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Once In 50 Years

Tuition given in the topic of A-Maths Tuition Questions from the desk of Miss Loi at 9:33 pm (Singapore time)

The sea of little flags proudly perched on all manner of vehicles serves to remind us that, once again, National Day is here.

Falling magnanimously on a long weekend, it’s also the perfect opportunity for patriotic families to flee leave the country en masse, thereby affording Miss Loi the opportunity to scale down this weekend’s joss sticks sessions in exchange for more leisurely activities like watering her plants, folding her clothes, and heading to town to catch some fireworks display.

With her Woodlands Customs-trained bumper-to-bumper driving skills, she managed to navigate her way out of the ubiquitous traffic jams, and promptly found what was arguably the last vacant (and legal) parking lot deep in the lowest basement of a carpark. (Couldn’t just anyhow park at the roadside you see, even though it’s a holiday.)

Soon, she was standing among the huge crowd at a prime spot with eyes transfixed at the night sky. And before long …


A collective cheer greeted the first of the fireworks as it lit up the sky.


Another one went up, streaking the heavens with brilliant y = k ln(x2), k ∈ ℝ arcs.


The next one was fierce, with straight explosive y = kx, k ∈ ℝ lines shooting out in all directions.


The night sky masked the storm clouds. The electrifying atmosphere absorbed all scent of impending rain. So when it came, the sudden, massive downpour caught everyone by surprise, and Miss Loi became an instant panicky member of the “Forget to Bring Umbrella” Club as she scrambled her way to the nearest shelter.

Shivering in the confines of the shelter, she stood and watched with fear as little streams of water on the floor merged into a raging river, carrying away anything in its path that had a lower density than water. And then …


A sudden realization dawned upon her, and the scene in her mind shifted quickly from the flash flood before her to her hapless car parked “deep in the lowest basement”.

With history about to repeat itself, she sacrificed her Charles & Keith platform shoes (again) and ran in the relentless rain towards the direction of the carpark.

Her worst nightmare was realized when she found the entrance to the carpark cordoned off by the police, and she had to be subsequently restrained by the police officer when she tried to barge her way through.

Let me in! My car is at the basement! LET ME IN!!!

Mdm! Get a hold of yourself! The flood water is rising inside! It’s too dangerous!

Let me in! My insurance doesn’t cover “Acts of God”! Let me in!!!

and she began to wail uncontrollably.

Perhaps it was her poor 凄凉 face that moved him, or perhaps it was her eerie wailing voice (in combination with her ‘gothic’ look created by her melting makeup) that spooked him. Either way, the police officer softened his stance …

I think I know you. Aren’t you that famous Sunday Times Maths Super Tutor?

A PUB government scholar has predicted that the height y (in cm) of the flood water in the lowest basement carpark will vary with time t (in minutes) as follows:

y = 40+ln { [ { te^{-{t-4}/2}}/{8-t} ]^{1/2} }, t > 0.

  1. As it’s only safe to enter when the water level is neither rising nor falling, find the first value of t for which y is a stationary point and determine the nature of this stationary point.
  2. Once you reach your car, it is only safe to drive out when the water level is falling. Find the set of values of t for which y is a decreasing function of t.

With that, the police officer held her shoulders, looked into her eyes and said,

Listen Mdm! This is a test of your understanding of the methods involved to obtain stationary points in a function! Do not use your illegal GC or exotic iPhone app to plot the curve as you won’t be able to obtain your answer this way!

Good luck and Happy National Day!

Afterword: So it didn’t rain tonight. But you still must help Miss Loi rescue her car in this INCEPTION-esque 9th August alternate reality 😛

*totem spinning*


Revision Exercise

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

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Comments & Reactions


  1. Kris's Avatar
    Kris commented in tuition class


    Hehe..i barely remember how to do differentiation anymore. But i believe, 1st questions require differentiation and there is 2 value of t to solve.

    2nd question , should do double differentiation. Replace, it with the value of t from 1st question. Determine which t, will produce the negative and that t should be the answer to the receding flood waters. 😛

  2. kris's Avatar
    kris commented in tuition class


    yaya..Miss Loi.i think so for the 2nd question..lol..

  3. Abigail's Avatar
    Abigail commented in tuition class


    For part two just differentiation 🙂

    y is decreasing function of t
    i.e. t = f(y)
    => dt/dy < 0

  4. Samantha69's Avatar
    Samantha69 commented in tuition class


    The first part is dy/dt=0 ( stationary point) .
    To determine nature of point, find d2y/dx2. If it is > 0 it is minimum point. Which means y is a minimum value. If it is < 0 then it is maximum point.
    The second part is Y is a decreasing function, therefore :
    dy/dt<0. From there set of t can be equated.

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