689 Miss Loi Fri, 09 Oct 2009 15:13:34 +0000 http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comment-30689 Alright, alright ... can we assume that, as the car was loaned to Little Miss Loi <span class="fineprint">(Note it's <em>Little</em> Miss Loi, not Miss Loi)</span>, her supreme sense of responsibility to the car far, far outweighs her need to visit the toilet - at least not till the very last minute. Besides, suing people costs a lot of time, karma and $$$! Alright, alright ... can we assume that, as the car was loaned to Little Miss Loi (Note it's Little Miss Loi, not Miss Loi), her supreme sense of responsibility to the car far, far outweighs her need to visit the toilet - at least not till the very last minute.

Besides, suing people costs a lot of time, karma and $$$!

]]> By: Capt. Chan http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comment-30679 Capt. Chan Fri, 09 Oct 2009 09:53:57 +0000 http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comment-30679 Erm... 'cher, the way you set the question, not only "Cheem", but also very wrong leh... You should have done what Nash suggested (You should have just ignored her nagging and just walk/ sprint to the nearest toilet, not much she can do with your car in the parking lot anyways… unless of course she goes violent and starts scratching, then you can sue her ^_^.) Erm... 'cher, the way you set the question, not only "Cheem", but also very wrong leh... You should have done what Nash suggested (You should have just ignored her nagging and just walk/ sprint to the nearest toilet, not much she can do with your car in the parking lot anyways… unless of course she goes violent and starts scratching, then you can sue her ^_^.)

]]> By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comment-30653 Miss Loi Thu, 08 Oct 2009 11:59:39 +0000 http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comment-30653 <b>Nash:</b> Added a diagram for visibility and marked your working - please pay attention to Miss Loi's notes on Part 2! Oh and the latest field report from Little Miss Loi was that the <i>Ah Lian</i>'s fingernails were Wolverine-like sharp! And, and ... coz of that, <var>h</var> became ... *a mysterious force from nowhere violently pushed Miss Loi away from the computer before she could finish typing* Nash: Added a diagram for visibility and marked your working - please pay attention to Miss Loi's notes on Part 2!

Oh and the latest field report from Little Miss Loi was that the Ah Lian's fingernails were Wolverine-like sharp!

And, and ... coz of that, h became ...

*a mysterious force from nowhere violently pushed Miss Loi away from the computer before she could finish typing*

