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Posted at 11:33 pm by Miss Loi in H1/H2 (A-Level) Pure Maths Questions


PROPERTY OF THE SEOUL METROPOLITAN POLICE AGENCY
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CASE NO.: 110629
DATE: 29 JUNE 2011
LOCATION: 서울특별시 남산 남산공원길KM 3
(KM 3 NAMSAN PARK WAY, NAMSAN-DONG, SEOUL - 300M FROM SEOUL TOWER)

DESCRIPTION: UNPUBLISHED BLOG CONTENT RETRIEVED FROM IPHONE RECOVERED AT LOCATION

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Miss Loi the Maid

Good morning Mdm. Good morning Sir. My name is Miss Loi and I am a Maths Tutor.

Life under Project A is tough.

When Miss Loi was being tricked into selling The Temple to the Takahashi brothers, little did she know that she had sold herself to a life of servitude.

Since then she has been banned from all blogging activities, and her usual shopping trips and Tuesday day-offs have been cruelly rescinded.

This was done, in her new bosses’ opinion, so that she can focus on her new role of “leading the company’s educational development and strategy in Singapore” – which currently involve very long hours of Leticia Bongnino-like chores – from scurrying around to pour sake into the brothers’ glasses whenever they’re empty, to carrying their young nephew’s schoolbag on his way to the Singapore Japanese School, to washing The Temple’s corridor as well as clean out the lizard **** from the corridor lights every Sunday :(

So imagine her unbridled maid tutor-like joy when they ‘magnanimously’ allowed her to finally take a break and go on a trip to South Korea, only because it was her birthday (Oh thanks for all the birthday wishes!).

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Unfortunately, any semblance of ‘body’ in her hair-do was instantly annihilated by the buckets of rain that fell on her the moment she landed in Seoul. As a result, she had to flee to the shelter of her hotel room, where she took a warm shower, grabbed a cup of coffee, and proceeded to spend the rest of the day watching with amusement people’s hair-dos being annihilated by buckets of rain falling on the streets below.

Gloomy Seoul
Day One itinerary
- watch locals’ hair get destroyed by rain

By the second day, she knew that she had definitely been on better trips to Korea.

Rain
Day Two itinerary
-watch locals’ hair get destroyed by rain (from another window)

The rain finally eased on the third day, and Miss Loi (along with fellow guests) slowly emerged from her (by now very familiar) hotel and ventured outdoors to visit some of the world-famous tourist sites that Korea is known for.

Foggy Seoul

Like the world-famous Gyeongbokgung Palace.

Foggy Gwanghwamun
Entrance to Gyeongbokgung Palace

And the world-famous Banpo Bridge Rainbow Fountain that has been featured in many romantic Korean dramas.

Foggy Banpo Bridge
Banpo Bridge (with imaginary fountain)

This time, she even made it to the world-famous tour to ‘view’ the world-famous North Korean border at Panmunjom.

Foggy North Korea
Th ever-secretive North Korea (do not adjust your monitor)

At least she was spared from further fog-induced cataract vision during the Cookin’ Nanta! performance (which was hilarious BTW).

Cookin' Nanta!
Cameras were disallowed so had to steal borrow this stock image

But when the fog ruined her planned birthday dinner with a ‘romantic view’ at Namsan Seoul Tower, she decided enough was enough and proceeded to return to her hotel.

Namsan Seoul Tower
Seoul’s top-secret long-range missile launch site at Namsan

Unfortunately, that happened to be the moment the fog was at its thickest yet – smothering the slopes and engulfing Namsan in a tight embrace as it rolled in like a scene off a Stephen King movie.

Nevertheless, she set off firmly in what she believed was the direction of the taxi stand. Such was her desire to return to her warm hotel room that a long-forgotten incident of her being discovered holding a map upside-down remained … umm … firmly forgotten.

Slowly but surely, the path got darker and the crickets chirped louder, but Miss Loi was dead sure that the taxi stand was still ‘just around the corner’.

Foggy Woods

Obviously, you don't expect Miss Loi to take pictures here hence another stock image

The fog got to a point where she could barely make out the intricate patterns on her manicured nails, and it took a distant howl from an unknown creature to remind her that her ‘corner’ could not be farther away.

With thoughts creeping in of werewolves and zombies and that evil girl from A Tale of Two Sisters lurking just beyond, her pace got faster and her heart beat louder.

Realising in panic that she might be lost, her ‘mental compass’ (if one exists in the first place) went into a tailspin as she spun round and round (like a record, baby right round round round) across bearings 000°-359° in search of any sign of life within the shapeless fog – Blair Witch-style.

Just when she was resigned to spending her xth birthday night cold and alone (maybe not!) in the woods, the unmistakable roar of an engine broke the silence and salvation duly arrived in the form of a black taxi that pulled up alongside her.

Seoul Ripoff Taxi
Obviously, Miss Loi was too elated for pictures at the time
so you’ll have to live with this earlier photo of a similar taxi

Ignoring every warning from her mother about “not hopping into mysterious cars”, she launched herself into the backseat of the mysterious taxi and shouted the name of her hotel to the driver, who then turned around and muttered to her in Korean something about the fare.

Being pretty used to the cheap taxi rides in Seoul and desperate to get out of this godforsaken place, the fare was the last thing on Miss Loi’s mind so she impatiently told the driver to get moving.

The smooth rev of the accelerating taxi couldn’t have sounded sweeter, and she was further delighted to find a mini-TV screen embedded in the seat in front of her – so she leaned forward to catch the local news that happened to be broadcasting at the time.

With her rudimentary Korean and from the TV images on the screen, she managed to roughly piece together the following breaking news story:

… several people are missing … all of them were last seen boarding a taxi … police on the hunt for a mentally-unsound taxi driver … police appeals to public to report immediately if they see the following person … *shows file photo of suspect* …

… who happens to be the taxi driver in front of her!!!

