NTU Interview

I will go straight to the point: the following is the detail of my Nanyang/ASEAN Undergraduate Scholarship Interview on 23 April, 2008 at Student Service Center, Nanyang Technological University. Minor details maybe inaccurate due to constraint of my memory capacity 😛

The interview (or should I say interrogation?) was conducted by three interviewers, in a large meeting room that made me feel like a criminal facing the judges.

<BEGIN>

Me : Good afternoon madam. (Tried to appear confident)

Interviewers : Good afternoon. What is your preference, ASEAN Undergraduate Scholarship or Nanyang Scholarship?

Me : ASEAN Undergraduate Scholarship.

Interviewers : Do you know their differences? Have you look through their objectives?

Me : The source for AUS is Singapore MOE, whereas for NS it is the campus itself. I apologize for not being able to tell their objectives.

Interviewers : Since you know the sources of the scholarship, can you tell us what do we expect from the scholars?

Me : (…after some cliche…)…the scholars are expected to become the human capital for Singapore Government.

Interviewers : So you are interested in becoming part of the Singapore human capital?

Me : I will go wherever I can acquire knowledge. (What am I talking about?)

Interviewers : What is your first choice? And why?

Me : Chemical and Biomolecular Engineering. blah blah blah…(True reason : Because it is the hardest to get into? I wish to slap myself for my thoughtlessness when I chose my first choice…)

Interviewers : But your subsequent choices are unrelated to chemistry and biology?

Me : (Stunned for a while) I am interested in all three science subjects but I am more inclined toward Physics than Biology. Chemical and Biomolecular Engineering enables me to study all three discipline of science….(messed up and completely unrelated to the question)

Interviewers : So you will be equally happy if we give you the other choices?

Me : Yes.

Interviewers : Why didn’t you study Biology in STPM?

Me : I would like to , but our school policy restraint me from doing so.

Interviewers : From your essay you seems passionate in teaching. Are you interested in becoming a lecturer in the future?

Me : Yes, etc. etc. etc.

Interviewers : You aren’t interested in SME?

Me : Yes. (Still in an unprepared state, forgot the meaning of SME out of sudden)

Interviewers : Why?

Me : (Too late when I realised what I have answered) Erm…I am inclined to join a profession that will enable me to contribute something to the society….etc etc

Interviewers : You are implying that SME aren’t making contribution to the society?

Me : (My mind went blank due to my previous imprudent reply) Well, Government sector is more related to the society…etc (Confidence shattered)

Interviewers : From the application form that you submitted, you got merit in etc etc but JUST a PASS for Grade 7 ABRSM exam?

Me : I learn music for fun, not for grade. I admit I don’t have enough talent for music.

Interviewers : What is your father business about?

Me : etc etc etc

Interviewers : What subject does your mother teach?

Me : Chinese.

Interviewers : Thank you, you may leave now. Any further question you wish to ask?

Me : No. (Feeling a little disheartened)

<END>

Mediocre/Below average performance I guess. It looks a little better in my post as it is written, not spoken.

For Howard : Howard, I have prepared to follow your foot step, apply a loan and be your junior…. T_T

Personality Test

I stumbled upon this test online. http://www.quizbox.com/personality/test82.aspx

That test really gives me a shiver….

Your view on yourself:

Other people find you very interesting, but you are really hiding your true self. Your friends love you because you are a good listener. They’ll probably still love you if you learn to be yourself with them.

The type of girlfriend/boyfriend you are looking for:

You like serious, smart and determined people. You don’t judge a book by its cover, so good-looking people aren’t necessarily your style. This makes you an attractive person in many people’s eyes.

Your readiness to commit to a relationship:

You are ready to commit as soon as you meet the right person. And you believe you will pretty much know as soon as you might that person.

The seriousness of your love:

Your have very sensible tactics when approaching the opposite sex. In many ways people find your straightforwardness attractive, so you will find yourself with plenty of dates.

