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2009
Fri
25
Sep
Miss Loi avatar

Inglourious *BEEP* Chapter One: The Crazy Cold Storage Aunty

(10)
Tuition given in the topic of E-Maths Tuition Questions from the desk of Miss Loi at 5:06 pm (Singapore time)

Based on a true story …

Scene 1

Scene 2

Scene 3

Scene 4

Scene 5

Scene 6

Scene 7

Scene 8

Scene 9

Scene 10

Scene 11

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

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

    Variation Graph Options

  2. Find the percentage change in F when t is tripled.
  3. 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

    1. the equation connecting F and t,
    2. 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.

Must be the Curse of Sadako Loi taking effect 🙁

頑張って!!!

Revision Exercise

To show that you have understood what Miss Loi just taught you from the centre, you must:

  1. Leave A Comment!
Comments & Reactions

9 Comments

  1. munak's Avatar
    munak commented in tuition class


    2009
    Sep
    25
    Fri
    5:22pm
     
    1

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

  2. mathslover's Avatar
    mathslover commented in tuition class


    2009
    Sep
    26
    Sat
    1:08am
     
    2

    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↑, x2↓ ⇔ F↓, x2↑ (⇒ Graphs I & II are out!)
    F1/x^2 (by definition)
    F = k/x^2

    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 y=a/x^2, 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 = k/x^2 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 = k/x 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.

    F = 490t−2 = 0.05
    490 = 0.05t2
    t2 = 490 / 0.05 = 9800
    t = 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 of x", "F falls to half of this value" etc.) in order to obtain the expression (F = k/x^2) 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...

  3. mathslover's Avatar
    mathslover commented in tuition class


    2009
    Sep
    26
    Sat
    1:13am
     
    3

    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*

  4. mathslover's Avatar
    mathslover commented in tuition class


    2009
    Sep
    26
    Sat
    1:21am
     
    4

    *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:

    • Original F = k/t^2
    • New F = k/(3t)^2 = (1/9)(k/t^2) = {1/9}F

    So the change in F = New F − New F = ({1/9}-1)F = -{8/9}F
    ∴ % change
    = (change in F/ original F) x 100%
    = -{{8/9}F}/F × 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%!!!!!!!!!!!!!!!

    attention 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%?????

    Sigh.. not going to check le...

  5. a_x's Avatar
    a_x commented in tuition class


    2009
    Sep
    26
    Sat
    8:19am
     
    5

    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?

  6. Stan's Avatar
    Stan commented in tuition class


    2009
    Sep
    26
    Sat
    3:53pm
     
    6

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

  7. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class


    2009
    Sep
    29
    Tue
    7:39pm
     
    7

    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 the young & gracious Miss Loi profusely.

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

  8. mathslover's Avatar
    mathslover commented in tuition class


    2009
    Sep
    30
    Wed
    1:44am
     
    8

    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。

  9. munak's Avatar
    munak commented in tuition class


    2009
    Oct
    7
    Wed
    2:58am

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    Sep
    25
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