Having heard the news himself, the taxi driver smiled and said to her in halting English,

Don’t worry I only punish those who cannot pay. You rich tourist sure can pay! *points to fare table on window*

당근 Taxi Company (Fare Table)

Distance Meter Readings (Korean Won ₩)
1st 100 m 2
2nd 100 m 4, 6
3rd 100 m 8, 10, 12
4th 100 m 14, 16, 18, 20

Note: This means the meter will start at ₩2, jumps to ₩4 (at 100 m), jumps to ₩6 (between 100-200 m), jumps to ₩8 (at 200 m) …

Total fare = Sum of all the meter readings from the very first reading to the final displayed reading.
E.g. If meter reads 12, total fare = 2 + 4 + 6 + 8 + 10 + 12 = ₩42.


From the GPS in the taxi, Miss Loi was exactly 3 km from her hotel the moment she boarded the taxi.

  1. Express in terms of n, the first meter reading of the nth 100 m. Hence state the taxi’s meter reading at the 3 km mark.
  2. Express in terms of n, the sum of all the meter readings from the 1st 100 m to the (n − 1)th 100 m. Hence state the total taxi fare at the 3 km mark.

As she watched with indescribable fear the taxi meter jumped and jumped and jumped at an astonishing rate, she hurriedly called Mr Loi for help.

The galloping horse taxi meter
… 1800 … 1802 … 1804 …
Obviously, Miss Loi was too frightened to …[photo source]

Nervous Miss Loi on the phone BRO! HELP! I’M CAUGHT IN A TAXI DRIVEN BY A MAD MAN! AND IF I DON’T HAVE ENOUGH MONEY TO PAY HIM YOU WON’T SEE ME AGAIN!

Mr Loi Yeah yeah yeah, another of your silly April Fools’ jokes. It’s already July for goodness sake!

Nervous Miss Loi on the phone I’M NOT JOKING! I NEED TO CALCULATE IF MY ₩200,000 IS ENOUGH FOR MY 3KM JOURNEY! I THINK NEED TO USE A.P. IN ‘A’ LEVEL H2 MATHS! BUT I’VE LOST TOUCH ALREADY SINCE I HAVEN’T BEEN TEACHING H2 MATHS FOR A WHILE!

Mr Loi Oh that’s simple. You just have to first identify the pattern flow, then determine the total number of terms in the progression …

***** Battery Flat *****

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THE SEOUL METROPOLITAN POLICE ARE APPEALING TO THE PUBLIC FOR HELP IN DETERMINING THE FATE OF VICTIM #6.

ALL STUDENTS AND MATHEMATICS ENTHUSIASTS WITH THE KNOWLEDGE TO SOLVE THIS CASE ARE STRONGLY URGED TO IMMEDIATELY LEAVE YOUR ANSWERS (WITH WORKINGS) IN THE COMMENTS BOX BELOW.

頑張って!!!

Revision Exercise

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Comments & Reactions

4 Comments



  1. 2011
    Jul
    22
    Fri
    11:51pm
     
    1

    Oh no! What fate awaits poor Ms Loi?
    From Dead Cockroach's blog: Terracotta Warriors: The First Emperor and His LegacyMy Profile



  2. 2011
    Jul
    23
    Sat
    1:33am
     
    2

    Hello? Hello? AP/GP questions while on holiday?

    Sigh ... think my sis sometimes misses her H2 maths a bit too much.

    *hangs up*

  3. clarionx's Avatar
    clarionx says


    2011
    Jul
    23
    Sat
    1:59pm
     
    3

    1) 1st meter reading at nth 100 meter = n^2 -n +2
    hence at 3km = 3000m = 30th 100 meter, 1st meter reading = 872 won.

    2) it is observed that at the (n−1)th 100 meter, final meter reading = n^2-n
    Also, at the (n−1)th 100 meter, no of meter readings = (n−1)
    In this AP, number of terms= n
    hence total sum of meter readings= n/2 (2+n^2-n)

    at 30km, total fare= 15(872)+872=13952 won.

    aiya 绰绰有余 la. can stop at Dongdaemun shop abit somemore :P



    • 2011
      Jul
      25
      Mon
      2:56pm
       
      3.1

      @clarionx: Hmmm ... this question requires a bit of 'eye power' ...

      1. This means the meter will start at ₩2, jumps to ₩4 (at 100 m), jumps to ₩6 (between 100-200 m), jumps to ₩8 (at 200 m) …

        ... which means that the 100 m mark occurs right at the start of the 2nd 100 m. Similarly the 200 m mark occurs right at the start of the 3rd 100 m.

        So at which '100 m' do you think the 3 km is at? Probably it would've been clearer to put 0-99 m, 100-199 m, 200-299 m ... on the fare table but then this is a Korean taxi we're tallking about :P

        Also, you managed to put down n2n + 2 like a flash of lightning. Care to share the pattern you used to arrive at it (but then it's kinda obvious now isn't it? :P )

      2. Total fare = Sum of all the meter readings from the very first reading to the final displayed reading.

        From the above, the total fare payable is the sum of all meter readings all the way from the very first one i.e. 2 to the final one displayed (not just the sum of the final 100 m row alone), else it won't be called 당근 Taxi Company for nothing :P

      Sadly, my sis would've told us excitedly about all her shopping exploits by now if she had been shopping at Dongdaemun :(

One Reaction

  1. Tweetback
    Miss Loi tweeted


    2011
    Jul
    22
    Fri
    3:42pm
     
    4

    Disturbing content retrieved from unpublished blog entry found in an iPhone recovered at Namsan Park, Seoul http://t.co/5NVuciY

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