2017 A-level H1 General Paper (8807) Paper 1

2017 A-level H1 General Paper (8807) Paper 1

JC Mathematics

Sharing the A-level H1 General Paper (8807) Paper 1…

 

  1. ‘The past is not dead; it is not even past.’ Discuss.
  2. Can the use of animals for scientific research ever be justified?
  3. In your society, to what extent is it acceptable for public money to be used for the acquisition of works of art?
  4. ‘Rehabilitation, not punishment, should be the purpose of the justice system.’ Discuss.
  5. Is regulation of the press desirable?
  6. Do events, rather than politicians, shape the future?
  7. How far is science fiction becoming fact?
  8. Examine the role of music in establishing a national identity in your society.
  9. To what extent are people judged more by their physical appearance than by their abilities?
  10. ‘Practical ability is just as important as intellectual skills.’ How far is this true in your society?
  11. Assess the view that attempts to control climate change can never be truly effective.
  12. The quality of written language is being destroyed by social media.’ What is your view?
  13.  

APGP Interest Rate Question

APGP Interest Rate Question

JC Mathematics, Mathematics

This is a question from TJC Promotion 2017 Question 10. Thank you Mr. Wee for sharing.

Mr. Scrimp started a savings account which pays compound interest at a rate of r% per year on the last day of each year.

He made an initial deposit of $ x on 1 January 2000. From 1 January 2001 onwards, he makes a deposit of $ x at the start of each year.

(i) Show that the total amount in the savings account at the end of the n ^{th} year is $ \frac{k}{k-1} (k^n - 1)x , where k = \frac{100 + r}{100}.

(ii) At the end of the year 2019, Mr. Scrimp has a total amount of $ 22x in the savings account. Find the value of r, giving your answer correct to one decimal place.

Assume that the last deposit is made on 1 January 2019 and that the total amount in the savings account is $50000 on 1 January 2020.

For a period of N years, where 1 \le N \le 20, Mr. Scrimp can either continue to keep this amount in the savings account to earn interest or invest this amount in a financial product. The financial product pays an upfront sign-up bonus of $2000 and a year-end profit of $200 in the first year. At the end of each subsequent year, the financial product pays $20 more profit that in the previous year.

(iii) Find the total amount Mr. Scrimp will have at the end of N years if he invests in the financial product.

(iv) Using the value of r found in (ii), find the maximum number of years Mr. Scrimp should invest in the financial product for it to be more profitable than keeping the money in the savings account.

(i)
(1 + \frac{r}{100})x  + (1 + \frac{r}{100})^2 x + (1 + \frac{r}{100})^3 x + \ldots + (1 + \frac{r}{100})^n x

= \frac{(1 + \frac{r}{100})x[(1 + \frac{r}{100})^n - 1]}{(1 + \frac{r}{100}) - 1}

= \frac{(\frac{100 + r}{100})x[(\frac{100 + r}{100})^n - 1]}{(\frac{100 + r}{100}) - 1}

Let k = \frac{100 + r}{100}

\Rightarrow \frac{k x[k^n - 1]}{k - 1}

Total Amount = \$ [\frac{k}{k-1}(k^n - 1 ) x ]

(ii)

\frac{k}{k-1}(k^{20} - 1 ) x  = 22 x

\frac{k}{k-1}(k^{20} - 1 )  = 22

Using GC, k = 1.0089905

\Rightarrow \frac{100 + r}{100} = 1.0089905

\therefore r = 0.89905 \approx 0.9 (1 decimal place)

(iii)

Total amount = 50000 + 2000 + \frac{N}{2}[2(200) + (N-1)(2)]

= 52000 + N(200 + N-1)

= 52000 + 199N + N^2

(iv)

With the savings account, he has $ [50000(1.009)^N] at the end of N years.

With the financial product, he has $ [52000 + 199N + N^2] at the end of N years.

For it to be more profitable,

[52000 + 199N + N^2] > [50000(1.009)^N]

Random Questions from 2017 Prelims #1

Random Questions from 2017 Prelims #1

JC Mathematics

Last year, I shared a handful of random interesting questions from the 2016 Prelims. Students feedback that they were quite helpful and gave them good exposure. I thought I share some that I’ve seen this year. I know, its a bit early for Prelims. But ACJC just had their paper 1. 🙂

This is from ACJC 2017 Prelims Paper 1 Question 7. And it is on complex numbers.