]]> By: Nash http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comment-30538 Nash Mon, 05 Oct 2009 00:55:49 +0000 http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comment-30538 1)Volume of a cone = [pmath]{1/3} pi hr^2[/pmath] To find the radius of the water level: [pmath]r/h = tan(tan^-1 (10/30))[/pmath] [pmath]r ={1/3} h[/pmath] Therefor : [pmath]V = {1/3} pi ({1/3}h)^2 (h)[/pmath] [pmath]V= {1/27} pi h^3[/pmath] <div class="highlight"> <strong>Miss Loi:</strong> Yes part 1 is straightforward. Main thing you'll need to recall is the expression for the volume of a cone that you've been drummed into since your lower-secondary days: [pmath]V = {1/3} pi hr^2[/pmath] --- (1) <img src="http://www.exampaper.com.sg/blog/wp-content/uploads/2009/10/inverted-cone-diagram-answer.gif" alt="Inverted cone answer Part 1" /> We're given <var>h</var> but not <var>r</var> and thus we'll need to express <var>r</var> in terms of <var>h</var> to obtain the final expression. To do this, we can make use of the tangent of the common angle (see diagram above) like what <b>Nash</b> has done or we can simply consider the ratios of the two similar triangles i.e. [pmath]r/h = 10/30 doubleright r = h/3[/pmath] Sub in this expression of <var>r</var> into (1) and you'll get [pmath]V= {1/27} pi h^3[/pmath] --- (2) </div> 2) To find rate of increase of h i.e. [pmath]dh/dt[/pmath], [pmath]dV/dh= {pi h^2}/9[/pmath] [pmath]dh/dV =9/{pi h^2}[/pmath] <span class="highlight">→ this step is unsafe!!!</span> [pmath]dh/dt = {dh/dV}*{dv/dt} = 180/{pi h^2}[/pmath] When h=24, [pmath]dh/dt = 5/{16 pi}[/pmath] cm/s = 0.0994 cm/s <div class="attention highlight"> Alright we're about to enter into a bit of <a href="http://en.wikipedia.org/wiki/Chain_rule" rel="nofollow">Chain Rule</a> Controversy here. You've established your Chain Rule expression as [pmath]dh/dt = {dh/dV}*{dV/dt}[/pmath], but you've differentiated <var>V</var> (in (2)) with respect to <var>h</var> and apparently looked to have simply <i>anyhow</i> <em>inverted</em> your [pmath]dV/dh[/pmath] to obtain your [pmath]dh/dV[/pmath] to in order to sub into your Chain Rule expression. While this will not affect your final (correct) answer, it's important to note that terms like [pmath]dy/dx[/pmath] are <em>derivatives</em> NOT fractions. So performing an Olympic-style backflip like this in your working has been known to get on the nerves of some mathematically-edgy teachers who may suspect that you don't actually know what you're doing! So since we've already established <var>V</var> in terms of <var>h</var> in Part 1, Miss Loi thinks it's safer to express your Chain Rule as: [pmath]dV/dt = {dV/dh}*{dh/dt}[/pmath] ... and obtain your [pmath]dh/dt = {dV/dt}*{1/{dV/dh}}[/pmath] <span class="fineprint">(note the use of [pmath]1/{dV/dh}[/pmath] instead of [pmath]dh/dV[/pmath])</span> Or if you wish to use your original expression of [pmath]dh/dt = {dh/dV}*{dV/dt}[/pmath], then it's safer to differentiate <var>h</var> with respect to <var>V</var> (i.e. [pmath]dh/dV[/pmath]) after first expressing <var>h</var> in terms of <var>V</var>. </div> 3) Total volume= [pmath]{1/3}(30)(pi)(10^3)[/pmath] = 1000π cm<sup>3</sup> <span class="highlight">Note:you should get the same value if you sub <var>h</var>=30 cm into your Part 1 expression i.e. [pmath]V= {1/27} pi h^3[/pmath]</span> Volume when h= 24, [pmath]V= {1/27}(pi)(24^3)[/pmath] = 512π cm<sup>3</sup> Time left before err... overflow = [pmath](1000 pi - 512 pi)/20[/pmath] = 76.6s <div class="highlight"> Part 3 is common-sensical and straightforward, but unfortunately many students keep thinking about "Rate of Change question means must dy/dx!" by the time they reach this stage! Since the rate of change of volume is constant at 20 cm<sup>3</sup>s<sup>−1</sup>, we simply obtain the time to overflow by: (Vol.<sub>overflow (i.e. <var>h</var>=30)</sub> − Vol.<sub><var>h</var>=24</sub>)/(Rate of change of vol.) = see <b>Nash</b>'s workings above ;) </div> I think its a bit wrong somewhere... You should have just ignored her nagging and just walk/ sprint to the nearest toilet, not much she can do with your car in the parking lot anyways... unless of course she goes violent and starts scratching, then you can sue her ^_^. 1)Volume of a cone = {1/3} pi hr^2
To find the radius of the water level:
r/h = tan(tan^-1 (10/30))
r ={1/3} h
Therefor : V = {1/3} pi ({1/3}h)^2 (h)
V= {1/27} pi h^3

Miss Loi: Yes part 1 is straightforward. Main thing you'll need to recall is the expression for the volume of a cone that you've been drummed into since your lower-secondary days:
V = {1/3} pi hr^2 --- (1)

Inverted cone answer Part 1

We're given h but not r and thus we'll need to express r in terms of h to obtain the final expression.

To do this, we can make use of the tangent of the common angle (see diagram above) like what Nash has done or we can simply consider the ratios of the two similar triangles i.e.
r/h = 10/30 doubleright r = h/3

Sub in this expression of r into (1) and you'll get
V= {1/27} pi h^3 --- (2)

2) To find rate of increase of h i.e. dh/dt,
dV/dh= {pi h^2}/9
dh/dV =9/{pi h^2} → this step is unsafe!!!
dh/dt = {dh/dV}*{dv/dt} = 180/{pi h^2}
When h=24, dh/dt = 5/{16 pi} cm/s = 0.0994 cm/s

Alright we're about to enter into a bit of Chain Rule Controversy here.

