Thinking [email protected] #3

JC Mathematics, Mathematics

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.

Thinking [email protected] is curated by KS. More of him can be found here.

This is a question from 1976 A’levels Paper 2. I thought it is pretty interesting to discuss the question with a little extension.

(a) In how many ways can 5 copies of a book be distributed among 10 people, if no-one gets more than one copy?

(b) In how many ways can 5 different books be distributed among 10 people if each person can get any number of books?

So now, let us modify it a bit.

(c) In how many ways can 5 copies of a book be distributed among 10 people if each person can get any number of books?

Notice that the difference between (b) and (c) is that the book distributed is not identical. So for (c), we are pretty much distributing r identical balls to n distinct boxes. Whereas for (b) , we are pretty much distributing r distinct balls to n distinct boxes.

Thinking [email protected] #2

JC Physics

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.

Thinking [email protected] is curated by Aaron. More of him can be found here.

Assuming an object is moving in a circular motion in a polar coordinate system given by x = r \text{cos} \theta and y = r \text{sin} \theta. Can you derive the formula of the centripetal acceleration? Hint: look at one of the axes and think of the direction and what is centripetal acceleration

Thinking [email protected] #1

JC Physics

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.

Thinking [email protected] is curated by Aaron. More of him can be found here.

Kepler’s Third Law states that the period of a planet’s orbit is directly proportional to the cube of the semi-major axis of its orbit. This allows scientists to calculate distances of planets in our solar system. Can you derive the equation using what you have learned in Motion in a Circle and Gravitational Field?

Physics@TheCulture #1

[email protected] #1

JC Physics

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.

Thinking [email protected] is curated by Aaron. More of him can be found here.

Why study Physics?

I have questioned many students and getting answers ranging from “Just a subject that I have to take in A-Level” to “I do not know what else to take?”

It is not just a subject:

Physics can be seen as a ‘tool’ to enable you to be more logical and you practise and learn to question ‘Why’, which is an invaluable asset to many other jobs or careers

A student’s dad was having a good chat with me and he was a control systems engineer back in his younger years in The States for a good decade or so. Thereafter he went on to take an MBA and he is now an MD in a local bank. Even if you are not going to major in engineering, it can be a good training.

Helping out with the house:

You can of course repair and fix things in the house without studying Physics but if you know more about topics like pressure, forces, electricity and how things work, won’t it be awesome that you are more knowledgeable? It can be a general knowledge and it will help you out in life along the way when things are screwed at home.

It puts your maths to good use:

Lots of formulas? Well, they help physicists and engineers to understand the world we live in.

Becoming an Engineer:

It is a myth that only bankers are being paid well. Only the good bankers are well paid, similar to engineers. If you excel in the things you do, you will be rewarded. Engineers are not technicians. Yes, they can fix things but they innovate and SOLVE problems too.

A world without Physics:

You will not be looking at this now on your computer/laptop or mobile device literally. Engineers continuously apply Physics to push the frontiers of technology.

It is not just a subject:

Physics can be seen as a ‘tool’ to enable you to be more logical and you practise and learn to question ‘Why’, which is an invaluable asset to many other jobs or careers

A student’s dad was having a good chat with me and he was a control systems engineer back in his younger years in The States for a good decade or so. Thereafter he went on to take an MBA and he is now an MD in a local bank. Even if you are not going to major in engineering, it can be a good training.

Helping out with the house:

You can of course repair and fix things in the house without studying Physics but if you know more about topics like pressure, forces, electricity and how things work, won’t it be awesome that you are more knowledgeable? It can be a general knowledge and it will help you out in life along the way when things are screwed at home.

It puts your maths to good use:

Lots of formulas? Well, they help physicists and engineers to understand the world we live in.

Becoming an Engineer:

It is a myth that only bankers are being paid well. Only the good bankers are well paid, similar to engineers. If you excel in the things you do, you will be rewarded. Engineers are not technicians. Yes, they can fix things but they innovate and SOLVE problems too.

A world without Physics:

You will not be looking at this now on your computer/laptop or mobile device literally. Engineers continuously apply Physics to push the frontiers of technology.

Should increased automation be embraced by our society?