Your views on education

You may not like to study but you have many practical ideas. You listen to your own instincts and tend to follow your heart, so you will probably end up with an unusual job.

The right job for you:

You’re a practical person and will choose a secure job with a steady income. Knowing what you like to do is important. Find a regular job doing just that and you’ll be set for life.

How do you view success:

You are afraid of failure and scared to have a go at the career you would like to have in case you don’t succeed. Don’t give up when you haven’t yet even started! Be courageous.

What are you most afraid of:

You are concerned about your image and the way others see you. This means that you try very hard to be accepted by other people. It’s time for you to believe in who you are, not what you wear.

Who is your true self:

You like privacy very much because you enjoy spending time with your own thoughts. You like to disappear when you cannot find solutions to your own problems, but you would feel better if you learned to share your thoughts with a person you trust.

Geodesic dome (I built a junk lol )

Basically geodesic dome is more or less identical to your foot ball in shape, consisting entirely only of pentagons and hexagons. For a clearer picture on geodesic dome you can refer to http://sci-toys.com/scitoys/scitoys/mathematics/dome/dome.html

I started constructing the geodesic dome out of straws when I came across the website. After all, it was one of the few projects listed on the site that I was capable of doing.

To be frank the geodesic dome I constructed was rather useless other than being a decoration, as my siblings pointed out to me. (They prefer the name “junk” over the name geodesic dome) But the reason I constructed the dome was not because of its use,  rather I was trying to prove that I could execute what I said and thought. The geodesic dome is the first step I took before I started constructing something more complicated.

Anyway, this is the geodesic dome I have built. It is only half completed. I took the photo using Jun Chiet’s cell phone (a big thanks to him)

And these are the raw materials:

It took me some days to cut the straws into the required length….

And this is the stapler I used for my project. I am not supposed to use stapler, but I really can’t find the material needed to connect the straws.

Au Revoir, My Past

Ever wonder why do I remove all the older entries all of a sudden? This post shall reveal the answer.

For those who have been constant readers of my blog, I owe them a thousand thanks—while it is unexpected that my blogger life still survive despite my lacking of perseverance, it is even more unexpected, and amazing that my blog has received more than a 1000 views.

Back then when I was posting my first blog entry, my life was a bed of roses. I led a care-free life, having a devil-may-care kind of attitude. The purpose of my blog, was to share my joy with the blog readers.

But then things changed. I would ponder in front of my monitor, wondering if there is anything worthy to write. My dream was shattered, and my life was forced to change it course—everyday I suffered from intensifying mental tumult and maelstrom. If there was anyone to be blamed it would be myself, my own skeptical, sensitive and weak mind.

Gradually my blog becomes a channel to vent all my frustration and depression. That, was the time that I posted only encrypted posts. How irony, I encrypted it because I hoped that the person would actually ask me for the password.

And eventually the quality of my post deteriorated to the extent that I deem it unworthy to the readers. It became nothing but despondent, hopeless and useless self-pithiness. Those posts were only meaningful to me while I was writing them.
I loathed the self-pithiness and meaningless of my older entries. I intended to delete my blog and started a new blog, but Chew suggested me to delete all my older entries instead. As for why I chose to turn this personal blog to an “educational” blog—

At least, mathematical truth doesn’t change over time. They will still be meaningful after eons.

Human feeling and emotion changes over time. They are only meaningful at the time when they still persist. When they are gone their history is worthless.

Perhaps, if I am leaving abroad for my tertiary study, I will rewrite personal post for my families, in order to inform them about my situation over there.

But now, this particular blog shall consist only of mathematical post.

Definite integrals of cos^n x cos nx

Question:

Solution:

Moments of Inertia

Moment of Inertia is defined as the product of mass and the square of the distance from the axis of rotation.

While less emphasized in STPM Physics, moment of inertia is studied in depth in A-Level Further Mechanics. (Derivation for the moment of inertia using integration is not required at this level.)