You've established your Chain Rule expression as dh/dt = {dh/dV}*{dV/dt}, but you've differentiated V (in (2)) with respect to h and apparently looked to have simply anyhow inverted your dV/dh to obtain your dh/dV to in order to sub into your Chain Rule expression.

While this will not affect your final (correct) answer, it's important to note that terms like dy/dx are derivatives NOT fractions. So performing an Olympic-style backflip like this in your working has been known to get on the nerves of some mathematically-edgy teachers who may suspect that you don't actually know what you're doing!

So since we've already established V in terms of h in Part 1, Miss Loi thinks it's safer to express your Chain Rule as:
dV/dt = {dV/dh}*{dh/dt}

... and obtain your dh/dt = {dV/dt}*{1/{dV/dh}} (note the use of 1/{dV/dh} instead of dh/dV)

Or if you wish to use your original expression of dh/dt = {dh/dV}*{dV/dt}, then it's safer to differentiate h with respect to V (i.e. dh/dV) after first expressing h in terms of V.

3) Total volume= {1/3}(30)(pi)(10^3)
= 1000π cm3
Note:you should get the same value if you sub h=30 cm into your Part 1 expression i.e. V= {1/27} pi h^3

Volume when h= 24, V= {1/27}(pi)(24^3)
= 512π cm3
Time left before err... overflow = (1000 pi - 512 pi)/20
= 76.6s

Part 3 is common-sensical and straightforward, but unfortunately many students keep thinking about "Rate of Change question means must dy/dx!" by the time they reach this stage!

Since the rate of change of volume is constant at 20 cm3s−1, we simply obtain the time to overflow by:

(Vol.overflow (i.e. h=30) − Vol.h=24)/(Rate of change of vol.) = see Nash's workings above ;)

I think its a bit wrong somewhere...
You should have just ignored her nagging and just walk/ sprint to the nearest toilet, not much she can do with your car in the parking lot anyways... unless of course she goes violent and starts scratching, then you can sue her ^_^.

]]> By: mathslover http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comment-30440 mathslover Fri, 02 Oct 2009 05:07:54 +0000 http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comment-30440 @Sadako Loi: Prove already! Go see and go back to where you belong! :( @Sadako Loi: Prove already! Go see and go back to where you belong! :(

]]> By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comment-30438 Miss Loi Fri, 02 Oct 2009 04:51:20 +0000 http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comment-30438 <b>Van:</b> Unfortunately, from the field report, it seemed pretty hard to do that with all the intense verbal bombardment going on *BOOMZ* <b>DC:</b> Such was the power of the <i>Ah Lian</i>'s @#$%^* 狮子吼. Quick! Go help Little Miss Loi flip the car back! <b>chanchinhong:</b> Fan? *shy* *blushes* <b>mathslover:</b> Unfortunately, as that Plane Geometry question wasn't proved within 7 days, she ended up 阴魂不散 ... and is now roaming around haunting all students studying late nights for the O-Levels :( Van: Unfortunately, from the field report, it seemed pretty hard to do that with all the intense verbal bombardment going on *BOOMZ*

DC: Such was the power of the Ah Lian's @#$%^* 狮子吼. Quick! Go help Little Miss Loi flip the car back!

chanchinhong: Fan? *shy* *blushes*

mathslover: Unfortunately, as that Plane Geometry question wasn't proved within 7 days, she ended up 阴魂不散 ... and is now roaming around haunting all students studying late nights for the O-Levels :(

]]> By: mathslover http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comment-30416 mathslover Thu, 01 Oct 2009 17:15:51 +0000 http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comment-30416 Feel like hijacking again.. but 不要啦。Sadako Loi 还没有放过我。 Feel like hijacking again.. but 不要啦。Sadako Loi 还没有放过我。

]]> By: chanchinhong http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comment-30412 chanchinhong Thu, 01 Oct 2009 15:52:22 +0000 http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comment-30412 i love how you link random scenarios to math questions. hahaha you're at a much higher level than me. All the way miss loi! -yourfan i love how you link random scenarios to math questions. hahaha you're at a much higher level than me. All the way miss loi!

-yourfan

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