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2008
Tue
1
Apr
Miss Loi avatar

Solve This Math Question And Win A Romantic Evening With Miss Loi!

(47)
Tuition given in the topic of A-Maths Tuition Questions from the desk of Miss Loi at 1:03 pm (Singapore time)
Singapore Flyer Night View

Oh what an evening in prospect.

In her excitement, one of Miss Loi’s students booked and paid for 4 x tickets for the 6 April (this coming Sunday) 9pm slot on the Singapore Flyer for she and her friends.

Since best friends are usually the best in flying aeroplanes at the last minute, it’s no surprise that she’s now desperately turning to Miss Loi for help, after two of her friends have pulled out of this little outing, and none of her other friends wants to lose a chunk of their pocket money are free to take their places.

Seeing that the introductory offer period is about to end soon And thus in a massive display of compassion, Miss Loi promises to buy the two extra tickets from her student (even though she had just ridden on another ferris wheel not too long ago), provided she can find another person to go with her.

But sadly, none of Miss Loi’s friends are free that evening too, as they’re all occupied with important stuffs like mahjong, EPL etc.

Anyway while Twittering this morning, NTT suggested holding a math contest on this blog. After seeing some early signs of enthusiasm and prompting, here we go …

* * *

Knowing that it takes a certain level of mathematical competency to be able to engage her in some meaningful conversation during the flight (like working out the geometric distance to some landmark), Miss Loi hereby propose that the *first person to answer correctly the following question:

Square within an equilateral triangle

In an equilateral triangle ABC, AB = 12 units. On vertex of a square lies at the midpoint of AB, with the adjacent vertices lying on the other two sides of the triangle.

The length of a side of the square may be expressed as

p√2 + q√6,

where p and q are rational numbers.

Find the values of p and q.

shall get to spend a romantic evening on the Singapore Flyer with her, where together we’ll be soaring high above the magnificent Singapore skyline, enjoying the cool night breeze, solve a math problem or two, and maybe even spot The Temple in the distance!

Moreover, you’ll have the dubious honour of being the first mortal from the blogosphere (apart from her students & their parents) to ever lay eyes on Miss Loi’s divine face … umm … if that really means anything.

NOTES:

This question is taken from a math workshop attended by (coincidentally) the same student, where the trainer was allegedly going so fast like a toot toot train, oblivious to the blank stares from the entire class.

Its kind is too mind-stimulating to EVER appear in the TYS, but this might help you in your upcoming Mids where anything can happen – especially with sadistic teachers out to exact revenge on students who gave them a torrid time in Semester I.

Lastly, this same question also managed to stump a GEP student – though in all due respect he was in a big, big hurry to get back to his DotA game.

P.S. To the student: Don’t say Miss Loi never try to help you har …

* Miss Loi reserves the right to reject any candidate whom she believes to be of dubious background, even though he/she might have answered the question correctly.

** Automatically disqualified: all students (and their immediate friends) who’d gone through this question in her class, the math workshop trainer, and cheekopeks who ask their school-going relatives to do the question on their behalf.

*** Do note that all visitors are to arrive at the Singapore flyer half an hour before their slot time.

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

46 Comments

  1. FoxTwo's Avatar
    FoxTwo commented in tuition class


    2008
    Apr
    1
    Tue
    1:57pm
  2. WishBoNe's Avatar
    WishBoNe  commented in tuition class


    2008
    Apr
    1
    Tue
    2:02pm
     
    2

    Ok, I'm guessing FoxTwo is part of one of the disclaimers. 😛

  3. xinyun's Avatar
    xinyun commented in tuition class


    2008
    Apr
    1
    Tue
    2:14pm
     
    3

    wah...
    nvm, i thought it was gonna be easy and i could meet our dear ping.sg lao shi... 😛

  4. ignorantsoup's Avatar
    ignorantsoup commented in tuition class


    2008
    Apr
    1
    Tue
    3:40pm
     
    4

    Haiz.. If can get 2 tickets then I try..haha..lazy to think too much!

