After collection of English paper 2...

Okay boys, please listen up. I have found a piece of foolscap paper and it is not attached to any scripts. It doesn't have any name on it as well. Please listen up as I read what is written on it. If it belongs to you please raise up your hand. This piece of paper has question 14 on it and it starts with, "Astrologers believe that the movement of the Moon..."

Before Mr Wong could finish, the whole hall was filled with laughter.

FYI, question 14 was the summary question and it has some 10 starting words given.

Oh and the thing is, Mr Wong still could not get why we were laughing. Well, he is a Chemistry teacher anyway.

Question: Prove that there are no positive integers x and y, such that 2(x² + xy + y²) is a perfect square.

Solution: Assume that there is some k² = 2(x² + xy + y²); where x, y and k are positive integers.

LHS = RHS --> Even number
So k² is divisible by 2.

If k is an odd number, then k² is an odd number.

So k is not an odd number.

So k is an even number

k² is divisible by 4.
k²/2 is an even number.

k²/2 = x² + xy + y²
So x and y are both even numbers (because if either is an odd number, LHS = odd number)

If such a positive solution exists, then there must be a value whereby k² is minimum. Let k² = 2(x² + xy + y²) be such a value.

Since x, y and k are even numbers, let x = 2p; y = 2q and k = 2r whereby p, q and r are positive integers.

(2r)²/2 = (2p)² + (2p)(2q) + (2q)²
2r² = 4p² + 4pq + 4q²
r² = 2p² + 2pq + 2q²
r² = 2(p² + pq + q²)

But we have assumed that k² is the minimum.
r² = k²/4 is smaller than k² which results in a contradiction.

Hence there are no positive integers x and y, such that 2(x² + xy + y²) is a perfect square.


N.B.: If you have no clue what I just did, I proved the question by contradiction. I assumed the opposite and found out that the results contradict each other. I've shown that if there exist some positive integers x and y which satisfy the equation, then x/2 and y/2 must also satisfy it. By using the same method, I prove that x/4 and y/4 must also satisfy it, etc. Eventually I will end up to an odd number or a fraction which does not satisfy the equation. An elegant way of proving by contradiction!

3A/4A. They are the most wonderful classes I have ever been in. I remember the first day in 3A. Everyone was so quiet waiting for the teacher to arrive. And when Mr Pang stepped in and talked to us, you can even hear the wind blow. All right, it's good to be in a class whereby there isn't much noise, but not until it was soooo quiet. I remembered making a lot of noise with the ex-2B gang near the back of the class.

After activities like the secondary three orientation camp, PE lessons and Victoria 130, our class became more bonded. Our class became more active. The most memorable thing about our class is the 131m-long banner, which was completed successfully during Victorian Challenge earlier this year.

Our class is indeed not like any other typical class. Our class can juggle our studies with our CCA and yet excelling in both. Being in 3A/4A is really a challenge, because you need to strive to keep up with the top. Even getting last in class is considered quite good in other classes. Look at this picture...

Source AIn 4A, it's not whether you get your A1 or not. It's whether you get 90% or not. This is what our class achieved for A-Maths and E-Maths respectively.

Because 4A is so competitive, you cannot afford to write crap answers like this:

Source B

In fact, to do well, you must know that time is an important factor. In exams, you cannot write long essays. You need to write quality ones... short enough to score the maximum marks possible.

Source C

One more point to take note. Being in 3A/4A, you must do everything with style and professionalism. You cannot let teachers or anyone criticise you, especially in examinations. In fact, whatever small mistakes you make may be exaggerated and laughed at by others.

