Given that Miss Loi’s body fluid level F (in units) is inversely proportional to the square of the time t (in seconds),

Which one of the graphs below could represent the relation between F and t?

Find the percentage change in F when t is tripled.

Given that Miss Loi’s fluid level F is dangerously low at 0.1 units when t=70 seconds, and that irreversible wrinkles and damage will occur on her silky smooth skin when F falls to half of this value, find

the equation connecting F and t,

the time t when Miss Loi needs to start drinking her barley water without paying , or kick the Crazy Aunty away with her 无影脚.

Miss Loi turn from story telling to manga drawing le... what next? 😛

Question hijacking time!

1) IV - I and II definitely out, inversely proportional means as t goes up F goes down. - V definitely out because inversely proportional to square of t means the F/t graph cannot be straight line. - III is out because F inversely proportional to t squared means F = kt^{−2} means t cannot be 0.

Hence by elimination of impossible answers, the answer of IV is obtained. 😛

Miss Loi: Yes the question states that "F is inversely proportional to the square of x".

Putting this English statement in mathematical context ⇒ F↑, x^{2}↓ ⇔ F↓, x^{2}↑ (⇒ Graphs I & II are out!) ⇒ F ∝ (by definition) ⇒ F =

If you're an upper sec student who's already familiar with the various sketches of important graphs, you should straightaway be able to identify the graph of , jump up from your seat and scream "It's IV! It's IV! IT'S IV" excitedly like a siao cha/ta boh (to the chagrin of those around you).

Else you may follow mathslover's wisdom of elimination and/or her comment below to arrive at the same conclusion.

P.S. It's good to write out the F = expression coz it's easy to forget that we're dealing with a square of x here, as many of us may already have the image of F = from textbooks/formula sheets burnt deep deep in our minds.

2) F = kt^{−2} When t is tripled, New F = k(3t)^{−2} New F = 9kt^{−2} → Aiyooo! Tsk tsk! Luckily you managed to 悬崖勒马 below BUT ...

New F = 9F Percentage change = change / original × 100% = 8F / F × 100% = 800%

*Puts up WRONG WORKING tape* Move along now ... see corrected workings below!

3) When t = 70, F = 0.1. By substituting, 0.1 = k (70^{−2}) 0.1 x 4900 = k k = 490

3i) F = 490t^{−2}

When F = 0.1/2 = 0.05, Miss Loi will start to challenge the law by drinking unpaid barley water.

Part 3 is one of the two typically standard kinds of proportion/variations questions (the other kind being something like this that you can expect to see in your O-Level E-Maths Paper 1.

As shown by mathslover's workings above, one can see that it's important to read the statement in the question carefully (i.e. pick out the critical words like "inversely", "square of x", "F falls to half of this value" etc.) in order to obtain the expression () and subsequently the value of k correct from the start.

After which it's simply sub, sub, sub in the given values to find that Miss Loi has about half a minute to take corrective action to prevent irreversible damage to her skin!

Miss Loi ah, next time don't wait till last minute then buy water...

"F inversely proportional to t squared means F = kt^{−2} means t cannot be 0." can be used to explain why all your graphs are wrong except IV already...

*really shouldn't have viewed Sadako Loi's video so late that night*

2) F = kt^{−2} When t is tripled, New F = k(3t)^{−2} New F = (1/9)kt^{−2} New F = (1/9)F Percentage change = change / original x 100% = −(8/9)F / F x 100% = −0.889%

Miss Loi: This part is actually a test on your concept of Percentages - a very basic Sec 1 topic that sadly managed to caught many students out.

After correcting your careless mistake in Comment #2, you're right to list that:

Original F = k/t^2

So the change in F = New F − New F = ∴ % change = (change in F/ original F) x 100% = × 100% ≈ −88.9%

So when t is tripled, F will decrease by 88.9% → not 11.1%, or 800%, and most certainly NOT a Sadako Loi-induced 0.889%!!!!!!!!!!!!!!!

On hindsight it would've served a greater purpose if this part of the question had been changed to "Find the percentage change in F when t is reduced by 3 times" to emphasize the importance of the formula: % change = change / original x 100%.

So in such a case, what would the % increase of F be? 900%? 800%? 90%?????

Put the math aside, I'm more curious about what happened to the crazy aunty? You smashed her with that bottle of barley drink? Seriously, though, the cashier didn't give in & serve her instead of you, right?

mathslover: Marked your workings. Aiyooo so many careless mistakes! Think you're the first victim of Sadako Loi's Curse!

a_x: Sadly, respect for aunties was the outcome of the day, and the poor cashier really had no choice but to apologize to the young & gracious Miss Loi profusely.

Stan: Ooi don't be rude to aunties here! This is an aunty-friendly blog! *BEEP*!!!

* Please refer to the relevant Ten-Year Series for the questions of these suggested solutions.

About Miss Loi

Miss Loi is a full-time private tutor in Singapore specializing in O-Level Maths tuition. Her life’s calling is to eradicate the terrifying LMBFH Syndrome off the face of this planet. For over years she has been a savior to countless students … [read more]

Gratitudes

I finally felt there was hope for Amath when I passed my first test. Towards the end of the year, I started scoring As for emath and no longer failed Amath! … [read more]

## 9 Comments

曜

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hahahaha i like how u narrate the story, very creative! and looking at all these maths questions, ahhh the school days

曜

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Miss Loi turn from story telling to manga drawing le... what next? 😛

Question hijacking time!