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


    2008
    Apr
    1
    Tue
    5:24pm
     
    5

    *Sneaks a peek and shakes head at all the non-attempts*

    HINTS:

    Whenever one sees surds and trigonometry and geometry together in one question, this should serve as a cue for you to recall your special angles:

    45o60o30o
    sin1/sqrt{2}sqrt{3}/21/2
    cos1/sqrt{2}1/2sqrt{3}/2
    tan1√31/sqrt{3}

    And when special angles come into play in a diagram like this, students must instinctively get to know the bigfoot Ah Soh of all trigonometric ratios known as TOA CAH SOH.

    And since trigo ratios are derived from right-angled triangles, students must instinctively know how to first slice the diagram into as many right-angled triangles as deemed necessary.

    *Runs away for tuition*

  6. FoxTwo's Avatar
    FoxTwo commented in tuition class


    2008
    Apr
    1
    Tue
    5:52pm
     
    6

    smc, the moment you put a non-number base question here, automatically I fail leow, no need to pass GO, no need to collect $200.

    So, since I can't solve it, what else can I do? tok kok lor! 😀

  7. Someone's Avatar
    Someone commented in tuition class


    2008
    Apr
    1
    Tue
    7:11pm
     
    7

    p=9
    q=-3

    sine rule would have been more convenient though...

  8. Horny Ang Moh's Avatar
    Horny Ang Moh commented in tuition class


    2008
    Apr
    1
    Tue
    7:19pm
     
    8

    I look at the 'condition' & I know I am not up to 'standard' already!
    But I am sure u have no problem finding partner to spend the weekend with u!
    Have a nice day!

  9. fearclif's Avatar
    fearclif commented in tuition class


    2008
    Apr
    1
    Tue
    8:20pm
  10. Stanleyliew's Avatar
    Stanleyliew commented in tuition class


    2008
    Apr
    1
    Tue
    9:51pm
     
    10

    WAH!!! The question so "keng" wan. Questions in Malaysia don't sound that hard....

    Btw, thx for dropping by my site!

  11. Daphne Maia's Avatar
    Daphne Maia commented in tuition class


    2008
    Apr
    1
    Tue
    11:05pm
     
    11

    Headlines on ST, 02 Apr 08:

    "Hello Kitty commits suicide!
    -- Hello Kitty jumps off Bukit Timah cliff in despair. Papers with Maths workings found on summit."

  12. precious's Avatar
    precious commented in tuition class


    2008
    Apr
    1
    Tue
    11:46pm
     
    12

    Now we know Miss Loi's number one criteria for a date. Must be able to solve mathematical problems!

  13. Mgccl's Avatar
    Mgccl commented in tuition class


    2008
    Apr
    2
    Wed
    5:51am
     
    13

    \frac{\sin(\frac{\pi}{3})}{6}=\frac{\sin(\frac{5\pi}{12})}{x}
    p=9
    q=-3
    law of sin... easy question...
    really... get this blog to use LaTeX instead of phpmathpublisher. LaTeX is the industrial standard for math equation formatting. It's not that hard... you can leech from wordpress with a simple code...

  14. Tianhong's Avatar
    Tianhong commented in tuition class


    2008
    Apr
    2
    Wed
    7:50am
  15. Tianhong's Avatar
    Tianhong commented in tuition class


    2008
    Apr
    2
    Wed
    7:56am
     
    15

    arrrgh too difficult le. maybe i can try to program something out and get the answer.

  16. WishBoNe's Avatar
    WishBoNe  commented in tuition class


    2008
    Apr
    2
    Wed
    9:16am
  17. Mgccl's Avatar
    Mgccl commented in tuition class


    2008
    Apr
    2
    Wed
    9:24am
     
    17

    oh nose... Someone(The name is actually Someone... guess there is no way to find who he is.) had the answer before me!

    but maybe I'm the only identifiable person.
    muhahahahaha. I'm so going to blog about this.

    now I just have to find a way to get to Singapore...

