### Differentiation Question #1

Given that $y = \frac{8}{x^3} - \frac{6}{x^2} + \frac{5}{2x}$, find the approximate percentage change in $y$ when $x$ increases from 2 by 2%.

### Probability Question #4

A gambler bets on one of the integers from 1 to 6. Three fair dice are then rolled. If the gambler’s number appears $k$ times ($k = 1, 2, 3$), he wins $$k$. If his number fails to appear, he loses$1. Calculate the gambler’s expected winnings

### Vectors Question #4

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.

### Vectors Question #3

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.

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.

### A little reminder to students doing Calculus now

When $\frac{dy}{dx} = 0$, it implies we have a stationary point.

To determine the nature of the stationary point, we can do either the first derivative test or the second derivative.

The first derivative test:

Students should write the actual values of $\alpha^-, \alpha, \alpha^+$ and $\frac{dy}{dx}$ in the table.

We use this under these two situations:
1. $\frac{d^2y}{dx^2}$ is difficult to solve for, that is, $\frac{dy}{dx}$ is tough to be differentiated
2. $\frac{d^2y}{dx^2} = 0$

The second derivative test:

Other things students should take note is concavity and drawing of the derivative graph.

### Responsibility of Protecting the Environment

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?

### Vectors Question #2

If $c = |a| b + |b| a$, where $a$ , $b$ and $c$ are all non-zero vectors, show that $c$ bisects the angle between $a$ and $b$.

### Post-Results 2016

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.

### Things to note for 9758 H2 Mathematics

It has been awhile since the A’levels. We talked and met up with several of our students. Some students are working and some are preparing their Personal Statements for overseas University Applications.

A few of them also remarked that they wish they put more efforts into studying A’levels.  An advice to this year JC2 – Do not wait till it is too late.

Students should also have a clear understanding of their syllabus, especially their scheme of exam. I still have JC2s this year who get stunned by the applications questions I threw at them (P.S. Aside from spending time with family, I wrote many sets of applied questions.). You may read more about your syllabus here. Or see the following images.

How much practice or emphasis your school put on this, is up to them. But it is clear that application takes up 25% of your marks. The entire syllabus can be found here.

PLEASE DON’T WALK INTO THE EXAM HALL BLUR BLUR…

### Release of A’levels Results 2016

For students who took A’levels in 2016, please note that information for the release of A’levels Results 2016 can be found in the following!

Release of A’levels 2016

Grade Profile (i.e. Number of As you need to get into courses for)

SMU

NTU

NUS

P.S. Results does not define you. When one door closes, another opens.