### Integration By Parts

Today, I’ll share a little something about Integration by Parts. I want to share this because I observe that several students are over-reliant on the LIATE to perform Integration by Parts. This caused them to overlook/ appreciate its use.

Lets start by reviewing the formula for Integration by Parts

$\int v \frac{du}{dx} ~dx = uv - \int u \frac{dv}{dx} ~dx$

I like to share with students that Integration by Parts have two interesting facts.

1. It allows us to integrate expression that we cannot integrate. Eg. $\text{ln}x$ or inverse trigonometric functions. This is also closely related to how LIATE is established.

2. This is closely related to point 1. That is, instead of trying to integrate the expression, we are differentiating it instead. And that itself, is a very important aspect.

Next, I like to point out to students that LIATE is a general rule of thumb.
GENERAL – because it does not work 100% of the times. And today, I’ll use an example to illustrate how LIATE actually fails.

$\int \frac{te^t}{(t+1)^2} ~ dt$

Here we observe two terms $\frac{t}{(t+1)^2}$ and $e^t$. Going by LIATE, we should be differentiating $\frac{t}{(t+1)^2}$ and integrating $e^t$.

$\int t^2 e^{t} ~ dt$
$= \frac{t}{(t+1)^2} e^{t} - \int \frac{(1)(t+1)^2 - t(2)(t+1)}{(t+1)^4} e^t ~dt$

Now observe what happened here, after applying integration by parts, it got “worst”. We are stuck to integrating $\frac{(1)(t+1)^2 - t(2)(t+1)}{(t+1)^4}$ with an exponential… This should raise some question marks. But we did follow LIATE.

I’ll leave students to try out this on their own. And feel free to ask questions here. Have fun!

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

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.

### 2016 A Level H2 Physics (9646) Paper 1 Suggested Solutions

All solutions here are SUGGESTED. Casey will hold no liability for any errors. Comments are entirely personal opinions.

1. B
2. C
3. B
4. D
5. D
6. C
7. D
8. D
9. B
10. C
11. A
12. D
13. D
14. C
15. C
16. A
17. D
18. A
19. B
20. D
21. Question 21 is a flawed question. When unpolarised light goes through a polarizer, the I is halved while the A is reduced by a factor of root 2. But based on the information Cambridge provides, the answer is C.
22. D
23. D
24. C
25. C
26. B
27. C
28. A
29. B
30. B
31. A
32. C
33. D
34. B
35. B
36. B
37. D
38. C
39. C
40. C

Note to all: Casey will not respond to most of the comments as he is busy. You may contact him by SMS at  +65 9474 5005 if you have a burning question.

Feel free to explain the answers, if you are confident. Many thanks.

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

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.

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### ‘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?

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.

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### ‘Countries experiencing conflict should be left to sort their own problems.’ How far do you agree?

‘Countries experiencing conflict should be left to sort their own problems.’ How far do you agree?

Question analysis- definition of key terms

Experiencing conflict: having issues dealing with domestic problems such as human rights; civil war; poverty

Left to sort: They should be left on their own terms to deal and resolve their own problems. There is no need for foreign intervention.

Assumption: The nation would know best in the reasons for their own conflicts, and that they would be the best person to resolve them. If the conflicts are really too complex and out of hand, then the countries should appeal for help on their own to the international community. Sovereignty of the state should be recognized at all costs and never to be infringed upon because the intervening state could abused and exploit the citizens.

To do well for this question, students need to consider the situations in which it is alright for the international community to come in to settle problems and even conflicts for the country. What are certain circumstances in which the sovereignty of the state could be violated? Also, students need to balance this against why the country itself should deal with their own problems and what are certain problems that intervention could possibly bring about.

Yes they should be left to sort their own problems

• Intervention by foreign powers could be for their own self-interest and they could end up exploiting the local people given their intervention. Very often, these foreign powers have an agenda for intervening in the country and due to past historical baggage, they could possibly take revenge on the locals.
• Intervention by foreign powers could bring about more problems than it solves. Intervention could possibly backfire especially if the peacekeeping troops choose to take sides in the conflict or try to impose their resolution on the people. Also, it is very difficult for an external power to understand the local situation and context of the place especially if the conflict is religious and racial in origin.