  18. ClappingTree's Avatar
    ClappingTree commented in tuition class


    2008
    Apr
    2
    Wed
    9:29am
     
    18

    Hmmm.... is this an April Fools' Day joke?

    Anyway, my math is rusty and my brain sluggish today. Good luck to all who try in hope. 🙂

  19. Dhope's Avatar
    Dhope commented in tuition class


    2008
    Apr
    2
    Wed
    4:46pm
     
    19

    Wow, mgccl looks correct... So is Miss Loi going on hot date? Take more photos!!! I heard it's really beautiful once nightfalls.

  20. Someone's Avatar
    Someone commented in tuition class


    2008
    Apr
    2
    Wed
    6:32pm
     
    20

    If you used the sine rule, you would have to use the sin(x+y) forumula to reduce to the surds though...

  21. La Papillion's Avatar
    La Papillion commented in tuition class


    2008
    Apr
    2
    Wed
    10:45pm
     
    21

    Alright, I don't know how to use the maths equation thingy...so here goes:

    Let x be the side of the square

    If we halve the triangle vertically, then look at the triangle bounded by the side of the square (x), the base of the equilateral triangle (6) and part of the side of the equilateral triangle (the side with total length of 12), and taking sine rule,

    6/sin75° = x/sin60°

    but sin 75°
    = sin (45°+30°)
    = sin 45° cos 30° + cos 45° sin 30°
    = [sqrt (6) + sqrt (2)]/4

    putting it all in,

    x= 9 sqrt(2) - 3sqrt(6)

    thus p = 9 and q = -3

    Quite fun, any more such questions Miss Loi? 🙂

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


    2008
    Apr
    3
    Thu
    12:28am
     
    22

    Wow Miss Loi is so touched by all your response *sob*

    First to reply all ...

    Xinyun: As you can see from the answers here, it's not very difficult leh ... just need to recall your basic AMaths knowledge.

    WishBoNe: Who? Who???

    FoxTwo: So Miss Loi take it that you're requesting for questions from the Numbers chapter? e.g. LCM, HCF? 😉

    HAM: 'Conditions' aside, you'll be in Singapore this weekend meh?

    fearclif: You're in Sec 3 right? Miss Loi believes some of the trigo stuff hasn't been taught to you yet. Maybe you can learn something here to show off to your 'cher & classmates (provided they're not foreign cyborgs) 😛

    Stanley: Looking at some of the cyborgs ASEAN scholars here, many have the perception that Malaysian math standards are lagi keng!

    Hello Kitty DON'T JUMP!!! WORKINGS STILL CARRY MARKS!!!!

    Precious: You're absolutely right. Miss Loi is sooo looking forward to solve some math problems with her date during the ride. Else it'll be really boring isn't it?

    MGCCL: You're back! You just made Miss Loi realise that she'd forgotten to put the disclaimer about transportation costs not included.

    And ... ummm ... actually LaTeX has been installed here since the beginning - you just need to enclose your LaTeX code with [tex][tex] (which has been done for you) and your beautiful expression will magically appear. This wasn't stated since Miss Loi doesn't want to confuse readers with too many options/syntax.

    Tianhong: Wei NUS comp science calibre - you should know! Miss Loi's faculty is just next door!

    ClappingTree: ...

    Dhope: Umm ... actually mgccl's not the first ... even if he is, not sure if he can get here by this Sunday.

    Wah Papillion! Nice workings! Welcome to Jφss Sticks and thanks for your interest in dating Miss Loi mathematics! Mids are coming = expect more questions (provided readers come and solve them)!

    Meanwhile if you browse through the AMaths and EMaths categories you'll find a number of questions still unsolved 😉

    Ok now with regards to the solution and results ...

