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.

Common Errors for Application Question(AQ)

Common Errors for Application Question(AQ)

JC General Paper

My previous posts have touched on the points that you would need to excel in your AQ. It is also important for you to understand what are some pitfalls so that you will not make these mistakes.

  • 1. Rehash of the author’s argument/ summary of the author’s argument- did not go on to elaborate or to even offer personal insight
  • 2. Lack of evaluation- paragraphs tend to be descriptive
  • 3.Poor selection of examples- they could be inaccurate or they are isolated case studies that are not representative of the whole society
  • 4.No examples given
  • 5.Evaluation lacks depth or it is done very superficially
  • 6.No link back to the requirements of the question
  • 7. No introduction or conclusion (of course this is a very obvious time management issue)

Alright, there you have it, the 7 deadly sins/pitfalls for your AQ.

Vectors Question #4

Vectors Question #4

JC Mathematics

Another interesting vectors question.

The fixed point A has position vector a relative to a fixed point O. A variable point P has position vector r relative to O. Find the locus of P if r \bullet (ra) = 0.

Evaluation for Application Question (AQ)

Evaluation for Application Question (AQ)

JC General Paper

Have you ever wonder what teachers mean by evaluation? Many students have asked me this during my classes.

Well to put it simply, evaluation for the AQ is not just simply stating whether you agree or disagree. You would need to provide a reason to support your point. So how exactly should you evaluate? Well you can consider commenting on the limitations or applicability of the author’s point or even how persuasive/convincing the author is in bringing across his point of view.

Here are some tricks that you could possibly use to help you in your evaluation to make it SUPER:

S– Span (whether the argument applies only to the past and not the present day context and vice versa)

U– Underlying assumption of the author

P– Perfect world vs Reality (does the argument exist only in theory/ in a perfect world, but not applicable in reality?)

E– Effectiveness of the argument

R– Reach (what are the different demographic groups which this argument applies to? surely it can’t apply to all?)

Using this framework, I’m sure you would be able to impress your tutors with your AQ from now on!

Vectors Question #3

Vectors Question #3

JC Mathematics

This is a question a student sent me a few days back, and I shared with my class.

Find the Cartesian equation of the locus of all points (plane) that is equidistant of the xy plane and xz plane.

The following should aid students to visualise.

xy-, xz-, yz-planes

Sidenote: I think Vectors is a very important topic for 9758 as its applications are wide. Students should do their best to understand the topic. I will share a few more applied questions next week when I have time.

Responsibility of Protecting the Environment

Responsibility of Protecting the Environment

JC General Paper

Environment is a common and easy essay question that could potentially come out for the exams… Students should always analyze their essays from a stakeholder’s perspective to give a more holistic evaluation.

Developed countries

Governments in developed countries have the necessary skills, influence and resources to aid the protection of the environment. They would have the financial means to invest in necessary science and technology which could improve the environment. At the same time, they would also possess political clout to enact policies to force companies to comply with their environmental standards. Education and campaigning to change the mindset of the people towards the environment would be within their means as people are generally more educated and aware.

Businesses could practise corporate social responsibility, and stand to gain since green consumers are more likely to purchase their products. Consumers are more concerned with the origins of their products they buy today. As such, MNCs could influence these green consumers to raise awareness about environmental issues using their products.

Individuals could make a difference by starting with themselves first. A small step could go a long way such as supporting Earth Hour or even car pooling.

NGOs no doubt would have more political clout than individuals, and do not have the same restrictions that are placed upon government agencies. They do not have to balance certain commitments such as the living standards in the country. This would result in them having greater flexibility when it comes to their operations and should be able to achieve more. \

Developing countries

Governments have the sole responsibility for the enactment and enforcement of policies to protect the environment. Unfortunately, their main priority is to ensure economic growth rather than the protection of the environment. Developing countries are more likely to have unstable government and corruption is usually rampant making it difficult to care for the environment. E.g Shell engaged in dodgy/shady dealings with the government officials in Nigeria in order to gain a foothold in the country.

Businesses are usually in the primary and secondary sector which focus on the harvesting of raw materials and manufacturing. These are highly damaging to the environment as the mining process results in large amounts of pollutants and waste. Many of their factories are owned by MNCs, and they would have little say in the production methods used.

Individuals concern would be to earn sufficient money to stay alive, they would not mind harnessing the earth for the raw materials or resorting to more efficient methods of clearing the land if they could help to save some money for them.

Considering the situation in both developed and developing countries, who do you think should be responsible for the environment?

