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2007
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Applications Of Integration – Beware Of Shady Areas

(10)
Posted at 10:55 pm by Miss Loi in A-Maths Questions

Mom and Dad will forever nag about the importance of being a goody two shoes and staying away from shady characters in shady areas. However, the A-Maths Syllabus dictates that every student’s integral-ity be tested by making him/her venture at least once into such areas during the exams. Hur hur hur.

The following question is designed to sieve out the street-smart students from the horribly naive, pampered, and unworldly ones (aren’t we all):

Diagram of Shaded Area Bounded By Curves The diagram shows part of the curve y = 1 + ex, intersecting the y-axis at Q. The tangent to the curve at the point P(1, 1+e) intersects the y-axis at R.

Find the area of the shaded region PQR.

Upon first glance, many of Miss Loi’s students will go: “Walau! So simple! Just integrate the curve to get the area beneath bounded by the points Q and P, and then integrate the straight line to get the area beneath bounded by the same x-coordinates for points R and P, and then subtract the two areas can already!”.

Miss Loi: “So how are you going to integrate that straight line without knowing its equation?”

Student: *frantically flips textbook for chapters on Differentiation and Coordinate Geometry*

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Miss Loi
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Boys Don’t Cry

(4)
Posted at 7:02 pm by Miss Loi in Study Break

Tickets

You first heard it from Japanese Whispers, but you wondered where’s the Catch. After all you’ve been waiting for A Night Like This since you were a Primary kid, catching The Caterpillar in A Forest In Between Days in school, and you could’ve waited for another One Hundred Years.

When the news broke, you might just be Standing On A Beach with a mobile phone in your hand, Staring At The Sea, staring at the sand.

Snapping out from that silly Lullaby of a Lovesong played at the beachside bar, you jumped into the nearest taxi, taking care not to knock The Head On The Door, much to the annoyance of the long queue at 10:15 Saturday Night.

Songs from the whole of Ten Imaginary Years played in your head as you made The Walk to the ticket booth.

To your mighty relief, tickets are still available else you would’ve been so Hot Hot Hot!!! that even Killing An Arab is Never Enough to stem your wrath.

The transaction was done in exactly Seventeen Seconds, but the joy would last you at least A Thousand Hours. You proudly held up the ticket and gave it The Kiss. You felt Just Like Heaven as tears started flowing from your eyes.

Now, now don’t do that here coz Boys Don’t Cry!

P.S. Remember to take some Pictures of You when you’re there!

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Miss Loi
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Vectors – Never In An E-Maths Question

(7)
Posted at 5:00 pm by Miss Loi in A-Maths Questions

Miss Loi’s mouthful of words from yesterday’s E-Maths vector question covered, as mentioned, almost 75% of the A-Maths Vector syllabus.

The remaining 25%, then, is summarized in the following commandments:

If |u| = 1, u is known as a unit vector. The unit vector in the direction of a given vector a is a/|u|.

With the two simple statements above, unit vectors are forever cast within the exclusive domain of the A-Maths Vectors Club, thus depriving the relieved masses of E-Maths students from ever needing to waste a single brain cell on a question like this:

The vector vec{OA} has magnitude 85 and is in the opposite direction of (matrix{2}{1}{8 {-15}}). Express vec{OA} as a column vector. The vector vec{BA} is (matrix{2}{1}{{-35} 63}). Obtain the unit vector in the direction of vec{OB}.

IMPORTANT: To avert a tragedy, always double-check the order of the letters in the vectors and don’t drive in the wrong direction against the traffic!

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Miss Loi
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Vectors – Almost An A-Maths Question

(21)
Posted at 7:04 pm by Miss Loi in E-Maths Questions

As D-Day draws nearer, Miss Loi’s Question of the Day gets longer … kekeke.

Besides the arrows and symbols looking exactly the same, there are few differences between E-Maths and A-Maths vector questions. In some schools vectors are even taught exclusively in E-Maths classes, much to the annoyance of the A-Maths student who happens to hate his/her E-Maths teacher!

Take the question below for example. This typical but tedious question is designed to test your elementary vector knowledge like Addition of Vectors, Difference of Two Vectors, Negative Vectors, Scalar Multiple of a Vector, Parallel Vectors, Position Vectors, and always a little bit more. *stops to catch breath*

Wow. That mouthful of words above already constitutes roughly 75% of your A-Maths vectors syllabus!

In the diagram, vec{OA} = a and vec{OB} = b. The points P and Q lie on AB and OB respectively so that AP/PB = 1/3 and OQ/QB = 3/4. The lines OP and AQ intersect at the point R.

  1. Express vec{AQ} in terms of a and b.
  2. Show that vec{OP} = 1/4 (3a + b).
  3. Given that vec{AR} = k vec{AQ}, show that vec{OR} = (1 – k)a + 3/7kb.
  4. Given also that vec{OR} = h vec{OP}, find the value of h.
  5. Find the numerical value of
    1. {Area of Delta OAR}/{Area of Delta OAP}
    2. {Area of Delta OAP}/{Area of Delta OAQ}

IMPORTANT: At this stage of the game, it is imperative that students to the scene appreciate the fact that long-ish vector questions have this evil tendency to ask for something a little off-tangent (like ratios and areas – can you spot this in the question?) that will usually require something beyond your vector abilities.

So approach all questions with a pure and open mind and don’t blindly Vector See Vector Do. 不要走火入魔! (literally: don’t keep firing when you’re already misfiring!)

You get the idea.

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Miss Loi
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Miss Loi’s Temple Goes Private!

(3)
Posted at 10:20 pm by Miss Loi in Miss Loi's Temple

No Miss Loi didn’t become a tycoon’s mistress overnight.

Rare photo of a privatus candidatus
Privatus Candidatus

Private Candidates (Privatus Candidatus) tend to be a bit of an enigmatic lot in Singapore. Due to their … umm … ‘private’ nature, they are often wrongly perceived by the outside world to be loners, slackers, unmotivated, and unloved.

This stereotype came about simply because they don’t attend school. At least not with the ones on this mighty list anyway. And when they don’t attend school, the spread of their kind can be best expressed by a Poisson Distribution (don’t worry this is not in the O-Level syllabus).

To put this in plain English, that is to say, (assuming they are not friends to begin with) the probability of a private candidate meeting another private candidate in Singapore is roughly equivalent to that of a white Bengal Tiger finding its mate within the Sundarbans National Park boundaries.

Yes they are here, living amongst us. One of them might have shared a seat with you on the bus yesterday. One of them might even have been that idiot who ‘stole’ your taxi on that rainy morning. Despite their undoubted presence, however, sightings of a concentrated population of private candidates (actual exam days not withstanding) have been few and far between.

And this poses a problem for the fate of the average private candidate. The absence of fellow schoolmates to check answers with, act as sources of encouragement, cohesion etc. makes it difficult in terms of study discipline and motivation. The real danger is, of course, that the private candidate do not even know if he/she is studying the right thing.

So in order to prevent inbreeding ensure the long-term survival of this unique species, the venerable Miss Loi has decided to open the Temple Gates for another joss sticks session specially for private candidates taking their O-Level Maths this year:

Lesson Time: Every Friday
1.00-3.00pm (Private Candidates ONLY!)
Venue: Miss Loi’s Temple
Class Size: Limited to 4 students

Yes, rekindle the spirit of study camaraderie! Confirm once and for all whether that question will come out! Re-indulge in the joy of getting spoonfed by your helpful classmate with your stupid noob questions! No more lonely unloving nights!

Contact Miss Loi today!

Privatus candidatus of the world unite!

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Miss Loi