  23. peewee's Avatar
    peewee  commented in tuition class


    2008
    Apr
    3
    Thu
    8:42am
     
    23

    i'm concerned whether the capsule will roll off the spindle while it's at the peak?

    i'm terrified of heights!

  24. FoxTwo's Avatar
    FoxTwo commented in tuition class


    2008
    Apr
    3
    Thu
    2:37pm
     
    24

    NooOoOo I suck at maths!!

    Even if you did, it'll be too late for this weekend anyway heheheh!

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


    2008
    Apr
    3
    Thu
    3:52pm
     
    25

    This question involves a student's understanding of Trigonometry and Surds basics.

    As mentioned, when you see a surd expression in a trigo question like this, it almost always involve trigo special angles - usually no calculators required 😉

    Since the question asks for p and q within the surd expression of the side of the square, your approach should be to 1) express the length of the side in surd form using all your trigo prowess, and then 2) equate it to p√2 + q√6.

    First of all do know that each interior angle of an equilateral triangle is 60o (duuuh!).

    So let the side of the square be x.

    Solution Diagram to the trigonometry surd problem

    Using Sine Rule

    As pointed out by Someone, MGCCL and Papillion, the quickest way would be to use the Sine Rule taught in your Sec 3 EMaths (and discussed here)

    And as Papillon pointed out, drawing a vertical line CD will bisect ∠FDE ⇒ ∠CDE = ∠EDB = 90o/2 = 45o.

    So you can form the following expresson for Δ BDE:

    x/{sin 60^o} = 6/{sin 75^o}

    And as Someone pointed out, sin 75o = sin (45o+30o) and using the Addition Formula from your AMaths New Syllabus:

    sin(A+B) = sin A cos B + cos A sin B

    ⇒ sin (45o+30o) = sin 45o cos 30o + cos 45o sin 30o

    And using the values from the special angle chart,
    sin 75^o = {sqrt{3}+1}/{2sqrt{2}}
    x/{sqrt{3}/2} = 6/{{sqrt{3}+1}/{2sqrt{2}}}

    x = {6 sqrt{3}sqrt{2}}/{sqrt{3}+1} = {6 sqrt{6}}/{sqrt{3}+1} since you should know that √ab = √ab

    Using Trigo Ratios

    But not everyone has been taught about the Addition Formula above (esp those retaking the Old Syllabus this year), and these unfortunate group of people will have to find x via trigo ratios - a little more tedious.

    When it comes to trigo ratios, you often need to slice your diagram into as many right-angled triangles you'll need to achieve your answer.

    Using Pythagoras Theorem,
    AC2 = AD2 + CD2CD = √[122 - 62] = √108

    But CD = OC + OD

    From the diagram,
    cos 45^o = OD/x doubleright OD = x/sqrt{2}
    sin 45^o = OF/x doubleright OF = x/sqrt{2}
    tan 60^o = OC/OF doubleright OC = {x sqrt{3}}/sqrt{2}

    sqrt{108} = {x sqrt{3}}/{sqrt{2}} + {x/sqrt{2}}

    x = {sqrt{2}sqrt{108}}/{sqrt{3}+1} = {sqrt{216}}/{sqrt{3}+1} = {sqrt{36} sqrt{6}}/{sqrt{3}+1} = {6 sqrt{6}}/{sqrt{3}+1}

    Which is the SAME expression you get using the sine rule method.

    * * *

    Now seeing surds at the denominator of a fraction, any AMaths student will know intuitively that you have to rationalise your surd.

    i.e.

    x = {{6 sqrt{6}}/{sqrt{3}+1}} * {{sqrt{3} -1}/{sqrt{3} -1}}

    Time to play around with your √ab = √ab once more, to bring out the √2!

    x = {6 sqrt{6} sqrt{3} - 6 sqrt{6}}/{3-1}
    x = 3 sqrt{6} sqrt{3} - 3 sqrt{6}
    x = 3 sqrt{18} - 3 sqrt{6}
    x = 3 sqrt{9}sqrt{2} - 3 sqrt{6}
    x = 9 sqrt{2} - 3 sqrt{6}

    So p = 9 and q = -3 😉

    Congratulations to Someone, MGCCL and Papillon for getting it right! Miss Loi knows that all of you are Level 99 math gurus, but please understand that this is just a humble blog dealing with O-Level Maths (read 13-16 year old Singaporean students) - so please bear with her if you find the problems and explanations here too basic for your liking.