No they should not be left to sort their own problems

• They should not especially if the state is committing human rights issue/genocide on the local people and this would require the intervention of the international community. In fact, once the state commits act of terror against its own citizens, they could be seen to be violating the citizens’ trust and rights as a legitimate government. As such, they should be taken to task by the international community. For instance, the UN has been criticized for intervening late in the Rwanda and Cambodian Crisis resulting in massive deaths.
• In times of humanitarian crisis and disasters that could potentially snowball into a conflict, it is only right that the international community comes in to help them, especially after they have made a formal request. This is to ensure that they do not violate the sovereignty of another nation in the process. The country should not be left to settle their own.

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### Is competition always desirable?

Is competition always desirable?

Defining competition

The activity of striving to gain or win something by establishing superiority over others, competition is highly prevalent in today’s fast paced and at times seemingly unforgiving society.

To do well for this question, there is a need to compare the benefits of competition to collaboration. Which one is actually more desirable? Students can approach this question from a cross country comparison, and decide which country culture is actually more inclined towards competition and which country is towards collaboration.
Thesis

It is true that competition can be unhealthy as it inevitably invokes stress, which in healthy amounts has the potential to not only decrease morale but also productivity. Some may also suggest that an overly competitive mindset deters collaboration and hence may even compromise on potential outcomes. However, I hold my stand that competition is mostly desirable. Competition compels us to work harder and strive further, empowering us to achieve levels of productivity and achievement which would otherwise be impossible. Also, competition ensures that the leaders who govern the way we live and consume products are optimal and behave in the best interest of society. As pointed out by Vince Lombardi, “Winning isn’t everything, but wanting to is.” As long as one does not get too fixated on the idea of ‘winning’, a healthy competitive mindset would most definitely generate the best results.

(Counter) Argument 1
Critics argue that competition can be unhealthy as it inevitably invokes stress which has the potential to not only decrease morale but also productivity.

Elaboration: This is in fact true, as an unhealthy obsession and mindset towards competition can prove to be counter-productive and ironically compel us to underperform. Rather than focusing on doing one’s best, an obsessive fixation on eventually winning and being the best is an unhealthy way to compete. The pressure to win rather than optimize the learning experience distracts individuals from placing full emphasis on doing quality work and bitterness with the knowledge that others may be currently ahead of them lowers morale which would in turn lower productivity.

Example: In Singapore’s highly competitive educational landscape, more and more students are being subject to psychological disorders as they are unable to cope with the mindless scramble to outcompete their fellow batch mates. Evidently, such unhealthy levels of stress has impeded their learning capabilities and has defeated the purpose of healthy competition altogether.

Link: Competition can become undesirable if the environment and competitive mindsets become too hostile and unhealthy.

(Counter) Argument 2
Some may also suggest that an overly competitive mindset deters collaboration and hence may even compromise on potential outcomes.

Elaboration: This is based on the premise that rather than trying to out compete each other, people should gather their resources, knowledge and talents together and achieve a better outcome via collaboration, especially if they are after the same mission. This results in lesser resources spent collectively to achieve the same goal.

Evidence: In the search for a cure for cancer, two of the world’s largest pharmaceutical companies, Pfizer and Merck, have entered a strategic partnership. The two competitors will pool resources in order to bring new cancer treatments to market faster.

Link: Collaboration is more desirable than competition in some cases.

Argument 3
Competition can empower us to achieve higher levels of productivity and achievement which would otherwise be impossible

Elaboration: Competition, by compelling us to set our competitors as standards to beat, constantly sets new feasible and progressive benchmarks and milestones for us to overcome. Empowered by a heightened sense of motivation to work harder in order to not fall behind the rest, we naturally do and achieve more.

Example: In the past, American miners had produced two tons of iron ore per hour for decades. When Brazilian iron ore suddenly became cheap enough to import in 1982, everything changed. In the span of five years, the miners doubled their productivity to four tons per hour.

Link: Competition is desirable as it increases productivity.