7
(a) Given that 2z + 1 = |w| and 2w-z = 4+8i, solve for w and z.

(b) Find the exact values of x and y, where x, y \in \mathbb{R} such that 2e^{-(\frac{3+x+iy}{i})} = 1 -i

I’ll put the solutions up if I’m free.

But for students stuck, consider checking this link here for (a) and this link here for (b). These links hopefully enlightens students.

Just FYI, you cannot \text{ln} complex numbers as they are not real…

H2 Mathematics (9740) 2016 Prelim Papers

H2 Mathematics (9740) 2016 Prelim Papers

JC Mathematics

So many students have been asking for more practice. I’ll put up all the Prelim Papers for 2016 here. Do note that the syllabus is 9740 so students should practice discretion and skip questions that are out of syllabus. 🙂

Here are the Prelim Paper 2016. Have fun!

Here is the MF26.


2016 ACJC H2 Math Prelim P1 QP
2016 ACJC H2 Math Prelim P2 QP


2016 CJC H2 Math Prelim P1 QP
2016 CJC H2 Math Prelim P2 QP


2016 HCI JC2 Prelim H2 Mathematics Paper 1
2016 HCI JC2 Prelim H2 Mathematics Paper 2


2016 IJC H2 Math Prelim P1 QP
2016 IJC H2 Math Prelim P2 QP


2016 JJC H2 Math Prelim P1 QP
2016 JJC H2 Math Prelim P2 QP


2016 MI H2 Math Prelim P1 QP
2016 MI H2 Math Prelim P2 QP


2016 MJC H2 Math Prelim P1 QP
2016 MJC H2 Math Prelim P2 QP


2016 NJC H2 Math Prelim P1 QP
2016 NJC H2 Math Prelim P2 QP


2016 NYJC H2 Math Prelim P1 QP
2016 NYJC H2 Math Prelim P2 QP


2016 PJC H2 Math Prelim P1 QP
2016 PJC H2 Math Prelim P2 QP


2016 SAJC H2 Math Prelim P1 QP
2016 SAJC H2 Math Prelim P2 QP


2016 SRJC H2 Math Prelim P1 QP
2016 SRJC H2 Math Prelim P2 QP


2016 TJC H2 Math Prelim P1 QP
2016 TJC H2 Math Prelim P2 QP


2016 TPJC H2 Math Prelim P1 QP
2016 TPJC H2 Math Prelim P2 QP


2016 VJC H2 Math Prelim P1 QP
2016 VJC H2 Math Prelim P2 QP


2016 YJC H2 Math Prelim P1 QP
2016 YJC H2 Math Prelim P2 QP


Students, test your Vectors!

Students, test your Vectors!

JC Mathematics

As the prelims examinations draw really close, many students were asking me to give questions to test their concepts for several topics. In class, I had the opportunity to explore several applications questions too. We saw several physics concepts mixed. We also have some conceptual questions that need students to be able to use the entire topic to solve it.

So I’ll share one here. This involves several concepts put together. I’ll put the solution up once I find the time. Concepts that will be involved, will be

  1. Vector Product
  2. Equations of Plane
  3. Finding foot of perpendicular of point

The question in one a reflection of a plane in another plane. I think such questions will come out in a few guided steps in exams. But should a student be able to solve it independently, it shows that he has good understanding.

The plane p has equation x + y + z = 9 and the plane p_1 contains the lines passing through (0, 2, 3) and are parallel to (1, -1, 0) and (0, 1, 1) respectively. Find, in scalar product form, the equation of the plane which is the reflection of p_1 in p.

Thinking Math@TheCulture #5

Thinking [email protected] #5

JC 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 very challenging trigonometry question from AJC Mid Years P1 Q10.

Using the formula for \text{sin}(A+B), prove that \text{sin}(3A) = 3 \text{sin} A - 4 \text{sin}^3 A .

(i) Hence show that \sum_{r=1}^n \dfrac{4}{3^r} \text{sin}^3 (3^r \theta) = \text{sin} (3 \theta) - \dfrac{1}{3^n} \text{sin}(3^{n+1} \theta).

(ii) Deduce the sum of the series \sum_{r=1}^n \text{sin}^2 (3^r \theta) \text{cos} (3^r \theta)

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.

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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?

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

‘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?

JC General Paper

‘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.

 

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

Is competition always desirable?

Is competition always desirable?

JC General Paper

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.

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