    As for the rest, hope that you've learnt something from Miss Loi's April Fools Day question 😉

  26. Mgccl's Avatar
    Mgccl commented in tuition class


    2008
    Apr
    3
    Thu
    6:47pm
     
    26

    level 99? nice 🙂

    nooooo..
    you destroyed my dreams... for a second there I thought math can get girls...
    maybe it's time for me to try physics for a change...

  27. Someone's Avatar
    Someone commented in tuition class


    2008
    Apr
    3
    Thu
    7:00pm
     
    27

    I see... I didn't know the addition formula was taught in A maths now; I split the triangles:

    Someone's Solution Diagram

    x being the side closer to the 60deg and y being the side closer to the 45deg; c is the common opposite.
    x+y=6
    tan{60}=c/x
    tan{45}=c/y
    ytan{45}=c
    xtan{60}=c
    ytan{45}=xtan{60}=(6-y)tan{60}=6tan{60}-ytan{60}
    ytan{45}+ytan{60}=6tan{60}
    y(tan{45}+tan{60})=6tan{60}
    y={6 tan 60}/{tan 45 +tan 60}=9-3sqrt{3}

    The relationship between an isosceles right angle triangle of equal sides x and the hypotenuse h is h={sqrt{2}}x

    s={sqrt{2}}y=9sqrt{2}-3sqrt{6}

    I don't like to ignore a mathematical challenge. Haha.

  28. Someone's Avatar
    Someone commented in tuition class


    2008
    Apr
    3
    Thu
    7:06pm
     
    28

    Opps. I somehow must have copied my equation twice. Haha.

  29. peewee's Avatar
    peewee  commented in tuition class


    2008
    Apr
    3
    Thu
    9:20pm
     
    29

    OMG, all these equations are giving me nightmares!

    Miss Loi, you mean this question is for 'O' Levels standard now?

    I should have met you for tuition 13 years ago! I scored F9 for maths...

  30. La Papillion's Avatar
    La Papillion commented in tuition class


    2008
    Apr
    4
    Fri
    12:06pm
     
    30

    Haha, lvl 99 🙂

    Like Someone, it's hard to resist a good maths challenge 🙂

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


    2008
    Apr
    4
    Fri
    9:32pm
     
    31

    Mgccl: Physics? Nah ... math girls are definitely sexier 😉

    Peeweeeeee: Actually O-Level questions tend to be a little easier and less involved, but all the concepts remain the same. But with the changing syllabus this year, nobody can be sure what's coming out though.

    Your math result that bad meh? Were you a terminal stage LMBFH Syndrome sufferer?

    Ahhh Someone nicely done 😀

    To be honest, Miss Loi spent a bit of time trying to figure out where's your x, y, c etc, (it would have been easier if you'd said which triangle you were referring to!) so hope you don't mind Miss Loi inserting a diagram in your comment for the benefit of readers 🙂

    Hope students can appreciate from this example that there can always be alternative approaches beyond what your teacher has taught you.

    Someone + Papillion: Something happened yesterday - let's see if Miss Loi can make this into a math challenge 😉

  32. Someone's Avatar
    Someone commented in tuition class


    2008
    Apr
    4
    Fri
    10:20pm
     
    32

    Is it just me, or when you enclose your equation with double { } it appears twice? I checked my previous equations, and it doesn't appear that I typed it twice; instead, the equation rendered twice. Haha.

  33. peewee's Avatar
    peewee  commented in tuition class


    2008
    Apr
    4
    Fri
    10:20pm
     
    33

    If you were my maths teacher, you could vomit blood teaching me. I scored 0/100 for my CAs...

