As we all know, essay questions on poverty are usually popular among students. It is an easy topic that usually asks about the reasons for poverty, whether this issue can be resolved, and whether people are poor due to their own personal failings.

With that, let’s take a look at some of the reasons why ppl are poor… Of course, one has to understand that world developments are not even, and that there is a need to discuss both relative and absolute poverty, and to differentiate reasons for poverty in the first and the third world.

First world context: Poverty can always happen due to the inability to keep up with the high cost of living, personal failings such as being lazy, engaging in vices such as gambling or being addicted to alcoholism, external and unfortunate circumstances such as racial discrimination, being afflicted with a terminal illness or even being born with disabilities that cut one off opportunities

Third world context: Poverty in this sense would be in absolute terms, define to be living less than USD1.25 a day. Reasons could be due to corruption of government, presence of incompetent government that could not harness the resources of the place efficiently, cultural stereotypes such as the caste system that entraps people’s minds, natural disasters and even the presence of war.

As we could see, the reasons for why an individual is poor are aplenty.  Could we possibly say that one is poor due to their own failings? Poverty is a very complex and entrenched problem that we see in our world today, it is systemic and could possibly take generations to eradicate it. At times, an individual could also be powerless to deal with the situations that they are born into. Thus, to what extent is really poverty the fault of an individual?

For societies that follow a fair and meritocratic system, should we take on a more compassionate and humane approach towards people who are poor?

Let me know what your thoughts are on this issue! I would love to hear from you 🙂

### June Crash Course

The team at The Culture SG has been really busy and we have a lot of things prepared to help you guys work for that A. First up! Crash course for June…

And we know it is a bit late to be announcing this on the site now, but we have really been caught up with preparing our students lately that we don’t have the time to properly update here. So here are the details for the Math Crash Course and the Chemistry Crash Course.

P.S. For SCIENCE students who wish to chiong in October, please take note that the H2 Chem/ Phy/ Bio Paper 4 (practical) is in October. So better start soon! Here are the details!

Click to view

For 3 hr lessons, they are priced at $105. For 2 hr lessons, they are priced at$70.

Lessons will be held at:
Newton Apple Learning Hub
Blk 131, Jurong Gateway Road #03-263/265/267 Singapore 600131
Tel: +65 6567 3606

For math enquiries, you may contact Mr. Teng at +65 9815 6827.

For chem enquiries, you may contact Ms. Chan at +65 93494384.

For GP enquiries, you may contact Ms. Chen at +65 91899133.

### Population problems eventually solve themselves-government meddling only makes things worse. Discuss

Government intervention solves population problems such as population decline, which will be left unresolved if left to the masses. With a preference for smaller families and a general unwillingness to start a family in today’s modern society, negative or zero population growth often ensues. These have detrimental impact on affected countries, such as a fall in tax revenues, a smaller workforce and a high dependence of an ageing population on the working population. As these socioeconomic perspectives are entrenched in the minds of young urban professionals, these population problems are incapable of eventually solving themselves. In this case, government intervention is beneficial. In developed countries like Italy and Spain, where fertility rates stand at a meagre 1.25, new generations are unable to replace past generations thus leading to population decline. The implementation of pro-natal policies could possibly help to increase the incentive for couples to procreate and boost total population numbers. Implemented measures include longer maternity and paternity leave in Switzerland, as well as cash incentives in Singapore. Another method of boosting population growth is through the relaxation of immigration policies, which allows for an influx of permanent residents.

Population problems such as the rampant spread of diseases are also combated more efficiently and effectively through government intervention. If left to solve by itself, this results in a higher death toll and increased spread of illnesses. The successful results of government intervention is exemplified through the World Health Organization and governments’ collaboration to wipe out smallpox, which was deadly enough to kill one in every four infected persons. With public health measures to increase hygiene standards and mandatory vaccinations, smallpox was eradicated worldwide in the 1800s.

Despite the effectiveness of government intervention in solving population problems, some policies and measures undoubtedly create new problems for countries. Firstly, policies to reduce overpopulation are often successful to the extent that they eventually lead to population decline. This is evident in Singapore, which, due to the overwhelming success of the “stop at two” policy, currently faces a replacement rate of 1.25. This has led to national concerns of unsustainable population growth and the possibility of a population decline in the near future. Furthermore,  the policy of migration to solve population problems has led to social segregation in some countries.