Argument 4.
Competition ensures that the leaders who govern the way we live and consume products, be it in politics or business, are optimal and behave in the best interest of society.

Elaboration: As one would have to emerge victorious from stringent competition in order to receive the recognition necessary for one to be considered a true winner, the product of competition would be of the highest caliber possible and would have to function to society’s best interest.

Example: Highly evident in business, companies continue to relentlessly work hard to outcompete competitors by delivering the highest quality goods and services at the lowest possible cost. The consumer benefits from such competition, as the majority are inclined to purchase from the leading and most worthy competitor.

Link: Competition is desirable as it ensures optimum output and influences business and political leaders to function at society’s best interest.

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

### Assess the view that most natural disasters are the result of human activity.

Assess the view that most natural disasters are the result of human activity.

Question analysis-definition of key terms

Natural disaster: Floods, landslides, tsunami,

Human activity: Deforestation, increasing urbanization, the pursuit of economic growth and the refusal to use environmentally friendly products

Assumption: Natural disasters today are on a very frequent and common basis, so much so that it is not seen to be in the natural state of things. Also, our impact on the environment is said to be more damaging and more exponential compared to before, resulting in these natural disasters.

This is a very simple and straightforward question for this year. Students just need to know the reasons and origins for the occurrence of natural disasters. They should attribute some of the reasons to man-made reasons and some to the natural state of how things are. I would expect most of the geography students to be doing this question due to their expertise.

Yes most natural disasters are man-made

1. Our human-related activity and our growing reliance on technology, and increasing levels of pollution actually leads to greater occurrence of natural disasters. A case in point would be the London Great Smog of 1952, where the city was overly polluted and covered in smog due to the rapid industrialization. It blanketed the whole street and killed at least 4000 people. Another instance would be the dust bowl, where decades of farming without bothering to rotate crops actually lead to the depletion of the top soil. It was considered one of the biggest ecological disaster in the history of the US, where dust storms consumed the entire communities from the South to the Midwest, forcing a lot of people to relocate in the process.
2. Most natural disasters today like floods and landslides are actually the making of human activities such as repeated construction and drilling of the land. Singapore is one nation that is relatively blessed not to have any natural disasters, however in recent years, she has been plauged with some flooding. A lot of these flooding have been attributed to the rapid construction that she has been doing over the years, especially in terms of building MRT. It is also arguable that the tsunami in Japan was caused by man actions of negligence over the nuclear reactor plants rather than just nature activity in itself.

No they are not due to man’s actions

1. A lot of natural disasters are still due to the earth’s mechanism rather than man actions themselves. For instance, earthquakes and volcanic eruptions are due to the earth’s tectonic movements and seismic activities. Of course, it is undeniable that underground mining is able to affect and cause instability that results in these earthquakes.

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### Evaluate the claim that equality of opportunity for females is a desirable, but unrealistic goal.

Evaluate the claim that equality of opportunity for females is a desirable, but unrealistic goal.

Question analysis-definition of key terms

Equality of opportunity: same chances to succeed in all aspects of life

Desirable: beneficial not just to the women, but towards the larger society as a whole

Unrealistic: impossible task to achieve; just a dream only

Assumption: This question assumes that giving women the same opportunities as men, would help to elevate their social status and position in society. However, this is too idealistic a scenario and that it is impossible to treat everyone in the same way. Inequality is part and parcel in our lives today.

To do well for this question, students need to consider why giving women the same opportunities are desirable to society. What are some aspects of society that would benefit from this and how would it improve and elevate the status of women overall? Also, students need to consider why is this goal unachievable? Could it be due to the women’s individual circumstances and context or could it be the larger external environment that is preventing this from occurring? Students should also realized that this is a matrix question and that they could answer this question from various angles: desirable and unrealistic; not desirable but realistic; not desirable and unrealistic and undesirable and unrealistic.

Yes it is desirable but unrealistic

• Feminist groups have not made much headway in the championing of women rights and the equal opportunities in terms of treatment for them. This is largely because these groups have been fighting for women’s rights by basing on men’s terms. Most women are also not strong supporters of these feminist groups as a result.
• It is impossible to accord everyone equal opportunities in this world, especially since inequality is something that is inherent. Every individual would have different conditions and abilities and hence it would not make sense to give someone the same opportunity. Biological differences could be one big factor as to why equality of opportunities are not given to women in industries that need more physical work and in the sporting arena.