    Haha...

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


    2008
    Apr
    4
    Fri
    11:34pm
     
    34

    Someone: Yes the additional { } appears to be the culprit. Anyway Miss Loi has taken the liberty to remove them for you 😉

    peewee: You have no idea how many liters of haemoglobin Miss Loi has produced through the years. Probably enough to fill a blood bank!

  35. tohkiatshengKEN's Avatar
    tohkiatshengKEN commented in tuition class


    2008
    Apr
    5
    Sat
    11:48am
  36. FoxTwo's Avatar
    FoxTwo commented in tuition class


    2008
    Apr
    5
    Sat
    3:54pm
     
    36

    Soooo.... after all these, you still haven't announced who's the lucky maths genius that gets to discuss the intricacies of maths with you on the Singapore Flyer....

    To the winnah - pls take lotsa pics ok? sneaky ones if you can 🙂

  37. peewee's Avatar
    peewee  commented in tuition class


    2008
    Apr
    5
    Sat
    4:30pm
     
    37

    I remembered my teacher mentioning about having to 'kill' a black chicken each week to nourish back the 'injury' she's sustained while teaching us (my class).

    Poor chickens...

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


    2008
    Apr
    6
    Sun
    1:00pm
     
    38

    Umm ... FoxTwo ... a bit late but ...

    ClappingTree: Hmmm…. is this an April Fools’ Day joke?

    Miss Loi: ...

  39. precious's Avatar
    precious commented in tuition class


    2008
    Apr
    6
    Sun
    5:17pm
     
    39

    April Fool's Joke?! I spent so much time persuading Nic to help me win a romantic date wif Miss Loi. Sighhh

  40. ignorantsoup's Avatar
    ignorantsoup commented in tuition class


    2008
    Apr
    6
    Sun
    7:46pm
     
    40

    Walau..thought teachers arn't suppose to lie? lol..but miss loi is a sexy math tutor..now that's different.. 😛

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


    2008
    Apr
    7
    Mon
    8:45am
     
    41

    Peewee: Miss Loi believes that your class has already graduated, since the population of black chickens is now flourishing.

    TOH KIAT SHENG!!! Made up with Julian already? Now so free to come here and leave silly comments huh?

    Precious: Huh? You should be spending the time on romantic dates with Nic instead!

    Soupie: Huh? Teachers cannot play April Fool's? What a sad, sad profession if that's really the case.

  42. Sam Windsor's Avatar
    Sam Windsor commented in tuition class


    2008
    Apr
    18
    Fri
    7:35pm
  43. Fred R's Avatar
    Fred R commented in tuition class


    2008
    Oct
    19
    Sun
    10:38am
     
    43

    Dear Miss Loi. I am too late to win the evening you spoke about in this article. However I am very interested in you. Intelligent women are the most beautiful. I am American Engineer. Will you marry me??!! 🙂

  44. Mgccl's Avatar
    Mgccl commented in tuition class


    2008
    Oct
    19
    Sun
    10:45am
     
    44

    @Fred...
    If you didn't already saw that this is an April fool's joke that broke my innocent heart... READ THE COMMENTS.
    Oh... I thought math can get me a date. Guess I was wrong...

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


    2008
    Oct
    20
    Mon
    9:13am
  46. qwerty1106's Avatar
    qwerty1106 commented in tuition class


    2010
    Jun
    27
    Sun
    3:19am
     
    46

    lol Chers/Tutors/anyone in the teaching sector are meant to have "faster-protein (ie.Haemoglobin) producing rate" as compared to us normal ppl XD

One Reaction

  1. Tweetback
    Miss Loi tweeted


    2008
    Apr
    1
    Tue
    7:35am
     
    47

    If you haven't heard, win a romantic evening on the Singapore Flyer with Miss Loi by solving this math question! (http://tinyurl.com/2pzzr5)

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