### A-level H2 Mathematics (9758) Suggested Solutions (2017)

Here is the suggested solutions for H2 Mathematics (9758). They are all typed in LaTeX, so if it does not render, please leave a comment and let me know. Thank you.

The suggested solutions for H2 Mathematics (9740) is here.

Students of mine should obtain the modified A’levels Paper, and the solutions to the additional questions can be found here.

Year 2017

MF26

### Thoughts on H2 Mathematics (9758) 2017 Paper 1

This is a new syllabus and this is the first time it will be tested. Personally, I don’t think it will be easy and students should not underestimate this upcoming A’levels. And I’m referring to the A’levels, on the whole. We saw how the Science Paper 4 were… unexpected.

The new H2 Mathematics (9758) syllabus has several topics removed, and these were mostly topics that were “drill-able”, aside from complex numbers. The new syllabus added in mainly, new integration forms, focus on parametric Equations with Cartesian equations, and of course, Discrete R.V. But let us leave the statistics out.

Students should familiarise themselves with the trigonometry Formulae in MF26. There are several topics that can be linked up with trigonometry, makes me wonder why it isn’t a chapter by itself. Complex numbers has a trigonometry form too, so make sure students know how to manipulate it, given the trigonometry Formulae.

Next, students should understand the use of Maclaurin’s. What does it mean for $x$ to be small, and the implications when they say $h$ is small compared to $R$… And also finding the general term of a Maclaurin’s Expansion.

It won’t hurt to review how to find the Area using Shoe-lace method. And not forgetting our Sine Rule and Cosine Rule.

Do know how to prove a one-one function… Non-graphically. (i.e. not using the Horizontal Line Test)

Do know that the oblique asymptote of $f(x)$ becomes $y=0$ when we do the $y = \frac{1}{f(x)}$ transformation too.

Lastly, students must READ really carefully and discern every information. Having marked many scripts, many students do not read carefully and lose marks here and there. And they do add up… Be alert and read, take note of the forms that they want. Here are 10 little things to take note when you read the question.

1. Cartesian/ Polar/ Exponential for complex
2. Scalar/ Parametric/ Cartesian for vectors
3. Set/ range/ interval of values
4. Algebraically => show all the workings without a GC.. usually discriminant, completing the square or maybe some differentiation will be involved.
5. Without using a calculator => show your workings and check with a GC (secretly)
6. Decimal places, etc…
7. Rounding off when you’re dealing with an inequality
8. Units used in the questions, (ten thousands, etc)
9. Rate of change; leaking means the rate is negative…
10. All answers should be in 3 SF UNLESS OTHERWISE STATED. Degrees to 1 DP. RADIANS to 3 SF.

Have fun and all the best!

### Temasek JC GP Prelim Paper 1 2017

Temasek Junior College 8807 H1 General Paper Paper 1 2017

1. Can government surveillance eradicate the threat of terrorism?
2. Examine the claim that globalization creates equal opportunities for all.
3. ‘The government is not doing enough to support local sportsmen in your society.’ What is your view?
4. To what extent is a universal language desirable?
5. Should people in your society be fearful of the future?
6. ‘Graciousness is lost as society progresses.’ Is this an accurate reflection of your society?
7. How far do you agree that technology gives us greater control in life?
8. Consider the view that what is posted online is all talk and no action.
9. ‘Failure should never be acceptable.’ Discuss.
10. Do you agree that only parents should be allowed to discipline their children?
11. Is volunteerism always good?
12. ‘The world today values appearance over substance.’ Is this a fair comment?

### Tampines GP Prelim Paper 1 2017

Tampines Junior College 8807 H1 General Paper Paper 1 2017

1. How realistic is it for your society to embrace diversity?
2. Protecting the environment should be given greater priority than eradicating poverty. How far do you agree?
3. ‘Appearance can be deceiving.’ To what extent is this true of the media today?
4. Discuss the view that smart devices have not made us smarter.
5. Education is the key to solving all social problems. Discuss.
6. Should firms have the responsibility to improve the quality of life of the communities they operate in?
7. Assess the view that literature is of little use to society.
8. Wealth is no guarantee of a better life. How far do you agree?
9. History is of little significance to a modern society. Discuss.
10. ‘Failure is always an option.’ Discuss.
11. A free and unrestricted media is essential for society to progress. How far do you agree?
12. How far is the arts a reflection of your society’s level of development?