Post-Results 2016

Post-Results 2016

Chemistry, JC Chemistry, JC General Paper, JC Mathematics, JC Physics, Mathematics, Studying Tips, University Mathematics

Let’s face it. Some of us will not get the dream results we want. Don’t give up and let fear conquer you.

For students unsure of the available courses, they can check out the following post. It contains the grade profile for local universities.

Our Team will be here if you need help/ advice. Feel free to text us.

P.S. Today, I saw an image shared by Mr Wee, which said that “You’re the architect of your own life”. So let’s not let the grades define us.

In times of economic hardship, should a country still be expected to provide financial or material aid to others?

In times of economic hardship, should a country still be expected to provide financial or material aid to others?

JC General Paper

Students are expected to address the criteria of this question throughout the essay; it being in times of economic hardship. For a quality essay, the terms “should” and “expected” should be addressed as well. For instance, a country should still give aid, but perhaps not be expected at a time when its survival is in question, and it does not have a healthy budget balance.

Financial aid- capital/loans/money

Material aid- manpower/distribution of basic goods and necessities

  • Provision of aid during economic hard times could be a political statement and commitment to the recipient country, helping to foster greater political relations in the long term. Giving of aid should be expected especially if the recipient country needs it more than the donor country. Such circumstances could be when the recipient country is facing civil war and there is urgent need of aid to cease the fighting etc. Another possible instance could be during times of natural disasters/emergencies. Also, for most of the donor country, aid takes up a small portion of their budget, hence it should not affect the current economy severely even if the country continues to give out aid during hard times. Aid accounts for 0.5% of the US budget yearly.
  • Governments should be responsible and accountable to their citizens first especially during hard times, hence aid should be allocated domestically rather than elsewhere. The dollar votes of the citizens and their voices are important, and it is only right that countries should be concerned with their own self-preservation before others. After all, an economically prosperous country will then be able to contribute more to the international community, rather than a slow and stagnate economy that is facing difficult times.
  • Perhaps a country should look at other means of support, rather than the provision of aid during bad times. It is presumptuous to assume that aid helps to alleviate the problems faced by the recipient countries. Often, aid may actually harm local industries and foster this sense of self-entitlement and dependency on the donor nations.
  • Legal obligations under international law could possibly bind countries to continue giving aid to another country. A short term economic difficulty does not suffice to repudiate this commitment, especially when contracts have been signed beforehand, and the donor country may risk ruining their legitimacy and international standing.

In dire situations, countries should still continue to give aid to one another. However, expectations to scale down in terms of aid is definitely reasonable and justifiable.

How far has modern technology made it unnecessary for individuals to possess mathematical skills?

How far has modern technology made it unnecessary for individuals to possess mathematical skills?

JC General Paper
  1. How far has modern technology made it unnecessary for individuals to possess mathematical skills?

Argument 1: Modern technology has provided us with tools that automate mathematical operations for us, making possessing mathematical skills redundant.

Elaboration: All we have to do are to insert the data we want to be processed into our modern technological tools, and their software automates the required operations and calculations for us, allowing us to attain the necessary processed data effortlessly.

Example: Calculators has made skills such as the ability simple mental calculations mostly redundant in everyday life. Online free tools such as desmos and Wolframalpha. Paid tools such as MatLab, Maple and R.

Link: Modern technology has provided us with tools that make certain mathematical skills such as doing simple mental calculations seemingly redundant.

(Counter) Argument 2: We still ultimately require mathematical knowledge and skills to utilize these technological tools

Elaboration: To say that possessing mathematical skills is unnecessary altogether would be too much of a far-fetched statement

Example: We still require intermediate knowledge on math to effectively operate a Graphic Calculator for more complex math problems. Basic knowledge for syntax used in programs in Graphic Calculator, or algorithm is needed.

Link: Mathematical skills are still required to allow modern technology to operate in our favor.

(Counter) Argument 3: Recognizing patterns, reasoning and logical thinking are important life skills which are largely mathematical.

Elaboration: These life skills are largely inculcated into our children via an education in mathematics.

Example: Number or shape pattern recognition is a skill inculcated into primary school children via math education. Over the years, this analytical skill is honed and eventually applied to solve industry-relevant problems such as market trends. Famous Hedge-fund owner James Simmons, only hires Mathematicians and Physicists, who do not need any business or banking background, to work as bankers in his company, Renaissance Technologies. The top Quantitative Analyst in the world has a doctorate in Physics and to quote him, in research he deals with 23 variables, but now in life and finance, he just has 3 to handle.

Link: Mathematical skills are a prerequisite to develop higher level cognitive and analytical skills in order for us to excel in society.