Some basic knowledge that you will need to know:

a) Equations for the moment of inertia for loop, solid cylinder, uniform sphere and rod.

(You can find the equations in any STPM Physics reference book)

b) Parallel Axis Theorem

c) Perpendicular Axis Theorem

Parallel and Perpendicular Axis Theorem

We know that the moment of inertia of a disc rotating around axis through the center of disc is given by 1/2 MR². But what if the disc is rotating around an axis perpendicular to the rim of the disc?

The parallel axis theorem states that if I’ is the moment of inertia of a body of total mass M about any axis, and I is the moment of inertia about an axis passing through the center of the mass and parallel to the first axis but a distance h away , then

I’ = I + Mh²

In the above case, I of the disc about axis Z is

I’ = 1/2 MR² + MR² (since h = R in this case)

= 3/2 MR²

The second theorem, Perpendicular Axis Theorem states that the sum of the moments of inertia of a plane body about any two perpendicular axes in the plane of the body is equals to the moment of inertia about an axis through their point of intersection perpendicular to the plane of the object.

Sounds confusing? Refer to the diagram above. The moment of inertia of the disc about the green axis is equals to the sum of the moments of inertia about the blue and red axis.

By symmetry, we can deduce that the moment of inertia about the blue axis and the red axis are equal. (Since the disc is uniform)

Hence, the moment of inertia of the disc about the red/blue axis, I is given by

I + I = 1/2 MR²

I = 1/4 MR²

Note : Proving of Perpendicular Axis Theorem and parallel Axis Theorem is not required at this stage.

 

 

 

 

 

 

 

 

Newton’s Law of Restitution

While having numerous similarities with STPM Physics Syllables, the mechanics section in A-Level Further Mathematics has different emphasis, and some equations that is not taught in STPM.

So far these are some of the new equations that I have discovered during my practice:

1) Newton’s Law of Restitution (Taught in STPM, but less emphasized)

2) Perpendicular Axis Theorem and Parallel Axis Theorem
3) Center of Mass for Certain Geometry Shape

I will disuss the Coefficient of Restitution today.

The Coefficient of Restitution, is the ratio of relative velocity of separation to relative velocity of approach. In equation form,

v2 – v1 = e (u1 – u2)

where e is the coefficient of restitution. e has a value between 0 and 1, 1 being the case for no kinetic energy is lost. The lower the coefficient, the more is the lost of kinetic energy from the system.

Sample Question :

A table tennis ball of mass 2.5 g strikes the smooth surface of a horizontal table. Calculate:

1) The speed of the ball immediately after impact,                                 [2]

2) The coefficient of restitution between the ball and the table.           [2]

(Adapted from A-Level Further Maths, Specimen Paper 1)

 Hints :

1) The vertical component of linear momentum is not conserved here, since the tennis ball will experience an impulsive force upon hitting the surface. Only the horizontal component is conserved.

2) In this case, u2 and v2 = 0, since the wall is not moving. Con sider only the vertical component of velocity.

 

 

Kinematic

A gun G fires a shell with initial speed V at an angle Θ above the horizontal. The shell hits a target T which is a distance d horizontally from G and a distance h below it. Given there is only one possible value for theta for which this occurs, show that

V² = g ( – h + ( h² + √( h² + d² ) )

(Adapted from A-Level Further Maths, Specimen Paper 1)

 

Well, I had a hard time solving this…crack my head, paid Chew a visit…just to discover that this question is meant to punish those who are thinking too much. 😦

I and Chew discussed the question for about an hour…poor Chew, he had to rush to the cinema after spending too much time on that question. He was the one who found the key to the question….

Initially I tried eliminating the parameter t, and the equation turn became a nasty trigonometry equation…..urgh…I thought I need knowledge on further trigonometry to solve that (which is, unnecessary, of course.)

It is simple, really. Look for equations for horizontal and vertical motion, then eliminate Θ as a parameter rather than t.

Have fun! Can be solved at SPM level. If you don’t make the same mistake as me 🙂