No it is desirable and realistic

1) Increasing presence of women rights movements and organizations that help to champion the rights of the women, and to ensure that equal opportunities are given to them increasingly. These feminist movements have made headways especially in the developed nations such as Singapore with AWARE. For instance, AWARE champions equal opportunities at work and promotion. The employers could be taken to task if they are found to have dismissed a female staff inappropriately due to her being pregnant and needing to pay maternity leave. These feminist organizations have also outlawed discrimination against women and champion equal opportunities in terms of schooling for them, as a first step towards empowerment especially in the developing world.

2) It is desirable as greater empowerment of women would mean that the world would be progressing towards greater respect of rights and be more accepting of women’s leadership. It is increasingly realistic as people are more educated and do not believe that only men are able to lead people due to “manly traits”. There are influential men who champion women’s rights and feel that there should be equality of opportunity such as Obama. Such influence though may take a long time, but they will gradually be more realistic in time to come.

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### ‘People who do the most worthwhile jobs rarely receive the best financial rewards.’ To what extent is this true in your society?

‘People who do the most worthwhile jobs rarely receive the best financial rewards.’ To what extent is this true in your society?

Question analysis- Definition of Key Terms

Most worthwhile jobs: occupations that are mostly serving the needs of the people for a very humanitarian and altruistic purpose. Such instances would be social workers, nurses, teachers, counselors, social entrepreneurs

Best financial rewards: In terms of monetary recognition, status and power in society.

Assumption: Jobs that are the most rewarding to one’s soul and conscience are not regarded highly in Singapore Society as people expect them to do it from their hearts, rather than to get a monetary reward for their good and charitable acts.

To do well for this question, students need to expand the scope of what it means to do ‘worthwhile jobs’. Could certain jobs that pay very highly not be seen to be worthwhile such as entrepreneurs, doctors, lawyers and even accountants? Are these jobs just regarded to be a ‘money-making’ occupation? Students should consider a variety of occupations and see how each and every single occupation is actually worthwhile in terms of their impact to society. No jobs should be seen to be above another just because it pays higher in terms of monetary value. That would be too narrow a perspective to take, since not every job contribution can be measured in a tangible manner.

Yes they rarely receive the best financial rewards:

• Jobs that tend to have a social impact in society are regarded lowly and viewed by locals to be charitable and should not be monetized as much. The ‘pureness’ of these jobs would be lost if money comes into place, since the individual could be tainted by monetary needs rather than the original aim of serving the larger community. For instance, jobs like counseling should be from the heart and empathy should be the driving force of why an individual would like to pursue this career rather than for the monetary incentive. Such jobs would only be able to attract the best and those who are the purest in intent to serve if monetary incentive is not present as a huge driving force.
• It is difficult to put an economic value or even to monetize all the skills needed for jobs that tend to be very people centric and focus. Certain things that a teacher does in her job would be hard to put a consistent monetary value on it. For instance, a teacher’s impact on a child’s development could be lifelong and this impact varies according to each child. It would be unreasonable to put an economic value on this impact since the impact can only be seen in the longer future or even after the teacher has retired from her profession.

No they receive the best financial rewards:

1) Some of the most rewarding jobs in terms of making a large contribution to society to save lives and to uphold justice pay and reward one handsomely in Singapore’ society. Doctors, lawyers and accountants are paid very highly here largely due to the demand and direction of the economy and the technical expertise needed for these jobs. It is not so much because these jobs are seen to be less altruistic or lesser in impact in serving the needs of the people. These jobs have to be paid highly in order to ensure the advancement of the sectors involved, so that their impact can be on a larger scale. For instance, doctors have to be paid highly so that the medical industry can attract the best and the brightest to serve the needs of the people, and to continually innovate and research for the best medicine to save lives. Medical technologies are expensive and it would only make sense if doctors are paid highly enough for them to want to improve the existing system.

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