(Counter) Argument 4: Being equipped with the most basic Mathematical skills provides us with much greater convenience as compared to having sole reliance on technological tools.

Elaboration: Simple day-to-day activities largely involve the use of mathematical skills and would ironically take a longer time and effort if we were to fully rely on technological tools. Moreover, it would be a hassle if we were to require such tools to physically be with us all the time as compared to solving problems on the spot with our mathematical knowledge.

Example: Mental calculations would greatly aid us in buying and selling as opposed to solely relying on a calculator even for simple operations. The absolute necessity of having a calculator around with you would often times become a hassle in that case. The basic skill of doing rough mental calculations and pattern recognition would enable us to have greater control over our finances in estimating and analyzing our spending habits and saving progress.

Back to the A’levels H1 General Paper 2016 Paper 1 Solutions

‘Everyone has an opinion, but not everyone’s opinion is of equal value.’ What is your view?

‘Everyone has an opinion, but not everyone’s opinion is of equal value.’ What is your view?

JC General Paper

‘Everyone has an opinion, but not everyone’s opinion is of equal value.’ What is your view?

Define opinion and its purpose.

An opinion is a view or judgment formed about something, not necessarily based on fact or knowledge. Opinions are predicated on the individual’s current understanding and analysis of perceived phenomena, and its dynamic nature brings value and meaning to the uniqueness of individuality and colorful context to otherwise mundane events.
Thesis statement

While everyone has an opinion and every opinion should be given fair amount consideration in order for society to best function and cater to the interest of every individual as much as possible, the harsh truth remains that not everyone’s opinion is of equal value. Firstly, opinions predicated upon evidence are more reliable to derive inspiration from compared to one which manifests purely from emotions and personal bias. Secondly, psychological bias renders the notion that everyone’s opinion holds equal value and be given the same amount of consideration to be impractical. Hence, everyone has an opinion and is indeed entitled to have one, but not everyone’s opinion is of equal value for society.

(Counter) Argument 1:
Every opinion should be equally considered in order for society to best function and cater to the interest of every individual as much as possible

Elaboration: The conscious societal effort to hold everyone’s opinion with equal regard protects the interest of every individual, especially of those from minority groups. If we were to disregard opinions which do not interest the majority of us, it can lead to immoral and biased behavior, policies and consequences.

Example: Severe racism against blacks in the US in the past was due to the majority group’s absolute lack of consideration of opinion and interests of the perceived minority group.

Link: Every opinion should be carefully regarded in order for society to not neglect the interest of certain groups in the midst of societal progress.

(Counter) Argument 2:
Every individual is unique and as valuable, and hence every opinion carries a perspective that has their own distinct and equal value which should not be ignored.

Elaboration: Based on the premise that “all lives are equal”, all opinions should be equally considered as every opinion represents a distinct and unique individual who is as valuable as another.

Evidence: In a democratic government, every vote from every eligible individual is considered and carries the same weight, acknowledging the notion that every individual citizen is of equal value.

Point: Every opinion matters as every individual is unique.

Argument 3:
Informed opinions hold more meaningful value

Elaboration: “You are not entitled to your opinion. You are entitled to your informed opinion. No one is entitled to be ignorant.” – Harlan Ellison

Opinions predicated upon evidence are more reliable to derive inspiration from compared to one which manifests purely from emotions and personal bias. Opinions direct societal progress, and hence informed opinions lead to more informed decisions which would allow society to function and develop in its best interest.

Example: In the political context, a deep understanding of politics and the local political scene would compel the informed citizen to support the most capable political party. This informed opinion leads to be more logical and rational political vote which brings great positive value to the country, as opposed to having disgruntled citizens angrily voting for political parties which capitalize on emotions without decent consideration for practicality.

Link: Informed opinions is of greater value than uninformed ones.

Argument 4:
Personal bias renders the notion of everyone’s opinion holding equal value impractical

Elaboration: Opinions generate the greatest amount of real tangible value when they resonate with the masses. And the extent of how well an opinion is received by the masses is influenced by psychological bias driven by factors such as age, the perceived credibility and prestige of the opinion-bearer and how well that opinion aligns with our own personal beliefs.

Example: In the campaign for gender equality, it is evident that Emma Watson’s efforts hold greater influence and are held in higher regard than most people who have been essentially advocating and saying the same thing. This is the reason why charities tend to tap onto the prestige of celebrities to amplify their impact.

Link: It is impossible for everyone’s opinion to be genuinely held with equal regard due to personal bias.

Back to the A’levels H1 General Paper 2016 Paper 1 Solutions