1) IV

- I and II definitely out, inversely proportional means as t goes up F goes down.

- V definitely out because inversely proportional to square of t means the F/t graph cannot be straight line.

- III is out because F inversely proportional to t squared means F = kt

^{−2}means t cannot be 0.Hence by elimination of impossible answers, the answer of IV is obtained. 😛

Miss Loi:Yes the question states that "Fisproportional to theinverselysquare of".xPutting this English statement in mathematical context

⇒

F↑,x^{2}↓ ⇔F↓,x^{2}↑ (⇒ Graphs I & II are out!)⇒

F∝ (by definition)⇒

F=If you're an upper sec student who's already familiar with the various sketches of important graphs, you should

straightawaybe able to identify the graph of , jump up from your seat and scream "It's IV! It's IV! IT'S IV" excitedly like asiao cha/ta boh(to the chagrin of those around you).Else you may follow

mathslover's wisdom of elimination and/or her comment below to arrive at the same conclusion.P.S. It's good to write out the

F= expression coz it's easy to forget that we're dealing with asquare ofhere, as many of us may already have the image ofxF= from textbooks/formula sheets burntdeep deepin our minds.2) F = kt

^{−2}When t is tripled,

New F = k(3t)

^{−2}New F = 9kt

^{−2}→ Aiyooo! Tsk tsk! Luckily you managed to 悬崖勒马 below BUT ...

~~New F = 9F~~~~Percentage change = change / original × 100%~~~~= 8F / F × 100% = 800%~~*Puts up WRONG WORKING tape* Move along now ... see corrected workings below!

3) When t = 70, F = 0.1.

By substituting,

0.1 = k (70

^{−2})0.1 x 4900 = k

k = 490

3i) F = 490t

^{−2}When F = 0.1/2 = 0.05, Miss Loi will start to challenge the law by drinking unpaid barley water.

F = 490t

^{−2}= 0.05490 = 0.05t

^{2}t

^{2}= 490 / 0.05 = 9800t = 98.995s = 99.0s (3.s.f)

3ii) t = 99.0s

Part 3 is one of the two typically standard kinds of proportion/variations questions (the other kind being something like this that you can expect to see in your O-Level E-Maths Paper 1.

As shown by

mathslover's workings above, one can see that it's important to read the statement in the question carefully (i.e. pick out the critical words like "inversely", "square ofx", "Ffalls to half of this value" etc.) in order to obtain the expression () and subsequently the value ofkcorrect from the start.After which it's simply sub, sub, sub in the given values to find that Miss Loi has about half a minute to take corrective action to prevent irreversible damage to her skin!

Miss Loi ah, next time don't wait till last minute then buy water...

曜

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Ahh just realised I wasted too much time.

"F inversely proportional to t squared means F = kt

^{−2}means t cannot be 0." can be used to explain why all your graphs are wrong except IV already...*really shouldn't have viewed Sadako Loi's video so late that night*

曜

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*and shouldn't have complained about Sadako Loi*

2) F = kt

^{−2}When t is tripled,

New F = k(3t)

^{−2}New F = (1/9)kt

^{−2}New F = (1/9)F

Percentage change = change / original x 100%

= −(8/9)F / F x 100% = −0.889%

Miss Loi:This part is actually a test on your concept of Percentages - a very basic Sec 1 topic that sadly managed to caught many students out.After correcting your careless mistake in Comment #2, you're right to list that:

So the change in

F= NewF− NewF=∴ % change

= (change in

F/ originalF) x 100%= × 100%

≈ −88.9%

So when

tis tripled,Fwilldecreaseby 88.9% → not 11.1%, or 800%, and most certainly NOT a Sadako Loi-induced 0.889%!!!!!!!!!!!!!!!On hindsight it would've served a greater purpose if this part of the question had been changed to "Find the percentage change in

Fwhentisreducedby 3 times" to emphasize the importance of the formula:% change = change / original x 100%.So in such a case, what would the % increase of

Fbe? 900%? 800%? 90%?????Sigh.. not going to check le...

曜

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Put the math aside, I'm more curious about what happened to the crazy aunty? You smashed her with that bottle of barley drink? Seriously, though, the cashier didn't give in & serve her instead of you, right?

曜

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Ja!! Did you give the siao cha bo a piece of your mind? Or did you just retort: hurry *BEEP* up you *BEEP*?

曜

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munak:Are you asrar in Plurk???mathslover:Marked your workings. Aiyooo so many careless mistakes! Think you're the first victim of Sadako Loi's Curse!a_x:Sadly, respect for aunties was the outcome of the day, and the poor cashier really had no choice but to apologize to theyoung & graciousMiss Loi profusely.Stan:Ooi don't be rude to aunties here! This is an aunty-friendly blog! *BEEP*!!!曜

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I'm the first victim because the others never try!!! 🙁

我知错了。:( I try to solve the Sadako Loi problem k? 不要再来找我了。

曜

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you is rite ms.loi, thats me on plurk