JC General Paper

In this latest May day’s speech by PM Lee, a lot of focus has been given to the future of jobs and the changing economy of Singapore. For a summary of the speech, you could refer to this link <a href=”http://www.straitstimes.com/politics/jobs-jobs-jobs-8-highlights-from-pm-lee-hsien-loongs-may-day-rally”>http://www.straitstimes.com/politics/jobs-jobs-jobs-8-highlights-from-pm-lee-hsien-loongs-may-day-rally</a>

This has got me thinking about the current trajectory of the economy and what the future could possibly bring. The future holds a promising outlook, yet very uncertain and challenging at the same time. Why has it been so? This could be due to increasing automation that we see in our society! According to World Economic Forum, the rise of technology will lead to more than 5 million jobs being eliminated. Redundancies would be widespread and companies would have to restructure in order to meet with this new challenge. We are already starting to see the rise of disruptive technologies, and a move towards the sharing economy through businesses like Uber, Grab, Airbnb, Deliveroo etc. In the process, many middleman are cut out and many taxi drivers worldwide have protested against their dwindling earnings. Retail industry growth has been sluggish, and many retail giants are struggling to keep afloat in an environment where consumers are increasingly looking at online spaces for shopping. Automation, disruptive technologies, and artificial intelligence are bound to eliminate even more jobs and spread to other industries such as healthcare, education etc.

This begs the question of whether society should embrace automation? We are going to see increasingly number of Singaporeans unemployed, unable to adapt and change according to the world economy and increased strain on government budget to sustain these people. The ones that are going to benefit from the future economy would be businesses that took advantage of these changes, and individuals who have the specialized skills and knowledge to adapt. What then is going to happen to the rest of the society? How then should we mitigate against such changes? Here’s something for you to consider about robot tax that is proposed by Bill Gates to mitigate against robots taking away human jobs:<a href=”http://www.businessinsider.com/bill-gates-robot-tax-brighter-future-2017-3?IR=T&amp;r=US&amp;IR=T”> http://www.businessinsider.com/bill-gates-robot-tax-brighter-future-2017-3?IR=T&amp;r=US&amp;IR=T</a>

A more comprehensive discussion would be done during class this week for my students 😛 See ya!

Thinking [email protected] #2

JC Mathematics, Mathematics

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.

Thinking [email protected] is curated by KS. More of him can be found here.

(i) Find the two possible values of z such that z^2 = 1 + \sqrt{3}i, leaving your answer in exact form a + bi, where a and b are real numbers.

(ii) Hence or otherwise, find the exact roots of the equation

2w^2 + 2 \sqrt{6}w + 1 - 2 \sqrt{3} i = 0

Junior College education: A path increasingly less traveled?

JC General Paper

Following up from the previous blog post about JC merger, it seems that there are more interesting and candid responses from the public. Here is one example that could interest you: <a href=”http://mothership.sg/2017/04/ex-nmp-calvin-cheng-makes-the-point-about-the-jc-mergers-that-no-one-wants-to-talk-about/”>http://mothership.sg/2017/04/ex-nmp-calvin-cheng-makes-the-point-about-the-jc-mergers-that-no-one-wants-to-talk-about/</a>

This begs the question whether the merger is an attempt to make JC education more exclusive/competitive, considering that 7 out of the 8 JCs involved in the merger “happened” to have the worst cut off points. Also, this attempt is seen as an elitist move to improve the quality of education for this system.

Considering this trend, poly education would be where the majority is heading towards… what then would be the purpose of JC education? We all know that for the more popular courses in poly such as accountancy, business admin and even engineering, some of the best students from the O levels are vying hard to get in. It is not uncommon to hear of 6 pointers who want to go to poly since they find the education there to be more broad-based,  Is it to train the academically inclined ppl to pursue academia in universities? would this system be slowly phased out in the years to come? (Many have criticized the JC education to be too theory-based; does not teach real life skills and applications. With all the technology-disruptions today and the move towards a sharing economy, where does the JC education fit?)

Thinking [email protected] #1

JC Mathematics, Mathematics

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.

Thinking [email protected] is curated by KS. More of him can be found here.

Each card in a deck of cards bear a single number from 1 to 5 such that there are n cards bearing the number n, where n = 1, 2, 3, 4, 5. One card is randomly drawn from the deck. Let X be the number on the card drawn.

(i) Find the probability distribution of X.

(ii) Show that \mathbb{E}(X) = \frac{11}{3} and find \text{Var}(X).

Andrew draws one card from the deck, notes the number and replaces it. The deck is shuffled and Beth also draws on card from the deck and notes the number. Andrew’s score is k times the number on teh card he draws, while Beth’s score is the square of the number on the card she draws. Find the value of k so that the game is a fair one.