Source DWhat a classic! "This was one point :("




Section A (Answer all questions)
1) Theme question: Does studying in 4A ensure good academic results?

a) Study Source A.
What does this source say? Explain your answer. [5]

b) Study Sources B and C.
How different are these two sources? Explain your answer. [6]

c) Study Source C.
Does this source prove that you can get high marks by writing less? Explain your answer. [7]

d) Study Source D.
How useful is this source in telling you that studying in 4A ensures good academic results? Explain your answer. [7]



Section B (Answer only one question)

2) Academics
a) How far is the education from teachers a factor in ensuring good academic results in 4A? Explain your answer. [12]

b) "4A studies more than they play". Do you agree with this statement? Explain your answer. [13]

3) Class bonding
a) How far does the Victoria 130 challenge forge a stronger bond between the students of 4A? Explain your answer. [12]

b) Here are 3 ways 4A bond with each other:

i) Buying of class jerseys

ii) Playing soccer during post-prelim break

iii) Going to LAN shops after school

Which of the above is the most crucial in bonding the class together? Explain your answer. [13]

Yesterday was officially the last day I was going to study in Victoria School. After studying for 4 years in VS, I must say I have grown from a young boy to a young man. The atmosphere I have experienced here in VS is something nobody in any other schools can experience. As the saying goes, "VS is something more, not something else".

Many people were feeling quite emo yesterday. I personally wasn't feeling so emo because I know that we will always meet again. Very soon we will be taking our 'O' levels together. We will meet again next year to collect our results slip. Also, during events like Chinese New Year Eve, we will definitely return to the place where we call home.

Anyway, something happened last week which I promised to post only after graduation.


(Gabriel, Jun Yuan, Wei Liang and I were playing cards (Gabriel's cards) in class after school. Miss Yeo suddenly walked into our class)

[Ms Yeo]: Why are you all playing cards?
[Us]: We want to reduce stress.
[Ms Yeo] (took the cards Jun Yuan was holding): I am going to tell Mr Pang about you all playing cards...
(Gabriel snatched the cards back from everyone including Ms Yeo, then placed them nicely into his case)
[Ms Yeo]: I am going to tell him to change all your conducts from "Excellent" to "Very Good".
[Gabriel] (hands over the whole deck of cards): Ma'am, take them.
[Ms Yeo]: Nah, it's OK. Don't play again next time.
[Gabriel] (quickly keeps his cards): I know you won't take!


The next day, Mr Pang saw Wei Liang and I walking across the 7th floor bridge...

[Mr Pang]: Walao, how can you all do such a thing?
[Me]: What thing?
[Mr Pang]: You all should know.
[Me]: Oh that one. Because we need to reduce stress!

The next day, we played cards in class yet again after school and after playing, we went to the canteen and saw Miss Yeo...)

[Gabriel]: Hi Ma'am.
[Ms Yeo]: You all never play cards already ah?
[Gabriel]: Erm, we never play already.


Haha. Oh and I got an "Excellent" for conduct this year.

Went to RJC's Open House today after school with Ryan and Wei Liang. Gabriel went earlier with his friends but we met him there eventually.

Seriously the open house discouraged me from going there. There was this performance in the amphi-theatre whereby CCAs will do a short performance of about 1 minute each. It was a big screw up. Especially when they tried to demonstrate sports there... A girl threw a volleyball right into the audience when she wanted to pass it to the people on the other side. And there were a lot of misses in sports like hockey, floorball and frisbee. The funniest one was when a soccer player tried to dribble past another player. He was supposed to dribble past him, but somehow the ball did not manage to pass through the other player's legs, and when the first player tried to turn back, he slipped on the smooth floor and fell. I guess soccer players can only play on fields, not on floors.

And hey, we found the RJC's Bridge Club and we played for more than an hour. We as in Ryan and one of the club members against Wei Liang and I. Hey not bad, the first game I actually made a 3NT... in fact I took 11 tricks when 9 was enough. Oh yeah, there was one very interesting bridge puzzle written on the whiteboard:

(modified slightly)

	North (dummy) ♠ AKQ ♥ JT9876 ♦ 56 ♣ 45
West Lead: ♠3	7NT	East
	South (declarer) ♠ - ♥ AKQ ♦ AK432 ♣ AKQ32

The contract is 7NT. South is the declarer and North is the dummy. West gives the opening lead with ♠3. Determine how all 13 tricks can be taken.