### Trigonometry Formulae & Applications (Part 1)

Upon request by some students, I’ll discuss a few trigonometry formulae here and also some of their uses in A’levels. I’ve previously discussed the use of factor formulae here under integration.

I’ll start with the R-Formulae. It should require no introduction as it is from secondary Add Math. This formulae is not given in MF26, although students can derive it out using existing formulae in MF26.

$a \text{cos} \theta \pm b \text{sin} \theta = R \text{cos} (\theta \mp \alpha)$

$a \text{sin} \theta \pm b \text{cos} \theta = R \text{sin} (\theta \pm \alpha)$

where $R = \sqrt{a^2 + b^2}$ and $\text{tan} \alpha = \frac{b}{a}$ for $a > 0, b > 0$ and $\alpha$ is acute.

Here is a quick example,

$f(x) = 3 \text{cos}t - 2 \text{sin}t$

Write $f(x)$ as a single trigonometric function exactly.

Here, we observe, we have to use the R-Formulae where

$R = \sqrt{3^2 + 2^2} = \sqrt{13}$

$\alpha = \text{tan}^{\text{-1}} (\frac{2}{3})$

We have that

$f(x) = \sqrt{13} \text{cos} ( t + \text{tan}^{\text{-1}} (\frac{2}{3}))$.

I’ll end with a question from HCI Midyear 2017 that uses R-Formulae in one part of the question.

A curve D has parametric equations

$x = e^{t} \text{sin}t, y = e^{t} \text{cos}t, \text{~for~} 0 \le t \le \frac{\pi}{2}$

(i) Prove that $\frac{dy}{dx} = \text{tan} (\frac{\pi}{4} - t)$.

I’ll discuss about Factor Formulae soon.  And then the difference and application between this two formulae.

### Let’s talk about money!!! (arts funding)

We all know that arts is a common topic that comes out year after year for the A levels. Should you choose to specialize in this topic, you would need to understand the issues and complexity that come along with state funding of the arts. Of course, funding does come with tangible and intangible benefits and let’s have a look at some of these.

Monetary benefits of funding: the arts put people to work; it attracts tourism revenue; creates a distinctive brand identity; it helps to develop rural development and infrastructure by allowing small businesses to be created through small handicraft sales; ability to attract the much needed foreign direct investment (FDI) into the state to improve the arts sector; link up with the overseas arts production houses for a collaboration.

Educational and work benefits of funding: arts students are apparently more critical and analytical; have better social and interpersonal skills that is needed for the new workforce, the arts industry also helps to address a shortage of creative workers; the arts help to keep students in schools by giving them a platform to express themselves etc.

Civic benefits of funding: the arts foster civic participation and a strong democracy; brings public spaces to life; contribute to community vitality etc.

As we can see there are various benefits that could be reaped through state funding of the arts. Next, this would beg the question of whether one would be overly dependent on state funding that it cripples the flourishing of the whole industry? Should states fund the arts when they are not doing well economically? Well to put things into perspective, most state funding for the arts take up around 2.8% of the total revenue of the state. So that is really up to you to decide right? 🙂

If you have any queries or comments that you would like to raise, let us know regarding this topic. We would be happy to engage.

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 🙂

### Thinking [email protected] #5

[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.

Given a chance to counter Sir Isaac Newton’s famous quote of “What goes up must come down”, do you think it is true in all scenarios?

### Thinking [email protected] #4

[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.

Can you explain how a privacy screen protector works on your smartphone?

### Thinking [email protected]Culture #3

[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.

In designing a circuit, an engineer needs to use five 5KΩ resistors to design a resistors network of approximately 4.3KΩ. How should he place the resistors to achieve that resistance?