### Thinking [email protected] #2

[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

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

### Thinking [email protected] #1

[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.

### Deriving integration formulae

Some inquisitive students have asked me before, how the MF15 integration formulas come about. I thought I should share it too then.

So we want to $\int\frac {1}{\sqrt{4-x^2}}dx$ and yes, we know the formula can be plugged directly… but what if we want to avoid the formula. Now actually, the trick here involves your trigonometry identities, along with substitution methods. We have a $sin$ here, so we only know one trigo identity that involves $sin$ and that is $sin^{2}x + cos^{2}x = 1$. Hmmm, so my approach here will be to let $x=2cost$. We will see shortly why I chose to put a 2 and that using $cost$ or $sint$ will make no difference. You can try them yourself!

lets first find that $dx=2sint dt$

$\int\frac {1}{\sqrt{4-x^2}}dx= \int \frac {1}{\sqrt{4-4cos^{2}t}}(2sint dt)$

If you notice, this explains why there is a need for us to introduce $2cost$ instead of just $cost$.

Having $4-4cos^{2}t$ allows us to simplify it to $4sin^{2}t$

We have $\int \frac{1}{\sqrt{4sin^{2}t}}(2sint dt)=\int\frac{1}{2sint}(2sint)dt=\int1dt$

Finally, $\int1dt=t+C = sin^{-1}(\frac{x}{2}) + C$

That was long! But i hope it give you some insights to the formulas.

### Integrating Trigonometric functions (part 4)

We shall now proceed to integrating $secx$ and similarly, lets refresh the formulas we should know.

$\frac {d}{dx}tanx = sec^{2}x$

$\frac {d}{dx}secx = secxtanx$

$\int tanx dx = ln|secx|+c$ (MF15)

$\int secx dx = ln|secx+tanx|+c$ (MF15)

$\int sec^{2}x dx = tanx+c$

$\int sec^{3}x dx = \int secx(sec^{2}x)dx = \int secx(tan^{2}x+1)dx = \int secxtan^{2}x+secx dx$
So how do we $\int secxtan^{2}x dx$? I’ll first rewrite it as $\int (secxtanx)(tanx)dx$ for some insights.

We can’t adopt the $\int f'(x)f(x) dx$ method here. So, Integration by parts?

$\int (secxtanx)(tanx)~dx$

$= secx(tanx) - \int secx(sec^{2})~ dx$

$= secxtanx-\int sec^{3}x~dx$

Wait! $\int sec^{3}x dx$ again? hmmm.

So we have that

$\int sec^{3}x ~dx$

$= \int secxtan^{2}x+secx ~dx$

$= secxtanx-\int sec^{3}xdx + \int secx ~dx$.

Then with a bit of juggling and manipulations, we have

$2\int sec^{3}x dx = secxtanx + ln|secx+tanx|+c$.

I do hope this gives you some insights. You should try $\int sec^{4}x dx$ on your own using the information here.

### Integrating Trigonometric functions (part 1)

Integration is topic that eludes several students. Many think that its those “you either see or don’t” topic. But its all practice and a bit of tricks. Let me touch on integrating trigonometric functions first and we shall start with $sinx$

$\int sinx dx = -cosx + c$

Easy!

$\int sin^{2}x dx$

This requires double angle formula: $sin^{2}A=\frac{1-cos2A}{2}$

$\int sin^{2}x dx = \int\frac{1-cos2x}{2}dx = \frac{1}{2}(x-\frac{sin2x}{2})+c$

$\int sin^{3}x dx$

Here we introduce trigo identity: $sin^{2}x + cos^{2}x = 1$

$\int sin^{3}x dx = \int sinx(1-cos^{2}x)dx= \int sinx - sinxcos^{2}x dx$

Here we have a problem! $sinxcos^{2}x dx=?$

Notice that $sinx$ is the derivative ($f'(x)$) of $cosx$.

So $sinxcos^{2}x dx=\frac{-cos^{3}x}{3}+c$.

Finally, $\int sinx - sinxcos^{2}x dx = -cosx + \frac{cos^{3}x}{3}+c$

$\int sin^{4}x dx = \int (sin^{2}x)(sin^{2}x) dx$

Here we can apply double angle a few times to break it down before integrating.

So if you notice, this is essentially like an algorithm, and as the power increases the treatment is really quite similar.

Let’s look at $cosx$ in the my next post!